Finite Group Databasebeta

← #13324437

Subgroups — #13324437

Order 1792.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2993C211yesmaximal, characteristic
2#11740581C211yesmaximal, characteristic
3#11736711C211yesmaximal, characteristic, complemented
4#11729506C211yesmaximal, characteristic
5#11728706C211yesmaximal, characteristic, complemented
6#11728705C211yesmaximal, characteristic, complemented
7#11728686C211yesmaximal, characteristic, complemented
8C8×#1144C211yesmaximal, characteristic, complemented
9#11728620C211yesmaximal, characteristic, complemented
10#11728614C211yesmaximal, characteristic, complemented
11C8×#1142C211yesmaximal, characteristic, complemented
12#11728593C211yesmaximal, characteristic, complemented
13#11728493C211yesmaximal, characteristic, complemented
14#11728255C211yesmaximal, characteristic, complemented
15#11728246C211yesmaximal, characteristic, complemented
16C7×#529C2211yescharacteristic
17#90161C2211yescharacteristic
18C7×#446C2211yescharacteristic
19C7×C8×Q8C2211yescharacteristic
20C7×#436—21no—
21C7×#436C2211yescharacteristic
22C7×#435—21no—
23C7×C8×D4C2211yescharacteristic
24C7×#433—21no—
25C7×#431C2211yescharacteristic
26C7×#424—21no—
27C7×#423C2211yescharacteristic
28#89841C411yescharacteristic
29#89837C411yescharacteristic
30#89832C411yescharacteristic
31#89827C411yescharacteristic
32#89824C411yescharacteristic
33#89824C411yescharacteristic
34#89814C411yescharacteristic
35#89814C411yescharacteristic
36C4×#1144C2211yescharacteristic
37C4×#1144C2211yescharacteristic
38C4×#1142C2211yescharacteristic
39C4×#1142C2211yescharacteristic
40#89698C2211yescharacteristic
41C4×#1136C2211yescharacteristic
42C2×C4×C7⋊C8C2211yescharacteristic
43#89600—21no—
44#89600—21no—
45#89492—21no—
46#89492—21no—
47#89451C2211yescharacteristic
48#89451C2211yescharacteristic
49C8×Dic14C2211yescharacteristic
50C8×Dic14C2211yescharacteristic
51Q8⋊(C7⋊C8)C2211yescharacteristic
52Q8⋊(C7⋊C8)C2211yescharacteristic
53D4⋊(C7⋊C8)C2211yescharacteristic
54D4⋊(C7⋊C8)C2211yescharacteristic
55#89279C2211yescharacteristic
56#89279C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89275C2211yescharacteristic
60#89275C2211yescharacteristic
61#89274C2211yescharacteristic
62#89274C2211yescharacteristic
63#89249C2211yescharacteristic
64#89249C2211yescharacteristic
65C8×C7⋊C8C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#17969—71nomaximal, Sylow
68C2×C7×M16—21no—
69C2×C7×M16—21no—
70C22×C7×C8—21no—
71C7×#126—21no—
72C7×#125C2×C411yescharacteristic
73C7×#124C2×C411yescharacteristic
74C7×#123—21no—
75C7×C22⋊Q8C2×C411yescharacteristic
76C7×#121C2×C411yescharacteristic
77C4×C7×Q8C2311yescharacteristic
78C4×C7×D4—21no—
79C4×C7×D4C2311yescharacteristic
80C7×#117—21no—
81C2×C42×C7C2311yescharacteristic
82C2×#1144C2×C411yescharacteristic
83C2×#1144C2×C411yescharacteristic
84C2×#1142C2×C411yescharacteristic
85C2×#1142C2×C411yescharacteristic
86#6489—21no—
87#6487—21no—
88#6487C2×C411yescharacteristic
89#6487C2×C411yescharacteristic
90C2×#1136C2×C411yescharacteristic
91C2×#1136C2×C411yescharacteristic
92C22×C7⋊C8—21no—
93#6433—21no—
94#6432C2×C411yescharacteristic
95#6432C2×C411yescharacteristic
96C4×Dic14—21no—
97C4×Dic14C2311yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×C4⋊C8—21no—
100C7×C4⋊C8—21no—
101C7×C4⋊C8—21no—
102C7×C4⋊C8D411yescharacteristic
103C7×C4⋊C8D411yescharacteristic
104C7×C4⋊C8C2311yescharacteristic
105C7×C4⋊C8C2311yescharacteristic
106C7×C22⋊C8—21no—
107C7×C22⋊C8—21no—
108C7×C22⋊C8D411yescharacteristic
109C7×C22⋊C8D411yescharacteristic
110C7×#97—21no—
111C4×C7×C8—21no—
112C4×C7×C8C2311yescharacteristic
113C4×C7×C8C2311yescharacteristic
114#6409C2×C411yescharacteristic
115#6409C2×C411yescharacteristic
116#6406C2×C411yescharacteristic
117#6406C2×C411yescharacteristic
118C22⋊(C7⋊C8)—21no—
119#6389—21no—
120#6389—21no—
121Dic7⋊C8—21no—
122Dic7⋊C8—21no—
123Dic7⋊C8—21no—
124Dic7⋊C8—21no—
125C8×Dic7—21no—
126C8×Dic7—21no—
127#6384C2×C411yescharacteristic
128#6384C2×C411yescharacteristic
129#6384C2×C411yescharacteristic
130#6384C2×C411yescharacteristic
131#6382C2×C411yescharacteristic
132#6382C2×C411yescharacteristic
133#6381C2×C411yescharacteristic
134#6381C2×C411yescharacteristic
135C4⋊(C7⋊C8)C2311yescharacteristic
136C4⋊(C7⋊C8)C2311yescharacteristic
137#6377—21no—
138#6377C2×C411yescharacteristic
139#6377C2×C411yescharacteristic
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3172—71no—
146#2993D711yescharacteristic
147#2985—71no—
148#1593—71no—
149#1592—71no—
150#1591—71no—
151#1590—71no—
152#1579—71no—
153SD16⋊C8—71no—
154C8×Q16—71no—
155C8×SD16—71no—
156#1569—71no—
157#1494—71no—
158#1493—71no—
159C8×M16—71no—
160C2×C7×Q8C22×C411yescharacteristic
161C2×C7×D4—21no—
162C2×C7×D4C22×C411yescharacteristic
163C22×C4×C7—21no—
164C22×C4×C7C22×C411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7#4111yescharacteristic
167C2×Dic14—21no—
168C2×Dic14C22×C411yescharacteristic
169C2×Dic14C22×C411yescharacteristic
170C7×M16—81no—
171C7×M16—81no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—81no—
175C2×C7×C8C2×D411yescharacteristic
176C2×C7×C8C2×D411yescharacteristic
177C2×C7×C8C2×D411yescharacteristic
178C2×C7×C8C2×D411yescharacteristic
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4C22×C411yescharacteristic
184C7×C4⋊C4C22×C411yescharacteristic
185C7×C22⋊C4—21no—
186C7×C22⋊C4—21no—
187C7×C22⋊C4—21no—
188C7×C22⋊C4—21no—
189C7×C22⋊C4—21no—
190C42×C7—21no—
191C42×C7C22×C411yescharacteristic
192C42×C7C2×D411yescharacteristic
193C42×C7#4111yescharacteristic
194C42×C7C2411yescharacteristic
195C22⋊Dic7—21no—
196C22⋊Dic7—21no—
197#1144—22no—
198#1144—22no—
199#1142—22no—
200#1142—22no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7C22×C411yescharacteristic
205C4⋊Dic7C22×C411yescharacteristic
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208Dic7⋊C4—21no—
209Dic7⋊C4—21no—
210C4×Dic7—21no—
211C4×Dic7—21no—
212#1136—22no—
213#1136—22no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—42no—
219C2×C7⋊C8C22×C411yescharacteristic
220C2×C7⋊C8C22×C411yescharacteristic
221C2×C7⋊C8C22×C411yescharacteristic
222C2×C7⋊C8C22×C411yescharacteristic
223#533—71no—
224#529C2×D711yescharacteristic
225#501—71no—
226#497—71no—
227#491—71no—
228#489—71no—
229#470—71no—
230#470—71no—
231#468—71no—
232#468—71no—
233#446—71no—
234#446—71no—
235#446—141no—
236#446—141no—
237#446C2×D711yescharacteristic
238C8×Q8—71no—
239C8×Q8—71no—
240C8×Q8C2×D711yescharacteristic
241C4×Q16—71no—
242C4×Q16—71no—
243C4×SD16—71no—
244C4×SD16—71no—
245#436—21no—
246#436C2×D711yescharacteristic
247#435—21no—
248C8×D4C2×D711yescharacteristic
249#433—21no—
250#433—141no—
251#433—141no—
252#432—71no—
253#431C2×D711yescharacteristic
254#424—21no—
255#423C2×D711yescharacteristic
256C4×M16—71no—
257C2×C4×C8—71no—
258#335—71no—
259#335—71no—
260#334—71no—
261#334—71no—
262Q8⋊C8—71no—
263Q8⋊C8—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268D4⋊C8—71no—
269D4⋊C8—71no—
270#322—71no—
271#322—71no—
272C82—71no—
273C82—71no—
274C23×C7—21no—
275C23×C7C4×D411yescharacteristic
276C7×Q8—21no—
277C7×Q8—21no—
278C7×D4—21no—
279C7×D4—21no—
280C7×D4—81no—
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—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7C4×D411yescharacteristic
292C2×C4×C7C4×D411yescharacteristic
293C2×C4×C7C4×D411yescharacteristic
294C2×C4×C7C23×C411yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301Dic14—21no—
302Dic14—21no—
303Dic14—21no—
304Dic14—21no—
305Dic14—81no—
306C7×C8—21no—
307C7×C8—21no—
308C7×C8—21no—
309C7×C8—21no—
310C7×C8—41no—
311C7×C8—41no—
312C7⋊C8—22no—
313C7⋊C8—21no—
314C7⋊C8—21no—
315C7⋊C8—41no—
316C7⋊C8—41no—
317C7⋊C8—41no—
318C7⋊C8#13112yes—
319C7⋊C8#13112yes—
320C2×Q16—71no—
321C2×Q16—71no—
322C2×SD16—71no—
323C2×SD16—71no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—71no—
327C2×M16—71no—
328C22×C8—21no—
329C22×C8—141no—
330C4⋊Q8—71no—
331C4⋊Q8—71no—
332#126—21no—
333#125—141no—
334#125C4×D711yescharacteristic
335#124C4×D711yescharacteristic
336#123—21no—
337C22⋊Q8—71no—
338C22⋊Q8—71no—
339C22⋊Q8—141no—
340C22⋊Q8C4×D711yescharacteristic
341#121C4×D711yescharacteristic
342C4×Q8—71no—
343C4×Q8—71no—
344C4×Q8—141no—
345C4×Q8C22×D711yescharacteristic
346C4×D4—21no—
347C4×D4C22×D711yescharacteristic
348#117—21no—
349#117—141no—
350C2×C42C22×D711yescharacteristic
351#107—71no—
352#107—71no—
353#106—71no—
354#106—71no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—71no—
359C4⋊C8—71no—
360C4⋊C8—141no—
361C4⋊C8—141no—
362C4⋊C8—141no—
363C4⋊C8—141no—
364C4⋊C8C22⋊D711yescharacteristic
365C4⋊C8C22⋊D711yescharacteristic
366C4⋊C8C22×D711yescharacteristic
367C4⋊C8C22×D711yescharacteristic
368#103—71no—
369#103—71no—
370#103—71no—
371#103—71no—
372#103—71no—
373#103—71no—
374#102—71no—
375#102—71no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—141no—
379C22⋊C8C22⋊D711yescharacteristic
380C22⋊C8C22⋊D711yescharacteristic
381#97—21no—
382#97—71no—
383#97—71no—
384#97—141no—
385#97—141no—
386#97—141no—
387C4×C8—21no—
388C4×C8—71no—
389C4×C8—71no—
390C4×C8—71no—
391C4×C8—71no—
392C4×C8—141no—
393C4×C8—141no—
394C4×C8—141no—
395C4×C8C22×D711yescharacteristic
396C4×C8C22×D711yescharacteristic
397C22×C7—21no—
398C22×C7—21no—
399C22×C7—21no—
400C22×C7—41no—
401C22×C7—41no—
402C22×C7—41no—
403C22×C7C2×C4×D411yescharacteristic
404C4×C7—21no—
405C4×C7—21no—
406C4×C7—21no—
407C4×C7—21no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7—41no—
411C4×C7C2×#13111yescharacteristic
412C4×C7C2×#13111yescharacteristic
413C4×C7#57711yescharacteristic
414C4×C7#57811yescharacteristic
415Dic7—41no—
416Dic7—41no—
417Dic7—41no—
418Dic7—41no—
419C2×Q8—71no—
420C2×Q8—71no—
421C2×Q8—141no—
422C2×Q8C2×C4×D711yescharacteristic
423C2×D4—21no—
424C2×D4C2×C4×D711yescharacteristic
425C22×C4—21no—
426C22×C4C2×C4×D711yescharacteristic
427C22×C4#115711yescharacteristic
428C22×C4C2×C22⋊D711yescharacteristic
429Q16—142no—
430Q16—142no—
431SD16—142no—
432SD16—142no—
433M16—81no—
434M16—81no—
435M16—142no—
436M16—142no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—71no—
440C2×C8—71no—
441C2×C8—71no—
442C2×C8—71no—
443C2×C8—81no—
444C2×C8—141no—
445C2×C8—141no—
446C2×C8—141no—
447C2×C8—141no—
448C2×C8—282no—
449C2×C8C2×C22⋊D711yescharacteristic
450C2×C8C2×C22⋊D711yescharacteristic
451C2×C8C2×C22⋊D711yescharacteristic
452C2×C8C2×C22⋊D711yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—71no—
458C4⋊C4—71no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4C2×C4×D711yescharacteristic
467C4⋊C4C2×C4×D711yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—141no—
474C22⋊C4—141no—
475C42—21no—
476C42—141no—
477C42—141no—
478C42C2×C4×D711yescharacteristic
479C42#115711yescharacteristic
480C42C2×C22⋊D711yescharacteristic
481C42C23×D711yescharacteristic
482C2×C7—41no—
483C2×C7—81no—
484C2×C7#293111yescharacteristic
485C2×C7#294711yescharacteristic
486C2×C7#295611yescharacteristic
487C23—21no—
488C23C4×C22⋊D711yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—141no—
492Q8—141no—
493Q8—141no—
494Q8—141no—
495Q8—561no—
496D4—21no—
497D4—21no—
498D4—81no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—141no—
512C2×C4—141no—
513C2×C4C4×C22⋊D711yescharacteristic
514C2×C4C4×C22⋊D711yescharacteristic
515C2×C4C4×C22⋊D711yescharacteristic
516C2×C4C22×C4×D711yescharacteristic
517C2×C4C2×#115711yescharacteristic
518C2×C4C22×C22⋊D711yescharacteristic
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—72no—
526C8—72no—
527C8—142no—
528C8—141no—
529C8—141no—
530C8—281no—
531C8—281no—
532C8—281no—
533C7#1796911yescharacteristic, complemented, Sylow
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—281no—
549C4—281no—
550C4—281no—
551C4—281no—
552C4D7×#13111yescharacteristic
553C4D7×#13111yescharacteristic
554C4#9052711yescharacteristic
555C4#9052911yescharacteristic
556C2—41no—
557C2—81no—
558C2#1174001611yescharacteristic
559C2#1174123111yescharacteristic
560C2#1174125611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#2993C2
socleC22×C7C2×C4×D4
prime radicalC7×#121C2×C4
cosocleC42×C7C24
hypercenter#2993D7
hypocenterC7#17969
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
3. #11736711C2semidirect
5. #11728706C2semidirect
6. #11728705C2semidirect
7. #11728686C2semidirect
8. C8×#1144C2semidirect
9. #11728620C2semidirect
10. #11728614C2semidirect
11. C8×#1142C2semidirect
12. #11728593C2semidirect
13. #11728493C2semidirect
14. #11728255C2semidirect
15. #11728246C2semidirect
533. C7#17969semidirect

Maximal subgroups

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

subgroupindex
C7×#29932
#117405812
#117367112
#117295062
#117287062
#117287052
#117286862
C8×#11442
#117286202
#117286142
C8×#11422
#117285932
#117284932
#117282552
#117282462
#179697