Finite Group Databasebeta

← #13325184

Subgroups — #13325184

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
1#11739892C211yesmaximal, characteristic
2#11739882C211yesmaximal, characteristic
3#11736712C211yesmaximal, characteristic
4C7×#1479C211yesmaximal, characteristic
5#11728525C211yesmaximal, characteristic
6#11728501C211yesmaximal, characteristic
7#11728498C211yesmaximal, characteristic
8#11725981C211yesmaximal, characteristic, complemented
9#11725979C211yesmaximal, characteristic, complemented
10#11725976C211yesmaximal, characteristic, complemented
11#11725975C211yesmaximal, characteristic, complemented
12#11725973C211yesmaximal, characteristic, complemented
13#11725972C211yesmaximal, characteristic, complemented
14#11725969C211yesmaximal, characteristic, complemented
15#11725967C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17#90161C2211yescharacteristic
18C7×#431C2211yescharacteristic
19C7×#431C2211yescharacteristic
20#90000C411yescharacteristic
21#90000C411yescharacteristic
22#89803C411yescharacteristic
23#89803C411yescharacteristic
24C4×#1144C2211yescharacteristic
25C4×#1144C2211yescharacteristic
26C4×#1144C2211yescharacteristic
27C4×#1144C2211yescharacteristic
28#89796—21no—
29#89796—21no—
30#89796C2211yescharacteristic
31#89796C2211yescharacteristic
32Q8×C7⋊C8C2211yescharacteristic
33Q8×C7⋊C8C2211yescharacteristic
34#89793C411yescharacteristic
35#89793C411yescharacteristic
36#89742C411yescharacteristic
37#89742C411yescharacteristic
38#89698—21no—
39#89698C2211yescharacteristic
40#89697—21no—
41#89697C2211yescharacteristic
42#89697C2211yescharacteristic
43#89603C2211yescharacteristic
44#89603C2211yescharacteristic
45#89602C2211yescharacteristic
46#89602C2211yescharacteristic
47#89492—21no—
48#89492—21no—
49#89451—21no—
50C8×Dic14—21no—
51C7×Q8⋊C8C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×Q8⋊C8C2211yescharacteristic
54C7×Q8⋊C8C2211yescharacteristic
55#89275C2211yescharacteristic
56#89275C2211yescharacteristic
57#89274C2211yescharacteristic
58#89274C2211yescharacteristic
59#89251C2211yescharacteristic
60#89251C2211yescharacteristic
61#89251C2211yescharacteristic
62#89251C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18032—71nomaximal, Sylow
68C22×C7×Q8C2×C411yescharacteristic
69C4×C7×Q8—21no—
70C4×C7×Q8—21no—
71C4×C7×Q8C2×C411yescharacteristic
72C4×C7×Q8C2×C411yescharacteristic
73C4×C7×Q8C2311yescharacteristic
74C4×C7×Q8C2311yescharacteristic
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4C2×C411yescharacteristic
77C2×C42×C7—21no—
78C2×C42×C7C2311yescharacteristic
79C2×#1144C2×C411yescharacteristic
80C2×#1144C2×C411yescharacteristic
81C2×#1144C2×C411yescharacteristic
82C2×#1144C2×C411yescharacteristic
83#6489—21no—
84#6487—21no—
85#6487C2×C411yescharacteristic
86#6487C2×C411yescharacteristic
87#6433—21no—
88#6432C2×C411yescharacteristic
89#6432C2×C411yescharacteristic
90C4×Dic14—21no—
91C4×Dic14C2311yescharacteristic
92C4×Dic14C2311yescharacteristic
93C7×C4⋊C8—21no—
94C7×C4⋊C8C2311yescharacteristic
95C7×C4⋊C8C2311yescharacteristic
96C7×C22⋊C8—21no—
97C7×C22⋊C8—21no—
98C4×C7×C8—21no—
99C4×C7×C8C2311yescharacteristic
100C4×C7×C8C2311yescharacteristic
101#6409C2×C411yescharacteristic
102#6409C2×C411yescharacteristic
103#6409C2×C411yescharacteristic
104#6409C2×C411yescharacteristic
105C22⋊(C7⋊C8)—21no—
106C22⋊(C7⋊C8)C2×C411yescharacteristic
107C22⋊(C7⋊C8)C2×C411yescharacteristic
108C22⋊(C7⋊C8)D411yescharacteristic
109C22⋊(C7⋊C8)D411yescharacteristic
110#6389—21no—
111#6389—21no—
112Dic7⋊C8—21no—
113Dic7⋊C8—21no—
114Dic7⋊C8—21no—
115Dic7⋊C8—21no—
116C8×Dic7—21no—
117C8×Dic7—21no—
118#6384C2×C411yescharacteristic
119#6384C2×C411yescharacteristic
120#6384C2×C411yescharacteristic
121#6384C2×C411yescharacteristic
122#6381C2×C411yescharacteristic
123#6381C2×C411yescharacteristic
124#6381C2×C411yescharacteristic
125#6381C2×C411yescharacteristic
126C4⋊(C7⋊C8)—21no—
127C4⋊(C7⋊C8)—21no—
128C4⋊(C7⋊C8)—21no—
129C4⋊(C7⋊C8)—21no—
130C4⋊(C7⋊C8)C2×C411yescharacteristic
131C4⋊(C7⋊C8)C2×C411yescharacteristic
132C4⋊(C7⋊C8)D411yescharacteristic
133C4⋊(C7⋊C8)D411yescharacteristic
134C4⋊(C7⋊C8)C2311yescharacteristic
135C4⋊(C7⋊C8)C2311yescharacteristic
136#6377—21no—
137#6377—21no—
138#6377—21no—
139C4×C7⋊C8—21no—
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3104—71no—
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#1479D711yescharacteristic
159#1454—71no—
160C2×C7×Q8—21no—
161C2×C7×Q8—22no—
162C2×C7×Q8—41no—
163C2×C7×Q8C22×C411yescharacteristic
164C2×C7×Q8C22×C411yescharacteristic
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7#4111yescharacteristic
170C2×Dic14—21no—
171C2×Dic14C22×C411yescharacteristic
172C2×Dic14C22×C411yescharacteristic
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4C22×C411yescharacteristic
183C7×C4⋊C4C22×C411yescharacteristic
184C42×C7—21no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—21no—
188C42×C7C22×C411yescharacteristic
189C42×C7C2×D411yescharacteristic
190C42×C7#4111yescharacteristic
191C42×C7C2411yescharacteristic
192C22⋊Dic7—21no—
193C22⋊Dic7—21no—
194#1144—22no—
195#1144—22no—
196#1144—41no—
197#1144—41no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7C22×C411yescharacteristic
202C4⋊Dic7C22×C411yescharacteristic
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8C22×C411yescharacteristic
212C2×C7⋊C8C22×C411yescharacteristic
213C2×C7⋊C8C22×C411yescharacteristic
214C2×C7⋊C8C22×C411yescharacteristic
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217C2×C7⋊C8C2×D411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219#533—71no—
220C2×C4×Q8C2×D711yescharacteristic
221#484—71no—
222#484—71no—
223#477—71no—
224#477—71no—
225#462—71no—
226#462—71no—
227#451—71no—
228#451—71no—
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×Q16—71no—
242C4×Q16—71no—
243C4×Q16—71no—
244C4×Q16—71no—
245#433—141no—
246#433—141no—
247#432—71no—
248#432—141no—
249#431—71no—
250#431—71no—
251#431—141no—
252#431C2×D711yescharacteristic
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⋊C8C2×D711yescharacteristic
263Q8⋊C8C2×D711yescharacteristic
264Q8⋊C8C2×D711yescharacteristic
265Q8⋊C8C2×D711yescharacteristic
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—42no—
275C7×Q8#13112yes—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—41no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7C4×D411yescharacteristic
288C2×C4×C7C4×D411yescharacteristic
289C2×C4×C7C4×D411yescharacteristic
290C2×C4×C7C23×C411yescharacteristic
291C2×C4×C7C22×D411yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297Dic14—21no—
298Dic14—21no—
299Dic14—21no—
300Dic14—21no—
301Dic14—42no—
302C7×C8—41no—
303C7×C8—41no—
304C7×C8—41no—
305C7×C8—41no—
306C7⋊C8—21no—
307C7⋊C8—21no—
308C7⋊C8—21no—
309C7⋊C8—21no—
310C7⋊C8—21no—
311C7⋊C8—21no—
312C7⋊C8—21no—
313C7⋊C8—21no—
314C7⋊C8—41no—
315C7⋊C8—41no—
316C22×Q8C4×D711yescharacteristic
317C2×Q16—71no—
318C2×Q16—71no—
319C2×Q16—71no—
320C2×Q16—71no—
321C4⋊Q8—71no—
322C4⋊Q8—71no—
323#125—141no—
324C22⋊Q8—71no—
325C22⋊Q8—71no—
326C22⋊Q8—141no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8—71no—
330C4×Q8—71no—
331C4×Q8—141no—
332C4×Q8C4×D711yescharacteristic
333C4×Q8C4×D711yescharacteristic
334C4×Q8C22×D711yescharacteristic
335C4×Q8C22×D711yescharacteristic
336#117—141no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C4×D711yescharacteristic
339C2×C42—21no—
340C2×C42C22×D711yescharacteristic
341#107—71no—
342#107—71no—
343#107—71no—
344#107—71no—
345C4⋊C8—21no—
346C4⋊C8—71no—
347C4⋊C8—71no—
348C4⋊C8—71no—
349C4⋊C8—71no—
350C4⋊C8—71no—
351C4⋊C8—71no—
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⋊C8C22×D711yescharacteristic
361C4⋊C8C22×D711yescharacteristic
362#103—71no—
363#103—71no—
364#103—71no—
365#103—71no—
366#103—71no—
367#103—71no—
368#103—71no—
369#103—71no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—71no—
373C22⋊C8—71no—
374C22⋊C8—71no—
375C22⋊C8—71no—
376C22⋊C8—141no—
377#97—141no—
378#97—141no—
379#97—141no—
380#97—141no—
381#97—141no—
382C4×C8—21no—
383C4×C8—71no—
384C4×C8—71no—
385C4×C8—71no—
386C4×C8—71no—
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×C7C2×#13111yescharacteristic
406C4×C7#56811yescharacteristic
407C4×C7#57811yescharacteristic
408C4×C7#57811yescharacteristic
409Dic7—41no—
410Dic7—41no—
411Dic7—41no—
412Dic7—41no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—41no—
416C2×Q8—71no—
417C2×Q8—71no—
418C2×Q8—141no—
419C2×Q8C2×C4×D711yescharacteristic
420C2×Q8C2×C4×D711yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4C2×C4×D711yescharacteristic
424C22×C4D4×D711yescharacteristic
425C22×C4#115911yescharacteristic
426Q16—142no—
427Q16—142no—
428Q16—281no—
429Q16—281no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—71no—
435C2×C8—71no—
436C2×C8—71no—
437C2×C8—71no—
438C2×C8—71no—
439C2×C8—71no—
440C2×C8—71no—
441C2×C8—71no—
442C2×C8—141no—
443C2×C8—141no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—71no—
450C4⋊C4—71no—
451C4⋊C4—141no—
452C4⋊C4—141no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4C2×C4×D711yescharacteristic
459C4⋊C4C2×C4×D711yescharacteristic
460C22⋊C4—141no—
461C22⋊C4—141no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—141no—
467C42—141no—
468C42C2×C4×D711yescharacteristic
469C42D4×D711yescharacteristic
470C42#115911yescharacteristic
471C42C23×D711yescharacteristic
472C2×C7—41no—
473C2×C7#293311yescharacteristic
474C2×C7#295011yescharacteristic
475C2×C7#295511yescharacteristic
476C23(C22⋊D7)⋊C411yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—42no—
481Q8—141no—
482Q8—141no—
483Q8—141no—
484Q8—141no—
485Q8—282no—
486Q8#646412yes—
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—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—141no—
499C2×C4—141no—
500C2×C4—141no—
501C2×C4—141no—
502C2×C4(C22⋊D7)⋊C411yescharacteristic
503C2×C4(C22⋊D7)⋊C411yescharacteristic
504C2×C4(C22⋊D7)⋊C411yescharacteristic
505C2×C4C22×C4×D711yescharacteristic
506C2×C4C2×D4×D711yescharacteristic
507C2×C4C2×#115911yescharacteristic
508C8—41no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—141no—
513C8—141no—
514C8—141no—
515C8—141no—
516C8—141no—
517C8—141no—
518C8—141no—
519C8—141no—
520C8—281no—
521C8—281no—
522C7#1803211yescharacteristic, complemented, Sylow
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×(C22⋊D7)⋊C411yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—281no—
536C4—281no—
537C4—281no—
538C4—281no—
539C4C2×#646411yescharacteristic
540C4#9043611yescharacteristic
541C4#9047011yescharacteristic
542C4#9047011yescharacteristic
543C2—41no—
544C2#1173604111yescharacteristic
545C2#1173639311yescharacteristic
546C2#1173643411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1479C2
socleC22×C7C2×C4×D4
prime radicalC23×C7C4×D4
cosocleC42×C7C24
hypercenter#1479D7
hypocenterC7#18032
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
8. #11725981C2semidirect
9. #11725979C2semidirect
10. #11725976C2semidirect
11. #11725975C2semidirect
12. #11725973C2semidirect
13. #11725972C2semidirect
14. #11725969C2semidirect
15. #11725967C2semidirect
522. C7#18032semidirect

Maximal subgroups

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

subgroupindex
#117398922
#117398822
#117367122
C7×#14792
#117285252
#117285012
#117284982
#117259812
#117259792
#117259762
#117259752
#117259732
#117259722
#117259692
#117259672
#180327