Finite Group Databasebeta

← #13321332

Subgroups — #13321332

Order 1792.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742835C211yesmaximal, characteristic
2C7×#2318C211yesmaximal, characteristic, complemented
3#11739748C211yesmaximal, characteristic, complemented
4#11727320C211yesmaximal, characteristic, complemented
5#11727319C211yesmaximal, characteristic, complemented
6#11727300C211yesmaximal, characteristic, complemented
7#11727298C211yesmaximal, characteristic, complemented
8#11727287C211yesmaximal, characteristic, complemented
9#11727286C211yesmaximal, characteristic, complemented
10#11727264C211yesmaximal, characteristic, complemented
11#11727262C211yesmaximal, characteristic, complemented
12#11727199C211yesmaximal, characteristic, complemented
13#11727197C211yesmaximal, characteristic, complemented
14C2×#89247C211yesmaximal, characteristic, complemented
15#11727152C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17#90497—21no—
18#90482C2211yescharacteristic
19#90482C2211yescharacteristic
20C2×#6487C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22#90255—21no—
23#90255—21no—
24#90252—21no—
25#90246C411yescharacteristic, complemented
26#90243C411yescharacteristic, complemented
27#90243C411yescharacteristic, complemented
28#90242C411yescharacteristic, complemented
29#90237—21no—
30#90233C411yescharacteristic, complemented
31#90232C411yescharacteristic, complemented
32#90232C411yescharacteristic, complemented
33D4×Dic14C411yescharacteristic, complemented
34#90202—21no—
35#90186—21no—
36#90186—21no—
37#90170C2211yescharacteristic
38#90161C2211yescharacteristic
39C7×#388—21no—
40C7×#387—21no—
41C7×#386—21no—
42C7×#385—21no—
43C7×#383C2211yescharacteristic
44C7×#382C2211yescharacteristic
45C7×#381C2211yescharacteristic
46C7×#380C2211yescharacteristic
47C4×C7×C22⋊C4C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49#89979C2211yescharacteristic
50#89979C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53#89784—21no—
54#89783—21no—
55#89783—21no—
56D4×C7⋊C8—21no—
57#89698C2211yescharacteristic
58#89697C2211yescharacteristic
59#89247C2211yescharacteristic
60#89247C2211yescharacteristic
61#89247C2211yescharacteristic
62#89247C2211yescharacteristic
63#89247C2211yescharacteristic
64#89247C2211yescharacteristic
65#89247C2211yescharacteristic
66#89247C2211yescharacteristic
67#89247C2211yescharacteristic
68#89247C2211yescharacteristic
69#89247C2211yescharacteristic
70#89247C2211yescharacteristic
71#89246C2211yescharacteristic
72#89246C2211yescharacteristic
73#89246C2211yescharacteristic
74#89246C2211yescharacteristic
75#17598—71nomaximal, Sylow
76C22×C7×D4D411yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C2×#1159—21no—
81C2×#1157C2×C411yescharacteristic
82C2×#1157C2×C411yescharacteristic, complemented
83C22×Dic14C2×C411yescharacteristic
84C22×Dic14C2×C411yescharacteristic, complemented
85C4×C7×D4C2×C411yescharacteristic
86C4×C7×D4C2×C411yescharacteristic
87C4×C7×D4C2×C411yescharacteristic
88C4×C7×D4C2×C411yescharacteristic
89C4×C7×D4D411yescharacteristic
90C4×C7×D4D411yescharacteristic
91C4×C7×D4D411yescharacteristic
92C4×C7×D4D411yescharacteristic
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C42×C7—21no—
102C2×C42×C7C2311yescharacteristic
103#6516—21no—
104#6516—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107#6502—21no—
108#6502—21no—
109#6501—21no—
110#6499—21no—
111#6498—21no—
112#6498—21no—
113D4×Dic7—21no—
114#6493C2×C411yescharacteristic
115#6493C2×C411yescharacteristic, complemented
116#6493C2311yescharacteristic
117#6492—21no—
118#6492—21no—
119#6492—21no—
120C4×C22⋊D7—21no—
121C4×C22⋊D7—21no—
122C4×C22⋊D7—21no—
123C4×C22⋊D7—21no—
124C4×C22⋊D7—21no—
125#6489—21no—
126#6489C2×C411yescharacteristic
127#6489C2×C411yescharacteristic, complemented
128C2×C4⋊Dic7C2×C411yescharacteristic
129C2×C4⋊Dic7C2×C411yescharacteristic, complemented
130#6487—21no—
131#6487—21no—
132#6487—21no—
133#6487—21no—
134#6487—21no—
135#6487C2×C411yescharacteristic
136#6487C2×C411yescharacteristic
137#6487C2×C411yescharacteristic
138#6487C2×C411yescharacteristic, complemented
139#6487C2×C411yescharacteristic, complemented
140#6487C2×C411yescharacteristic, complemented
141#6487C2311yescharacteristic
142#6487C2311yescharacteristic
143#6487C2311yescharacteristic
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×#1136—21no—
147C2×#1136—21no—
148C22×C7⋊C8—21no—
149C22×C7⋊C8—21no—
150#6460—21no—
151#6459—21no—
152#6459—21no—
153D7×C4⋊C4—21no—
154#6452—21no—
155#6452—21no—
156#6451—21no—
157#6450—21no—
158#6449—21no—
159#6449—21no—
160#6448—21no—
161#6448—21no—
162#6446—21no—
163#6446—21no—
164(C22⋊D7)⋊C4—21no—
165(C22⋊D7)⋊C4—21no—
166#6442—21no—
167#6442—21no—
168#6442—21no—
169#6442—21no—
170#6441—21no—
171#6441—21no—
172#6440—21no—
173#6440—21no—
174#6439—21no—
175#6438C2×C411yescharacteristic, complemented
176C4×D28C2×C411yescharacteristic, complemented
177#6435—21no—
178#6433—21no—
179#6433C2×C411yescharacteristic, complemented
180#6432C2×C411yescharacteristic, complemented
181#6432C2×C411yescharacteristic, complemented
182C4×Dic14—21no—
183C4×Dic14C2×C411yescharacteristic, complemented
184C4×Dic14C2×C411yescharacteristic, complemented
185C4×Dic14C2×C411yescharacteristic, complemented
186C7×#95—21no—
187C7×#95—21no—
188C7×#95—21no—
189C7×#95—21no—
190C7×#95—21no—
191C7×#95C2311yescharacteristic
192C7×#95C2311yescharacteristic
193C7×#95C2311yescharacteristic
194C7×#95C2311yescharacteristic
195C22⋊(C7⋊C8)—21no—
196C22⋊(C7⋊C8)—21no—
197C22⋊(C7⋊C8)—21no—
198C22⋊(C7⋊C8)—21no—
199C22⋊(C7⋊C8)C2311yescharacteristic
200C22⋊(C7⋊C8)C2311yescharacteristic
201C22⋊(C7⋊C8)C2311yescharacteristic
202C22⋊(C7⋊C8)C2311yescharacteristic
203C4⋊(C7⋊C8)—21no—
204C4⋊(C7⋊C8)—21no—
205#6377—21no—
206C4×C7⋊C8—21no—
207#3520—71no—
208#2974—71no—
209#2318D711yescharacteristic, complemented
210#1521—71no—
211#1520—71no—
212#1518—71no—
213#1516—71no—
214#1515—71no—
215#1513—71no—
216#1512—71no—
217#1511—71no—
218#1508—71no—
219#1504—71no—
220#1501—71no—
221C2×#328—71no—
222C24×C7C2×D411yescharacteristic
223C24×C7C2×D411yescharacteristic
224C2×C7×D4—42no—
225C2×C7×D4C22⋊C411yescharacteristic
226C2×C7×D4C22⋊C411yescharacteristic
227C2×C7×D4C22⋊C411yescharacteristic
228C2×C7×D4C22⋊C411yescharacteristic
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—42no—
234C22×C4×C7—81no—
235C22×C4×C7—81no—
236C22×C4×C7—81no—
237C22×C4×C7—81no—
238C22×C4×C7C22×C411yescharacteristic
239C22×C4×C7C22×C411yescharacteristic
240C22×C4×C7C22×C411yescharacteristic
241C22×C4×C7C22×C411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C2×C22⋊D7—21no—
252C2×C22⋊D7—21no—
253C2×C22⋊D7—21no—
254C2×C22⋊D7—21no—
255C2×C22⋊D7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260#1159—44no—
261#1157—81no—
262#1157—81no—
263C2×D28C22×C411yescharacteristic
264C2×C4×D7—21no—
265C2×C4×D7—21no—
266C2×C4×D7—21no—
267C2×Dic14—21no—
268C2×Dic14—21no—
269C2×Dic14—21no—
270C2×Dic14—81no—
271C2×Dic14—81no—
272C2×Dic14C22×C411yescharacteristic
273C2×Dic14C22×C411yescharacteristic
274C2×Dic14C22×C411yescharacteristic
275C7×C4⋊C4—81no—
276C7×C4⋊C4—81no—
277C7×C4⋊C4C22⋊C411yescharacteristic
278C7×C4⋊C4C22⋊C411yescharacteristic
279C7×C4⋊C4C22⋊C411yescharacteristic
280C7×C4⋊C4C22⋊C411yescharacteristic
281C7×C22⋊C4—42no—
282C7×C22⋊C4—81no—
283C7×C22⋊C4—81no—
284C7×C22⋊C4C22⋊C411yescharacteristic
285C7×C22⋊C4C22⋊C411yescharacteristic
286C7×C22⋊C4C22⋊C411yescharacteristic
287C7×C22⋊C4C22⋊C411yescharacteristic
288C7×C22⋊C4C22⋊C411yescharacteristic
289C7×C22⋊C4C22⋊C411yescharacteristic
290C7×C22⋊C4C22⋊C411yescharacteristic
291C7×C22⋊C4C22⋊C411yescharacteristic
292C42×C7—81no—
293C42×C7C22×C411yescharacteristic
294C42×C7C22×C411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C22⋊Dic7—21no—
298C22⋊Dic7—21no—
299C22⋊Dic7—21no—
300C22⋊Dic7—21no—
301C22⋊Dic7—21no—
302C22⋊Dic7—21no—
303C22⋊Dic7—21no—
304C22⋊Dic7—21no—
305C22⋊Dic7—21no—
306C22⋊Dic7—21no—
307C22⋊Dic7—21no—
308(C2×D7)⋊C4—21no—
309(C2×D7)⋊C4—21no—
310(C2×D7)⋊C4—21no—
311(C2×D7)⋊C4—21no—
312(C2×D7)⋊C4—21no—
313(C2×D7)⋊C4—21no—
314C4⋊Dic7—21no—
315C4⋊Dic7—21no—
316C4⋊Dic7—21no—
317C4⋊Dic7—21no—
318C4⋊Dic7—21no—
319C4⋊Dic7C22×C411yescharacteristic
320C4⋊Dic7C22×C411yescharacteristic
321C4⋊Dic7C22×C411yescharacteristic
322C4⋊Dic7C22×C411yescharacteristic
323Dic7⋊C4—21no—
324Dic7⋊C4—21no—
325Dic7⋊C4—21no—
326Dic7⋊C4—21no—
327Dic7⋊C4—21no—
328Dic7⋊C4—21no—
329Dic7⋊C4—21no—
330Dic7⋊C4—21no—
331Dic7⋊C4—21no—
332Dic7⋊C4—21no—
333Dic7⋊C4—21no—
334Dic7⋊C4—21no—
335Dic7⋊C4—21no—
336Dic7⋊C4—21no—
337C4×Dic7—21no—
338C4×Dic7—21no—
339C4×Dic7—21no—
340C4×Dic7—21no—
341C4×Dic7—21no—
342#1136—81no—
343#1136—81no—
344C2×C7⋊C8—21no—
345C2×C7⋊C8—21no—
346C2×C7⋊C8—21no—
347C2×C7⋊C8—21no—
348C2×C7⋊C8—81no—
349C2×C7⋊C8—81no—
350#556—71no—
351#554—141no—
352#552—71no—
353#552—71no—
354#551—141no—
355#551—141no—
356D4×Q8—71no—
357#548—71no—
358#548—71no—
359#547—71no—
360#547—71no—
361#546—141no—
362#542—141no—
363#539—141no—
364#539—141no—
365#533—71no—
366#529—71no—
367#525—71no—
368#525—71no—
369C2×C22⋊Q8—71no—
370C2×C22⋊Q8—71no—
371#520—141no—
372C2×C4×D4C2×D711yescharacteristic
373#436—141no—
374#435—141no—
375#435—141no—
376C8×D4—141no—
377#432—71no—
378#431—71no—
379#407—71no—
380#407—71no—
381C2×C22⋊C8—71no—
382C2×C22⋊C8—71no—
383#388—21no—
384#387—21no—
385#386—21no—
386#385—21no—
387#383C2×D711yescharacteristic
388#382C2×D711yescharacteristic
389#381C2×D711yescharacteristic
390#380C2×D711yescharacteristic
391C4×C22⋊C4C2×D711yescharacteristic
392C2×#95C2×D711yescharacteristic
393#328—71no—
394#328—71no—
395#328—71no—
396#328—71no—
397#328—71no—
398#328—71no—
399#328—71no—
400#328—71no—
401#328—71no—
402#328—71no—
403#328—71no—
404#328—71no—
405#327—71no—
406#327—71no—
407#327—71no—
408#327—71no—
409C23×C7—21no—
410C23×C7—21no—
411C23×C7—22no—
412C23×C7—21no—
413C23×C7—21no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7C2×C22⋊C411yescharacteristic
418C23×C7C2×C22⋊C411yescharacteristic
419C23×C7C2×C22⋊C411yescharacteristic
420C23×C7C2×C22⋊C411yescharacteristic
421C23×C7C22×D411yescharacteristic
422C22×D7—21no—
423C7×D4—22no—
424C7×D4—22no—
425C7×D4—41no—
426C7×D4—41no—
427C2×C4×C7—21no—
428C2×C4×C7—21no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—84no—
454C2×C4×C7C2×C22⋊C411yescharacteristic
455C2×C4×C7C2×C22⋊C411yescharacteristic
456C2×C4×C7C2×C22⋊C411yescharacteristic
457C2×C4×C7C2×C22⋊C411yescharacteristic
458C2×C4×C7C2×C22⋊C411yescharacteristic
459C2×C4×C7C2×C22⋊C411yescharacteristic
460C2×C4×C7C2×C22⋊C411yescharacteristic
461C2×C4×C7C2×C22⋊C411yescharacteristic
462C2×C4×C7C23×C411yescharacteristic
463C2×C4×C7C22×D411yescharacteristic
464C22⋊D7—42no—
465C22⋊D7—41no—
466C22⋊D7—41no—
467C22⋊D7—42no—
468C22⋊D7—81no—
469C22⋊D7—81no—
470C2×Dic7—21no—
471C2×Dic7—21no—
472C2×Dic7—21no—
473C2×Dic7—21no—
474C2×Dic7—21no—
475C2×Dic7—21no—
476C2×Dic7—21no—
477C2×Dic7—42no—
478C2×Dic7—42no—
479C2×Dic7—81no—
480C2×Dic7—81no—
481D28—41no—
482C4×D7—42no—
483C4×D7—81no—
484C4×D7—81no—
485Dic14—42no—
486Dic14—41no—
487Dic14—41no—
488Dic14—41no—
489Dic14—81no—
490Dic14—81no—
491C7⋊C8—41no—
492C7⋊C8—41no—
493C7⋊C8—41no—
494C7⋊C8—41no—
495C2×#41—71no—
496C2×#41—71no—
497C2×#41—141no—
498C22×Q8—71no—
499C22×Q8—71no—
500C22×D4C22⋊D711yescharacteristic
501C23×C4—21no—
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C2×M16—141no—
505C2×M16—141no—
506C22×C8—141no—
507C22×C8—141no—
508C4⋊Q8—71no—
509C4⋊Q8—71no—
510C4⋊Q8—141no—
511#126—141no—
512#126—141no—
513#126—141no—
514#126—141no—
515#126—141no—
516#125—71no—
517#125—141no—
518#125—141no—
519#125—141no—
520#124—71no—
521#124—141no—
522#124—141no—
523#124—141no—
524#123—141no—
525#123—141no—
526#123—141no—
527#123—141no—
528#123—141no—
529#123—141no—
530#123—141no—
531#123—141no—
532#123—141no—
533C22⋊Q8—71no—
534C22⋊Q8—71no—
535C22⋊Q8—71no—
536C22⋊Q8—71no—
537C22⋊Q8—71no—
538C22⋊Q8—71no—
539C22⋊Q8—71no—
540C22⋊Q8—71no—
541C22⋊Q8—71no—
542C22⋊Q8—141no—
543C22⋊Q8—141no—
544C22⋊Q8—141no—
545C22⋊Q8—141no—
546C22⋊Q8—141no—
547C22⋊Q8—141no—
548C22⋊Q8—141no—
549C22⋊Q8—141no—
550C22⋊Q8—141no—
551C22⋊Q8—141no—
552#121—71no—
553#121—71no—
554#121—71no—
555#121—141no—
556#121—141no—
557#121—141no—
558#120—141no—
559#120—141no—
560C4×Q8—71no—
561C4×Q8—71no—
562C4×Q8—71no—
563C4×Q8—141no—
564C4×Q8—141no—
565C4×D4—71no—
566C4×D4—141no—
567C4×D4—141no—
568C4×D4—141no—
569C4×D4—141no—
570C4×D4—141no—
571C4×D4—141no—
572C4×D4—141no—
573C4×D4—141no—
574C4×D4C4×D711yescharacteristic
575C4×D4C4×D711yescharacteristic
576C4×D4C4×D711yescharacteristic
577C4×D4C4×D711yescharacteristic
578C4×D4D2811yescharacteristic
579C4×D4D2811yescharacteristic
580C4×D4D2811yescharacteristic
581C4×D4D2811yescharacteristic
582#117—71no—
583#117—71no—
584#117—141no—
585#117—141no—
586#117—141no—
587#117—141no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—71no—
591C2×C4⋊C4—71no—
592C2×C4⋊C4—141no—
593C2×C4⋊C4—141no—
594C2×C4⋊C4—141no—
595C2×C4⋊C4C22⋊D711yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—141no—
600C2×C22⋊C4—141no—
601C2×C22⋊C4C22⋊D711yescharacteristic
602C2×C22⋊C4C22⋊D711yescharacteristic
603C2×C42—21no—
604C2×C42C22×D711yescharacteristic
605C4⋊C8—141no—
606C4⋊C8—141no—
607C22⋊C8—71no—
608C22⋊C8—71no—
609C22⋊C8—71no—
610C22⋊C8—71no—
611C22⋊C8—141no—
612C22⋊C8—141no—
613C22⋊C8—141no—
614C22⋊C8—141no—
615#97—141no—
616C4×C8—141no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622#95C22×D711yescharacteristic
623#95C22×D711yescharacteristic
624#95C22×D711yescharacteristic
625#95C22×D711yescharacteristic
626C22×C7—21no—
627C22×C7—21no—
628C22×C7—21no—
629C22×C7—21no—
630C22×C7—21no—
631C22×C7—21no—
632C22×C7—21no—
633C22×C7—21no—
634C22×C7—21no—
635C22×C7—21no—
636C22×C7—21no—
637C22×C7—21no—
638C22×C7—21no—
639C22×C7—42no—
640C22×C7—42no—
641C22×C7—81no—
642C22×C7—81no—
643C22×C7#42112yes—
644C22×C7C22×C22⋊C411yescharacteristic
645C22×C7#57711yescharacteristic
646C22×C7#57811yescharacteristic
647C2×D7—41no—
648C2×D7—41no—
649C2×D7—41no—
650C4×C7—21no—
651C4×C7—21no—
652C4×C7—21no—
653C4×C7—21no—
654C4×C7—21no—
655C4×C7—21no—
656C4×C7—21no—
657C4×C7—21no—
658C4×C7—21no—
659C4×C7—21no—
660C4×C7—81no—
661C4×C7—81no—
662C4×C7—81no—
663C4×C7—81no—
664Dic7—41no—
665Dic7—41no—
666Dic7—41no—
667Dic7—41no—
668Dic7—41no—
669Dic7—41no—
670Dic7—41no—
671C24C2×C22⋊D711yescharacteristic
672C24C2×C22⋊D711yescharacteristic
673#41—284no—
674#41—561no—
675#41—561no—
676C2×Q8—71no—
677C2×Q8—71no—
678C2×Q8—71no—
679C2×Q8—141no—
680C2×Q8—141no—
681C2×Q8—141no—
682C2×Q8—561no—
683C2×Q8—561no—
684C2×D4—42no—
685C2×D4—71no—
686C2×D4—141no—
687C2×D4—141no—
688C2×D4—141no—
689C2×D4—141no—
690C2×D4—141no—
691C2×D4(C2×D7)⋊C411yescharacteristic
692C2×D4(C2×D7)⋊C411yescharacteristic
693C2×D4(C2×D7)⋊C411yescharacteristic
694C2×D4(C2×D7)⋊C411yescharacteristic
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4C2×C4×D711yescharacteristic
712C22×C4C2×C4×D711yescharacteristic
713C22×C4C2×C4×D711yescharacteristic
714C22×C4C2×C4×D711yescharacteristic
715C22×C4C2×D2811yescharacteristic
716C22×C4C2×D2811yescharacteristic
717C22×C4C2×D2811yescharacteristic
718C22×C4C2×D2811yescharacteristic
719C22×C4C2×C22⋊D711yescharacteristic
720C22×C4C2×C22⋊D711yescharacteristic
721C22×C4C2×C22⋊D711yescharacteristic
722C22×C4C2×C22⋊D711yescharacteristic
723C22×C4C23×D711yescharacteristic
724M16—561no—
725M16—561no—
726C2×C8—141no—
727C2×C8—141no—
728C2×C8—141no—
729C2×C8—141no—
730C2×C8—561no—
731C2×C8—561no—
732C4⋊C4—71no—
733C4⋊C4—71no—
734C4⋊C4—71no—
735C4⋊C4—71no—
736C4⋊C4—81no—
737C4⋊C4—81no—
738C4⋊C4—141no—
739C4⋊C4—141no—
740C4⋊C4—141no—
741C4⋊C4—141no—
742C4⋊C4—141no—
743C4⋊C4—141no—
744C4⋊C4—141no—
745C4⋊C4—141no—
746C4⋊C4—141no—
747C4⋊C4—141no—
748C4⋊C4—141no—
749C4⋊C4—141no—
750C4⋊C4—141no—
751C4⋊C4—141no—
752C4⋊C4—141no—
753C4⋊C4—141no—
754C4⋊C4—141no—
755C4⋊C4—141no—
756C4⋊C4—141no—
757C4⋊C4(C2×D7)⋊C411yescharacteristic
758C4⋊C4(C2×D7)⋊C411yescharacteristic
759C4⋊C4(C2×D7)⋊C411yescharacteristic
760C4⋊C4(C2×D7)⋊C411yescharacteristic
761C22⋊C4—42no—
762C22⋊C4—81no—
763C22⋊C4—81no—
764C22⋊C4—141no—
765C22⋊C4—141no—
766C22⋊C4—141no—
767C22⋊C4—141no—
768C22⋊C4—141no—
769C22⋊C4—141no—
770C22⋊C4—141no—
771C22⋊C4—141no—
772C22⋊C4—141no—
773C22⋊C4—141no—
774C22⋊C4—141no—
775C22⋊C4—141no—
776C22⋊C4—141no—
777C22⋊C4—141no—
778C22⋊C4—141no—
779C22⋊C4—141no—
780C22⋊C4—141no—
781C22⋊C4(C2×D7)⋊C411yescharacteristic
782C22⋊C4(C2×D7)⋊C411yescharacteristic
783C22⋊C4(C2×D7)⋊C411yescharacteristic
784C22⋊C4(C2×D7)⋊C411yescharacteristic
785C22⋊C4(C2×D7)⋊C411yescharacteristic
786C22⋊C4(C2×D7)⋊C411yescharacteristic
787C22⋊C4(C2×D7)⋊C411yescharacteristic
788C22⋊C4(C2×D7)⋊C411yescharacteristic
789C42—81no—
790C42—141no—
791C42—141no—
792C42—141no—
793C42—141no—
794C42—141no—
795C42C2×C4×D711yescharacteristic
796C42C2×C4×D711yescharacteristic
797C42C2×D2811yescharacteristic
798C42C2×D2811yescharacteristic
799C2×C7—21no—
800C2×C7—21no—
801C2×C7—22no—
802C2×C7—41no—
803C2×C7—41no—
804C2×C7—41no—
805C2×C7#288311yescharacteristic
806C2×C7#289811yescharacteristic
807C2×C7C2×#42111yescharacteristic
808D7—81no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—141no—
818C23C2×(C2×D7)⋊C411yescharacteristic
819C23C2×(C2×D7)⋊C411yescharacteristic
820C23C2×(C2×D7)⋊C411yescharacteristic
821C23C2×(C2×D7)⋊C411yescharacteristic
822C23C22×C22⋊D711yescharacteristic
823Q8—281no—
824Q8—281no—
825Q8—281no—
826Q8—282no—
827Q8—561no—
828Q8—561no—
829D4—22no—
830D4—22no—
831D4—41no—
832D4—41no—
833D4—281no—
834D4—282no—
835D4—281no—
836D4—281no—
837D4—282no—
838D4—561no—
839D4—561no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—84no—
867C2×C4—141no—
868C2×C4—141no—
869C2×C4—141no—
870C2×C4—141no—
871C2×C4—141no—
872C2×C4—141no—
873C2×C4—141no—
874C2×C4—282no—
875C2×C4—282no—
876C2×C4—282no—
877C2×C4—561no—
878C2×C4—561no—
879C2×C4—561no—
880C2×C4—561no—
881C2×C4C2×(C2×D7)⋊C411yescharacteristic
882C2×C4C2×(C2×D7)⋊C411yescharacteristic
883C2×C4C2×(C2×D7)⋊C411yescharacteristic
884C2×C4C2×(C2×D7)⋊C411yescharacteristic
885C2×C4C2×(C2×D7)⋊C411yescharacteristic
886C2×C4C2×(C2×D7)⋊C411yescharacteristic
887C2×C4C2×(C2×D7)⋊C411yescharacteristic
888C2×C4C2×(C2×D7)⋊C411yescharacteristic
889C2×C4C22×C4×D711yescharacteristic
890C2×C4C22×D2811yescharacteristic
891C8—281no—
892C8—281no—
893C8—281no—
894C8—281no—
895C7#1759811yescharacteristic, complemented, Sylow
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—281no—
914C22—281no—
915C22—281no—
916C22#8977712yes—
917C22C22×(C2×D7)⋊C411yescharacteristic
918C22#9052711yescharacteristic
919C22#9052911yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C4—281no—
935C4—281no—
936C4—281no—
937C4—281no—
938C4—281no—
939C4—281no—
940C4—281no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—561no—
948C2C2×#8977711yescharacteristic
949C2#1173999111yescharacteristic
950C2#1174001511yescharacteristic
subgroupG/H
centerC22C22×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2318C2
socleC22×C7C22×C22⋊C4
prime radical#11742835C2
cosocleC22×C4×C7C24
hypercenter#2318D7
hypocenterC7#17598
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. C7×#2318C2semidirect
3. #11739748C2semidirect
4. #11727320C2semidirect
5. #11727319C2semidirect
6. #11727300C2semidirect
7. #11727298C2semidirect
8. #11727287C2semidirect
9. #11727286C2semidirect
10. #11727264C2semidirect
11. #11727262C2semidirect
12. #11727199C2semidirect
13. #11727197C2semidirect
14. C2×#89247C2semidirect
15. #11727152C2semidirect
25. #90246C4semidirect
26. #90243C4semidirect
27. #90243C4semidirect
28. #90242C4semidirect
30. #90233C4semidirect
31. #90232C4semidirect
32. #90232C4semidirect
33. D4×Dic14C4semidirect
82. C2×#1157C2×C4semidirect
84. C22×Dic14C2×C4semidirect
115. #6493C2×C4semidirect
127. #6489C2×C4semidirect
129. C2×C4⋊Dic7C2×C4semidirect
138. #6487C2×C4semidirect
139. #6487C2×C4semidirect
140. #6487C2×C4semidirect
175. #6438C2×C4semidirect
176. C4×D28C2×C4semidirect
179. #6433C2×C4semidirect
180. #6432C2×C4semidirect
181. #6432C2×C4semidirect
183. C4×Dic14C2×C4semidirect
184. C4×Dic14C2×C4semidirect
185. C4×Dic14C2×C4semidirect
209. #2318D7semidirect
895. C7#17598semidirect

Maximal subgroups

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

subgroupindex
#117428352
C7×#23182
#117397482
#117273202
#117273192
#117273002
#117272982
#117272872
#117272862
#117272642
#117272622
#117271992
#117271972
C2×#892472
#117271522
#175987