Finite Group Databasebeta

← #13324616

Subgroups — #13324616

Order 1792.

606 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737392C211yesmaximal, characteristic, complemented
2#11737109C211yesmaximal, characteristic
3#11736876C211yesmaximal, characteristic, complemented
4C7×#1582C211yesmaximal, characteristic, complemented
5#11728708C211yesmaximal, characteristic, complemented
6#11728652C211yesmaximal, characteristic, complemented
7#11728598C211yesmaximal, characteristic, complemented
8#11726285C211yesmaximal, characteristic, complemented
9#11726275C211yesmaximal, characteristic, complemented
10#11725995C211yesmaximal, characteristic, complemented
11#11725971C211yesmaximal, characteristic, complemented
12#11725930C211yesmaximal, characteristic, complemented
13#11725907C211yesmaximal, characteristic, complemented
14#11725832C211yesmaximal, characteristic, complemented
15#11725824C211yesmaximal, characteristic, complemented
16#90271C2211yescharacteristic
17#90239C2211yescharacteristic
18C7×#446C2211yescharacteristic
19C4×C7×SD16C2211yescharacteristic
20C7×C8×D4C2211yescharacteristic
21#89948C411yescharacteristic
22#89946C411yescharacteristic
23#89883—21no—
24#89882—21no—
25C4×#1143C2211yescharacteristic
26Q8×C7⋊C8C2211yescharacteristic
27C4×#1141C2211yescharacteristic
28#89784C2211yescharacteristic
29#89637C411yescharacteristic
30#89628C411yescharacteristic
31#89611—21no—
32#89610—21no—
33#89610C2211yescharacteristic
34#89609C2211yescharacteristic
35#89607C2211yescharacteristic
36#89606C2211yescharacteristic
37#89584C411yescharacteristic
38#89567C411yescharacteristic
39#89554C411yescharacteristic
40#89536C411yescharacteristic
41#89500—21no—
42#89499—21no—
43#89481—21no—
44#89478—21no—
45C4×D56C2211yescharacteristic
46#89460C2211yescharacteristic
47C4×#1131C2211yescharacteristic
48C8×D28C2211yescharacteristic
49#89457C2211yescharacteristic
50C4×C8×D7C2211yescharacteristic
51C7×#334C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×#322C2211yescharacteristic
55Q8⋊(C7⋊C8)C2211yescharacteristic
56D4⋊(C7⋊C8)C2211yescharacteristic
57#89278C2211yescharacteristic
58#89278C2211yescharacteristic
59#89275C2211yescharacteristic
60#89274C2211yescharacteristic
61#89254C2211yescharacteristic
62#89254C2211yescharacteristic
63#89253C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66#89249C2211yescharacteristic
67#17987—71nomaximal, Sylow
68C2×#1157—21no—
69C2×C7×SD16C2×C411yescharacteristic
70C22×C7×C8—21no—
71C4×C7×Q8C2311yescharacteristic
72C4×C7×D4C2311yescharacteristic
73#6510C2×C411yescharacteristic
74#6509C2×C411yescharacteristic
75C2×#1143C2×C411yescharacteristic
76#6503C2×C411yescharacteristic
77#6501C2×C411yescharacteristic
78C2×#1141C2×C411yescharacteristic
79C4×C22⋊D7—21no—
80C2×#1136—21no—
81C2×D56C2×C411yescharacteristic
82C2×#1131—21no—
83C2×#1131—21no—
84C2×#1131—21no—
85C2×#1131C2×C411yescharacteristic
86C2×#1131C2×C411yescharacteristic
87C2×C8×D7—21no—
88C2×C8×D7—21no—
89C2×C8×D7—21no—
90#6461—21no—
91#6458C2×C411yescharacteristic
92#6458C2×C411yescharacteristic
93#6457—21no—
94#6453C2×C411yescharacteristic
95#6451C2×C411yescharacteristic
96#6448—21no—
97#6447—21no—
98C4×D28—21no—
99C4×D28C2311yescharacteristic
100C4×D28C2311yescharacteristic
101#6435—21no—
102C42×D7C2311yescharacteristic
103C7×#106C2×C411yescharacteristic
104C7×C4⋊C8—21no—
105C7×C4⋊C8C2311yescharacteristic
106C7×C4⋊C8C2311yescharacteristic
107C7×#103C2×C411yescharacteristic
108C7×#102C2×C411yescharacteristic
109C7×C22⋊C8—21no—
110C7×#97—21no—
111C4×C7×C8C2311yescharacteristic
112C4×C7×C8C2311yescharacteristic
113C4×C7×C8C2311yescharacteristic
114#6409C2×C411yescharacteristic
115#6406C2×C411yescharacteristic
116C22⋊(C7⋊C8)—21no—
117#6395C2×C411yescharacteristic
118#6395C2×C411yescharacteristic
119(C2×D7)⋊C8—21no—
120(C2×D7)⋊C8—21no—
121(C2×D7)⋊C8—21no—
122(C2×D7)⋊C8—21no—
123(C2×D7)⋊C8—21no—
124(C2×D7)⋊C8D411yescharacteristic
125(C2×D7)⋊C8D411yescharacteristic
126#6392C2×C411yescharacteristic
127#6389—21no—
128#6389C2×C411yescharacteristic
129#6389C2×C411yescharacteristic
130Dic7⋊C8—21no—
131Dic7⋊C8D411yescharacteristic
132Dic7⋊C8D411yescharacteristic
133C8×Dic7—21no—
134#6383C2×C411yescharacteristic
135#6383C2×C411yescharacteristic
136#6382C2×C411yescharacteristic
137#6381C2×C411yescharacteristic
138C4⋊(C7⋊C8)—21no—
139C4⋊(C7⋊C8)C2311yescharacteristic
140C4⋊(C7⋊C8)C2311yescharacteristic
141C4×C7⋊C8—21no—
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3171—71no—
146#2993—71no—
147#2981—71no—
148#1588—71no—
149#1586—71no—
150#1586—71no—
151#1585—71no—
152#1583—71no—
153#1582D711yescharacteristic, complemented
154#1581—71no—
155#1581—71no—
156#1569—71no—
157#1494—71no—
158#1492—71no—
159#1451—71no—
160C2×C7×Q8C22×C411yescharacteristic
161C2×C7×D4C22×C411yescharacteristic
162C22×C4×C7—21no—
163C2×C22⋊D7—21no—
164C2×C22⋊D7—21no—
165C2×C22⋊D7—21no—
166#1157—81no—
167#1157—81no—
168C2×D28—21no—
169C2×D28—21no—
170C2×D28C22×C411yescharacteristic
171C2×D28C22×C411yescharacteristic
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7C22×C411yescharacteristic
175C2×C4×D7C2×D411yescharacteristic
176C2×C4×D7#4111yescharacteristic
177C2×Dic14—21no—
178C7×SD16—41no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8—81no—
183C2×C7×C8C22×C411yescharacteristic
184C2×C7×C8C22×C411yescharacteristic
185C2×C7×C8C2×D411yescharacteristic
186C2×C7×C8C2×D411yescharacteristic
187C7×C4⋊C4—21no—
188C7×C4⋊C4C22×C411yescharacteristic
189C7×C4⋊C4C22×C411yescharacteristic
190C7×C22⋊C4—21no—
191C42×C7—21no—
192C42×C7C2411yescharacteristic
193C22⋊Dic7—21no—
194#1143—41no—
195#1141—41no—
196(C2×D7)⋊C4—21no—
197(C2×D7)⋊C4—21no—
198(C2×D7)⋊C4—21no—
199(C2×D7)⋊C4—21no—
200(C2×D7)⋊C4—21no—
201(C2×D7)⋊C4—21no—
202(C2×D7)⋊C4—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7C22×C411yescharacteristic
205C4⋊Dic7C22×C411yescharacteristic
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208Dic7⋊C4—21no—
209C4×Dic7C22×C411yescharacteristic
210C4×Dic7C2×D411yescharacteristic
211C4×Dic7#4111yescharacteristic
212#1136—81no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8C22×C411yescharacteristic
217C2×C7⋊C8C22×C411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219C2×C7⋊C8C2×D411yescharacteristic
220D56—41no—
221#1131—41no—
222#1131—41no—
223#1131—81no—
224#1131—81no—
225#1131—81no—
226C8×D7—42no—
227C8×D7—81no—
228C8×D7—81no—
229#532—71no—
230#529—71no—
231#501—71no—
232#496—71no—
233#490—71no—
234#489—71no—
235#469—71no—
236#469—71no—
237#468—71no—
238#468—71no—
239#446C2×D711yescharacteristic
240C8×Q8—71no—
241C4×SD16—71no—
242C4×SD16C2×D711yescharacteristic
243C4×D8—71no—
244C4×D8—71no—
245#436—71no—
246#436—71no—
247#436—71no—
248#436—141no—
249#435—141no—
250#435—141no—
251#435—141no—
252C8×D4—71no—
253C8×D4—71no—
254C8×D4C2×D711yescharacteristic
255#433—141no—
256#432—71no—
257#431—71no—
258#424—141no—
259#423—71no—
260#408—141no—
261#408—141no—
262C4×M16—71no—
263C2×C4×C8—71no—
264#335—71no—
265#335—71no—
266#334—71no—
267#334C2×D711yescharacteristic
268Q8⋊C8—71no—
269Q8⋊C8C2×D711yescharacteristic
270D4⋊C8—71no—
271D4⋊C8—71no—
272D4⋊C8—71no—
273D4⋊C8—71no—
274D4⋊C8—71no—
275D4⋊C8C2×D711yescharacteristic
276#322—71no—
277#322—71no—
278#322—71no—
279#322C2×D711yescharacteristic
280C23×C7—21no—
281C22×D7—21no—
282C22×D7—21no—
283C22×D7C4×D411yescharacteristic
284C7×Q8—21no—
285C7×Q8—21no—
286C7×D4—21no—
287C7×D4—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7C23×C411yescharacteristic
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C22⋊D7—81no—
297C22⋊D7—81no—
298C22⋊D7—81no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7C4×D411yescharacteristic
302C2×Dic7C4×D411yescharacteristic
303C2×Dic7C4×D411yescharacteristic
304D28—21no—
305D28—21no—
306D28—21no—
307D28—21no—
308D28—81no—
309D28—81no—
310C4×D7—21no—
311C4×D7—21no—
312C4×D7—21no—
313C4×D7—21no—
314C4×D7—41no—
315C4×D7—41no—
316C4×D7—41no—
317C4×D7—41no—
318C4×D7—41no—
319Dic14—81no—
320C7×C8—21no—
321C7×C8—21no—
322C7×C8—21no—
323C7×C8—21no—
324C7×C8—41no—
325C7×C8—41no—
326C7×C8—41no—
327C7⋊C8—22no—
328C7⋊C8—21no—
329C7⋊C8—21no—
330C7⋊C8—21no—
331C7⋊C8—21no—
332C7⋊C8—41no—
333C7⋊C8—41no—
334C2×#41—141no—
335C2×SD16—71no—
336C2×SD16C4×D711yescharacteristic
337C2×D8—71no—
338C2×D8—71no—
339C2×M16—71no—
340C2×M16—71no—
341C2×M16—141no—
342C2×M16—141no—
343C2×M16—141no—
344C2×M16—141no—
345C22×C8—21no—
346C22×C8—141no—
347C22×C8—141no—
348C22×C8—141no—
349C4⋊Q8—71no—
350#127—71no—
351#126—141no—
352#125—71no—
353#124—71no—
354#124—141no—
355#123—141no—
356C22⋊Q8—71no—
357#121—71no—
358#121—71no—
359#121—71no—
360#121—141no—
361C4×Q8C22×D711yescharacteristic
362C4×D4—71no—
363C4×D4—71no—
364C4×D4—141no—
365C4×D4—141no—
366C4×D4C22×D711yescharacteristic
367#117—141no—
368C2×C42—71no—
369#107—71no—
370#107—71no—
371#106—71no—
372#106C4×D711yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—71no—
375C4⋊C8—71no—
376C4⋊C8—71no—
377C4⋊C8—71no—
378C4⋊C8—141no—
379C4⋊C8—141no—
380C4⋊C8C22×D711yescharacteristic
381C4⋊C8C22×D711yescharacteristic
382#103—71no—
383#103C4×D711yescharacteristic
384#102—71no—
385#102—71no—
386#102—71no—
387#102—71no—
388#102—71no—
389#102C4×D711yescharacteristic
390C22⋊C8—21no—
391C22⋊C8—71no—
392C22⋊C8—71no—
393C22⋊C8—141no—
394C22⋊C8—141no—
395C22⋊C8—141no—
396C22⋊C8—141no—
397C22⋊C8—141no—
398C22⋊C8—141no—
399#97—21no—
400#97—71no—
401#97—71no—
402#97—141no—
403C4×C8—71no—
404C4×C8—71no—
405C4×C8—71no—
406C4×C8—141no—
407C4×C8—141no—
408C4×C8C22×D711yescharacteristic
409C4×C8C22×D711yescharacteristic
410C4×C8C22×D711yescharacteristic
411C22×C7—41no—
412C22×C7—41no—
413C22×C7—41no—
414C22×C7C2×C4×D411yescharacteristic
415C2×D7—21no—
416C2×D7—21no—
417C2×D7—21no—
418C2×D7—41no—
419C2×D7—41no—
420C2×D7—41no—
421C2×D7—41no—
422C2×D7—41no—
423C2×D7—41no—
424C4×C7—21no—
425C4×C7—41no—
426C4×C7—41no—
427C4×C7—41no—
428C4×C7#56811yescharacteristic
429C4×C7#56811yescharacteristic
430C4×C7#57611yescharacteristic
431C4×C7#57711yescharacteristic
432Dic7—21no—
433Dic7—21no—
434Dic7—21no—
435Dic7—41no—
436Dic7—41no—
437#41—561no—
438#41—561no—
439C2×Q8—141no—
440C2×Q8C2×C4×D711yescharacteristic
441C2×D4—71no—
442C2×D4—71no—
443C2×D4—141no—
444C2×D4—141no—
445C2×D4—141no—
446C2×D4—141no—
447C2×D4—141no—
448C2×D4C2×C4×D711yescharacteristic
449C22×C4—21no—
450C22×C4—71no—
451C22×C4—71no—
452C22×C4—71no—
453C22×C4—141no—
454C22×C4—141no—
455SD16—41no—
456SD16—281no—
457D8—281no—
458D8—281no—
459M16—281no—
460M16—281no—
461M16—561no—
462M16—561no—
463M16—561no—
464M16—561no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—71no—
469C2×C8—71no—
470C2×C8—71no—
471C2×C8—71no—
472C2×C8—81no—
473C2×C8—141no—
474C2×C8—141no—
475C2×C8—141no—
476C2×C8—282no—
477C2×C8—561no—
478C2×C8—561no—
479C2×C8C2×C4×D711yescharacteristic
480C2×C8C2×C4×D711yescharacteristic
481C2×C8D4×D711yescharacteristic
482C2×C8D4×D711yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—71no—
485C4⋊C4—71no—
486C4⋊C4—141no—
487C4⋊C4—141no—
488C4⋊C4—141no—
489C4⋊C4—141no—
490C4⋊C4C2×C4×D711yescharacteristic
491C4⋊C4C2×C4×D711yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—141no—
494C22⋊C4—141no—
495C22⋊C4—141no—
496C22⋊C4—141no—
497C22⋊C4—141no—
498C22⋊C4—141no—
499C22⋊C4—141no—
500C22⋊C4—141no—
501C42—21no—
502C42—71no—
503C42—71no—
504C42—71no—
505C42C23×D711yescharacteristic
506C2×C7—81no—
507C2×C7#293211yescharacteristic
508C2×C7#294611yescharacteristic
509C2×C7#295611yescharacteristic
510D7—41no—
511D7—81no—
512D7—81no—
513C23—21no—
514C23—71no—
515C23—141no—
516C23—141no—
517Q8—21no—
518Q8—21no—
519Q8—561no—
520D4—21no—
521D4—21no—
522D4—141no—
523D4—141no—
524D4—141no—
525D4—141no—
526D4—561no—
527D4—561no—
528D4—561no—
529D4—561no—
530D4—561no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—71no—
537C2×C4—71no—
538C2×C4—71no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—141no—
543C2×C4—141no—
544C2×C4—141no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4C22×C4×D711yescharacteristic
551C2×C4C2×D4×D711yescharacteristic
552C2×C4D7×#4111yescharacteristic
553C8—21no—
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—142no—
561C8—141no—
562C8—141no—
563C8—141no—
564C8—141no—
565C8—281no—
566C8—281no—
567C7#1798711yescharacteristic, complemented, Sylow
568C22—41no—
569C22—41no—
570C22—41no—
571C22—141no—
572C22—141no—
573C22—141no—
574C22—281no—
575C22—281no—
576C22—281no—
577C22—281no—
578C22—281no—
579C22—281no—
580C22C4×D4×D711yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—141no—
586C4—141no—
587C4—141no—
588C4—281no—
589C4—281no—
590C4#9043611yescharacteristic
591C4#9044111yescharacteristic
592C4#9045311yescharacteristic
593C4#9046011yescharacteristic
594C2—81no—
595C2—281no—
596C2—561no—
597C2—561no—
598C2#1173692511yescharacteristic
599C2#1173709211yescharacteristic
600C2#1173734311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1582C2
socleC22×C7C2×C4×D4
prime radical#11737109C2
cosocleC42×C7C24
hypercenter#1582D7
hypocenterC7#17987
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #11737392C2semidirect
3. #11736876C2semidirect
4. C7×#1582C2semidirect
5. #11728708C2semidirect
6. #11728652C2semidirect
7. #11728598C2semidirect
8. #11726285C2semidirect
9. #11726275C2semidirect
10. #11725995C2semidirect
11. #11725971C2semidirect
12. #11725930C2semidirect
13. #11725907C2semidirect
14. #11725832C2semidirect
15. #11725824C2semidirect
153. #1582D7semidirect
567. C7#17987semidirect

Maximal subgroups

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

subgroupindex
#117373922
#117371092
#117368762
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