Finite Group Databasebeta

← #13320809

Subgroups — #13320809

Order 1792.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742911C211yesmaximal, characteristic
2C7×#2922C211yesmaximal, characteristic, complemented
3#11739967C211yesmaximal, characteristic, complemented
4#11728519C211yesmaximal, characteristic, complemented
5#11728518C211yesmaximal, characteristic, complemented
6#11728517C211yesmaximal, characteristic, complemented
7#11728516C211yesmaximal, characteristic, complemented
8#11728514C211yesmaximal, characteristic, complemented
9#11728512C211yesmaximal, characteristic, complemented
10#11728511C211yesmaximal, characteristic, complemented
11#11728509C211yesmaximal, characteristic, complemented
12#11727609C211yesmaximal, characteristic, complemented
13#11727606C211yesmaximal, characteristic, complemented
14#11727490C211yesmaximal, characteristic, complemented
15C2×#89254C211yesmaximal, characteristic, complemented
16C4×C7×#41C2211yescharacteristic
17#90520—21no—
18#90276C411yescharacteristic
19#90271—21no—
20#90270C411yescharacteristic
21#90256C411yescharacteristic
22#90256C411yescharacteristic
23#90241C411yescharacteristic
24#90241C411yescharacteristic
25D4×D28C411yescharacteristic
26#90238—21no—
27#90238—21no—
28C4×D4×D7—21no—
29#90234C411yescharacteristic
30#90221—21no—
31#90218—21no—
32#90218—21no—
33#90170C2211yescharacteristic
34#90170C2211yescharacteristic
35#90168C2211yescharacteristic
36C4×#1157C2211yescharacteristic
37C2×C4×D28C2211yescharacteristic
38C2×C4×D28C2211yescharacteristic
39C7×#433—21no—
40C7×#433—21no—
41C7×#431C2211yescharacteristic, complemented
42C7×#431C2211yescharacteristic, complemented
43C7×#431C2211yescharacteristic, complemented
44C7×#431C2211yescharacteristic, complemented
45C7×#424—21no—
46C7×#408—21no—
47C4×C7×M16C2211yescharacteristic, complemented
48C2×C4×C7×C8C2211yescharacteristic, complemented
49#89796—21no—
50#89783—21no—
51#89783—21no—
52D4×C7⋊C8—21no—
53#89698C2211yescharacteristic, complemented
54#89698C2211yescharacteristic, complemented
55#89697C2211yescharacteristic, complemented
56#89696C2211yescharacteristic, complemented
57C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
58C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
59#89254C2211yescharacteristic
60#89254C2211yescharacteristic
61#89254C2211yescharacteristic
62#89254C2211yescharacteristic
63#89254C2211yescharacteristic, complemented
64#89254C2211yescharacteristic, complemented
65#89254C2211yescharacteristic, complemented
66#89254C2211yescharacteristic, complemented
67#89254C2211yescharacteristic, complemented
68#89254C2211yescharacteristic, complemented
69#89254C2211yescharacteristic, complemented
70#89254C2211yescharacteristic, complemented
71#89251C2211yescharacteristic, complemented
72#89251C2211yescharacteristic, complemented
73#89251C2211yescharacteristic, complemented
74#89251C2211yescharacteristic, complemented
75#17521—71nomaximal, Sylow
76C2×C7×#41D411yescharacteristic
77C2×D4×D7—21no—
78C2×#1157—21no—
79C2×#1157C2×C411yescharacteristic
80C22×D28C2×C411yescharacteristic
81C22×D28C2×C411yescharacteristic
82C22×C4×D7—21no—
83C22×C4×D7—21no—
84C2×C7×M16—21no—
85C22×C7×C8—21no—
86C4×C7×Q8C2×C411yescharacteristic
87C4×C7×Q8D411yescharacteristic
88C4×C7×D4C2×C411yescharacteristic
89C4×C7×D4C2×C411yescharacteristic
90C4×C7×D4C2×C411yescharacteristic
91C4×C7×D4D411yescharacteristic
92C4×C7×D4D411yescharacteristic
93C4×C7×D4D411yescharacteristic
94C7×#117D411yescharacteristic
95C7×#117D411yescharacteristic
96C7×#117D411yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C42×C7C2311yescharacteristic
99C2×C42×C7C2311yescharacteristic
100#6510—21no—
101#6509—21no—
102#6502—21no—
103#6502—21no—
104#6500—21no—
105#6500—21no—
106D4×Dic7—21no—
107#6493—21no—
108#6493C2×C411yescharacteristic
109#6493C2×C411yescharacteristic
110#6493C2×C411yescharacteristic
111#6493C2×C411yescharacteristic
112#6492—21no—
113#6492—21no—
114C4×C22⋊D7—21no—
115C4×C22⋊D7—21no—
116C4×C22⋊D7—21no—
117C4×C22⋊D7—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120#6489C2×C411yescharacteristic
121C2×C4⋊Dic7C2×C411yescharacteristic
122C2×C4⋊Dic7C2×C411yescharacteristic
123#6487C2×C411yescharacteristic
124#6487C2×C411yescharacteristic
125C2×#1136—21no—
126C22×C7⋊C8—21no—
127C22×C7⋊C8—21no—
128#6461—21no—
129#6461—21no—
130#6459—21no—
131#6459—21no—
132#6458—21no—
133#6457—21no—
134#6457—21no—
135#6457—21no—
136#6457—21no—
137#6456—21no—
138D7×C4⋊C4—21no—
139#6453—21no—
140#6447—21no—
141#6447—21no—
142#6446—21no—
143#6446—21no—
144#6445—21no—
145#6445—21no—
146(C22⋊D7)⋊C4—21no—
147(C22⋊D7)⋊C4—21no—
148D7×C22⋊C4—21no—
149D7×C22⋊C4—21no—
150#6441—21no—
151#6441—21no—
152#6439—21no—
153#6439—21no—
154#6438—21no—
155#6438C2×C411yescharacteristic
156#6438C2×C411yescharacteristic
157#6437C2×C411yescharacteristic
158C4×D28—21no—
159C4×D28—21no—
160C4×D28—21no—
161C4×D28—21no—
162C4×D28—21no—
163C4×D28C2×C411yescharacteristic
164C4×D28C2×C411yescharacteristic
165C4×D28C2×C411yescharacteristic
166C4×D28C2×C411yescharacteristic
167C4×D28C2×C411yescharacteristic
168C4×D28C2311yescharacteristic
169C4×D28C2311yescharacteristic
170C4×D28C2311yescharacteristic
171#6435—21no—
172#6435—21no—
173#6435—21no—
174C42×D7—21no—
175#6433C2×C411yescharacteristic
176#6433C2×C411yescharacteristic
177#6432C2×C411yescharacteristic
178C4×Dic14C2×C411yescharacteristic
179C4×Dic14C2311yescharacteristic
180C7×C4⋊C8—21no—
181C7×C4⋊C8—21no—
182C7×C4⋊C8—21no—
183C7×C4⋊C8—21no—
184C7×C22⋊C8—21no—
185C7×C22⋊C8—21no—
186C7×C22⋊C8—21no—
187C7×C22⋊C8—21no—
188C7×#97—21no—
189C4×C7×C8—21no—
190C4×C7×C8C2311yescharacteristic
191C4×C7×C8C2311yescharacteristic
192C4×C7×C8C2311yescharacteristic
193C4×C7×C8C2311yescharacteristic
194C22⋊(C7⋊C8)—21no—
195C22⋊(C7⋊C8)—21no—
196C22⋊(C7⋊C8)—21no—
197C4⋊(C7⋊C8)—21no—
198C4⋊(C7⋊C8)—21no—
199C4⋊(C7⋊C8)—21no—
200C4⋊(C7⋊C8)C2311yescharacteristic
201C4⋊(C7⋊C8)C2311yescharacteristic
202C4⋊(C7⋊C8)C2311yescharacteristic
203C4⋊(C7⋊C8)C2311yescharacteristic
204#6377—21no—
205#6377—21no—
206C4×C7⋊C8—21no—
207#3481—71no—
208#2990—71no—
209#2922D711yescharacteristic, complemented
210#1496—71no—
211#1495—71no—
212#1494—71no—
213#1490—71no—
214#1488—71no—
215#1486—71no—
216#1483—71no—
217#1482—71no—
218#1480—71no—
219#1478—71no—
220#1477—71no—
221C2×D4⋊C8—71no—
222C23×D7—21no—
223C23×D7—21no—
224C7×#41—42no—
225C2×C7×Q8C22⋊C411yescharacteristic
226C2×C7×D4C22⋊C411yescharacteristic
227C2×C7×D4C22⋊C411yescharacteristic
228C2×C7×D4C22⋊C411yescharacteristic
229C22×C4×C7C22×C411yescharacteristic
230C22×C4×C7C22×C411yescharacteristic
231C22×C4×C7C22×C411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C2×C22⋊D7—21no—
239C2×C22⋊D7—21no—
240C2×C22⋊D7—21no—
241C2×C22⋊D7—21no—
242C2×C22⋊D7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245D4×D7—44no—
246#1157—22no—
247#1157—41no—
248#1157—81no—
249#1157—81no—
250C2×D28—22no—
251C2×D28—22no—
252C2×D28—21no—
253C2×D28—21no—
254C2×D28—21no—
255C2×D28—21no—
256C2×D28—41no—
257C2×D28—41no—
258C2×D28C22×C411yescharacteristic
259C2×D28C22×C411yescharacteristic
260C2×D28C22×C411yescharacteristic
261C2×C4×D7—21no—
262C2×C4×D7—21no—
263C2×C4×D7—21no—
264C2×C4×D7—21no—
265C2×C4×D7—21no—
266C2×C4×D7—21no—
267C2×C4×D7—21no—
268C2×C4×D7—21no—
269C2×C4×D7—21no—
270C2×C4×D7—81no—
271C2×C4×D7—81no—
272C2×C4×D7—81no—
273C2×C4×D7—81no—
274C2×Dic14—21no—
275C2×Dic14C22×C411yescharacteristic
276C7×M16—42no—
277C2×C7×C8—21no—
278C2×C7×C8—21no—
279C2×C7×C8—21no—
280C2×C7×C8—21no—
281C2×C7×C8—42no—
282C7×C4⋊C4C22⋊C411yescharacteristic
283C7×C4⋊C4C22⋊C411yescharacteristic
284C7×C4⋊C4C22⋊C411yescharacteristic
285C7×C4⋊C4C22⋊C411yescharacteristic
286C7×C4⋊C4C22⋊C411yescharacteristic
287C7×C4⋊C4C22⋊C411yescharacteristic
288C7×C22⋊C4C22⋊C411yescharacteristic
289C7×C22⋊C4C22⋊C411yescharacteristic
290C7×C22⋊C4C22⋊C411yescharacteristic
291C7×C22⋊C4C22⋊C411yescharacteristic
292C7×C22⋊C4C22⋊C411yescharacteristic
293C7×C22⋊C4C22⋊C411yescharacteristic
294C42×C7C22×C411yescharacteristic
295C42×C7C22×C411yescharacteristic
296C42×C7C22×C411yescharacteristic
297C42×C7C2×D411yescharacteristic
298C42×C7C2×D411yescharacteristic
299C42×C7C2×D411yescharacteristic
300C42×C7C2×D411yescharacteristic
301C42×C7C2×D411yescharacteristic
302C42×C7C2×D411yescharacteristic
303C42×C7C2411yescharacteristic
304C22⋊Dic7—21no—
305C22⋊Dic7—21no—
306C22⋊Dic7—21no—
307(C2×D7)⋊C4—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—
314(C2×D7)⋊C4—21no—
315(C2×D7)⋊C4—21no—
316(C2×D7)⋊C4—21no—
317(C2×D7)⋊C4—21no—
318(C2×D7)⋊C4—21no—
319(C2×D7)⋊C4—21no—
320(C2×D7)⋊C4—21no—
321(C2×D7)⋊C4—21no—
322(C2×D7)⋊C4—21no—
323C4⋊Dic7—21no—
324C4⋊Dic7—21no—
325C4⋊Dic7—21no—
326C4⋊Dic7C22×C411yescharacteristic
327C4⋊Dic7C22×C411yescharacteristic
328C4⋊Dic7C22×C411yescharacteristic
329C4⋊Dic7C22×C411yescharacteristic
330Dic7⋊C4—21no—
331Dic7⋊C4—21no—
332Dic7⋊C4—21no—
333Dic7⋊C4—21no—
334Dic7⋊C4—21no—
335Dic7⋊C4—21no—
336Dic7⋊C4—21no—
337Dic7⋊C4—21no—
338C4×Dic7—21no—
339C4×Dic7—21no—
340C4×Dic7—21no—
341#1136—81no—
342C2×C7⋊C8—21no—
343C2×C7⋊C8—21no—
344C2×C7⋊C8—21no—
345C2×C7⋊C8—21no—
346C2×C7⋊C8—81no—
347C2×C7⋊C8—81no—
348#559—71no—
349#554—71no—
350#554—71no—
351#553—71no—
352#553—71no—
353#553—141no—
354#551—141no—
355#551—141no—
356#546—71no—
357#546—71no—
358#546—141no—
359D42—71no—
360#532—71no—
361#529—71no—
362#529—71no—
363#529—141no—
364#525—141no—
365#525—141no—
366C4×#41—71no—
367C4×#41C2×D711yescharacteristic
368C2×C4×D4—71no—
369C2×C4×D4—71no—
370C2×C4×D4—141no—
371#446—141no—
372#435—141no—
373#435—141no—
374C8×D4—141no—
375#433—21no—
376#433—21no—
377#432—71no—
378#432—71no—
379#431—71no—
380#431C2×D711yescharacteristic, complemented
381#431C2×D711yescharacteristic, complemented
382#431C2×D711yescharacteristic, complemented
383#431C2×D711yescharacteristic, complemented
384#424—21no—
385#423—71no—
386C2×C4⋊C8—71no—
387C2×C4⋊C8—71no—
388#408—21no—
389C4×M16C2×D711yescharacteristic, complemented
390C2×C4×C8C2×D711yescharacteristic, complemented
391Q8⋊C8—71no—
392Q8⋊C8—71no—
393Q8⋊C8—71no—
394Q8⋊C8—71no—
395D4⋊C8—71no—
396D4⋊C8—71no—
397D4⋊C8—71no—
398D4⋊C8—71no—
399D4⋊C8—71no—
400D4⋊C8—71no—
401D4⋊C8—71no—
402D4⋊C8—71no—
403D4⋊C8—71no—
404D4⋊C8—71no—
405D4⋊C8—71no—
406D4⋊C8—71no—
407C23×C7C2×C22⋊C411yescharacteristic
408C23×C7C2×C22⋊C411yescharacteristic
409C23×C7C2×C22⋊C411yescharacteristic
410C22×D7—21no—
411C22×D7—21no—
412C22×D7—21no—
413C22×D7—42no—
414C22×D7—42no—
415C22×D7—42no—
416C22×D7—42no—
417C22×D7—81no—
418C22×D7—81no—
419C7×Q8—41no—
420C7×D4—22no—
421C7×D4—22no—
422C7×D4—41no—
423C2×C4×C7—22no—
424C2×C4×C7—21no—
425C2×C4×C7—21no—
426C2×C4×C7—21no—
427C2×C4×C7—21no—
428C2×C4×C7—21no—
429C2×C4×C7—21no—
430C2×C4×C7—21no—
431C2×C4×C7—21no—
432C2×C4×C7—21no—
433C2×C4×C7—21no—
434C2×C4×C7—21no—
435C2×C4×C7—21no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7C2×C22⋊C411yescharacteristic
439C2×C4×C7C2×C22⋊C411yescharacteristic
440C2×C4×C7C2×C22⋊C411yescharacteristic
441C2×C4×C7C2×C22⋊C411yescharacteristic
442C2×C4×C7C2×C22⋊C411yescharacteristic
443C2×C4×C7C2×C22⋊C411yescharacteristic
444C2×C4×C7C2×C22⋊C411yescharacteristic
445C2×C4×C7C2×C22⋊C411yescharacteristic
446C2×C4×C7C2×C22⋊C411yescharacteristic
447C2×C4×C7C23×C411yescharacteristic
448C2×C4×C7C22×D411yescharacteristic
449C2×C4×C7C22×D411yescharacteristic
450C22⋊D7—42no—
451C22⋊D7—42no—
452C22⋊D7—42no—
453C22⋊D7—81no—
454C22⋊D7—81no—
455C2×Dic7—21no—
456C2×Dic7—21no—
457C2×Dic7—21no—
458C2×Dic7—21no—
459C2×Dic7—21no—
460C2×Dic7—81no—
461C2×Dic7—81no—
462D28—21no—
463D28—21no—
464D28—21no—
465D28—21no—
466D28—21no—
467D28—42no—
468D28—42no—
469D28—42no—
470D28—81no—
471D28#13112yes—
472C4×D7—42no—
473C4×D7—42no—
474C4×D7—41no—
475C4×D7—41no—
476C4×D7—41no—
477C4×D7—41no—
478C4×D7—41no—
479C4×D7—41no—
480C4×D7—81no—
481C4×D7—81no—
482C4×D7—81no—
483C4×D7—81no—
484Dic14—21no—
485Dic14—21no—
486Dic14—81no—
487C7×C8—41no—
488C7×C8—41no—
489C7×C8—41no—
490C7×C8—41no—
491C7⋊C8—41no—
492C7⋊C8—41no—
493C7⋊C8—41no—
494C7⋊C8—41no—
495C2×#41—71no—
496C2×#41—141no—
497C2×#41C22⋊D711yescharacteristic
498C22×D4—71no—
499C22×D4—71no—
500C22×D4—141no—
501C23×C4—141no—
502C23×C4—141no—
503C2×M16—21no—
504C2×M16—141no—
505C22×C8—21no—
506C22×C8—141no—
507C22×C8—141no—
508C4⋊Q8—71no—
509#127—71no—
510#126—141no—
511#126—141no—
512#126—141no—
513#126—141no—
514#125—71no—
515#125—71no—
516#125—141no—
517#124—71no—
518#124—71no—
519#124—141no—
520#124—141no—
521#123—141no—
522#123—141no—
523#123—141no—
524#123—141no—
525#123—141no—
526#123—141no—
527#123—141no—
528#123—141no—
529C22⋊Q8—71no—
530C22⋊Q8—71no—
531C22⋊Q8—141no—
532C22⋊Q8—141no—
533C22⋊Q8—141no—
534C22⋊Q8—141no—
535C22⋊Q8—141no—
536#121—71no—
537#121—71no—
538#121—71no—
539#121—71no—
540#121—141no—
541#121—141no—
542#121—141no—
543#121—141no—
544#121—141no—
545#121—141no—
546#120—141no—
547#120—141no—
548#120—141no—
549#120—141no—
550C4×Q8—71no—
551C4×Q8—71no—
552C4×Q8C4×D711yescharacteristic
553C4×Q8D2811yescharacteristic
554C4×D4—71no—
555C4×D4—71no—
556C4×D4—71no—
557C4×D4—71no—
558C4×D4—71no—
559C4×D4—71no—
560C4×D4—71no—
561C4×D4—71no—
562C4×D4—141no—
563C4×D4—141no—
564C4×D4—141no—
565C4×D4—141no—
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×D4—141no—
575C4×D4C4×D711yescharacteristic
576C4×D4C4×D711yescharacteristic
577C4×D4C4×D711yescharacteristic
578C4×D4D2811yescharacteristic
579C4×D4D2811yescharacteristic
580C4×D4D2811yescharacteristic
581#117—71no—
582#117—141no—
583#117—141no—
584#117—141no—
585#117C22⋊D711yescharacteristic
586#117C22⋊D711yescharacteristic
587#117C22⋊D711yescharacteristic
588C2×C4⋊C4—71no—
589C2×C4⋊C4—71no—
590C2×C4⋊C4—141no—
591C2×C22⋊C4—141no—
592C2×C22⋊C4—141no—
593C2×C22⋊C4—141no—
594C2×C22⋊C4—141no—
595C2×C42—141no—
596C2×C42C22×D711yescharacteristic
597C2×C42C22×D711yescharacteristic
598C2×C42C22×D711yescharacteristic
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—21no—
602C4⋊C8—21no—
603C4⋊C8—71no—
604C4⋊C8—71no—
605C4⋊C8—71no—
606C4⋊C8—71no—
607C4⋊C8—141no—
608C4⋊C8—141no—
609C4⋊C8—141no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612C22⋊C8—21no—
613C22⋊C8—21no—
614C22⋊C8—141no—
615C22⋊C8—141no—
616C22⋊C8—141no—
617#97—21no—
618#97—141no—
619#97—141no—
620C4×C8—21no—
621C4×C8—141no—
622C4×C8C22×D711yescharacteristic
623C4×C8C22×D711yescharacteristic
624C4×C8C22×D711yescharacteristic
625C4×C8C22×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#42112yes—
635C22×C7C22×C22⋊C411yescharacteristic
636C2×D7—22no—
637C2×D7—41no—
638C2×D7—41no—
639C2×D7—41no—
640C2×D7—41no—
641C2×D7—41no—
642C2×D7—41no—
643C2×D7—41no—
644C2×D7—41no—
645C2×D7—84no—
646C2×D7—84no—
647C4×C7—21no—
648C4×C7—21no—
649C4×C7—21no—
650C4×C7—21no—
651C4×C7—21no—
652C4×C7—21no—
653C4×C7—21no—
654C4×C7—21no—
655C4×C7—21no—
656C4×C7—21no—
657C4×C7C2×#13111yescharacteristic
658C4×C7#56811yescharacteristic
659C4×C7#57611yescharacteristic
660C4×C7#57711yescharacteristic
661Dic7—41no—
662Dic7—41no—
663Dic7—41no—
664Dic7—41no—
665Dic7—41no—
666C24—141no—
667C24—141no—
668#41—42no—
669#41—142no—
670#41—281no—
671#41—561no—
672#41—561no—
673C2×Q8—71no—
674C2×Q8—141no—
675C2×Q8(C2×D7)⋊C411yescharacteristic
676C2×D4—71no—
677C2×D4—71no—
678C2×D4—71no—
679C2×D4—142no—
680C2×D4—142no—
681C2×D4—141no—
682C2×D4—141no—
683C2×D4—141no—
684C2×D4—141no—
685C2×D4—141no—
686C2×D4—141no—
687C2×D4—141no—
688C2×D4—141no—
689C2×D4—141no—
690C2×D4—281no—
691C2×D4—281no—
692C2×D4—284no—
693C2×D4(C2×D7)⋊C411yescharacteristic
694C2×D4(C2×D7)⋊C411yescharacteristic
695C2×D4(C2×D7)⋊C411yescharacteristic
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—561no—
708C22×C4—561no—
709C22×C4—561no—
710C22×C4—561no—
711C22×C4C2×C4×D711yescharacteristic
712C22×C4C2×C4×D711yescharacteristic
713C22×C4C2×C4×D711yescharacteristic
714C22×C4C2×D2811yescharacteristic
715C22×C4C2×D2811yescharacteristic
716C22×C4C2×D2811yescharacteristic
717C22×C4C2×C22⋊D711yescharacteristic
718C22×C4C2×C22⋊D711yescharacteristic
719C22×C4C2×C22⋊D711yescharacteristic
720M16—42no—
721M16—561no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—42no—
727C2×C8—141no—
728C2×C8—141no—
729C2×C8—141no—
730C2×C8—141no—
731C2×C8—561no—
732C2×C8—561no—
733C4⋊C4—71no—
734C4⋊C4—71no—
735C4⋊C4—71no—
736C4⋊C4—71no—
737C4⋊C4—141no—
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(C2×D7)⋊C411yescharacteristic
749C4⋊C4(C2×D7)⋊C411yescharacteristic
750C4⋊C4(C2×D7)⋊C411yescharacteristic
751C4⋊C4(C2×D7)⋊C411yescharacteristic
752C4⋊C4(C2×D7)⋊C411yescharacteristic
753C4⋊C4(C2×D7)⋊C411yescharacteristic
754C22⋊C4—141no—
755C22⋊C4—141no—
756C22⋊C4—141no—
757C22⋊C4—141no—
758C22⋊C4—141no—
759C22⋊C4—141no—
760C22⋊C4—141no—
761C22⋊C4—141no—
762C22⋊C4—141no—
763C22⋊C4—141no—
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(C2×D7)⋊C411yescharacteristic
774C22⋊C4(C2×D7)⋊C411yescharacteristic
775C22⋊C4(C2×D7)⋊C411yescharacteristic
776C22⋊C4(C2×D7)⋊C411yescharacteristic
777C22⋊C4(C2×D7)⋊C411yescharacteristic
778C22⋊C4(C2×D7)⋊C411yescharacteristic
779C42—141no—
780C42—141no—
781C42—141no—
782C42C2×C4×D711yescharacteristic
783C42C2×C4×D711yescharacteristic
784C42C2×C4×D711yescharacteristic
785C42C2×D2811yescharacteristic
786C42C2×D2811yescharacteristic
787C42C2×D2811yescharacteristic
788C42C2×C22⋊D711yescharacteristic
789C42C2×C22⋊D711yescharacteristic
790C42C2×C22⋊D711yescharacteristic
791C42C23×D711yescharacteristic
792C2×C7—22no—
793C2×C7—41no—
794C2×C7—41no—
795C2×C7#288011yescharacteristic
796C2×C7#289711yescharacteristic
797C2×C7C2×#42111yescharacteristic
798D7—42no—
799D7—81no—
800D7—81no—
801C23—141no—
802C23—141no—
803C23—141no—
804C23—282no—
805C23—282no—
806C23—282no—
807C23—282no—
808C23—561no—
809C23—561no—
810C23C2×(C2×D7)⋊C411yescharacteristic
811C23C2×(C2×D7)⋊C411yescharacteristic
812C23C2×(C2×D7)⋊C411yescharacteristic
813Q8—41no—
814Q8—141no—
815Q8—141no—
816Q8—561no—
817D4—22no—
818D4—22no—
819D4—41no—
820D4—72no—
821D4—141no—
822D4—141no—
823D4—141no—
824D4—141no—
825D4—141no—
826D4—282no—
827D4—282no—
828D4—282no—
829D4—282no—
830D4—282no—
831D4—282no—
832D4—561no—
833D4—561no—
834D4—561no—
835C2×C4—22no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—141no—
851C2×C4—141no—
852C2×C4—141no—
853C2×C4—141no—
854C2×C4—141no—
855C2×C4—282no—
856C2×C4—282no—
857C2×C4—281no—
858C2×C4—281no—
859C2×C4—281no—
860C2×C4—281no—
861C2×C4—281no—
862C2×C4—281no—
863C2×C4—561no—
864C2×C4—561no—
865C2×C4—561no—
866C2×C4—561no—
867C2×C4—561no—
868C2×C4—561no—
869C2×C4C2×(C2×D7)⋊C411yescharacteristic
870C2×C4C2×(C2×D7)⋊C411yescharacteristic
871C2×C4C2×(C2×D7)⋊C411yescharacteristic
872C2×C4C2×(C2×D7)⋊C411yescharacteristic
873C2×C4C2×(C2×D7)⋊C411yescharacteristic
874C2×C4C2×(C2×D7)⋊C411yescharacteristic
875C2×C4C2×(C2×D7)⋊C411yescharacteristic
876C2×C4C2×(C2×D7)⋊C411yescharacteristic
877C2×C4C2×(C2×D7)⋊C411yescharacteristic
878C2×C4C22×C4×D711yescharacteristic
879C2×C4C22×D2811yescharacteristic
880C2×C4C22×C22⋊D711yescharacteristic
881C8—41no—
882C8—41no—
883C8—41no—
884C8—41no—
885C8—281no—
886C8—281no—
887C8—281no—
888C8—281no—
889C7#1752111yescharacteristic, complemented, Sylow
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—142no—
899C22—281no—
900C22—281no—
901C22—281no—
902C22—281no—
903C22—281no—
904C22—281no—
905C22—281no—
906C22—281no—
907C22—564no—
908C22—564no—
909C22#8977712yes—
910C22C22×(C2×D7)⋊C411yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—281no—
922C4—281no—
923C4—281no—
924C4—281no—
925C4—281no—
926C4D7×#13111yescharacteristic
927C4#9044111yescharacteristic
928C4#9044211yescharacteristic
929C4#9044311yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—282no—
934C2—561no—
935C2—561no—
936C2C2×#8977711yescharacteristic
937C2#1174123811yescharacteristic
938C2#1174124211yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#2922C2
socleC22×C7C22×C22⋊C4
prime radical#11742911C2
cosocleC42×C7C24
hypercenter#2922D7
hypocenterC7#17521
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. C7×#2922C2semidirect
3. #11739967C2semidirect
4. #11728519C2semidirect
5. #11728518C2semidirect
6. #11728517C2semidirect
7. #11728516C2semidirect
8. #11728514C2semidirect
9. #11728512C2semidirect
10. #11728511C2semidirect
11. #11728509C2semidirect
12. #11727609C2semidirect
13. #11727606C2semidirect
14. #11727490C2semidirect
15. C2×#89254C2semidirect
41. C7×#431C22semidirect
42. C7×#431C22semidirect
43. C7×#431C22semidirect
44. C7×#431C22semidirect
47. C4×C7×M16C22semidirect
48. C2×C4×C7×C8C22semidirect
53. #89698C22semidirect
54. #89698C22semidirect
55. #89697C22semidirect
56. #89696C22semidirect
57. C2×C4⋊(C7⋊C8)C22semidirect
58. C2×C4⋊(C7⋊C8)C22semidirect
63. #89254C22semidirect
64. #89254C22semidirect
65. #89254C22semidirect
66. #89254C22semidirect
67. #89254C22semidirect
68. #89254C22semidirect
69. #89254C22semidirect
70. #89254C22semidirect
71. #89251C22semidirect
72. #89251C22semidirect
73. #89251C22semidirect
74. #89251C22semidirect
209. #2922D7semidirect
380. #431C2×D7semidirect
381. #431C2×D7semidirect
382. #431C2×D7semidirect
383. #431C2×D7semidirect
389. C4×M16C2×D7semidirect
390. C2×C4×C8C2×D7semidirect
889. C7#17521semidirect

Maximal subgroups

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

subgroupindex
#117429112
C7×#29222
#117399672
#117285192
#117285182
#117285172
#117285162
#117285142
#117285122
#117285112
#117285092
#117276092
#117276062
#117274902
C2×#892542
#175217