Finite Group Databasebeta

← #13524715

Subgroups — #13524715

Order 1792.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2612C211yesmaximal, characteristic, complemented
2#11735631C211yesmaximal, characteristic, complemented
3#11735577C211yesmaximal, characteristic, complemented
4#11735245C211yesmaximal, characteristic, complemented
5#11735233C211yesmaximal, characteristic
6#11735186C211yesmaximal, characteristic, complemented
7#11735183C211yesmaximal, characteristic
8#11734633C211yesmaximal, characteristic, complemented
9#11734615C211yesmaximal, characteristic, complemented
10#11733975C211yesmaximal, characteristic, complemented
11#11733961C211yesmaximal, characteristic
12#11733924C211yesmaximal, characteristic, complemented
13#11733922C211yesmaximal, characteristic, complemented
14#11733501C211yesmaximal, characteristic, complemented
15#11733467C211yesmaximal, characteristic
16#11733411C211yesmaximal, characteristic, complemented
17#11733408C211yesmaximal, characteristic, complemented
18#11732519C211yesmaximal, characteristic, complemented
19#11732508C211yesmaximal, characteristic, complemented
20#11732462C211yesmaximal, characteristic, complemented
21#11732458C211yesmaximal, characteristic, complemented
22#11732387C211yesmaximal, characteristic, complemented
23#11732385C211yesmaximal, characteristic
24#11732384C211yesmaximal, characteristic, complemented
25#11732382C211yesmaximal, characteristic
26#11731688C211yesmaximal, characteristic
27#11731595C211yesmaximal, characteristic, complemented
28#11730872C211yesmaximal, characteristic, complemented
29#11730872C211yesmaximal, characteristic, complemented
30#11730827C211yesmaximal, characteristic, complemented
31#11730827C211yesmaximal, characteristic, complemented
32C2×#6509C2211yescharacteristic
33C2×Q8×Dic7C2211yescharacteristic
34C2×#6461C2211yescharacteristic
35C2×#6457C2211yescharacteristic
36C2×#6456C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6435C2211yescharacteristic
41C2×#6435C2211yescharacteristic
42C2×#6435C2211yescharacteristic
43C2×#6435C2211yescharacteristic
44C2×C42×D7C2211yescharacteristic
45C2×C42×D7C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47C7×#400C2211yescharacteristic
48C7×#398C2211yescharacteristic
49C7×#398C2211yescharacteristic
50C7×#395C2211yescharacteristic
51C7×#391C2211yescharacteristic
52C7×#391C2211yescharacteristic
53C7×#389C2211yescharacteristic
54C7×#389C2211yescharacteristic
55C7×#387C2211yescharacteristic
56C7×#387C2211yescharacteristic
57C7×#387C2211yescharacteristic
58C7×#387C2211yescharacteristic
59C7×#382C2211yescharacteristic
60C7×#376C2211yescharacteristic
61C7×#376C2211yescharacteristic
62#90003C2211yescharacteristic
63#90002C2211yescharacteristic
64#89766C2211yescharacteristic
65#89766C2211yescharacteristic
66#89766C2211yescharacteristic
67#89765C2211yescharacteristic
68#89765C2211yescharacteristic
69#89763C2211yescharacteristic
70#89763C2211yescharacteristic
71#89762C2211yescharacteristic
72#89762C2211yescharacteristic
73#89761C2211yescharacteristic
74#89761C2211yescharacteristic
75#89761C2211yescharacteristic
76#89759C2211yescharacteristic
77#89758C2211yescharacteristic
78#89758C2211yescharacteristic
79#89758C2211yescharacteristic
80#89757C2211yescharacteristic
81#89756C2211yescharacteristic
82#89755C2211yescharacteristic
83#89754C2211yescharacteristic
84#89753C2211yescharacteristic
85#89753C2211yescharacteristic
86#89750C2211yescharacteristic
87#89750C2211yescharacteristic
88#89750C2211yescharacteristic
89#89749C2211yescharacteristic
90C4⋊C4×Dic7C2211yescharacteristic
91C4⋊C4×Dic7C2211yescharacteristic
92C4⋊C4×Dic7C2211yescharacteristic
93C4⋊C4×Dic7C2211yescharacteristic
94C4⋊C4×Dic7C2211yescharacteristic
95C4⋊C4×Dic7C2211yescharacteristic
96C4⋊C4×Dic7C2211yescharacteristic
97C4⋊C4×Dic7C2211yescharacteristic
98#89745C2211yescharacteristic
99#89745C2211yescharacteristic
100#89745C2211yescharacteristic
101#89745C2211yescharacteristic
102#89712C2211yescharacteristic
103#89712C2211yescharacteristic
104#89712C2211yescharacteristic
105#89712C2211yescharacteristic
106#89704C2211yescharacteristic
107#89704C2211yescharacteristic
108C42×Dic7C2211yescharacteristic
109C42×Dic7C2211yescharacteristic
110C42×Dic7C2211yescharacteristic
111#89700C2211yescharacteristic
112#89700C2211yescharacteristic
113#89700C2211yescharacteristic
114#89700C2211yescharacteristic
115#89449C2211yescharacteristic
116#89449C2211yescharacteristic
117#89447C2211yescharacteristic
118#89446C2211yescharacteristic
119#89446C2211yescharacteristic
120#89446C2211yescharacteristic
121#89442C2211yescharacteristic
122#89442C2211yescharacteristic
123#89442C2211yescharacteristic
124#89441C2211yescharacteristic
125#89441C2211yescharacteristic
126#89440C2211yescharacteristic
127#89440C2211yescharacteristic
128#89440C2211yescharacteristic
129#89440C2211yescharacteristic
130#89440C2211yescharacteristic
131#89440C2211yescharacteristic
132#89438C2211yescharacteristic
133#89438C2211yescharacteristic
134#89438C2211yescharacteristic
135#89438C2211yescharacteristic
136#89438C2211yescharacteristic
137#89438C2211yescharacteristic
138#89438C2211yescharacteristic
139#89438C2211yescharacteristic
140#89438C2211yescharacteristic
141#89438C2211yescharacteristic
142#89438C2211yescharacteristic
143#89438C2211yescharacteristic
144#89437C2211yescharacteristic
145#89437C2211yescharacteristic
146#89437C2211yescharacteristic
147#89436C2211yescharacteristic
148C7⋊#401C2211yescharacteristic
149#89433C2211yescharacteristic
150#89433C2211yescharacteristic
151#89433C2211yescharacteristic
152#89432C2211yescharacteristic
153#89432C2211yescharacteristic
154#89431C2211yescharacteristic
155#89431C2211yescharacteristic
156#89427C2211yescharacteristic
157#89427C2211yescharacteristic
158#89427C2211yescharacteristic
159#89426C2211yescharacteristic
160#89426C2211yescharacteristic
161#89426C2211yescharacteristic
162#89425C2211yescharacteristic
163#89425C2211yescharacteristic
164#89425C2211yescharacteristic
165#89425C2211yescharacteristic
166#89425C2211yescharacteristic
167#89425C2211yescharacteristic
168#89424C2211yescharacteristic
169#89424C2211yescharacteristic
170#89424C2211yescharacteristic
171#89424C2211yescharacteristic
172#89423C2211yescharacteristic
173#89421C2211yescharacteristic
174#89421C2211yescharacteristic
175#89421C2211yescharacteristic
176#89421C2211yescharacteristic
177#89421C2211yescharacteristic
178#89421C2211yescharacteristic
179#89421C2211yescharacteristic
180#89421C2211yescharacteristic
181#89421C2211yescharacteristic
182#89421C2211yescharacteristic
183#89421C2211yescharacteristic
184#89421C2211yescharacteristic
185#89420C2211yescharacteristic
186#89420C2211yescharacteristic
187#34873—71nomaximal, Sylow
188C22×C7×Q8C2311yescharacteristic
189C22×D28C2311yescharacteristic
190C22×C4×D7C2311yescharacteristic
191C22×C4×D7C2311yescharacteristic
192C22×C4×D7C2311yescharacteristic
193C22×C4×D7C2311yescharacteristic
194C22×C4×D7C2311yescharacteristic
195C22×C4×D7C2311yescharacteristic
196C2×C7×C4⋊C4C2311yescharacteristic
197C2×C7×C4⋊C4C2311yescharacteristic
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
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×C42×C7C2311yescharacteristic
208C2×C42×C7C2311yescharacteristic
209C2×C42×C7C2311yescharacteristic
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2311yescharacteristic
212#6509—24no—
213Q8×Dic7—24no—
214C2×(C2×D7)⋊C4C2311yescharacteristic
215C2×(C2×D7)⋊C4C2311yescharacteristic
216C2×(C2×D7)⋊C4C2311yescharacteristic
217C2×(C2×D7)⋊C4C2311yescharacteristic
218C2×(C2×D7)⋊C4C2311yescharacteristic
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×C4⋊Dic7C2311yescharacteristic
237C2×C4⋊Dic7C2311yescharacteristic
238C2×C4⋊Dic7C2311yescharacteristic
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×Dic7⋊C4C2311yescharacteristic
250C2×Dic7⋊C4C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2311yescharacteristic
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×C4×Dic7C2311yescharacteristic
266C2×C4×Dic7C2311yescharacteristic
267C2×C4×Dic7C2311yescharacteristic
268C2×C4×Dic7C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
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
288C2×C4×Dic7C2311yescharacteristic
289#6461—24no—
290#6457—24no—
291#6456—24no—
292#6455—24no—
293#6455—24no—
294#6453—24no—
295#6435—24no—
296#6435—24no—
297#6435—24no—
298#6435—24no—
299C42×D7—24no—
300C42×D7—24no—
301#6433—24no—
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#2612D711yescharacteristic, complemented
359#2611—71no—
360#2611—71no—
361#2609—71no—
362#2585—71no—
363#2573—71no—
364#2556—71no—
365#2553—71no—
366#2533—71no—
367#2530—71no—
368#2528—71no—
369#2527—71no—
370#2478—71no—
371#2477—71no—
372#2475—71no—
373#2470—71no—
374#2402—71no—
375#2401—71no—
376#2396—71no—
377#2395—71no—
378C4×#125—71no—
379C4×#125—71no—
380C4×#126—71no—
381C4×C22⋊Q8—71no—
382C4×#123—71no—
383#2298—71no—
384#2296—71no—
385#2295—71no—
386#2290—71no—
387C4×#117—71no—
388C4×#117—71no—
389C23×D7C2411yescharacteristic
390C23×D7C2411yescharacteristic
391C2×C7×Q8—22no—
392C2×C7×Q8—22no—
393C2×C7×Q8—41no—
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×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C22×Dic7C2411yescharacteristic
410C22×Dic7C2411yescharacteristic
411C22×Dic7C2411yescharacteristic
412C22×Dic7C2411yescharacteristic
413C22×Dic7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C2×D28—22no—
424C2×D28—22no—
425C2×D28—41no—
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—22no—
434C2×C4×D7—22no—
435C2×C4×D7—22no—
436C2×C4×D7—22no—
437C2×C4×D7—22no—
438C2×C4×D7—22no—
439C2×C4×D7—22no—
440C2×C4×D7—22no—
441C2×C4×D7—41no—
442C2×C4×D7—41no—
443C2×C4×D7#4114yes—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—22no—
447C7×C4⋊C4—22no—
448C7×C4⋊C4—22no—
449C7×C4⋊C4—22no—
450C7×C4⋊C4—41no—
451C7×C4⋊C4—41no—
452C7×C4⋊C4—41no—
453C7×C4⋊C4—41no—
454C7×C4⋊C4—41no—
455C42×C7—22no—
456C42×C7—22no—
457C42×C7—22no—
458C42×C7—22no—
459C42×C7#4114yes—
460(C2×D7)⋊C4—22no—
461(C2×D7)⋊C4—22no—
462(C2×D7)⋊C4—22no—
463(C2×D7)⋊C4—22no—
464(C2×D7)⋊C4—22no—
465(C2×D7)⋊C4—22no—
466(C2×D7)⋊C4—22no—
467(C2×D7)⋊C4—22no—
468(C2×D7)⋊C4—22no—
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—41no—
480(C2×D7)⋊C4—41no—
481(C2×D7)⋊C4#4114yes—
482C4⋊Dic7—22no—
483C4⋊Dic7—22no—
484C4⋊Dic7—22no—
485C4⋊Dic7—22no—
486C4⋊Dic7—22no—
487C4⋊Dic7—22no—
488C4⋊Dic7—22no—
489C4⋊Dic7—22no—
490C4⋊Dic7—22no—
491C4⋊Dic7—22no—
492C4⋊Dic7—22no—
493C4⋊Dic7—22no—
494C4⋊Dic7—41no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
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—22no—
508Dic7⋊C4—22no—
509Dic7⋊C4—22no—
510Dic7⋊C4#4114yes—
511C4×Dic7—22no—
512C4×Dic7—22no—
513C4×Dic7—22no—
514C4×Dic7—22no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—22no—
521C4×Dic7—22no—
522C4×Dic7—22no—
523C4×Dic7—22no—
524C4×Dic7—22no—
525C4×Dic7—22no—
526C4×Dic7—22no—
527C4×Dic7—22no—
528C4×Dic7—22no—
529C4×Dic7—22no—
530C4×Dic7—22no—
531C4×Dic7—41no—
532C4×Dic7—41no—
533C4×Dic7—41no—
534C4×Dic7#4114yes—
535C2×#126—71no—
536C2×#125—71no—
537C2×#125—71no—
538C2×#123—71no—
539C2×C22⋊Q8—71no—
540C2×C4×Q8—71no—
541C2×C4×D4—71no—
542C2×#117—71no—
543C2×#117—71no—
544C2×#117—71no—
545C2×#117—71no—
546C2×#117—71no—
547C2×#117—71no—
548C22×C42—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#400C2×D711yescharacteristic
560#399—71no—
561#399—71no—
562#398—71no—
563#398—71no—
564#398—71no—
565#398—71no—
566#398—71no—
567#398C2×D711yescharacteristic
568#398C2×D711yescharacteristic
569#397—71no—
570#397—71no—
571#397—71no—
572#397—71no—
573#397—71no—
574#397—71no—
575#396—71no—
576#396—71no—
577#396—71no—
578#395C2×D711yescharacteristic
579#394—71no—
580#394—71no—
581#393—71no—
582#391—71no—
583#391C2×D711yescharacteristic
584#391C2×D711yescharacteristic
585#389—71no—
586#389—71no—
587#389—71no—
588#389—71no—
589#389—71no—
590#389—71no—
591#389—71no—
592#389—71no—
593#389—71no—
594#389C2×D711yescharacteristic
595#389C2×D711yescharacteristic
596#388—71no—
597#388—71no—
598#388—71no—
599#388—71no—
600#388—71no—
601#388—71no—
602#388—71no—
603#388—71no—
604#388—71no—
605#388—71no—
606#388—71no—
607#387—71no—
608#387—71no—
609#387—71no—
610#387—71no—
611#387—71no—
612#387—71no—
613#387—71no—
614#387—71no—
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387—71no—
623#387—71no—
624#387—71no—
625#387—71no—
626#387—71no—
627#387—71no—
628#387C2×D711yescharacteristic
629#387C2×D711yescharacteristic
630#387C2×D711yescharacteristic
631#387C2×D711yescharacteristic
632#386—71no—
633#386—71no—
634#386—71no—
635#385—71no—
636#385—71no—
637#385—71no—
638#385—71no—
639#385—71no—
640#385—71no—
641#385—71no—
642#385—71no—
643#385—71no—
644#383—71no—
645#382—71no—
646#382C2×D711yescharacteristic
647#381—71no—
648#380—71no—
649C4×C4⋊C4—71no—
650C4×C4⋊C4—71no—
651C4×C4⋊C4—71no—
652C4×C4⋊C4—71no—
653C4×C4⋊C4—71no—
654C4×C4⋊C4—71no—
655C4×C4⋊C4—71no—
656C4×C4⋊C4—71no—
657C4×C4⋊C4—71no—
658C4×C4⋊C4—71no—
659C4×C4⋊C4—71no—
660C4×C4⋊C4—71no—
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C4⋊C4—71no—
668C4×C4⋊C4—71no—
669C4×C22⋊C4—71no—
670C4×C22⋊C4—71no—
671C4×C22⋊C4—71no—
672C4×C22⋊C4—71no—
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4—71no—
677C4×C22⋊C4—71no—
678C4×C22⋊C4—71no—
679C4×C22⋊C4—71no—
680C4×C22⋊C4—71no—
681#376—71no—
682#376—71no—
683#376—71no—
684#376—71no—
685#376C2×D711yescharacteristic
686#376C2×D711yescharacteristic
687C43—71no—
688C43—71no—
689C43—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×D7—21no—
703C22×D7C2×#4112yes—
704C22×D7C2×#4112yes—
705C7×Q8—44no—
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×C7C2×#4112yes—
745C2×C4×C7C2×#4112yes—
746C2×C4×C7C2×#4112yes—
747C2×C4×C7C2×#4112yes—
748C2×C4×C7C2×#4112yes—
749C2×C4×C7C2×#4112yes—
750C2×C4×C7C2×#4112yes—
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×Dic7C2×#4112yes—
787C2×Dic7C2×#4112yes—
788C2×Dic7C2×#4112yes—
789C2×Dic7C2×#4112yes—
790C2×Dic7C2×#4112yes—
791C2×Dic7C2×#4112yes—
792C2×Dic72−1+412yes—
793D28—44no—
794C4×D7—28no—
795C4×D7—28no—
796C4×D7—28no—
797C4×D7—44no—
798C4×D7—44no—
799C4×D7—44no—
800C22×Q8C22×D711yescharacteristic
801C22×D4—71no—
802C23×C4—71no—
803C23×C4—71no—
804C23×C4—71no—
805C23×C4—71no—
806C23×C4—71no—
807C23×C4—71no—
808#126—144no—
809#125—144no—
810#125—144no—
811#123—144no—
812C22⋊Q8—144no—
813C4×Q8—144no—
814C4×D4—144no—
815#117—144no—
816#117—144no—
817#117—144no—
818#117—144no—
819#117—144no—
820#117—144no—
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×C4⋊C4C22×D711yescharacteristic
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×C42—71no—
884C2×C42—71no—
885C2×C42—71no—
886C2×C42—71no—
887C2×C42—71no—
888C2×C42—71no—
889C2×C42—71no—
890C2×C42—71no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—71no—
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×C42—71no—
905C2×C42—71no—
906C2×C42—71no—
907C2×C42—144no—
908C2×C42—144no—
909C2×C42C22×D711yescharacteristic
910C2×C42C22×D711yescharacteristic
911C2×C42C22×D711yescharacteristic
912C2×C42C22×D711yescharacteristic
913C2×C42C22×D711yescharacteristic
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#95C22×D711yescharacteristic
953#95C22×D711yescharacteristic
954#95C22×D711yescharacteristic
955#95C22×D711yescharacteristic
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
970C22×C7C22×#4111yescharacteristic
971C22×C7C22×#4111yescharacteristic
972C22×C7C22×#4111yescharacteristic
973C22×C7C22×#4111yescharacteristic
974C22×C7C22×#4111yescharacteristic
975C22×C7C2×2−1+411yescharacteristic
976C22×C7#58511yescharacteristic
977C2×D7—22no—
978C2×D7—22no—
979C2×D7—22no—
980C2×D7—22no—
981C2×D7—22no—
982C2×D7—22no—
983C2×D7—41no—
984C2×D7—41no—
985C2×D7—41no—
986C2×D7—41no—
987C2×D7—41no—
988C2×D7—41no—
989C2×D7—41no—
990C2×D7—41no—
991C4×C7—22no—
992C4×C7—22no—
993C4×C7—22no—
994C4×C7—22no—
995C4×C7—22no—
996C4×C7—22no—
997C4×C7—22no—
998C4×C7—41no—
999C4×C7—41no—
1000C4×C7—41no—
1001C4×C7—41no—
1002C4×C7—41no—
1003C4×C7—41no—
1004C4×C7—41no—
1005C4×C7—41no—
1006Dic7—22no—
1007Dic7—22no—
1008Dic7—22no—
1009Dic7—22no—
1010Dic7—41no—
1011Dic7—41no—
1012Dic7—41no—
1013Dic7—41no—
1014Dic7—41no—
1015Dic7—41no—
1016Dic7—41no—
1017Dic7—41no—
1018Dic7—41no—
1019Dic7#55214yes—
1020C24—71no—
1021C24—71no—
1022C2×Q8—22no—
1023C2×Q8—22no—
1024C2×Q8—41no—
1025C2×D4—142no—
1026C2×D4—142no—
1027C2×D4—281no—
1028C22×C4—71no—
1029C22×C4—71no—
1030C22×C4—71no—
1031C22×C4—71no—
1032C22×C4—71no—
1033C22×C4—74no—
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—142no—
1044C22×C4—142no—
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—142no—
1056C22×C4—142no—
1057C22×C4—142no—
1058C22×C4—281no—
1059C22×C4—281no—
1060C22×C4C23×D711yescharacteristic
1061C22×C4C23×D711yescharacteristic
1062C22×C4C23×D711yescharacteristic
1063C22×C4C23×D711yescharacteristic
1064C22×C4C23×D711yescharacteristic
1065C22×C4C23×D711yescharacteristic
1066C22×C4C23×D711yescharacteristic
1067C22×C4C23×D711yescharacteristic
1068C22×C4C23×D711yescharacteristic
1069C22×C4C23×D711yescharacteristic
1070C22×C4C23×D711yescharacteristic
1071C22×C4C23×D711yescharacteristic
1072C22×C4C23×D711yescharacteristic
1073C22×C4C23×D711yescharacteristic
1074C22×C4C23×D711yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—74no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—142no—
1090C4⋊C4—142no—
1091C4⋊C4—142no—
1092C4⋊C4—142no—
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—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—142no—
1114C4⋊C4—281no—
1115C22⋊C4—74no—
1116C22⋊C4—142no—
1117C22⋊C4—142no—
1118C22⋊C4—142no—
1119C22⋊C4—142no—
1120C22⋊C4—142no—
1121C22⋊C4—142no—
1122C22⋊C4—142no—
1123C22⋊C4—142no—
1124C22⋊C4—142no—
1125C22⋊C4—142no—
1126C22⋊C4—142no—
1127C22⋊C4—142no—
1128C22⋊C4—142no—
1129C22⋊C4—142no—
1130C22⋊C4—142no—
1131C22⋊C4—142no—
1132C22⋊C4—142no—
1133C22⋊C4—142no—
1134C22⋊C4—142no—
1135C22⋊C4—281no—
1136C22⋊C4—281no—
1137C42—22no—
1138C42—22no—
1139C42—22no—
1140C42—22no—
1141C42—74no—
1142C42—142no—
1143C42—142no—
1144C42—142no—
1145C42—142no—
1146C42—142no—
1147C42—142no—
1148C42—142no—
1149C42—142no—
1150C42—142no—
1151C42—142no—
1152C42—142no—
1153C42—142no—
1154C42—142no—
1155C42—142no—
1156C42—142no—
1157C42—142no—
1158C42—142no—
1159C42—142no—
1160C42—142no—
1161C42—142no—
1162C42—281no—
1163C42—281no—
1164C42—281no—
1165C42#116114yes—
1166C2×C7#344411yescharacteristic
1167C2×C7#344411yescharacteristic
1168C2×C7#346111yescharacteristic
1169C2×C7C2×#55211yescharacteristic
1170C2×C7#347511yescharacteristic
1171C2×C7#347511yescharacteristic
1172C2×C7#348211yescharacteristic
1173D7—42no—
1174D7—42no—
1175C23—72no—
1176C23—72no—
1177C23—141no—
1178C23—141no—
1179C23—141no—
1180C23—141no—
1181C23—141no—
1182C23—141no—
1183C23—141no—
1184C23—141no—
1185C23—141no—
1186C23—141no—
1187C23—141no—
1188C23—141no—
1189C23C24×D711yescharacteristic
1190Q8—44no—
1191D4—284no—
1192C2×C4—21no—
1193C2×C4—21no—
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—72no—
1231C2×C4—72no—
1232C2×C4—72no—
1233C2×C4—72no—
1234C2×C4—72no—
1235C2×C4—72no—
1236C2×C4—72no—
1237C2×C4—148no—
1238C2×C4—148no—
1239C2×C4—148no—
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—284no—
1276C2×C4—284no—
1277C2×C4—284no—
1278C2×C4C2×#116112yes—
1279C2×C4C2×#116112yes—
1280C2×C4C2×#116112yes—
1281C2×C4D7×#4112yes—
1282C2×C4D7×#4112yes—
1283C2×C4D7×#4112yes—
1284C2×C4D7×#4112yes—
1285C7#3487311yescharacteristic, complemented, Sylow
1286C22—142no—
1287C22—142no—
1288C22—142no—
1289C22—142no—
1290C22—142no—
1291C22—142no—
1292C22—281no—
1293C22—281no—
1294C22—281no—
1295C22—281no—
1296C22—281no—
1297C22—281no—
1298C22—281no—
1299C22—281no—
1300C22C22×#116111yescharacteristic
1301C22C2×D7×#4111yescharacteristic
1302C22C2×D7×#4111yescharacteristic
1303C22C2×D7×#4111yescharacteristic
1304C22C2×D7×#4111yescharacteristic
1305C22#9061811yescharacteristic
1306C22D7×2−1+411yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—74no—
1323C4—142no—
1324C4—142no—
1325C4—142no—
1326C4—142no—
1327C4—281no—
1328C4—281no—
1329C4—281no—
1330C4—281no—
1331C4—281no—
1332C4—281no—
1333C4—281no—
1334C4—281no—
1335C4—281no—
1336C2—282no—
1337C2—282no—
1338C2#1174332511yescharacteristic
1339C2#1174332511yescharacteristic
1340C2#1174365111yescharacteristic
1341C2#1174385811yescharacteristic
1342C2#1174389611yescharacteristic
1343C2D7×#55211yescharacteristic
1344C2#1174402611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2612C2
prime radicalC22×D28C23
hypercenter#2612D7
hypocenterC7#34873
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2612

Complements

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

NH ≅ G/Ntype
1. C7×#2612C2semidirect
2. #11735631C2semidirect
3. #11735577C2semidirect
4. #11735245C2semidirect
6. #11735186C2semidirect
8. #11734633C2semidirect
9. #11734615C2semidirect
10. #11733975C2semidirect
12. #11733924C2semidirect
13. #11733922C2semidirect
14. #11733501C2semidirect
16. #11733411C2semidirect
17. #11733408C2semidirect
18. #11732519C2semidirect
19. #11732508C2semidirect
20. #11732462C2semidirect
21. #11732458C2semidirect
22. #11732387C2semidirect
24. #11732384C2semidirect
27. #11731595C2semidirect
28. #11730872C2semidirect
29. #11730872C2semidirect
30. #11730827C2semidirect
31. #11730827C2semidirect
358. #2612D7semidirect
1285. C7#34873semidirect

Maximal subgroups

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

subgroupindex
C7×#26122
#117356312
#117355772
#117352452
#117352332
#117351862
#117351832
#117346332
#117346152
#117339752
#117339612
#117339242
#117339222
#117335012
#117334672
#117334112
#117334082
#117325192
#117325082
#117324622
#117324582
#117323872
#117323852
#117323842
#117323822
#117316882
#117315952
#117308722
#117308272
#348737