Finite Group Databasebeta

← #13325192

Subgroups — #13325192

Order 1792.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3104C211yesmaximal, characteristic
2#11740777C211yesmaximal, characteristic
3#11739882C211yesmaximal, characteristic
4#11729581C211yesmaximal, characteristic
5#11729375C211yesmaximal, characteristic
6#11728660C211yesmaximal, characteristic, complemented
7#11728659C211yesmaximal, characteristic, complemented
8#11728658C211yesmaximal, characteristic, complemented
9#11728658C211yesmaximal, characteristic, complemented
10#11728657C211yesmaximal, characteristic, complemented
11#11728657C211yesmaximal, characteristic, complemented
12#11728656C211yesmaximal, characteristic, complemented
13Q16×C7⋊C8C211yesmaximal, characteristic, complemented
14#11728505C211yesmaximal, characteristic
15#11728498C211yesmaximal, characteristic
16C7×#533C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C7×#484C411yescharacteristic
19C7×#484C411yescharacteristic
20C7×#477C411yescharacteristic
21C7×#477C411yescharacteristic
22C7×#462C411yescharacteristic
23C7×#462C411yescharacteristic
24C7×#451C411yescharacteristic
25C7×#451C411yescharacteristic
26C4×C7×Q16C2211yescharacteristic
27C4×C7×Q16C2211yescharacteristic
28C4×C7×Q16C2211yescharacteristic
29C4×C7×Q16C2211yescharacteristic
30C7×#431C2211yescharacteristic
31#89796—21no—
32#89796—21no—
33#89796—21no—
34#89796C2211yescharacteristic
35#89796C2211yescharacteristic
36#89796C2211yescharacteristic
37#89796C2211yescharacteristic
38Q8×C7⋊C8—21no—
39Q8×C7⋊C8C2211yescharacteristic
40Q8×C7⋊C8C2211yescharacteristic
41Q8×C7⋊C8C2211yescharacteristic
42Q8×C7⋊C8C2211yescharacteristic
43#89772—21no—
44#89772—21no—
45#89698—21no—
46#89698C2211yescharacteristic
47#89697—21no—
48#89697C2211yescharacteristic
49#89697C2211yescharacteristic
50#89697C2211yescharacteristic
51Q8⋊(C7⋊C8)C2211yescharacteristic
52Q8⋊(C7⋊C8)C2211yescharacteristic
53Q8⋊(C7⋊C8)C2211yescharacteristic
54Q8⋊(C7⋊C8)C2211yescharacteristic
55Q8⋊(C7⋊C8)C2211yescharacteristic
56Q8⋊(C7⋊C8)C2211yescharacteristic
57Q8⋊(C7⋊C8)C2211yescharacteristic
58Q8⋊(C7⋊C8)C2211yescharacteristic
59#89253C2211yescharacteristic
60#89253C2211yescharacteristic
61#89252C2211yescharacteristic
62#89252C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18032—71nomaximal, Sylow
68C22×C7×Q8C2×C411yescharacteristic
69C2×C7×Q16C2×C411yescharacteristic
70C2×C7×Q16C2×C411yescharacteristic
71C2×C7×Q16C2×C411yescharacteristic
72C2×C7×Q16C2×C411yescharacteristic
73C7×C4⋊Q8C2×C411yescharacteristic
74C7×C4⋊Q8C2×C411yescharacteristic
75C7×#125—21no—
76C7×C22⋊Q8—21no—
77C7×C22⋊Q8C2×C411yescharacteristic
78C7×C22⋊Q8C2×C411yescharacteristic
79C4×C7×Q8—21no—
80C4×C7×Q8—21no—
81C4×C7×Q8—21no—
82C4×C7×Q8C2×C411yescharacteristic
83C4×C7×Q8C2×C411yescharacteristic
84C4×C7×Q8C2311yescharacteristic
85C4×C7×Q8C2311yescharacteristic
86C4×C7×Q8C2311yescharacteristic
87C4×C7×Q8C2311yescharacteristic
88C7×#117—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4C2×C411yescharacteristic
91C2×C42×C7—21no—
92C2×C42×C7C2311yescharacteristic
93C7×#107C2×C411yescharacteristic
94C7×#107C2×C411yescharacteristic
95C7×#107C2×C411yescharacteristic
96C7×#107C2×C411yescharacteristic
97C7×C4⋊C8C2×C411yescharacteristic
98C7×C4⋊C8C2×C411yescharacteristic
99C7×#103C2×C411yescharacteristic
100C7×#103C2×C411yescharacteristic
101C7×#103C2×C411yescharacteristic
102C7×#103C2×C411yescharacteristic
103C7×#103C2×C411yescharacteristic
104C7×#103C2×C411yescharacteristic
105C7×#103C2×C411yescharacteristic
106C7×#103C2×C411yescharacteristic
107C7×C22⋊C8C2×C411yescharacteristic
108C7×C22⋊C8C2×C411yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111C22⋊(C7⋊C8)—21no—
112C22⋊(C7⋊C8)—21no—
113C22⋊(C7⋊C8)—21no—
114C22⋊(C7⋊C8)D411yescharacteristic
115C22⋊(C7⋊C8)D411yescharacteristic
116C4⋊(C7⋊C8)—21no—
117C4⋊(C7⋊C8)—21no—
118C4⋊(C7⋊C8)—21no—
119C4⋊(C7⋊C8)—21no—
120C4⋊(C7⋊C8)—21no—
121C4⋊(C7⋊C8)—21no—
122C4⋊(C7⋊C8)—21no—
123C4⋊(C7⋊C8)—21no—
124C4⋊(C7⋊C8)—21no—
125C4⋊(C7⋊C8)D411yescharacteristic
126C4⋊(C7⋊C8)D411yescharacteristic
127C4⋊(C7⋊C8)C2311yescharacteristic
128C4⋊(C7⋊C8)C2311yescharacteristic
129C4⋊(C7⋊C8)C2311yescharacteristic
130C4⋊(C7⋊C8)C2311yescharacteristic
131#6377—21no—
132#6377—21no—
133#6377—21no—
134#6377—21no—
135#6377—21no—
136C4×C7⋊C8—21no—
137C4×C7⋊C8—21no—
138C4×C7⋊C8—21no—
139C4×C7⋊C8—21no—
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3104D711yescharacteristic
146#2986—71no—
147#2984—71no—
148#1593—71no—
149#1591—71no—
150#1587—71no—
151#1587—71no—
152#1584—71no—
153#1584—71no—
154#1579—71no—
155C8×Q16—71no—
156#1572—71no—
157#1497—71no—
158#1479—71no—
159#1454—71no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—22no—
163C2×C7×Q8—41no—
164C2×C7×Q8C22×C411yescharacteristic
165C2×C7×Q8C22×C411yescharacteristic
166C2×C7×Q8C22×C411yescharacteristic
167C2×C7×Q8C22×C411yescharacteristic
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7C22×C411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7#4111yescharacteristic
173C7×Q16—22no—
174C7×Q16—22no—
175C7×Q16—41no—
176C7×Q16—41no—
177C2×C7×C8C22×C411yescharacteristic
178C2×C7×C8C22×C411yescharacteristic
179C2×C7×C8C22×C411yescharacteristic
180C2×C7×C8C22×C411yescharacteristic
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4C22×C411yescharacteristic
194C7×C4⋊C4C22×C411yescharacteristic
195C7×C4⋊C4C22×C411yescharacteristic
196C7×C4⋊C4C22×C411yescharacteristic
197C7×C22⋊C4—21no—
198C7×C22⋊C4—21no—
199C42×C7—21no—
200C42×C7—21no—
201C42×C7—21no—
202C42×C7—21no—
203C42×C7—21no—
204C42×C7—21no—
205C42×C7C22×C411yescharacteristic
206C42×C7C2×D411yescharacteristic
207C42×C7#4111yescharacteristic
208C42×C7C2411yescharacteristic
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217C2×C7⋊C8C2×D411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219#533C2×D711yescharacteristic
220C2×C4×Q8C2×D711yescharacteristic
221#484Dic711yescharacteristic
222#484Dic711yescharacteristic
223#477Dic711yescharacteristic
224#477Dic711yescharacteristic
225#462Dic711yescharacteristic
226#462Dic711yescharacteristic
227#451Dic711yescharacteristic
228#451Dic711yescharacteristic
229#446—71no—
230#446—71no—
231#446—71no—
232#446—71no—
233#446—141no—
234#446—141no—
235#446—141no—
236C8×Q8—71no—
237C8×Q8—71no—
238C8×Q8—71no—
239C8×Q8—71no—
240C8×Q8—141no—
241C4×Q16C2×D711yescharacteristic
242C4×Q16C2×D711yescharacteristic
243C4×Q16C2×D711yescharacteristic
244C4×Q16C2×D711yescharacteristic
245#433—141no—
246#433—141no—
247#432—71no—
248#432—141no—
249#431—71no—
250#431—71no—
251#431—71no—
252#431—141no—
253#431C2×D711yescharacteristic
254#335—71no—
255#335—71no—
256#334—71no—
257#334—71no—
258Q8⋊C8—71no—
259Q8⋊C8—71no—
260Q8⋊C8—71no—
261Q8⋊C8—71no—
262Q8⋊C8—71no—
263Q8⋊C8—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266#322—71no—
267#322—71no—
268#322—71no—
269C82—71no—
270C23×C7C4×D411yescharacteristic
271C7×Q8—21no—
272C7×Q8—21no—
273C7×Q8—21no—
274C7×Q8—21no—
275C7×Q8—21no—
276C7×Q8—21no—
277C7×Q8—21no—
278C7×Q8—42no—
279C7×Q8—42no—
280C7×Q8#13112yes—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—41no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7C4×D411yescharacteristic
297C2×C4×C7C4×D411yescharacteristic
298C2×C4×C7C4×D411yescharacteristic
299C2×C4×C7C23×C411yescharacteristic
300C2×C4×C7C22×D411yescharacteristic
301C2×C4×C7C2×#4111yescharacteristic
302C7×C8—21no—
303C7×C8—21no—
304C7×C8—21no—
305C7×C8—21no—
306C7⋊C8—21no—
307C7⋊C8—21no—
308C7⋊C8—21no—
309C7⋊C8—21no—
310C7⋊C8—41no—
311C7⋊C8—41no—
312C7⋊C8—41no—
313C7⋊C8—41no—
314C7⋊C8—41no—
315C7⋊C8—41no—
316C22×Q8C2×Dic711yescharacteristic
317C2×Q16C2×Dic711yescharacteristic
318C2×Q16C2×Dic711yescharacteristic
319C2×Q16C2×Dic711yescharacteristic
320C2×Q16C2×Dic711yescharacteristic
321C4⋊Q8C2×Dic711yescharacteristic
322C4⋊Q8C2×Dic711yescharacteristic
323#125—21no—
324C22⋊Q8—21no—
325C22⋊Q8C2×Dic711yescharacteristic
326C22⋊Q8C2×Dic711yescharacteristic
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8C2×Dic711yescharacteristic
331C4×Q8C2×Dic711yescharacteristic
332C4×Q8C22×D711yescharacteristic
333C4×Q8C22×D711yescharacteristic
334C4×Q8C22×D711yescharacteristic
335C4×Q8C22×D711yescharacteristic
336#117—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C2×Dic711yescharacteristic
339C2×C42—21no—
340C2×C42C22×D711yescharacteristic
341#107C2×Dic711yescharacteristic
342#107C2×Dic711yescharacteristic
343#107C2×Dic711yescharacteristic
344#107C2×Dic711yescharacteristic
345C4⋊C8—71no—
346C4⋊C8—71no—
347C4⋊C8—71no—
348C4⋊C8—71no—
349C4⋊C8—71no—
350C4⋊C8—71no—
351C4⋊C8—141no—
352C4⋊C8—141no—
353C4⋊C8—141no—
354C4⋊C8—141no—
355C4⋊C8—141no—
356C4⋊C8—141no—
357C4⋊C8—141no—
358C4⋊C8—141no—
359C4⋊C8—141no—
360C4⋊C8C2×Dic711yescharacteristic
361C4⋊C8C2×Dic711yescharacteristic
362#103C2×Dic711yescharacteristic
363#103C2×Dic711yescharacteristic
364#103C2×Dic711yescharacteristic
365#103C2×Dic711yescharacteristic
366#103C2×Dic711yescharacteristic
367#103C2×Dic711yescharacteristic
368#103C2×Dic711yescharacteristic
369#103C2×Dic711yescharacteristic
370C22⋊C8—71no—
371C22⋊C8—71no—
372C22⋊C8—141no—
373C22⋊C8—141no—
374C22⋊C8—141no—
375C22⋊C8C2×Dic711yescharacteristic
376C22⋊C8C2×Dic711yescharacteristic
377#97—141no—
378#97—141no—
379#97—141no—
380#97—141no—
381#97—141no—
382C4×C8—71no—
383C4×C8—71no—
384C4×C8—71no—
385C4×C8—71no—
386C4×C8—141no—
387C4×C8—141no—
388C4×C8—141no—
389C4×C8—141no—
390C4×C8—141no—
391C4×C8C22×D711yescharacteristic
392C4×C8C22×D711yescharacteristic
393C22×C7—21no—
394C22×C7—21no—
395C22×C7—21no—
396C22×C7C2×C4×D411yescharacteristic
397C4×C7—21no—
398C4×C7—22no—
399C4×C7—21no—
400C4×C7—21no—
401C4×C7—21no—
402C4×C7—41no—
403C4×C7—41no—
404C4×C7—41no—
405C4×C7—41no—
406C4×C7—41no—
407C4×C7—41no—
408C4×C7—41no—
409C4×C7C2×#13111yescharacteristic
410C4×C7#56811yescharacteristic
411C4×C7#57811yescharacteristic
412C4×C7#57811yescharacteristic
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—41no—
417C2×Q8C22×Dic711yescharacteristic
418C2×Q8C22×Dic711yescharacteristic
419C2×Q8C22×Dic711yescharacteristic
420C2×Q8C22×Dic711yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4D4×D711yescharacteristic
424C22×C4#115911yescharacteristic
425C22×C4C22×Dic711yescharacteristic
426Q16—22no—
427Q16—22no—
428Q16—41no—
429Q16—41no—
430C2×C8—71no—
431C2×C8—71no—
432C2×C8—71no—
433C2×C8—71no—
434C2×C8—141no—
435C2×C8—141no—
436C2×C8—141no—
437C2×C8—141no—
438C2×C8—141no—
439C2×C8—141no—
440C2×C8C22×Dic711yescharacteristic
441C2×C8C22×Dic711yescharacteristic
442C2×C8C22×Dic711yescharacteristic
443C2×C8C22×Dic711yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4C22×Dic711yescharacteristic
457C4⋊C4C22×Dic711yescharacteristic
458C4⋊C4C22×Dic711yescharacteristic
459C4⋊C4C22×Dic711yescharacteristic
460C22⋊C4—21no—
461C22⋊C4—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42D4×D711yescharacteristic
469C42#115911yescharacteristic
470C42C22×Dic711yescharacteristic
471C42C23×D711yescharacteristic
472C2×C7—41no—
473C2×C7#293311yescharacteristic
474C2×C7#295011yescharacteristic
475C2×C7#295511yescharacteristic
476C23D4×Dic711yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—42no—
485Q8—42no—
486Q8#651112yes—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4D4×Dic711yescharacteristic
503C2×C4D4×Dic711yescharacteristic
504C2×C4D4×Dic711yescharacteristic
505C2×C4C2×D4×D711yescharacteristic
506C2×C4C2×#115911yescharacteristic
507C2×C4C23×Dic711yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—141no—
513C8—141no—
514C8—141no—
515C8—141no—
516C8—281no—
517C8—281no—
518C8—281no—
519C8—281no—
520C8—281no—
521C8—281no—
522C7#1803211yescharacteristic, complemented, Sylow
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×Dic711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4#9045711yescharacteristic
540C4#9045711yescharacteristic
541C4C2×#651111yescharacteristic
542C4#9051011yescharacteristic
543C2—41no—
544C2#1174036311yescharacteristic
545C2#1174131911yescharacteristic
546C2#1174144411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#3104C2
socleC22×C7C2×C4×D4
prime radicalC23×C7C4×D4
cosocleC42×C7C24
hypercenter#3104D7
hypocenterC7#18032
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
6. #11728660C2semidirect
7. #11728659C2semidirect
8. #11728658C2semidirect
9. #11728658C2semidirect
10. #11728657C2semidirect
11. #11728657C2semidirect
12. #11728656C2semidirect
13. Q16×C7⋊C8C2semidirect
522. C7#18032semidirect

Maximal subgroups

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

subgroupindex
C7×#31042
#117407772
#117398822
#117295812
#117293752
#117286602
#117286592
#117286582
#117286572
#117286562
Q16×C7⋊C82
#117285052
#117284982
#180327