Finite Group Databasebeta

← #13563569

Subgroups — #13563569

Order 1792.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2719C211yesmaximal, characteristic, complemented
2#11740517C211yesmaximal, characteristic, complemented
3#11740498C211yesmaximal, characteristic, complemented
4#11740498C211yesmaximal, characteristic, complemented
5#11740477C211yesmaximal, characteristic, complemented
6#11735808C211yesmaximal, characteristic, complemented
7#11735807C211yesmaximal, characteristic
8#11735753C211yesmaximal, characteristic, complemented
9#11735721C211yesmaximal, characteristic, complemented
10#11735711C211yesmaximal, characteristic, complemented
11#11735589C211yesmaximal, characteristic
12#11735406C211yesmaximal, characteristic, complemented
13#11735311C211yesmaximal, characteristic, complemented
14#11735310C211yesmaximal, characteristic, complemented
15#11735297C211yesmaximal, characteristic, complemented
16#11735203C211yesmaximal, characteristic, complemented
17#11735191C211yesmaximal, characteristic, complemented
18#11733709C211yesmaximal, characteristic, complemented
19#11733657C211yesmaximal, characteristic
20D7×#389C211yesmaximal, characteristic, complemented
21#11733600C211yesmaximal, characteristic, complemented
22#11732891C211yesmaximal, characteristic
23#11732851C211yesmaximal, characteristic, complemented
24#11732815C211yesmaximal, characteristic
25#11732745C211yesmaximal, characteristic, complemented
26#11732720C211yesmaximal, characteristic, complemented
27#11732635C211yesmaximal, characteristic, complemented
28#11732611C211yesmaximal, characteristic, complemented
29#11732465C211yesmaximal, characteristic
30#11731671C211yesmaximal, characteristic
31#11731647C211yesmaximal, characteristic, complemented
32C2×C7×#125C2211yescharacteristic
33C2×C7×#125C2211yescharacteristic
34C2×#6461C2211yescharacteristic
35C2×#6461C2211yescharacteristic
36C2×#6461C2211yescharacteristic
37C2×#6460C2211yescharacteristic
38C2×#6460C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×D7×C4⋊C4C2211yescharacteristic
42C2×D7×C4⋊C4C2211yescharacteristic
43C2×#6453C2211yescharacteristic
44C2×#6452C2211yescharacteristic
45C2×C4×D28C2211yescharacteristic
46C2×C42×D7C2211yescharacteristic
47C7×#400C2211yescharacteristic
48C7×#400C2211yescharacteristic
49C7×#400C2211yescharacteristic
50C7×#398C2211yescharacteristic
51C7×#398C2211yescharacteristic
52C7×#398C2211yescharacteristic
53C7×#389C2211yescharacteristic
54C7×#389C2211yescharacteristic
55C7×#387C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C7×#387C2211yescharacteristic
58C7×#387C2211yescharacteristic
59C7×#382C2211yescharacteristic
60#89766C2211yescharacteristic
61#89766C2211yescharacteristic
62#89766C2211yescharacteristic
63#89766C2211yescharacteristic
64#89766C2211yescharacteristic
65#89765C2211yescharacteristic
66#89765C2211yescharacteristic
67#89762C2211yescharacteristic
68#89762C2211yescharacteristic
69#89762C2211yescharacteristic
70#89761C2211yescharacteristic
71#89761C2211yescharacteristic
72#89761C2211yescharacteristic
73#89761C2211yescharacteristic
74#89761C2211yescharacteristic
75#89761C2211yescharacteristic
76#89761C2211yescharacteristic
77#89761C2211yescharacteristic
78#89761C2211yescharacteristic
79#89759C2211yescharacteristic
80#89759C2211yescharacteristic
81#89759C2211yescharacteristic
82#89759C2211yescharacteristic
83#89758C2211yescharacteristic
84#89758C2211yescharacteristic
85#89758C2211yescharacteristic
86#89757C2211yescharacteristic
87#89757C2211yescharacteristic
88#89757C2211yescharacteristic
89#89756C2211yescharacteristic
90#89756C2211yescharacteristic
91#89756C2211yescharacteristic
92#89755C2211yescharacteristic
93#89755C2211yescharacteristic
94#89753C2211yescharacteristic
95#89753C2211yescharacteristic
96#89752C2211yescharacteristic
97#89752C2211yescharacteristic
98#89751C2211yescharacteristic
99#89750C2211yescharacteristic
100#89750C2211yescharacteristic
101#89750C2211yescharacteristic
102#89750C2211yescharacteristic
103#89750C2211yescharacteristic
104#89745C2211yescharacteristic
105#89745C2211yescharacteristic
106#89745C2211yescharacteristic
107#89745C2211yescharacteristic
108#89744C2211yescharacteristic
109#89744C2211yescharacteristic
110#89744C2211yescharacteristic
111#89744C2211yescharacteristic
112#89744C2211yescharacteristic
113#89712C2211yescharacteristic
114#89712C2211yescharacteristic
115C4×(C2×D7)⋊C4C2211yescharacteristic
116#89709C2211yescharacteristic
117#89708C2211yescharacteristic
118#89705C2211yescharacteristic
119#89705C2211yescharacteristic
120#89701C2211yescharacteristic
121#89700C2211yescharacteristic
122#89700C2211yescharacteristic
123#89448C2211yescharacteristic
124#89448C2211yescharacteristic
125#89447C2211yescharacteristic
126#89447C2211yescharacteristic
127#89446C2211yescharacteristic
128#89441C2211yescharacteristic
129#89441C2211yescharacteristic
130#89440C2211yescharacteristic
131#89440C2211yescharacteristic
132#89440C2211yescharacteristic
133#89440C2211yescharacteristic
134#89440C2211yescharacteristic
135#89439C2211yescharacteristic
136#89439C2211yescharacteristic
137#89439C2211yescharacteristic
138#89438C2211yescharacteristic
139#89438C2211yescharacteristic
140#89437C2211yescharacteristic
141#89437C2211yescharacteristic
142#89437C2211yescharacteristic
143#89437C2211yescharacteristic
144#89437C2211yescharacteristic
145#89437C2211yescharacteristic
146#89436C2211yescharacteristic
147D7×#95C2211yescharacteristic
148D7×#95C2211yescharacteristic
149C7⋊#401C2211yescharacteristic
150#89433C2211yescharacteristic
151#89433C2211yescharacteristic
152#89433C2211yescharacteristic
153#89433C2211yescharacteristic
154#89432C2211yescharacteristic
155#89432C2211yescharacteristic
156#89431C2211yescharacteristic
157#89431C2211yescharacteristic
158#89431C2211yescharacteristic
159#89431C2211yescharacteristic
160#89430C2211yescharacteristic
161#89430C2211yescharacteristic
162#89430C2211yescharacteristic
163#89429C2211yescharacteristic
164#89429C2211yescharacteristic
165#89429C2211yescharacteristic
166#89429C2211yescharacteristic
167#89428C2211yescharacteristic
168#89427C2211yescharacteristic
169#89427C2211yescharacteristic
170#89426C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89425C2211yescharacteristic
174#89425C2211yescharacteristic
175#89425C2211yescharacteristic
176#89424C2211yescharacteristic
177#89424C2211yescharacteristic
178#89423C2211yescharacteristic
179#89422C2211yescharacteristic
180#89419C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89419C2211yescharacteristic
184#89419C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#36825—71nomaximal, Sylow
188C22×D28C2311yescharacteristic
189C22×C4×D7C2311yescharacteristic
190C22×C4×D7C2311yescharacteristic
191C22×C4×D7C2311yescharacteristic
192C22×C4×D7C2311yescharacteristic
193C22×C4×D7C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C22×C4×D7C2311yescharacteristic
197C22×Dic14C2311yescharacteristic
198C7×#125—42no—
199C7×#125—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×C4⋊C4C2311yescharacteristic
211C2×C7×C4⋊C4C2311yescharacteristic
212C2×C7×C4⋊C4C2311yescharacteristic
213C2×C7×C4⋊C4C2311yescharacteristic
214C2×C7×C4⋊C4C2311yescharacteristic
215C2×C7×C4⋊C4C2311yescharacteristic
216C2×C42×C7C2311yescharacteristic
217C2×C42×C7C2311yescharacteristic
218C2×C42×C7C2311yescharacteristic
219C2×(C2×D7)⋊C4C2311yescharacteristic
220C2×(C2×D7)⋊C4C2311yescharacteristic
221C2×(C2×D7)⋊C4C2311yescharacteristic
222C2×(C2×D7)⋊C4C2311yescharacteristic
223C2×(C2×D7)⋊C4C2311yescharacteristic
224C2×(C2×D7)⋊C4C2311yescharacteristic
225C2×(C2×D7)⋊C4C2311yescharacteristic
226C2×(C2×D7)⋊C4C2311yescharacteristic
227C2×(C2×D7)⋊C4C2311yescharacteristic
228C2×(C2×D7)⋊C4C2311yescharacteristic
229C2×(C2×D7)⋊C4C2311yescharacteristic
230C2×(C2×D7)⋊C4C2311yescharacteristic
231C2×(C2×D7)⋊C4C2311yescharacteristic
232C2×(C2×D7)⋊C4C2311yescharacteristic
233C2×(C2×D7)⋊C4C2311yescharacteristic
234C2×(C2×D7)⋊C4C2311yescharacteristic
235C2×(C2×D7)⋊C4C2311yescharacteristic
236C2×(C2×D7)⋊C4C2311yescharacteristic
237C2×(C2×D7)⋊C4C2311yescharacteristic
238C2×(C2×D7)⋊C4C2311yescharacteristic
239C2×C4⋊Dic7C2311yescharacteristic
240C2×C4⋊Dic7C2311yescharacteristic
241C2×C4⋊Dic7C2311yescharacteristic
242C2×C4⋊Dic7C2311yescharacteristic
243C2×C4⋊Dic7C2311yescharacteristic
244C2×C4⋊Dic7C2311yescharacteristic
245C2×C4⋊Dic7C2311yescharacteristic
246C2×C4⋊Dic7C2311yescharacteristic
247C2×C4⋊Dic7C2311yescharacteristic
248C2×C4⋊Dic7C2311yescharacteristic
249C2×C4⋊Dic7C2311yescharacteristic
250C2×C4⋊Dic7C2311yescharacteristic
251C2×C4⋊Dic7C2311yescharacteristic
252C2×C4⋊Dic7C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2311yescharacteristic
255C2×Dic7⋊C4C2311yescharacteristic
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×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285#6461—42no—
286#6461—42no—
287#6461—42no—
288#6460—24no—
289#6460—42no—
290D7×C4⋊C4—24no—
291D7×C4⋊C4—42no—
292D7×C4⋊C4—42no—
293D7×C4⋊C4—42no—
294#6453—42no—
295#6452—42no—
296C4×D28—24no—
297C42×D7—42no—
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
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356C7⋊#95C2311yescharacteristic
357C7⋊#95C2311yescharacteristic
358#2852—71no—
359#2851—71no—
360#2802—71no—
361#2802—71no—
362#2776—71no—
363#2772—71no—
364#2766—71no—
365#2758—71no—
366#2755—71no—
367#2739—71no—
368#2725—71no—
369#2725—71no—
370#2725—71no—
371#2722—71no—
372#2719—71no—
373#2719D711yescharacteristic, complemented
374#2704—71no—
375#2698—71no—
376#2646—71no—
377#2643—71no—
378#2583—71no—
379#2579—71no—
380#2481—71no—
381#2481—71no—
382#2473—71no—
383#2473—71no—
384#2442—71no—
385#2417—71no—
386#2329—71no—
387#2318—71no—
388C2×#389—71no—
389C23×D7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C22×C4×C7C2411yescharacteristic
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
405C22×C4×C7C2411yescharacteristic
406C22×Dic7C2411yescharacteristic
407C22×Dic7C2411yescharacteristic
408C22×Dic7C2411yescharacteristic
409C22×Dic7C2411yescharacteristic
410C22×Dic7C2411yescharacteristic
411C22×Dic7C2411yescharacteristic
412C22×Dic7C2411yescharacteristic
413C22×Dic7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C2×D28—22no—
421C2×D28—22no—
422C2×D28—22no—
423C2×C4×D7—22no—
424C2×C4×D7—22no—
425C2×C4×D7—22no—
426C2×C4×D7—22no—
427C2×C4×D7—22no—
428C2×C4×D7—22no—
429C2×C4×D7—22no—
430C2×C4×D7—22no—
431C2×C4×D7—22no—
432C2×C4×D7—22no—
433C2×C4×D7—41no—
434C2×C4×D7—41no—
435C2×C4×D7—41no—
436C2×C4×D7—41no—
437C2×C4×D7—41no—
438C2×C4×D7—41no—
439C2×C4×D7—41no—
440C2×C4×D7—41no—
441C2×C4×D7—41no—
442C2×C4×D7—41no—
443C2×C4×D7—41no—
444C2×C4×D7—41no—
445C2×C4×D7—41no—
446C2×C4×D7#4114yes—
447C2×Dic14—22no—
448C2×Dic14—41no—
449C2×Dic14—41no—
450C7×C4⋊C4—22no—
451C7×C4⋊C4—22no—
452C7×C4⋊C4—22no—
453C7×C4⋊C4—22no—
454C7×C4⋊C4—22no—
455C7×C4⋊C4—22no—
456C7×C4⋊C4—22no—
457C7×C4⋊C4—22no—
458C7×C4⋊C4—22no—
459C7×C4⋊C4—41no—
460C7×C4⋊C4—41no—
461C7×C4⋊C4—41no—
462C7×C4⋊C4—41no—
463C7×C4⋊C4—41no—
464C7×C4⋊C4—41no—
465C7×C4⋊C4—41no—
466C42×C7—22no—
467C42×C7—22no—
468C42×C7—41no—
469(C2×D7)⋊C4—22no—
470(C2×D7)⋊C4—22no—
471(C2×D7)⋊C4—22no—
472(C2×D7)⋊C4—22no—
473(C2×D7)⋊C4—22no—
474(C2×D7)⋊C4—22no—
475(C2×D7)⋊C4—22no—
476(C2×D7)⋊C4—22no—
477(C2×D7)⋊C4—22no—
478(C2×D7)⋊C4—22no—
479(C2×D7)⋊C4—22no—
480(C2×D7)⋊C4—41no—
481(C2×D7)⋊C4—41no—
482(C2×D7)⋊C4—41no—
483(C2×D7)⋊C4—41no—
484(C2×D7)⋊C4—41no—
485(C2×D7)⋊C4—41no—
486(C2×D7)⋊C4—41no—
487(C2×D7)⋊C4—41no—
488(C2×D7)⋊C4—41no—
489C4⋊Dic7—22no—
490C4⋊Dic7—22no—
491C4⋊Dic7—22no—
492C4⋊Dic7—22no—
493C4⋊Dic7—22no—
494C4⋊Dic7—22no—
495C4⋊Dic7—22no—
496C4⋊Dic7—41no—
497C4⋊Dic7—41no—
498C4⋊Dic7—41no—
499C4⋊Dic7—41no—
500C4⋊Dic7—41no—
501C4⋊Dic7—41no—
502C4⋊Dic7—41no—
503Dic7⋊C4—22no—
504Dic7⋊C4—22no—
505Dic7⋊C4—22no—
506Dic7⋊C4—22no—
507Dic7⋊C4—22no—
508Dic7⋊C4—22no—
509Dic7⋊C4—22no—
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—
521Dic7⋊C4—41no—
522Dic7⋊C4—41no—
523Dic7⋊C4—41no—
524Dic7⋊C4—41no—
525Dic7⋊C4—41no—
526Dic7⋊C4—41no—
527C4×Dic7—22no—
528C4×Dic7—41no—
529C4×Dic7—41no—
530C4×Dic7—41no—
531C4×Dic7—41no—
532C4×Dic7—41no—
533C4×Dic7—41no—
534C4×Dic7—41no—
535C2×#126—71no—
536C2×#126—71no—
537C2×#126—71no—
538C2×#125—71no—
539C2×#125—71no—
540C2×#125C2×D711yescharacteristic
541C2×#125C2×D711yescharacteristic
542C2×C22⋊Q8—71no—
543C2×C22⋊Q8—71no—
544C2×C4×D4—71no—
545C22×C4⋊C4—71no—
546C22×C4⋊C4—71no—
547C22×C4⋊C4—71no—
548C22×C4⋊C4—71no—
549C22×C42—71no—
550#401—71no—
551#400—71no—
552#400—71no—
553#400—71no—
554#400—71no—
555#400—71no—
556#400—71no—
557#400—71no—
558#400—71no—
559#400—71no—
560#400—71no—
561#400—71no—
562#400—71no—
563#400C2×D711yescharacteristic
564#400C2×D711yescharacteristic
565#400C2×D711yescharacteristic
566#398—71no—
567#398—71no—
568#398—71no—
569#398—71no—
570#398—71no—
571#398—71no—
572#398—71no—
573#398—71no—
574#398—71no—
575#398—71no—
576#398—71no—
577#398—71no—
578#398—71no—
579#398—71no—
580#398—71no—
581#398C2×D711yescharacteristic
582#398C2×D711yescharacteristic
583#398C2×D711yescharacteristic
584#397—71no—
585#397—71no—
586#397—71no—
587#397—71no—
588#397—71no—
589#396—71no—
590#396—71no—
591#396—71no—
592#396—71no—
593#396—71no—
594#396—71no—
595#396—71no—
596#395—71no—
597#395—71no—
598#391—71no—
599#391—71no—
600#391—71no—
601#389—71no—
602#389—71no—
603#389—71no—
604#389—71no—
605#389—71no—
606#389—71no—
607#389—71no—
608#389—71no—
609#389—71no—
610#389—71no—
611#389—71no—
612#389—71no—
613#389—71no—
614#389—71no—
615#389—71no—
616#389—71no—
617#389—71no—
618#389—71no—
619#389—71no—
620#389C2×D711yescharacteristic
621#389C2×D711yescharacteristic
622#388—71no—
623#388—71no—
624#388—71no—
625#388—71no—
626#388—71no—
627#388—71no—
628#388—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#387C2×D711yescharacteristic
649#387C2×D711yescharacteristic
650#387C2×D711yescharacteristic
651#387C2×D711yescharacteristic
652#386—71no—
653#386—71no—
654#386—71no—
655#386—71no—
656#386—71no—
657#386—71no—
658#385—71no—
659#385—71no—
660#385—71no—
661#385—71no—
662#385—71no—
663#385—71no—
664#385—71no—
665#385—71no—
666#385—71no—
667#385—71no—
668#385—71no—
669#385—71no—
670#385—71no—
671#385—71no—
672#383—71no—
673#383—71no—
674#382—71no—
675#382—71no—
676#382C2×D711yescharacteristic
677#381—71no—
678#380—71no—
679#380—71no—
680#380—71no—
681#380—71no—
682#380—71no—
683#380—71no—
684#380—71no—
685C4×C22⋊C4—71no—
686C4×C22⋊C4—71no—
687C4×C22⋊C4—71no—
688C2×#95—71no—
689C2×#95—71no—
690C23×C7C2511yescharacteristic
691C22×D7—21no—
692C22×D7—21no—
693C22×D7—21no—
694C22×D7—21no—
695C22×D7—21no—
696C22×D7—21no—
697C22×D7—21no—
698C22×D7—21no—
699C22×D7—21no—
700C22×D7—21no—
701C22×D7—21no—
702C22×D7C2×#4112yes—
703C22×D72−1+412yes—
704C22×D72−1+412yes—
705C2×C4×C7—21no—
706C2×C4×C7—21no—
707C2×C4×C7—21no—
708C2×C4×C7—21no—
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—21no—
747C2×C4×C7C2×#4112yes—
748C2×C4×C7H(5,𝔽2)12yes—
749C2×C4×C7H(5,𝔽2)12yes—
750C2×Dic7—21no—
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×Dic7C2×#4112yes—
791C2×Dic72−1+412yes—
792D28—44no—
793C4×D7—28no—
794C4×D7—44no—
795C4×D7—44no—
796C4×D7—44no—
797C4×D7—44no—
798C4×D7—82no—
799C4×D7—82no—
800C4×D7—82no—
801Dic14—82no—
802C22×Q8—71no—
803C22×D4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4—71no—
807C23×C4—71no—
808C23×C4—71no—
809C23×C4—71no—
810C23×C4—71no—
811C23×C4—71no—
812#126—282no—
813#126—282no—
814#126—282no—
815#125—42no—
816#125—42no—
817#125—282no—
818#125—282no—
819C22⋊Q8—144no—
820C22⋊Q8—282no—
821C4×D4—144no—
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⋊C4—71no—
851C2×C4⋊C4—71no—
852C2×C4⋊C4—71no—
853C2×C4⋊C4—71no—
854C2×C4⋊C4—71no—
855C2×C4⋊C4—71no—
856C2×C4⋊C4—71no—
857C2×C4⋊C4—71no—
858C2×C4⋊C4—71no—
859C2×C4⋊C4—71no—
860C2×C4⋊C4—144no—
861C2×C4⋊C4—282no—
862C2×C4⋊C4—282no—
863C2×C4⋊C4—282no—
864C2×C4⋊C4C22×D711yescharacteristic
865C2×C4⋊C4C22×D711yescharacteristic
866C2×C4⋊C4C22×D711yescharacteristic
867C2×C4⋊C4C22×D711yescharacteristic
868C2×C4⋊C4C22×D711yescharacteristic
869C2×C4⋊C4C22×D711yescharacteristic
870C2×C4⋊C4C22×D711yescharacteristic
871C2×C4⋊C4C22×D711yescharacteristic
872C2×C4⋊C4C22×D711yescharacteristic
873C2×C4⋊C4C22×D711yescharacteristic
874C2×C4⋊C4C22×D711yescharacteristic
875C2×C4⋊C4C22×D711yescharacteristic
876C2×C4⋊C4C22×D711yescharacteristic
877C2×C4⋊C4C22×D711yescharacteristic
878C2×C4⋊C4C22×D711yescharacteristic
879C2×C4⋊C4C22×D711yescharacteristic
880C2×C22⋊C4—71no—
881C2×C22⋊C4—71no—
882C2×C22⋊C4—71no—
883C2×C22⋊C4—71no—
884C2×C22⋊C4—71no—
885C2×C22⋊C4—71no—
886C2×C22⋊C4—71no—
887C2×C22⋊C4—71no—
888C2×C22⋊C4—71no—
889C2×C22⋊C4—71no—
890C2×C22⋊C4—71no—
891C2×C22⋊C4—71no—
892C2×C22⋊C4—71no—
893C2×C22⋊C4—71no—
894C2×C22⋊C4—71no—
895C2×C22⋊C4—71no—
896C2×C22⋊C4—71no—
897C2×C22⋊C4—71no—
898C2×C22⋊C4—71no—
899C2×C22⋊C4—71no—
900C2×C42—71no—
901C2×C42—71no—
902C2×C42—71no—
903C2×C42—71no—
904C2×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
907C2×C42—71no—
908C2×C42—282no—
909C2×C42C22×D711yescharacteristic
910C2×C42C22×D711yescharacteristic
911C2×C42C22×D711yescharacteristic
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#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959#95C22×D711yescharacteristic
960#95C22×D711yescharacteristic
961#95C22×D711yescharacteristic
962#95C22×D711yescharacteristic
963#95C22×D711yescharacteristic
964#95C22×D711yescharacteristic
965#95C22×D711yescharacteristic
966#95C22×D711yescharacteristic
967#95C22×D711yescharacteristic
968#95C22×D711yescharacteristic
969#95C22×D711yescharacteristic
970#95C22×D711yescharacteristic
971#95C22×D711yescharacteristic
972C22×C7C22×#4111yescharacteristic
973C22×C7C2×H(5,𝔽2)11yescharacteristic
974C22×C7C2×H(5,𝔽2)11yescharacteristic
975C22×C7C2×2−1+411yescharacteristic
976C22×C7C2×2−1+411yescharacteristic
977C22×C7C2×2−1+411yescharacteristic
978C22×C7#58511yescharacteristic
979C2×D7—22no—
980C2×D7—22no—
981C2×D7—22no—
982C2×D7—22no—
983C2×D7—22no—
984C2×D7—22no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C2×D7—41no—
992C2×D7#54114yes—
993C4×C7—22no—
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—
1007C4×C7—41no—
1008Dic7—22no—
1009Dic7—22no—
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—
1023C24—71no—
1024C2×Q8—142no—
1025C2×Q8—281no—
1026C2×Q8—281no—
1027C2×D4—142no—
1028C2×D4—142no—
1029C2×D4—142no—
1030C22×C4—71no—
1031C22×C4—71no—
1032C22×C4—74no—
1033C22×C4—71no—
1034C22×C4—71no—
1035C22×C4—71no—
1036C22×C4—71no—
1037C22×C4—71no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4—71no—
1041C22×C4—71no—
1042C22×C4—71no—
1043C22×C4—71no—
1044C22×C4—71no—
1045C22×C4—142no—
1046C22×C4—142no—
1047C22×C4—142no—
1048C22×C4—142no—
1049C22×C4—142no—
1050C22×C4—142no—
1051C22×C4—142no—
1052C22×C4—142no—
1053C22×C4—142no—
1054C22×C4—142no—
1055C22×C4—281no—
1056C22×C4—281no—
1057C22×C4—281no—
1058C22×C4—281no—
1059C22×C4—281no—
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×C4C23×D711yescharacteristic
1069C22×C4C23×D711yescharacteristic
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—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—142no—
1100C4⋊C4—142no—
1101C4⋊C4—142no—
1102C4⋊C4—142no—
1103C4⋊C4—142no—
1104C4⋊C4—142no—
1105C4⋊C4—142no—
1106C4⋊C4—142no—
1107C4⋊C4—142no—
1108C4⋊C4—142no—
1109C4⋊C4—142no—
1110C4⋊C4—142no—
1111C4⋊C4—142no—
1112C4⋊C4—142no—
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—
1122C4⋊C4—281no—
1123C4⋊C4—281no—
1124C4⋊C4—281no—
1125C4⋊C4—281no—
1126C4⋊C4—281no—
1127C4⋊C4—281no—
1128C4⋊C4—281no—
1129C4⋊C4—281no—
1130C4⋊C4—281no—
1131C4⋊C4—281no—
1132C4⋊C4—281no—
1133C4⋊C4—281no—
1134C4⋊C4—281no—
1135C4⋊C4—281no—
1136C4⋊C4—281no—
1137C22⋊C4—142no—
1138C22⋊C4—142no—
1139C22⋊C4—142no—
1140C22⋊C4—142no—
1141C22⋊C4—142no—
1142C22⋊C4—142no—
1143C22⋊C4—142no—
1144C22⋊C4—142no—
1145C22⋊C4—142no—
1146C22⋊C4—142no—
1147C22⋊C4—142no—
1148C22⋊C4—281no—
1149C22⋊C4—281no—
1150C22⋊C4—281no—
1151C22⋊C4—281no—
1152C22⋊C4—281no—
1153C22⋊C4—281no—
1154C22⋊C4—281no—
1155C22⋊C4—281no—
1156C22⋊C4—281no—
1157C42—22no—
1158C42—22no—
1159C42—41no—
1160C42—142no—
1161C42—281no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42—281no—
1166C42—281no—
1167C42—281no—
1168C2×C7C2×#54111yescharacteristic
1169C2×C7#349211yescharacteristic
1170C2×C7#350511yescharacteristic
1171C2×C7#353611yescharacteristic
1172C2×C7#354111yescharacteristic
1173C2×C7#355211yescharacteristic
1174C2×C7#356311yescharacteristic
1175D7—24no—
1176D7—81no—
1177C23—72no—
1178C23—72no—
1179C23—72no—
1180C23—141no—
1181C23—141no—
1182C23—141no—
1183C23—141no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23—141no—
1189C23—141no—
1190C23—141no—
1191C23C24×D711yescharacteristic
1192Q8—562no—
1193D4—284no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
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—72no—
1237C2×C4—72no—
1238C2×C4—148no—
1239C2×C4—141no—
1240C2×C4—141no—
1241C2×C4—141no—
1242C2×C4—141no—
1243C2×C4—141no—
1244C2×C4—141no—
1245C2×C4—141no—
1246C2×C4—141no—
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—284no—
1280C2×C4—284no—
1281C2×C4—284no—
1282C2×C4—284no—
1283C2×C4—562no—
1284C2×C4—562no—
1285C2×C4—562no—
1286C2×C4#654812yes—
1287C2×C4D7×#4112yes—
1288C2×C4#655312yes—
1289C7#3682511yescharacteristic, complemented, Sylow
1290C22—74no—
1291C22—142no—
1292C22—142no—
1293C22—142no—
1294C22—142no—
1295C22—142no—
1296C22—142no—
1297C22—281no—
1298C22—281no—
1299C22—281no—
1300C22—281no—
1301C22—281no—
1302C22—281no—
1303C22—281no—
1304C22C2×#654811yescharacteristic
1305C22C2×D7×#4111yescharacteristic
1306C22C2×#655311yescharacteristic
1307C22D7×2−1+411yescharacteristic
1308C22D7×2−1+411yescharacteristic
1309C22D7×2−1+411yescharacteristic
1310C22#9062011yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—142no—
1327C4—142no—
1328C4—281no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C4—281no—
1333C4—281no—
1334C4—281no—
1335C4—281no—
1336C4—281no—
1337C4—281no—
1338C4—281no—
1339C4—281no—
1340C2—144no—
1341C2—561no—
1342C2#1174342811yescharacteristic
1343C2D7×#54111yescharacteristic
1344C2#1174358511yescharacteristic
1345C2#1174376911yescharacteristic
1346C2#1174380711yescharacteristic
1347C2#1174393011yescharacteristic
1348C2#1174421211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2719C2
prime radicalC22×D28C23
hypercenter#2719D7
hypocenterC7#36825
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2719

Complements

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

NH ≅ G/Ntype
1. C7×#2719C2semidirect
2. #11740517C2semidirect
3. #11740498C2semidirect
4. #11740498C2semidirect
5. #11740477C2semidirect
6. #11735808C2semidirect
8. #11735753C2semidirect
9. #11735721C2semidirect
10. #11735711C2semidirect
12. #11735406C2semidirect
13. #11735311C2semidirect
14. #11735310C2semidirect
15. #11735297C2semidirect
16. #11735203C2semidirect
17. #11735191C2semidirect
18. #11733709C2semidirect
20. D7×#389C2semidirect
21. #11733600C2semidirect
23. #11732851C2semidirect
25. #11732745C2semidirect
26. #11732720C2semidirect
27. #11732635C2semidirect
28. #11732611C2semidirect
31. #11731647C2semidirect
373. #2719D7semidirect
1289. C7#36825semidirect

Maximal subgroups

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

subgroupindex
C7×#27192
#117405172
#117404982
#117404772
#117358082
#117358072
#117357532
#117357212
#117357112
#117355892
#117354062
#117353112
#117353102
#117352972
#117352032
#117351912
#117337092
#117336572
D7×#3892
#117336002
#117328912
#117328512
#117328152
#117327452
#117327202
#117326352
#117326112
#117324652
#117316712
#117316472
#368257