Finite Group Databasebeta

← #13324630

Subgroups — #13324630

Order 1792.

566 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
1#11736740C211yesmaximal, characteristic
2#11736711C211yesmaximal, characteristic, complemented
3#11735984C211yesmaximal, characteristic
4C7×#1451C211yesmaximal, characteristic, complemented
5#11727605C211yesmaximal, characteristic, complemented
6#11727492C211yesmaximal, characteristic, complemented
7#11727490C211yesmaximal, characteristic
8#11725842C211yesmaximal, characteristic, complemented
9#11725841C211yesmaximal, characteristic, complemented
10#11725841C211yesmaximal, characteristic, complemented
11#11725840C211yesmaximal, characteristic, complemented
12#11725840C211yesmaximal, characteristic, complemented
13#11725839C211yesmaximal, characteristic, complemented
14#11725834C211yesmaximal, characteristic, complemented
15#11725833C211yesmaximal, characteristic, complemented
16#90170C2211yescharacteristic
17#90161C2211yescharacteristic
18C7×#431C2211yescharacteristic
19C4×C7×M16C2211yescharacteristic
20C2×C4×C7×C8C2211yescharacteristic
21#89909C411yescharacteristic
22#89909C411yescharacteristic
23#89906C411yescharacteristic
24#89906C411yescharacteristic
25#89698C2211yescharacteristic
26#89696C2211yescharacteristic
27#89612—21no—
28#89611—21no—
29#89600—21no—
30#89600—21no—
31#89501—21no—
32#89500—21no—
33#89492—21no—
34#89492—21no—
35#89487C411yescharacteristic
36#89486C411yescharacteristic
37#89475C411yescharacteristic
38#89474C411yescharacteristic
39C4×Dic28C2211yescharacteristic
40C4×Dic28C2211yescharacteristic
41C4×#1132C2211yescharacteristic
42C4×#1132C2211yescharacteristic
43#89460C2211yescharacteristic
44C8×D28C2211yescharacteristic
45#89451C2211yescharacteristic
46#89451C2211yescharacteristic
47#89451C2211yescharacteristic
48C8×Dic14C2211yescharacteristic
49C8×Dic14C2211yescharacteristic
50C8×Dic14C2211yescharacteristic
51C7×#322C2211yescharacteristic
52C7×#322C2211yescharacteristic
53C7×#322C2211yescharacteristic
54C7×#322C2211yescharacteristic
55#89254C2211yescharacteristic
56#89254C2211yescharacteristic
57#89253C2211yescharacteristic
58#89253C2211yescharacteristic
59#89252C2211yescharacteristic
60#89252C2211yescharacteristic
61#89251C2211yescharacteristic
62#89251C2211yescharacteristic
63#89251C2211yescharacteristic
64#89251C2211yescharacteristic
65#89251C2211yescharacteristic
66#89251C2211yescharacteristic
67#17988—71nomaximal, Sylow
68C2×C7×M16C2×C411yescharacteristic
69C2×C7×M16C2×C411yescharacteristic
70C22×C7×C8—21no—
71C2×C42×C7C2311yescharacteristic
72#6493C2×C411yescharacteristic
73#6492—21no—
74C4×C22⋊D7—21no—
75#6489—21no—
76#6487—21no—
77#6487C2×C411yescharacteristic
78#6487C2×C411yescharacteristic
79#6487C2×C411yescharacteristic
80C2×#1136—21no—
81C2×Dic28C2×C411yescharacteristic
82C2×Dic28C2×C411yescharacteristic
83C2×#1132C2×C411yescharacteristic
84C2×#1132C2×C411yescharacteristic
85C2×#1131—21no—
86C2×C8×D7—21no—
87#6439—21no—
88#6438C2×C411yescharacteristic
89C4×D28C2311yescharacteristic
90#6435—21no—
91#6433—21no—
92#6433C2×C411yescharacteristic
93#6432C2×C411yescharacteristic
94#6432C2×C411yescharacteristic
95C4×Dic14—21no—
96C4×Dic14C2311yescharacteristic
97C4×Dic14C2311yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×C4⋊C8D411yescharacteristic
100C7×C4⋊C8D411yescharacteristic
101C7×C22⋊C8D411yescharacteristic
102C7×C22⋊C8D411yescharacteristic
103C7×#97C2×C411yescharacteristic
104C7×#97C2×C411yescharacteristic
105C4×C7×C8—21no—
106C4×C7×C8C2311yescharacteristic
107C4×C7×C8C2311yescharacteristic
108C4×C7×C8C2311yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111C4×C7×C8C2311yescharacteristic
112C22⋊(C7⋊C8)—21no—
113#6395C2×C411yescharacteristic
114#6395C2×C411yescharacteristic
115(C2×D7)⋊C8—21no—
116(C2×D7)⋊C8—21no—
117#6392C2×C411yescharacteristic
118#6392C2×C411yescharacteristic
119#6391C2×C411yescharacteristic
120#6391C2×C411yescharacteristic
121#6390C2×C411yescharacteristic
122#6390C2×C411yescharacteristic
123#6390C2×C411yescharacteristic
124#6390C2×C411yescharacteristic
125#6390C2×C411yescharacteristic
126#6390C2×C411yescharacteristic
127#6389—21no—
128#6389—21no—
129#6389—21no—
130Dic7⋊C8—21no—
131Dic7⋊C8—21no—
132Dic7⋊C8—21no—
133Dic7⋊C8—21no—
134Dic7⋊C8—21no—
135Dic7⋊C8—21no—
136C8×Dic7—21no—
137C8×Dic7—21no—
138C8×Dic7—21no—
139C4⋊(C7⋊C8)—21no—
140C4⋊(C7⋊C8)C2311yescharacteristic
141C4⋊(C7⋊C8)C2311yescharacteristic
142C4⋊(C7⋊C8)C2311yescharacteristic
143C4⋊(C7⋊C8)C2311yescharacteristic
144#6377—21no—
145#3172—71no—
146#2993—71no—
147#2985—71no—
148#1588—71no—
149#1587—71no—
150#1587—71no—
151#1585—71no—
152#1584—71no—
153#1584—71no—
154#1583—71no—
155#1582—71no—
156#1569—71no—
157#1494—71no—
158#1493—71no—
159#1451D711yescharacteristic, complemented
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7#4111yescharacteristic
163C2×C22⋊D7—21no—
164C2×D28C22×C411yescharacteristic
165C2×C4×D7—21no—
166C2×Dic14—21no—
167C2×Dic14C22×C411yescharacteristic
168C2×Dic14C22×C411yescharacteristic
169C2×Dic14C22×C411yescharacteristic
170C7×M16—41no—
171C7×M16—41no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—42no—
175C2×C7×C8C22×C411yescharacteristic
176C2×C7×C8C22×C411yescharacteristic
177C2×C7×C8C22×C411yescharacteristic
178C2×C7×C8C22×C411yescharacteristic
179C2×C7×C8C2×D411yescharacteristic
180C2×C7×C8C2×D411yescharacteristic
181C2×C7×C8C2×D411yescharacteristic
182C2×C7×C8C2×D411yescharacteristic
183C42×C7C22×C411yescharacteristic
184C42×C7C2×D411yescharacteristic
185C42×C7#4111yescharacteristic
186C42×C7C2411yescharacteristic
187C22⋊Dic7—21no—
188C22⋊Dic7—21no—
189C22⋊Dic7—21no—
190(C2×D7)⋊C4—21no—
191(C2×D7)⋊C4—21no—
192(C2×D7)⋊C4—21no—
193(C2×D7)⋊C4—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7C22×C411yescharacteristic
198C4⋊Dic7C22×C411yescharacteristic
199C4⋊Dic7C22×C411yescharacteristic
200C4⋊Dic7C22×C411yescharacteristic
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208Dic7⋊C4—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C4×Dic7—21no—
212#1136—81no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217Dic28—41no—
218Dic28—41no—
219#1132—41no—
220#1132—41no—
221#1131—81no—
222C8×D7—81no—
223#533—71no—
224#529—71no—
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—71no—
236#446—141no—
237#446—141no—
238C8×Q8—71no—
239C8×Q8—71no—
240C8×Q8—71no—
241C4×Q16—71no—
242C4×Q16—71no—
243C4×SD16—71no—
244C4×SD16—71no—
245#436—71no—
246#436—141no—
247#435—141no—
248C8×D4—71no—
249#433—141no—
250#433—141no—
251#433—141no—
252#432—71no—
253#431C2×D711yescharacteristic
254#424—141no—
255#423—71no—
256C4×M16C2×D711yescharacteristic
257C2×C4×C8C2×D711yescharacteristic
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#322C2×D711yescharacteristic
271#322C2×D711yescharacteristic
272#322C2×D711yescharacteristic
273#322C2×D711yescharacteristic
274C23×C7C4×D411yescharacteristic
275C22×D7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—41no—
281C2×C4×C7C4×D411yescharacteristic
282C2×C4×C7C4×D411yescharacteristic
283C2×C4×C7C4×D411yescharacteristic
284C2×C4×C7C23×C411yescharacteristic
285C2×C4×C7C22×D411yescharacteristic
286C2×C4×C7C2×#4111yescharacteristic
287C22⋊D7—81no—
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295D28—21no—
296D28—21no—
297C4×D7—41no—
298C4×D7—41no—
299Dic14—21no—
300Dic14—21no—
301Dic14—21no—
302Dic14—21no—
303Dic14—21no—
304Dic14—21no—
305Dic14—81no—
306C7×C8—22no—
307C7×C8—21no—
308C7×C8—21no—
309C7×C8—21no—
310C7×C8—21no—
311C7×C8—21no—
312C7×C8—21no—
313C7×C8—21no—
314C7×C8—21no—
315C7×C8—41no—
316C7⋊C8—41no—
317C7⋊C8—41no—
318C7⋊C8—41no—
319C7⋊C8—41no—
320C2×Q16—71no—
321C2×Q16—71no—
322C2×SD16—71no—
323C2×SD16—71no—
324C2×M16—141no—
325C2×M16—141no—
326C2×M16C4×D711yescharacteristic
327C2×M16C4×D711yescharacteristic
328C22×C8—21no—
329C22×C8—141no—
330C4⋊Q8—71no—
331C4⋊Q8—71no—
332#126—141no—
333#125—71no—
334#125—141no—
335#124—71no—
336#123—141no—
337C22⋊Q8—71no—
338C22⋊Q8—71no—
339C22⋊Q8—71no—
340C22⋊Q8—141no—
341#121—71no—
342C4×Q8—71no—
343C4×Q8—71no—
344C4×Q8—71no—
345C4×Q8—141no—
346C4×D4—71no—
347C4×D4—141no—
348#117—141no—
349#117—141no—
350C2×C42C22×D711yescharacteristic
351#107—71no—
352#107—71no—
353#106—71no—
354#106—71no—
355C4⋊C8—71no—
356C4⋊C8—71no—
357C4⋊C8—71no—
358C4⋊C8—71no—
359C4⋊C8—141no—
360C4⋊C8—141no—
361C4⋊C8—141no—
362C4⋊C8—141no—
363C4⋊C8—141no—
364C4⋊C8—141no—
365C4⋊C8—141no—
366C4⋊C8D2811yescharacteristic
367C4⋊C8D2811yescharacteristic
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—141no—
377C22⋊C8—141no—
378C22⋊C8—141no—
379C22⋊C8D2811yescharacteristic
380C22⋊C8D2811yescharacteristic
381#97—141no—
382#97—141no—
383#97—141no—
384#97—141no—
385#97C4×D711yescharacteristic
386#97C4×D711yescharacteristic
387C4×C8—21no—
388C4×C8—141no—
389C4×C8—141no—
390C4×C8—141no—
391C4×C8C22×D711yescharacteristic
392C4×C8C22×D711yescharacteristic
393C4×C8C22×D711yescharacteristic
394C4×C8C22×D711yescharacteristic
395C4×C8C22×D711yescharacteristic
396C4×C8C22×D711yescharacteristic
397C22×C7—21no—
398C22×C7—21no—
399C22×C7—21no—
400C22×C7C2×C4×D411yescharacteristic
401C2×D7—41no—
402C2×D7—41no—
403C2×D7—41no—
404C4×C7—21no—
405C4×C7—21no—
406C4×C7—21no—
407C4×C7—21no—
408C4×C7#56811yescharacteristic
409C4×C7#56811yescharacteristic
410C4×C7#57711yescharacteristic
411C4×C7#57811yescharacteristic
412Dic7—41no—
413Dic7—41no—
414Dic7—41no—
415Dic7—41no—
416Dic7—41no—
417Dic7—41no—
418Dic7—41no—
419C2×Q8—71no—
420C2×Q8—71no—
421C2×Q8—71no—
422C2×Q8—141no—
423C2×D4—71no—
424C2×D4—141no—
425C22×C4—141no—
426C22×C4C2×C4×D711yescharacteristic
427C22×C4C2×D2811yescharacteristic
428C22×C4#115711yescharacteristic
429Q16—281no—
430Q16—281no—
431SD16—281no—
432SD16—281no—
433M16—41no—
434M16—41no—
435M16—561no—
436M16—561no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—42no—
440C2×C8—141no—
441C2×C8—141no—
442C2×C8—141no—
443C2×C8—141no—
444C2×C8—561no—
445C2×C8C2×C4×D711yescharacteristic
446C2×C8C2×C4×D711yescharacteristic
447C2×C8C2×C4×D711yescharacteristic
448C2×C8C2×C4×D711yescharacteristic
449C2×C8C2×D2811yescharacteristic
450C2×C8C2×D2811yescharacteristic
451C2×C8C2×D2811yescharacteristic
452C2×C8C2×D2811yescharacteristic
453C4⋊C4—71no—
454C4⋊C4—71no—
455C4⋊C4—71no—
456C4⋊C4—71no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4—141no—
467C4⋊C4—141no—
468C22⋊C4—141no—
469C22⋊C4—141no—
470C22⋊C4—141no—
471C22⋊C4—141no—
472C22⋊C4—141no—
473C22⋊C4—141no—
474C22⋊C4—141no—
475C42—141no—
476C42—141no—
477C42—141no—
478C42C2×C4×D711yescharacteristic
479C42C2×D2811yescharacteristic
480C42#115711yescharacteristic
481C42C23×D711yescharacteristic
482C2×C7—41no—
483C2×C7#293211yescharacteristic
484C2×C7#294711yescharacteristic
485C2×C7#295611yescharacteristic
486D7—81no—
487C23—141no—
488C23C4×D2811yescharacteristic
489Q8—141no—
490Q8—141no—
491Q8—141no—
492Q8—141no—
493Q8—141no—
494Q8—141no—
495Q8—561no—
496D4—141no—
497D4—141no—
498D4—561no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—141no—
505C2×C4—141no—
506C2×C4—141no—
507C2×C4—141no—
508C2×C4—141no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—281no—
512C2×C4—281no—
513C2×C4C4×D2811yescharacteristic
514C2×C4C4×D2811yescharacteristic
515C2×C4C4×D2811yescharacteristic
516C2×C4C22×C4×D711yescharacteristic
517C2×C4C22×D2811yescharacteristic
518C2×C4C2×#115711yescharacteristic
519C8—22no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—281no—
530C8—281no—
531C8—281no—
532C8—281no—
533C7#1798811yescharacteristic, complemented, Sylow
534C22—21no—
535C22—21no—
536C22—21no—
537C22—281no—
538C22—281no—
539C22—281no—
540C22C2×C4×D2811yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—281no—
546C4—281no—
547C4—281no—
548C4—281no—
549C4—281no—
550C4—281no—
551C4—281no—
552C4#9043611yescharacteristic
553C4#9043611yescharacteristic
554C4#9044211yescharacteristic
555C4#9044411yescharacteristic
556C2—41no—
557C2—561no—
558C2#1173593611yescharacteristic
559C2#1173598611yescharacteristic
560C2#1173601611yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1451C2
socleC22×C7C2×C4×D4
prime radical#6493C2×C4
cosocleC42×C7C24
hypercenter#1451D7
hypocenterC7#17988
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #11736711C2semidirect
4. C7×#1451C2semidirect
5. #11727605C2semidirect
6. #11727492C2semidirect
8. #11725842C2semidirect
9. #11725841C2semidirect
10. #11725841C2semidirect
11. #11725840C2semidirect
12. #11725840C2semidirect
13. #11725839C2semidirect
14. #11725834C2semidirect
15. #11725833C2semidirect
159. #1451D7semidirect
533. C7#17988semidirect

Maximal subgroups

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

subgroupindex
#117367402
#117367112
#117359842
C7×#14512
#117276052
#117274922
#117274902
#117258422
#117258412
#117258402
#117258392
#117258342
#117258332
#179887