Finite Group Databasebeta

← #13568281

Subgroups — #13568281

Order 1792.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2479C211yesmaximal, characteristic, complemented
2#11740561C211yesmaximal, characteristic, complemented
3#11740538C211yesmaximal, characteristic, complemented
4#11739697C211yesmaximal, characteristic, complemented
5#11739670C211yesmaximal, characteristic, complemented
6#11735528C211yesmaximal, characteristic, complemented
7#11735521C211yesmaximal, characteristic, complemented
8#11735520C211yesmaximal, characteristic, complemented
9#11735516C211yesmaximal, characteristic, complemented
10#11735447C211yesmaximal, characteristic, complemented
11#11735322C211yesmaximal, characteristic, complemented
12#11734502C211yesmaximal, characteristic
13#11734467C211yesmaximal, characteristic, complemented
14#11733916C211yesmaximal, characteristic
15#11733849C211yesmaximal, characteristic, complemented
16#11733667C211yesmaximal, characteristic, complemented
17#11733638C211yesmaximal, characteristic, complemented
18#11733397C211yesmaximal, characteristic, complemented
19#11733267C211yesmaximal, characteristic, complemented
20#11733191C211yesmaximal, characteristic, complemented
21#11733070C211yesmaximal, characteristic, complemented
22#11732941C211yesmaximal, characteristic, complemented
23#11732902C211yesmaximal, characteristic, complemented
24#11732689C211yesmaximal, characteristic, complemented
25#11732649C211yesmaximal, characteristic, complemented
26#11732348C211yesmaximal, characteristic
27#11732234C211yesmaximal, characteristic, complemented
28#11732060C211yesmaximal, characteristic, complemented
29#11731950C211yesmaximal, characteristic, complemented
30#11731209C211yesmaximal, characteristic, complemented
31#11731176C211yesmaximal, characteristic, complemented
32C2×C7×#126C2211yescharacteristic
33C2×C7×#117C2211yescharacteristic
34C2×C4×C22⋊D7C2211yescharacteristic
35C2×#6459C2211yescharacteristic
36C2×#6459C2211yescharacteristic
37C2×(C22⋊D7)⋊C4C2211yescharacteristic
38C2×#6442C2211yescharacteristic
39C2×#6441C2211yescharacteristic
40C2×#6435C2211yescharacteristic
41C7×#399C2211yescharacteristic
42C7×#399C2211yescharacteristic
43C7×#398C2211yescharacteristic
44C7×#394C2211yescharacteristic
45C7×#390C2211yescharacteristic
46C7×#389C2211yescharacteristic
47C7×#388C2211yescharacteristic
48C7×#388C2211yescharacteristic
49C7×#388C2211yescharacteristic
50C7×#387C2211yescharacteristic
51C7×#386C2211yescharacteristic
52C7×#385C2211yescharacteristic
53C4×C7×C4⋊C4C2211yescharacteristic
54#89995C2211yescharacteristic
55#89994C2211yescharacteristic
56#89994C2211yescharacteristic
57#89992C2211yescharacteristic
58#89982C2211yescharacteristic
59#89982C2211yescharacteristic
60C4×C22⋊Dic7C2211yescharacteristic
61#89762C2211yescharacteristic
62#89762C2211yescharacteristic
63#89762C2211yescharacteristic
64#89761C2211yescharacteristic
65#89761C2211yescharacteristic
66#89761C2211yescharacteristic
67#89759C2211yescharacteristic
68#89759C2211yescharacteristic
69#89757C2211yescharacteristic
70#89756C2211yescharacteristic
71#89756C2211yescharacteristic
72#89755C2211yescharacteristic
73#89755C2211yescharacteristic
74#89755C2211yescharacteristic
75#89754C2211yescharacteristic
76#89754C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89753C2211yescharacteristic
80#89753C2211yescharacteristic
81#89752C2211yescharacteristic
82#89751C2211yescharacteristic
83#89751C2211yescharacteristic
84#89751C2211yescharacteristic
85#89750C2211yescharacteristic
86#89750C2211yescharacteristic
87#89750C2211yescharacteristic
88#89750C2211yescharacteristic
89#89750C2211yescharacteristic
90#89749C2211yescharacteristic
91#89749C2211yescharacteristic
92#89749C2211yescharacteristic
93#89745C2211yescharacteristic
94#89744C2211yescharacteristic
95#89744C2211yescharacteristic
96#89744C2211yescharacteristic
97#89744C2211yescharacteristic
98#89744C2211yescharacteristic
99#89733C2211yescharacteristic
100#89733C2211yescharacteristic
101#89731C2211yescharacteristic
102#89731C2211yescharacteristic
103#89729C2211yescharacteristic
104#89729C2211yescharacteristic
105#89728C2211yescharacteristic
106#89728C2211yescharacteristic
107#89728C2211yescharacteristic
108#89728C2211yescharacteristic
109#89725C2211yescharacteristic
110#89725C2211yescharacteristic
111#89724C2211yescharacteristic
112#89724C2211yescharacteristic
113#89724C2211yescharacteristic
114#89724C2211yescharacteristic
115#89724C2211yescharacteristic
116#89724C2211yescharacteristic
117#89723C2211yescharacteristic
118#89723C2211yescharacteristic
119#89723C2211yescharacteristic
120#89723C2211yescharacteristic
121#89723C2211yescharacteristic
122#89721C2211yescharacteristic
123#89720C2211yescharacteristic
124#89720C2211yescharacteristic
125#89719C2211yescharacteristic
126#89719C2211yescharacteristic
127#89719C2211yescharacteristic
128#89718C2211yescharacteristic
129#89717C2211yescharacteristic
130#89717C2211yescharacteristic
131#89717C2211yescharacteristic
132#89717C2211yescharacteristic
133#89717C2211yescharacteristic
134#89717C2211yescharacteristic
135#89716C2211yescharacteristic
136#89716C2211yescharacteristic
137#89715C2211yescharacteristic
138#89714C2211yescharacteristic
139#89714C2211yescharacteristic
140#89712C2211yescharacteristic
141#89712C2211yescharacteristic
142C4×(C2×D7)⋊C4C2211yescharacteristic
143#89705C2211yescharacteristic
144#89705C2211yescharacteristic
145#89705C2211yescharacteristic
146#89705C2211yescharacteristic
147#89705C2211yescharacteristic
148#89705C2211yescharacteristic
149C4×Dic7⋊C4C2211yescharacteristic
150C4×Dic7⋊C4C2211yescharacteristic
151C42×Dic7C2211yescharacteristic
152#89701C2211yescharacteristic
153#89701C2211yescharacteristic
154#89700C2211yescharacteristic
155#89447C2211yescharacteristic
156#89447C2211yescharacteristic
157#89446C2211yescharacteristic
158#89442C2211yescharacteristic
159#89440C2211yescharacteristic
160#89439C2211yescharacteristic
161#89436C2211yescharacteristic
162D7×#95C2211yescharacteristic
163C7⋊#401C2211yescharacteristic
164C7⋊#401C2211yescharacteristic
165#89432C2211yescharacteristic
166#89430C2211yescharacteristic
167#89430C2211yescharacteristic
168#89430C2211yescharacteristic
169#89430C2211yescharacteristic
170#89429C2211yescharacteristic
171#89429C2211yescharacteristic
172#89427C2211yescharacteristic
173#89426C2211yescharacteristic
174#89426C2211yescharacteristic
175#89425C2211yescharacteristic
176#89425C2211yescharacteristic
177#89425C2211yescharacteristic
178#89424C2211yescharacteristic
179#89424C2211yescharacteristic
180#89424C2211yescharacteristic
181#89424C2211yescharacteristic
182#89423C2211yescharacteristic
183#89419C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#36996—71nomaximal, Sylow
188C22×C7×D4C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C22×C22⋊D7C2311yescharacteristic
191C22×C22⋊D7C2311yescharacteristic
192C23×Dic7C2311yescharacteristic
193C22×C4×D7C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C22×Dic14C2311yescharacteristic
197C22×Dic14C2311yescharacteristic
198C7×#126—42no—
199C7×#117—42no—
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊C4C2311yescharacteristic
206C2×C7×C4⋊C4C2311yescharacteristic
207C2×C7×C4⋊C4C2311yescharacteristic
208C2×C7×C4⋊C4C2311yescharacteristic
209C2×C7×C4⋊C4C2311yescharacteristic
210C2×C7×C22⋊C4C2311yescharacteristic
211C2×C7×C22⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4C2311yescharacteristic
213C2×C7×C22⋊C4C2311yescharacteristic
214C2×C7×C22⋊C4C2311yescharacteristic
215C2×C7×C22⋊C4C2311yescharacteristic
216C2×C7×C22⋊C4C2311yescharacteristic
217C2×C7×C22⋊C4C2311yescharacteristic
218C2×C7×C22⋊C4C2311yescharacteristic
219C2×C7×C22⋊C4C2311yescharacteristic
220C2×C7×C22⋊C4C2311yescharacteristic
221C2×C42×C7C2311yescharacteristic
222C2×C42×C7C2311yescharacteristic
223C2×C42×C7C2311yescharacteristic
224C2×C42×C7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226C2×C22⋊Dic7C2311yescharacteristic
227C2×C22⋊Dic7C2311yescharacteristic
228C2×C22⋊Dic7C2311yescharacteristic
229C2×C22⋊Dic7C2311yescharacteristic
230C2×C22⋊Dic7C2311yescharacteristic
231C2×C22⋊Dic7C2311yescharacteristic
232C2×C22⋊Dic7C2311yescharacteristic
233C2×C22⋊Dic7C2311yescharacteristic
234C2×C22⋊Dic7C2311yescharacteristic
235C2×C22⋊Dic7C2311yescharacteristic
236C2×C22⋊Dic7C2311yescharacteristic
237C2×C22⋊Dic7C2311yescharacteristic
238C4×C22⋊D7—24no—
239C2×(C2×D7)⋊C4C2311yescharacteristic
240C2×(C2×D7)⋊C4C2311yescharacteristic
241C2×(C2×D7)⋊C4C2311yescharacteristic
242C2×(C2×D7)⋊C4C2311yescharacteristic
243C2×(C2×D7)⋊C4C2311yescharacteristic
244C2×(C2×D7)⋊C4C2311yescharacteristic
245C2×(C2×D7)⋊C4C2311yescharacteristic
246C2×(C2×D7)⋊C4C2311yescharacteristic
247C2×(C2×D7)⋊C4C2311yescharacteristic
248C2×(C2×D7)⋊C4C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
252C2×C4⋊Dic7C2311yescharacteristic
253C2×C4⋊Dic7C2311yescharacteristic
254C2×C4⋊Dic7C2311yescharacteristic
255C2×C4⋊Dic7C2311yescharacteristic
256C2×Dic7⋊C4C2311yescharacteristic
257C2×Dic7⋊C4C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
260C2×Dic7⋊C4C2311yescharacteristic
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×Dic7⋊C4C2311yescharacteristic
264C2×Dic7⋊C4C2311yescharacteristic
265C2×Dic7⋊C4C2311yescharacteristic
266C2×Dic7⋊C4C2311yescharacteristic
267C2×Dic7⋊C4C2311yescharacteristic
268C2×Dic7⋊C4C2311yescharacteristic
269C2×Dic7⋊C4C2311yescharacteristic
270C2×Dic7⋊C4C2311yescharacteristic
271C2×Dic7⋊C4C2311yescharacteristic
272C2×Dic7⋊C4C2311yescharacteristic
273C2×Dic7⋊C4C2311yescharacteristic
274C2×Dic7⋊C4C2311yescharacteristic
275C2×Dic7⋊C4C2311yescharacteristic
276C2×Dic7⋊C4C2311yescharacteristic
277C2×Dic7⋊C4C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288#6459—24no—
289#6459—42no—
290(C22⋊D7)⋊C4—24no—
291#6442—42no—
292#6441—42no—
293#6435—42no—
294C7×#95C2311yescharacteristic
295C7×#95C2311yescharacteristic
296C7×#95C2311yescharacteristic
297C7×#95C2311yescharacteristic
298C7×#95C2311yescharacteristic
299C7×#95C2311yescharacteristic
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7⋊#95C2311yescharacteristic
303C7⋊#95C2311yescharacteristic
304C7⋊#95C2311yescharacteristic
305C7⋊#95C2311yescharacteristic
306C7⋊#95C2311yescharacteristic
307C7⋊#95C2311yescharacteristic
308C7⋊#95C2311yescharacteristic
309C7⋊#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352#2865—71no—
353#2864—71no—
354#2797—71no—
355#2787—71no—
356#2787—71no—
357#2786—71no—
358#2773—71no—
359#2766—71no—
360#2759—71no—
361#2755—71no—
362#2753—71no—
363#2742—71no—
364#2741—71no—
365#2740—71no—
366#2723—71no—
367#2702—71no—
368#2702—71no—
369#2698—71no—
370#2653—71no—
371#2652—71no—
372#2600—71no—
373#2594—71no—
374#2588—71no—
375#2564—71no—
376#2479D711yescharacteristic, complemented
377#2478—71no—
378#2438—71no—
379#2415—71no—
380#2332—71no—
381#2318—71no—
382#2293—71no—
383C24×C7C2411yescharacteristic
384C24×C7C2411yescharacteristic
385C23×D7C2411yescharacteristic
386C2×C7×D4—41no—
387C2×C7×D4—41no—
388C2×C7×D4—41no—
389C22×C4×C7—22no—
390C22×C4×C7—41no—
391C22×C4×C7—41no—
392C22×C4×C7C2411yescharacteristic
393C22×C4×C7C2411yescharacteristic
394C22×C4×C7C2411yescharacteristic
395C22×C4×C7C2411yescharacteristic
396C22×C4×C7C2411yescharacteristic
397C22×C4×C7C2411yescharacteristic
398C22×C4×C7C2411yescharacteristic
399C22×C4×C7C2411yescharacteristic
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C2×C22⋊D7—22no—
406C2×C22⋊D7—22no—
407C2×C22⋊D7—22no—
408C2×C22⋊D7—41no—
409C2×C22⋊D7—41no—
410C2×C22⋊D7—41no—
411C22×Dic7—22no—
412C22×Dic7—41no—
413C22×Dic7—41no—
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C2×C4×D7—41no—
430C2×C4×D7—41no—
431C2×C4×D7—41no—
432C2×C4×D7—41no—
433C2×C4×D7—41no—
434C2×C4×D7—41no—
435C2×C4×D7—41no—
436C2×C4×D7—41no—
437C2×C4×D7#4114yes—
438C2×Dic14—22no—
439C2×Dic14—41no—
440C2×Dic14—41no—
441C2×Dic14—41no—
442C2×Dic14—41no—
443C2×Dic14—41no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—22no—
447C7×C4⋊C4—41no—
448C7×C4⋊C4—41no—
449C7×C4⋊C4—41no—
450C7×C4⋊C4—41no—
451C7×C4⋊C4—41no—
452C7×C4⋊C4—41no—
453C7×C4⋊C4—41no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—41no—
458C7×C22⋊C4—41no—
459C7×C22⋊C4—41no—
460C7×C22⋊C4—41no—
461C7×C22⋊C4—41no—
462C7×C22⋊C4—41no—
463C7×C22⋊C4—41no—
464C7×C22⋊C4—41no—
465C42×C7—22no—
466C42×C7—41no—
467C42×C7—41no—
468C42×C7—41no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—41no—
472C22⋊Dic7—41no—
473C22⋊Dic7—41no—
474C22⋊Dic7—41no—
475C22⋊Dic7—41no—
476C22⋊Dic7—41no—
477C22⋊Dic7—41no—
478C22⋊Dic7—41no—
479C22⋊Dic7—41no—
480C22⋊Dic7—41no—
481C22⋊Dic7—41no—
482(C2×D7)⋊C4—22no—
483(C2×D7)⋊C4—22no—
484(C2×D7)⋊C4—22no—
485(C2×D7)⋊C4—22no—
486(C2×D7)⋊C4—22no—
487(C2×D7)⋊C4—41no—
488(C2×D7)⋊C4—41no—
489(C2×D7)⋊C4—41no—
490(C2×D7)⋊C4—41no—
491(C2×D7)⋊C4—41no—
492C4⋊Dic7—22no—
493C4⋊Dic7—41no—
494C4⋊Dic7—41no—
495C4⋊Dic7—41no—
496C4⋊Dic7—41no—
497C4⋊Dic7—41no—
498C4⋊Dic7—41no—
499Dic7⋊C4—22no—
500Dic7⋊C4—22no—
501Dic7⋊C4—22no—
502Dic7⋊C4—22no—
503Dic7⋊C4—22no—
504Dic7⋊C4—22no—
505Dic7⋊C4—22no—
506Dic7⋊C4—22no—
507Dic7⋊C4—41no—
508Dic7⋊C4—41no—
509Dic7⋊C4—41no—
510Dic7⋊C4—41no—
511Dic7⋊C4—41no—
512Dic7⋊C4—41no—
513Dic7⋊C4—41no—
514Dic7⋊C4—41no—
515Dic7⋊C4—41no—
516Dic7⋊C4—41no—
517Dic7⋊C4—41no—
518Dic7⋊C4—41no—
519Dic7⋊C4—41no—
520Dic7⋊C4—41no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C2×#126—71no—
532C2×#126C2×D711yescharacteristic
533C2×C22⋊Q8—71no—
534C2×C22⋊Q8—71no—
535C2×C22⋊Q8—71no—
536C2×C4×D4—71no—
537C2×C4×D4—71no—
538C2×#117—71no—
539C2×#117C2×D711yescharacteristic
540#401—71no—
541#401—71no—
542#400—71no—
543#400—71no—
544#400—71no—
545#400—71no—
546#400—71no—
547#400—71no—
548#400—71no—
549#399—71no—
550#399C2×D711yescharacteristic
551#399C2×D711yescharacteristic
552#398—71no—
553#398—71no—
554#398—71no—
555#398—71no—
556#398—71no—
557#398—71no—
558#398—71no—
559#398—71no—
560#398C2×D711yescharacteristic
561#397—71no—
562#397—71no—
563#397—71no—
564#397—71no—
565#397—71no—
566#397—71no—
567#397—71no—
568#397—71no—
569#397—71no—
570#397—71no—
571#397—71no—
572#396—71no—
573#396—71no—
574#395—71no—
575#395—71no—
576#395—71no—
577#394—71no—
578#394—71no—
579#394—71no—
580#394—71no—
581#394—71no—
582#394—71no—
583#394C2×D711yescharacteristic
584#393—71no—
585#393—71no—
586#393—71no—
587#392—71no—
588#391—71no—
589#391—71no—
590#391—71no—
591#391—71no—
592#391—71no—
593#390—71no—
594#390—71no—
595#390C2×D711yescharacteristic
596#389—71no—
597#389—71no—
598#389—71no—
599#389—71no—
600#389—71no—
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389C2×D711yescharacteristic
606#388—71no—
607#388—71no—
608#388—71no—
609#388—71no—
610#388—71no—
611#388—71no—
612#388—71no—
613#388—71no—
614#388—71no—
615#388—71no—
616#388—71no—
617#388—71no—
618#388—71no—
619#388—71no—
620#388—71no—
621#388—71no—
622#388—71no—
623#388—71no—
624#388—71no—
625#388C2×D711yescharacteristic
626#388C2×D711yescharacteristic
627#388C2×D711yescharacteristic
628#387—71no—
629#387—71no—
630#387—71no—
631#387—71no—
632#387—71no—
633#387—71no—
634#387—71no—
635#387—71no—
636#387—71no—
637#387—71no—
638#387—71no—
639#387—71no—
640#387—71no—
641#387—71no—
642#387—71no—
643#387—71no—
644#387—71no—
645#387—71no—
646#387—71no—
647#387—71no—
648#387—71no—
649#387—71no—
650#387—71no—
651#387—71no—
652#387—71no—
653#387C2×D711yescharacteristic
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#386—71no—
659#386C2×D711yescharacteristic
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385—71no—
667#385C2×D711yescharacteristic
668#383—71no—
669#382—71no—
670#382—71no—
671#382—71no—
672#381—71no—
673#381—71no—
674#380—71no—
675#380—71no—
676#380—71no—
677#380—71no—
678#380—71no—
679C4×C4⋊C4—71no—
680C4×C4⋊C4—71no—
681C4×C4⋊C4C2×D711yescharacteristic
682C4×C22⋊C4—71no—
683C4×C22⋊C4—71no—
684C2×#95—71no—
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7—21no—
693C23×C7—21no—
694C23×C7—21no—
695C23×C7—21no—
696C23×C7—21no—
697C23×C7—21no—
698C23×C7—21no—
699C23×C7—21no—
700C23×C7C2511yescharacteristic
701C22×D7—21no—
702C22×D7—21no—
703C22×D7—21no—
704C22×D7—21no—
705C22×D7—21no—
706C22×D7—21no—
707C22×D7C2×#4112yes—
708C7×D4—82no—
709C2×C4×C7—21no—
710C2×C4×C7—21no—
711C2×C4×C7—21no—
712C2×C4×C7—21no—
713C2×C4×C7—21no—
714C2×C4×C7—21no—
715C2×C4×C7—21no—
716C2×C4×C7—21no—
717C2×C4×C7—21no—
718C2×C4×C7—21no—
719C2×C4×C7—21no—
720C2×C4×C7—21no—
721C2×C4×C7—21no—
722C2×C4×C7—21no—
723C2×C4×C7—21no—
724C2×C4×C7—21no—
725C2×C4×C7—21no—
726C2×C4×C7—21no—
727C2×C4×C7—21no—
728C2×C4×C7—21no—
729C2×C4×C7—21no—
730C2×C4×C7—21no—
731C2×C4×C7—21no—
732C2×C4×C7—21no—
733C2×C4×C7—21no—
734C2×C4×C7—21no—
735C2×C4×C7—21no—
736C2×C4×C7—21no—
737C2×C4×C7—21no—
738C2×C4×C7—21no—
739C2×C4×C7—21no—
740C2×C4×C7—21no—
741C2×C4×C7—21no—
742C2×C4×C7—21no—
743C2×C4×C7—21no—
744C2×C4×C7—21no—
745C2×C4×C7—21no—
746C2×C4×C7—44no—
747C2×C4×C7C2×#4112yes—
748C2×C4×C7H(5,𝔽2)12yes—
749C22⋊D7—44no—
750C22⋊D7—44no—
751C2×Dic7—21no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7—21no—
781C2×Dic7—21no—
782C2×Dic7—21no—
783C2×Dic7—21no—
784C2×Dic7—21no—
785C2×Dic7—21no—
786C2×Dic7—21no—
787C2×Dic7—21no—
788C2×Dic7—21no—
789C2×Dic7—21no—
790C2×Dic7—21no—
791C2×Dic7—21no—
792C2×Dic7—21no—
793C2×Dic7—21no—
794C2×Dic7—82no—
795C2×Dic7C2×#4112yes—
796C2×Dic72−1+412yes—
797C4×D7—44no—
798C4×D7—82no—
799C4×D7—82no—
800Dic14—82no—
801Dic14—82no—
802C22×Q8—71no—
803C22×Q8—71no—
804C22×D4—71no—
805C22×D4—71no—
806C22×D4C22×D711yescharacteristic
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4C22×D711yescharacteristic
812#126—42no—
813#126—282no—
814C22⋊Q8—144no—
815C22⋊Q8—282no—
816C22⋊Q8—282no—
817C4×D4—144no—
818C4×D4—144no—
819#117—42no—
820#117—282no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—71no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—71no—
839C2×C4⋊C4—71no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—71no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—71no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—71no—
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C4⋊C4C22×D711yescharacteristic
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
860C2×C22⋊C4—71no—
861C2×C22⋊C4—71no—
862C2×C22⋊C4—71no—
863C2×C22⋊C4—71no—
864C2×C22⋊C4—71no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4—71no—
867C2×C22⋊C4—71no—
868C2×C22⋊C4—71no—
869C2×C22⋊C4—71no—
870C2×C22⋊C4—71no—
871C2×C22⋊C4—71no—
872C2×C22⋊C4—71no—
873C2×C22⋊C4—71no—
874C2×C22⋊C4—71no—
875C2×C22⋊C4—71no—
876C2×C22⋊C4—71no—
877C2×C22⋊C4—71no—
878C2×C22⋊C4—71no—
879C2×C22⋊C4—71no—
880C2×C22⋊C4—71no—
881C2×C22⋊C4—71no—
882C2×C22⋊C4—71no—
883C2×C22⋊C4C22×D711yescharacteristic
884C2×C22⋊C4C22×D711yescharacteristic
885C2×C22⋊C4C22×D711yescharacteristic
886C2×C22⋊C4C22×D711yescharacteristic
887C2×C22⋊C4C22×D711yescharacteristic
888C2×C22⋊C4C22×D711yescharacteristic
889C2×C22⋊C4C22×D711yescharacteristic
890C2×C22⋊C4C22×D711yescharacteristic
891C2×C22⋊C4C22×D711yescharacteristic
892C2×C22⋊C4C22×D711yescharacteristic
893C2×C22⋊C4C22×D711yescharacteristic
894C2×C42—71no—
895C2×C42—71no—
896C2×C42—71no—
897C2×C42—71no—
898C2×C42—71no—
899C2×C42—71no—
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42C22×D711yescharacteristic
905C2×C42C22×D711yescharacteristic
906C2×C42C22×D711yescharacteristic
907C2×C42C22×D711yescharacteristic
908#95—71no—
909#95—71no—
910#95—71no—
911#95—71no—
912#95—71no—
913#95—71no—
914#95—71no—
915#95—71no—
916#95—71no—
917#95—71no—
918#95—71no—
919#95—71no—
920#95—71no—
921#95—71no—
922#95—71no—
923#95—71no—
924#95—71no—
925#95—71no—
926#95—71no—
927#95—71no—
928#95—71no—
929#95—71no—
930#95—71no—
931#95—71no—
932#95—71no—
933#95—71no—
934#95—71no—
935#95—71no—
936#95—71no—
937#95—71no—
938#95—71no—
939#95—71no—
940#95—71no—
941#95—71no—
942#95—71no—
943#95—71no—
944#95—71no—
945#95—71no—
946#95—71no—
947#95—71no—
948#95—71no—
949#95—71no—
950#95—71no—
951#95—71no—
952#95—71no—
953#95—71no—
954#95—71no—
955#95—71no—
956#95—71no—
957#95—71no—
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964#95C22×D711yescharacteristic
965#95C22×D711yescharacteristic
966C22×C7—41no—
967C22×C7—41no—
968C22×C7—41no—
969C22×C7—41no—
970C22×C7—41no—
971C22×C7—41no—
972C22×C7—41no—
973C22×C7—41no—
974C22×C7—41no—
975C22×C7—41no—
976C22×C7—41no—
977C22×C7—41no—
978C22×C7—41no—
979C22×C7—41no—
980C22×C7C22×#4111yescharacteristic
981C22×C7C2×H(5,𝔽2)11yescharacteristic
982C22×C7C2×2−1+411yescharacteristic
983C22×C7#58511yescharacteristic
984C22×C7#58511yescharacteristic
985C22×C7#58511yescharacteristic
986C22×C7#58511yescharacteristic
987C2×D7—22no—
988C2×D7—22no—
989C2×D7—22no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7—41no—
993C2×D7—41no—
994C4×C7—22no—
995C4×C7—22no—
996C4×C7—41no—
997C4×C7—41no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006C4×C7—41no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—41no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7—41no—
1020Dic7—41no—
1021Dic7—41no—
1022C24—71no—
1023C24C23×D711yescharacteristic
1024C24C23×D711yescharacteristic
1025C2×Q8—142no—
1026C2×Q8—281no—
1027C2×Q8—281no—
1028C2×Q8—281no—
1029C2×Q8—281no—
1030C2×Q8—281no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4—41no—
1034C2×D4—142no—
1035C2×D4—142no—
1036C2×D4—142no—
1037C2×D4—281no—
1038C2×D4—281no—
1039C2×D4—281no—
1040C22×C4—22no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—74no—
1046C22×C4—71no—
1047C22×C4—71no—
1048C22×C4—71no—
1049C22×C4—71no—
1050C22×C4—71no—
1051C22×C4—71no—
1052C22×C4—71no—
1053C22×C4—71no—
1054C22×C4—71no—
1055C22×C4—71no—
1056C22×C4—71no—
1057C22×C4—71no—
1058C22×C4—71no—
1059C22×C4—142no—
1060C22×C4—281no—
1061C22×C4—281no—
1062C22×C4—281no—
1063C22×C4—281no—
1064C22×C4—281no—
1065C22×C4—281no—
1066C22×C4—281no—
1067C22×C4—281no—
1068C22×C4—281no—
1069C22×C4—281no—
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C22×C4C23×D711yescharacteristic
1076C22×C4C23×D711yescharacteristic
1077C22×C4C23×D711yescharacteristic
1078C22×C4C23×D711yescharacteristic
1079C22×C4C23×D711yescharacteristic
1080C22×C4C23×D711yescharacteristic
1081C22×C4C23×D711yescharacteristic
1082C22×C4C23×D711yescharacteristic
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—142no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—142no—
1097C4⋊C4—142no—
1098C4⋊C4—142no—
1099C4⋊C4—142no—
1100C4⋊C4—142no—
1101C4⋊C4—142no—
1102C4⋊C4—281no—
1103C4⋊C4—281no—
1104C4⋊C4—281no—
1105C4⋊C4—281no—
1106C4⋊C4—281no—
1107C4⋊C4—281no—
1108C4⋊C4—281no—
1109C4⋊C4—281no—
1110C4⋊C4—281no—
1111C4⋊C4—281no—
1112C4⋊C4—281no—
1113C4⋊C4—281no—
1114C4⋊C4—281no—
1115C4⋊C4—281no—
1116C4⋊C4—281no—
1117C4⋊C4—281no—
1118C4⋊C4—281no—
1119C4⋊C4—281no—
1120C4⋊C4—281no—
1121C4⋊C4—281no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—142no—
1136C22⋊C4—142no—
1137C22⋊C4—142no—
1138C22⋊C4—142no—
1139C22⋊C4—142no—
1140C22⋊C4—281no—
1141C22⋊C4—281no—
1142C22⋊C4—281no—
1143C22⋊C4—281no—
1144C22⋊C4—281no—
1145C22⋊C4—281no—
1146C22⋊C4—281no—
1147C22⋊C4—281no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C22⋊C4—281no—
1155C22⋊C4—281no—
1156C42—22no—
1157C42—41no—
1158C42—41no—
1159C42—41no—
1160C42—142no—
1161C42—142no—
1162C42—142no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C42—281no—
1169C42—281no—
1170C2×C7—81no—
1171C2×C7—81no—
1172C2×C7#345511yescharacteristic
1173C2×C7#349511yescharacteristic
1174C2×C7#350511yescharacteristic
1175C2×C7#355711yescharacteristic
1176C2×C7#355911yescharacteristic
1177C2×C7#356211yescharacteristic
1178C2×C7#356811yescharacteristic
1179D7—42no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—72no—
1195C23—141no—
1196C23—141no—
1197C23—141no—
1198C23—141no—
1199C23—141no—
1200C23—141no—
1201C23C24×D711yescharacteristic
1202Q8—562no—
1203Q8—562no—
1204D4—82no—
1205D4—284no—
1206D4—284no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—44no—
1245C2×C4—72no—
1246C2×C4—72no—
1247C2×C4—141no—
1248C2×C4—141no—
1249C2×C4—141no—
1250C2×C4—141no—
1251C2×C4—141no—
1252C2×C4—141no—
1253C2×C4—141no—
1254C2×C4—141no—
1255C2×C4—141no—
1256C2×C4—141no—
1257C2×C4—141no—
1258C2×C4—141no—
1259C2×C4—141no—
1260C2×C4—141no—
1261C2×C4—141no—
1262C2×C4—141no—
1263C2×C4—141no—
1264C2×C4—141no—
1265C2×C4—141no—
1266C2×C4—141no—
1267C2×C4—141no—
1268C2×C4—141no—
1269C2×C4—141no—
1270C2×C4—141no—
1271C2×C4—141no—
1272C2×C4—141no—
1273C2×C4—141no—
1274C2×C4—141no—
1275C2×C4—141no—
1276C2×C4—141no—
1277C2×C4—141no—
1278C2×C4—141no—
1279C2×C4—141no—
1280C2×C4—141no—
1281C2×C4—141no—
1282C2×C4—141no—
1283C2×C4—141no—
1284C2×C4—141no—
1285C2×C4—141no—
1286C2×C4—141no—
1287C2×C4—141no—
1288C2×C4—141no—
1289C2×C4—141no—
1290C2×C4—284no—
1291C2×C4—562no—
1292C2×C4—562no—
1293C2×C4—562no—
1294C2×C4#654812yes—
1295C2×C4D7×#4112yes—
1296C7#3699611yescharacteristic, complemented, Sylow
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—142no—
1312C22—142no—
1313C22—142no—
1314C22—281no—
1315C22—281no—
1316C22—281no—
1317C22—281no—
1318C22C2×#654811yescharacteristic
1319C22C2×D7×#4111yescharacteristic
1320C22#9061611yescharacteristic
1321C22#9061611yescharacteristic
1322C22#9061611yescharacteristic
1323C22#9061811yescharacteristic
1324C22D7×2−1+411yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—142no—
1339C4—142no—
1340C4—281no—
1341C4—281no—
1342C4—281no—
1343C4—281no—
1344C4—281no—
1345C4—281no—
1346C4—281no—
1347C4—281no—
1348C4—281no—
1349C4—281no—
1350C4—281no—
1351C4—281no—
1352C4—281no—
1353C2—81no—
1354C2—81no—
1355C2—282no—
1356C2#1174311211yescharacteristic
1357C2#1174321411yescharacteristic
1358C2#1174361911yescharacteristic
1359C2#1174376311yescharacteristic
1360C2#1174384911yescharacteristic
1361C2#1174388111yescharacteristic
1362C2#1174391811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2479C2
prime radical#89995C22
hypercenter#2479D7
hypocenterC7#36996
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2479

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#2479C2semidirect
2. #11740561C2semidirect
3. #11740538C2semidirect
4. #11739697C2semidirect
5. #11739670C2semidirect
6. #11735528C2semidirect
7. #11735521C2semidirect
8. #11735520C2semidirect
9. #11735516C2semidirect
10. #11735447C2semidirect
11. #11735322C2semidirect
13. #11734467C2semidirect
15. #11733849C2semidirect
16. #11733667C2semidirect
17. #11733638C2semidirect
18. #11733397C2semidirect
19. #11733267C2semidirect
20. #11733191C2semidirect
21. #11733070C2semidirect
22. #11732941C2semidirect
23. #11732902C2semidirect
24. #11732689C2semidirect
25. #11732649C2semidirect
27. #11732234C2semidirect
28. #11732060C2semidirect
29. #11731950C2semidirect
30. #11731209C2semidirect
31. #11731176C2semidirect
376. #2479D7semidirect
1296. C7#36996semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#24792
#117405612
#117405382
#117396972
#117396702
#117355282
#117355212
#117355202
#117355162
#117354472
#117353222
#117345022
#117344672
#117339162
#117338492
#117336672
#117336382
#117333972
#117332672
#117331912
#117330702
#117329412
#117329022
#117326892
#117326492
#117323482
#117322342
#117320602
#117319502
#117312092
#117311762
#369967