Finite Group Databasebeta

← #13324439

Subgroups — #13324439

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
1#11736761C211yesmaximal, characteristic, complemented
2#11736498C211yesmaximal, characteristic
3#11735984C211yesmaximal, characteristic
4C7×#1569C211yesmaximal, characteristic, complemented
5#11728554C211yesmaximal, characteristic
6#11728255C211yesmaximal, characteristic, complemented
7M16×C7⋊C8C211yesmaximal, characteristic, complemented
8#11726319C211yesmaximal, characteristic, complemented
9#11726318C211yesmaximal, characteristic, complemented
10#11726312C211yesmaximal, characteristic, complemented
11#11726311C211yesmaximal, characteristic, complemented
12#11726278C211yesmaximal, characteristic, complemented
13#11726277C211yesmaximal, characteristic, complemented
14#11726271C211yesmaximal, characteristic, complemented
15#11726270C211yesmaximal, characteristic, complemented
16#90170C2211yescharacteristic
17#90161C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C7×#423C2211yescharacteristic
20C4×C7×M16C2211yescharacteristic
21#89909C411yescharacteristic
22#89909C411yescharacteristic
23#89906C411yescharacteristic
24#89906C411yescharacteristic
25#89900—21no—
26#89899—21no—
27#89697C2211yescharacteristic
28C2×C4×C7⋊C8C2211yescharacteristic
29#89612—21no—
30#89611—21no—
31#89610C2211yescharacteristic
32#89606C2211yescharacteristic
33#89603C2211yescharacteristic
34#89603C2211yescharacteristic
35#89603C2211yescharacteristic
36#89602C2211yescharacteristic
37#89602C2211yescharacteristic
38#89602C2211yescharacteristic
39#89492—21no—
40#89492—21no—
41#89487C411yescharacteristic
42#89486C411yescharacteristic
43#89475C411yescharacteristic
44#89474C411yescharacteristic
45#89473—21no—
46#89473—21no—
47C4×Dic28C2211yescharacteristic
48C4×Dic28C2211yescharacteristic
49C4×#1132C2211yescharacteristic
50C4×#1132C2211yescharacteristic
51C7×#335C2211yescharacteristic
52C7×#335C2211yescharacteristic
53C7×#334C2211yescharacteristic
54C7×#334C2211yescharacteristic
55#89279C2211yescharacteristic
56#89279C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89279C2211yescharacteristic
60#89279C2211yescharacteristic
61#89278C2211yescharacteristic
62#89278C2211yescharacteristic
63#89250C2211yescharacteristic
64#89250C2211yescharacteristic
65C8×C7⋊C8C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#17969—71nomaximal, Sylow
68C2×C7×M16—21no—
69C2×C7×M16C2×C411yescharacteristic
70C2×C7×M16C2×C411yescharacteristic
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
80C22×C7⋊C8—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⋊C8—21no—
100C7×C4⋊C8C2311yescharacteristic
101C7×C4⋊C8C2311yescharacteristic
102C7×C4⋊C8C2311yescharacteristic
103C7×C4⋊C8C2311yescharacteristic
104C7×C22⋊C8—21no—
105C7×#97—21no—
106C7×#97C2×C411yescharacteristic
107C7×#97C2×C411yescharacteristic
108C4×C7×C8C2311yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C22⋊(C7⋊C8)D411yescharacteristic
111C22⋊(C7⋊C8)D411yescharacteristic
112#6395C2×C411yescharacteristic
113#6395C2×C411yescharacteristic
114(C2×D7)⋊C8—21no—
115(C2×D7)⋊C8—21no—
116#6392C2×C411yescharacteristic
117#6392C2×C411yescharacteristic
118#6391C2×C411yescharacteristic
119#6391C2×C411yescharacteristic
120#6390C2×C411yescharacteristic
121#6390C2×C411yescharacteristic
122#6390C2×C411yescharacteristic
123#6390C2×C411yescharacteristic
124#6390C2×C411yescharacteristic
125#6390C2×C411yescharacteristic
126#6389—21no—
127#6389—21no—
128#6389—21no—
129Dic7⋊C8—21no—
130Dic7⋊C8—21no—
131Dic7⋊C8—21no—
132Dic7⋊C8—21no—
133Dic7⋊C8—21no—
134Dic7⋊C8—21no—
135C8×Dic7—21no—
136C8×Dic7—21no—
137C8×Dic7—21no—
138C4⋊(C7⋊C8)D411yescharacteristic
139C4⋊(C7⋊C8)D411yescharacteristic
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3172—71no—
146#2993—71no—
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#1569D711yescharacteristic, complemented
157#1494—71no—
158#1493—71no—
159C8×M16—71no—
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—22no—
171C7×M16—22no—
172C7×M16—81no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8C22×C411yescharacteristic
178C2×C7×C8C22×C411yescharacteristic
179C2×C7×C8C22×C411yescharacteristic
180C2×C7×C8C22×C411yescharacteristic
181C42×C7C22×C411yescharacteristic
182C42×C7C2×D411yescharacteristic
183C42×C7#4111yescharacteristic
184C42×C7C2411yescharacteristic
185C22⋊Dic7—21no—
186C22⋊Dic7—21no—
187C22⋊Dic7—21no—
188(C2×D7)⋊C4—21no—
189(C2×D7)⋊C4—21no—
190(C2×D7)⋊C4—21no—
191(C2×D7)⋊C4—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7C22×C411yescharacteristic
196C4⋊Dic7C22×C411yescharacteristic
197C4⋊Dic7C22×C411yescharacteristic
198C4⋊Dic7C22×C411yescharacteristic
199Dic7⋊C4—21no—
200Dic7⋊C4—21no—
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—42no—
213C2×C7⋊C8C2×D411yescharacteristic
214C2×C7⋊C8C2×D411yescharacteristic
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217Dic28—22no—
218Dic28—22no—
219#1132—22no—
220#1132—22no—
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#432C2×D711yescharacteristic
253#431—71no—
254#424—141no—
255#423C2×D711yescharacteristic
256C4×M16C2×D711yescharacteristic
257C2×C4×C8—71no—
258#335C2×D711yescharacteristic
259#335C2×D711yescharacteristic
260#334C2×D711yescharacteristic
261#334C2×D711yescharacteristic
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×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—21no—
307C7×C8—21no—
308C7×C8—41no—
309C7×C8—41no—
310C7×C8—41no—
311C7×C8—41no—
312C7×C8#13112yes—
313C7×C8#13112yes—
314C7⋊C8—22no—
315C7⋊C8—21no—
316C7⋊C8—21no—
317C7⋊C8—21no—
318C7⋊C8—21no—
319C7⋊C8—41no—
320C2×Q16—71no—
321C2×Q16—71no—
322C2×SD16—71no—
323C2×SD16—71no—
324C2×M16—21no—
325C2×M16—141no—
326C2×M16C4×D711yescharacteristic
327C2×M16C4×D711yescharacteristic
328C22×C8—141no—
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—21no—
356C4⋊C8—71no—
357C4⋊C8—71no—
358C4⋊C8—141no—
359C4⋊C8—141no—
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—71no—
378C22⋊C8—71no—
379C22⋊C8—141no—
380C22⋊C8—141no—
381#97—21no—
382#97—141no—
383#97—141no—
384#97—141no—
385#97C4×D711yescharacteristic
386#97C4×D711yescharacteristic
387C4×C8—71no—
388C4×C8—71no—
389C4×C8—71no—
390C4×C8—71no—
391C4×C8—141no—
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×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×C7C2×#13111yescharacteristic
409C4×C7C2×#13111yescharacteristic
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×C4D4×D711yescharacteristic
428C22×C4#116111yescharacteristic
429Q16—142no—
430Q16—142no—
431SD16—142no—
432SD16—142no—
433M16—22no—
434M16—22no—
435M16—81no—
436M16—561no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—71no—
442C2×C8—71no—
443C2×C8—71no—
444C2×C8—71no—
445C2×C8—141no—
446C2×C8—141no—
447C2×C8—282no—
448C2×C8—561no—
449C2×C8C2×C4×D711yescharacteristic
450C2×C8C2×C4×D711yescharacteristic
451C2×C8C2×C4×D711yescharacteristic
452C2×C8C2×C4×D711yescharacteristic
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
479C42D4×D711yescharacteristic
480C42#116111yescharacteristic
481C42C23×D711yescharacteristic
482C2×C7—41no—
483C2×C7#293111yescharacteristic
484C2×C7#294711yescharacteristic
485C2×C7#295611yescharacteristic
486D7—81no—
487C23—141no—
488C23#645611yescharacteristic
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×C4#645611yescharacteristic
514C2×C4#645611yescharacteristic
515C2×C4#645611yescharacteristic
516C2×C4C22×C4×D711yescharacteristic
517C2×C4C2×D4×D711yescharacteristic
518C2×C4C2×#116111yescharacteristic
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—142no—
526C8—141no—
527C8—141no—
528C8—141no—
529C8—141no—
530C8—281no—
531C8#647012yes—
532C8#647012yes—
533C7#1796911yescharacteristic, complemented, Sylow
534C22—21no—
535C22—21no—
536C22—21no—
537C22—281no—
538C22—281no—
539C22—281no—
540C22C2×#645611yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—281no—
546C4—281no—
547C4—281no—
548C4—281no—
549C4—281no—
550C4—281no—
551C4—281no—
552C4C2×#647011yescharacteristic
553C4C2×#647011yescharacteristic
554C4#9046611yescharacteristic
555C4#9047011yescharacteristic
556C2—41no—
557C2—561no—
558C2#1173648611yescharacteristic
559C2#1173664711yescharacteristic
560C2#1173670311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1569C2
socleC22×C7C2×C4×D4
prime radical#6493C2×C4
cosocleC42×C7C24
hypercenter#1569D7
hypocenterC7#17969
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
1. #11736761C2semidirect
4. C7×#1569C2semidirect
6. #11728255C2semidirect
7. M16×C7⋊C8C2semidirect
8. #11726319C2semidirect
9. #11726318C2semidirect
10. #11726312C2semidirect
11. #11726311C2semidirect
12. #11726278C2semidirect
13. #11726277C2semidirect
14. #11726271C2semidirect
15. #11726270C2semidirect
156. #1569D7semidirect
533. C7#17969semidirect

Maximal subgroups

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

subgroupindex
#117367612
#117364982
#117359842
C7×#15692
#117285542
#117282552
M16×C7⋊C82
#117263192
#117263182
#117263122
#117263112
#117262782
#117262772
#117262712
#117262702
#179697