Finite Group Databasebeta

← #14738606

Subgroups — #14738606

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic
2#13079126C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic
4#13068124C211yesmaximal, characteristic, complemented
5#13068120C211yesmaximal, characteristic, complemented
6#13068117C211yesmaximal, characteristic, complemented
7#13068113C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13068003C211yesmaximal, characteristic, complemented
12#13067374C211yesmaximal, characteristic, complemented
13#13067346C211yesmaximal, characteristic, complemented
14#13067344C211yesmaximal, characteristic, complemented
15C11×#3252C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#479—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#470—21no—
23C11×#468—21no—
24C11×#464—21no—
25C11×#462C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622692C2211yescharacteristic
29#10622692C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622677—21no—
33#10622677—21no—
34#10622676—21no—
35#10622667—21no—
36#10622665—21no—
37#10622655—21no—
38#10622644C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622625C2211yescharacteristic
44#10622624—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47#10622621C2211yescharacteristic
48#10622613—21no—
49#10622611—21no—
50#10622611—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53#10622537C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622117C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×SD16—21no—
69C2×C11×M16—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#126—21no—
73C11×#125—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121D411yescharacteristic
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4324—21no—
91#66979—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66923—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113#66899—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66872—21no—
121#66872—21no—
122#66872—21no—
123#66872—21no—
124#66872—21no—
125#66871—21no—
126#66871—21no—
127#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19361—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C11×Q16—81no—
157C11×SD16—81no—
158C11×M16—81no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
179C42×C11—21no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—41no—
186#4326—81no—
187#4324—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194C4×Dic11—41no—
195#4318—42no—
196#4318—81no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3252—111no—
209#3252D1111yescharacteristic
210#3160—111no—
211#2966—111no—
212#1692—111no—
213#1692—111no—
214#1691—111no—
215#1691—111no—
216#1676—111no—
217#1675—111no—
218#1674—111no—
219#1673—111no—
220#1567—111no—
221#1559—111no—
222#1559—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—81no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—42no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—41no—
252C2×Dic11—41no—
253Dic22—41no—
254Dic22—41no—
255Dic22—81no—
256C8×C11—41no—
257C8×C11—41no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8#13712yes—
265C11⋊C8#13712yes—
266#533—111no—
267#533C2×D1111yescharacteristic
268#529C2×D1111yescharacteristic
269#500—111no—
270#500—111no—
271#499—221no—
272#499—221no—
273#498—111no—
274#498—111no—
275#479—21no—
276#479—221no—
277#477—111no—
278#477C2×D1111yescharacteristic
279#476—111no—
280#476C2×D1111yescharacteristic
281#470—21no—
282#470—221no—
283#468—21no—
284#468—221no—
285#464—21no—
286#464—221no—
287#462—111no—
288#462C2×D1111yescharacteristic
289#461—111no—
290#461C2×D1111yescharacteristic
291#446—111no—
292C8×Q8—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—221no—
297#433—221no—
298#432—111no—
299#427—221no—
300#427—221no—
301#423—111no—
302#423C2×D1111yescharacteristic
303#405—221no—
304C2×C4×C8—111no—
305#335—111no—
306#335—111no—
307#335—111no—
308#335—111no—
309#333—111no—
310#333—111no—
311#333—111no—
312#333—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C2×#12111yescharacteristic
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C2×#13711yescharacteristic
334C4×C11C2×#13711yescharacteristic
335C4×C11#57611yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—81no—
338Dic11—81no—
339C2×Q16—21no—
340C2×Q16—221no—
341C2×SD16—21no—
342C2×SD16—221no—
343C2×M16—21no—
344C2×M16—221no—
345C2×M16—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—221no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#126—21no—
354#125—21no—
355#125—221no—
356#125C22⋊D1111yescharacteristic
357#124C22⋊D1111yescharacteristic
358#123—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C22⋊Q8C22⋊D1111yescharacteristic
364#121C22⋊D1111yescharacteristic
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8C22×D1111yescharacteristic
370C4×D4—21no—
371C4×D4C22×D1111yescharacteristic
372#117—21no—
373#117—21no—
374#117—221no—
375C2×C42C22×D1111yescharacteristic
376#107—21no—
377#107—221no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—21no—
383#106—221no—
384#106—221no—
385#106—221no—
386#106—221no—
387#106—221no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409#97—221no—
410#97—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C2×C11—41no—
417C2×C11—81no—
418C2×C11#303911yescharacteristic
419C2×C11#306111yescharacteristic
420C2×C11#306711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8C2×C22⋊D1111yescharacteristic
426C2×D4—21no—
427C2×D4C2×C22⋊D1111yescharacteristic
428C22×C4—21no—
429C22×C4D4×D1111yescharacteristic
430C22×C4#434111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432Q16—81no—
433Q16—881no—
434SD16—81no—
435SD16—881no—
436M16—81no—
437M16—442no—
438M16—881no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—442no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C4⋊C4C2×C22⋊D1111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—441no—
477C42—21no—
478C42—41no—
479C42—441no—
480C42D4×D1111yescharacteristic
481C42#434111yescharacteristic
482C42C2×C22⋊D1111yescharacteristic
483C42C23×D1111yescharacteristic
484C11#1936111yescharacteristic, complemented, Sylow
485C23—21no—
486C23#6699211yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—441no—
493Q8—441no—
494Q8—881no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4#6699211yescharacteristic
513C2×C4#6699211yescharacteristic
514C2×C4#6699211yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—41no—
519C8—41no—
520C8—112no—
521C8—112no—
522C8—221no—
523C8—221no—
524C8—441no—
525C8—441no—
526C8—441no—
527C8—441no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#6699211yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—881no—
545C4—881no—
546C4D11×#13711yescharacteristic
547C4D11×#13711yescharacteristic
548C4#1062336611yescharacteristic
549C4#1062336911yescharacteristic
550C2—41no—
551C2—81no—
552C2#1307810111yescharacteristic
553C2#1307828311yescharacteristic
554C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3252C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3252D11
hypocenterC11#19361
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #13079126C2semidirect
4. #13068124C2semidirect
5. #13068120C2semidirect
6. #13068117C2semidirect
7. #13068113C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13068008C2semidirect
11. #13068003C2semidirect
12. #13067374C2semidirect
13. #13067346C2semidirect
14. #13067344C2semidirect
484. C11#19361semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130791262
#130775922
#130681242
#130681202
#130681172
#130681132
#130680182
#130680132
#130680082
#130680032
#130673742
#130673462
#130673442
C11×#32522
#1936111