Finite Group Databasebeta

← #14724702

Subgroups — #14724702

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078653C211yesmaximal, characteristic
2Q8×#4313C211yesmaximal, characteristic
3#13077558C211yesmaximal, characteristic
4#13067514C211yesmaximal, characteristic, complemented
5#13067510C211yesmaximal, characteristic, complemented
6#13067467C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067466C211yesmaximal, characteristic, complemented
9#13067465C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067389C211yesmaximal, characteristic
12#13067069C211yesmaximal, characteristic
13D11×Q8⋊C8C211yesmaximal, characteristic
14C8×#4313C211yesmaximal, characteristic
15C8×C11×Q16C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622795C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622497C411yescharacteristic
28#10622488C411yescharacteristic
29#10622452—21no—
30#10622450—21no—
31#10622450C2211yescharacteristic
32D11×C4⋊C8C2211yescharacteristic
33#10622444—21no—
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622422C411yescharacteristic
38#10622421C411yescharacteristic
39#10622407C411yescharacteristic
40#10622406C411yescharacteristic
41C4×Dic44C2211yescharacteristic
42#10622302—21no—
43C4×#4313—21no—
44C4×#4313C2211yescharacteristic
45#10622298C2211yescharacteristic
46C4×C8×D11C2211yescharacteristic
47#10622292—21no—
48#10622292—21no—
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313D411yescharacteristic
79C2×#4313D411yescharacteristic
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82#66950C2×C411yescharacteristic
83#66949—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11C2×C411yescharacteristic
86#66942—21no—
87#66941C2×C411yescharacteristic
88#66940—21no—
89#66940C2×C411yescharacteristic
90#66925—21no—
91C42×D11—21no—
92C42×D11C2311yescharacteristic
93C4×Dic22—21no—
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×#107C2×C411yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C4×C8×C11—21no—
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66899C2×C411yescharacteristic
111(C2×D11)⋊C8C2×C411yescharacteristic
112(C2×D11)⋊C8C2×C411yescharacteristic
113#66882C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—21no—
117#66879—21no—
118#66879—21no—
119#66879D411yescharacteristic
120#66879D411yescharacteristic
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129C8×Dic11—21no—
130C8×Dic11—21no—
131#66874C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17998—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—41no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C11×Q16—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C4⋊C4C22×C411yescharacteristic
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2411yescharacteristic
173#4326—22no—
174#4326—41no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—41no—
204#4313—22no—
205#4313—42no—
206#4313Q1614yescomplemented
207C8×D11—42no—
208C8×D11—42no—
209#3104—111no—
210Q8×M16—111no—
211#2962—111no—
212#1591—111no—
213#1591—111no—
214#1584—111no—
215#1584—111no—
216#1584—111no—
217#1584—111no—
218C8×Q16—111no—
219C8×Q16D1111yescharacteristic, complemented
220#1571—111no—
221#1493—111no—
222C2×Q8⋊C8—111no—
223C8×M16—111no—
224C22×D11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11#13112yes—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—41no—
246C4×D11—42no—
247C4×D11—81no—
248C4×D11C2×Q1612yes—
249C4×D11#13512yes—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—42no—
255Dic22—81no—
256C8×C11—22no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11C2×Q1612yes—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8C2×Q1612yes—
270#533—111no—
271C2×C4×Q8—111no—
272#484—111no—
273#484—111no—
274#477—111no—
275#477—111no—
276#462—111no—
277#462—111no—
278#451—111no—
279#451—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286#446—221no—
287#446—221no—
288C8×Q8—111no—
289C8×Q8—111no—
290C8×Q8C2×D1111yescharacteristic
291C8×Q8C2×D1111yescharacteristic
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×Q16C2×D1111yescharacteristic
296#431—111no—
297#424—221no—
298#423—111no—
299#423—221no—
300C2×C4⋊C8—111no—
301#405—221no—
302C4×M16—111no—
303C4×M16—221no—
304C2×C4×C8—111no—
305#335—111no—
306#335—111no—
307#335—111no—
308#335C2×D1111yescharacteristic
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8C2×D1111yescharacteristic
316Q8⋊C8C2×D1111yescharacteristic
317#322—111no—
318#322—111no—
319C82—111no—
320C82C2×D1111yescharacteristic
321C22×C11C2×C4×D411yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11C4×Q1612yes—
325C4×C11—22no—
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11C2×#13111yescharacteristic
331C4×C11#56811yescharacteristic
332C4×C11C22×Q1611yescharacteristic
333C4×C11C2×#13511yescharacteristic
334Dic11—21no—
335Dic11—21no—
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11C4×Q1612yes—
341C22×Q8—111no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×Q16—111no—
345C2×Q16C4×D1111yescharacteristic
346C2×M16—111no—
347C2×M16—111no—
348C2×M16—221no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#125—221no—
354C22⋊Q8—111no—
355C22⋊Q8—111no—
356C22⋊Q8—221no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366#117—221no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C42—111no—
370C2×C42—221no—
371#107—111no—
372#107—111no—
373#107—111no—
374#107C4×D1111yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103C4×D1111yescharacteristic
398#103C4×D1111yescharacteristic
399C22⋊C8—111no—
400C22⋊C8—111no—
401#97—111no—
402#97—111no—
403#97—221no—
404#97—221no—
405#97—221no—
406#97—221no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11#293311yescharacteristic
419C2×C11C2×C4×Q1611yescharacteristic
420C2×C11#295611yescharacteristic
421D11—22no—
422C2×Q8—111no—
423C2×Q8—111no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—222no—
427C2×Q8—441no—
428C2×Q8C2×C4×D1111yescharacteristic
429C2×Q8C2×C4×D1111yescharacteristic
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—221no—
434C22×C4—221no—
435Q16—22no—
436Q16—222no—
437Q16—441no—
438Q16—441no—
439M16—114no—
440M16—222no—
441M16—442no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—442no—
453C2×C8—442no—
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8D4×D1111yescharacteristic
457C2×C8D4×D1111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—111no—
461C4⋊C4—111no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4C2×C4×D1111yescharacteristic
473C4⋊C4C2×C4×D1111yescharacteristic
474C22⋊C4—221no—
475C22⋊C4—221no—
476C42—21no—
477C42—21no—
478C42—111no—
479C42—111no—
480C42—111no—
481C42—221no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42C23×D1111yescharacteristic
486C11#1799811yescharacteristic, complemented, Sylow
487C23—111no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—442no—
496Q8—881no—
497Q8#6695412yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—111no—
503C2×C4—112no—
504C2×C4—112no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—881no—
516C2×C4C22×C4×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4#41×D1111yescharacteristic
519C8—22no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—112no—
526C8—221no—
527C8—221no—
528C8—221no—
529C8—441no—
530C8—441no—
531C8—441no—
532C8Q16×D1112yes—
533C22—112no—
534C22—221no—
535C22—221no—
536C22C4×D4×D1111yescharacteristic
537C4—21no—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—112no—
543C4—221no—
544C4—221no—
545C4—441no—
546C4—441no—
547C4—441no—
548C4—441no—
549C4C2×#6695411yescharacteristic
550C4#1062328111yescharacteristic
551C4C2×Q16×D1111yescharacteristic
552C4D11×#13511yescharacteristic
553C2—222no—
554C2#1307733611yescharacteristic
555C2C4×Q16×D1111yescharacteristic
556C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×Q16C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenterC8×Q16D11
hypocenterC11#17998
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
4. #13067514C2semidirect
5. #13067510C2semidirect
6. #13067467C2semidirect
7. #13067466C2semidirect
8. #13067466C2semidirect
9. #13067465C2semidirect
10. #13067420C2semidirect
15. C8×C11×Q16C2semidirect
206. #4313Q16semidirect
219. C8×Q16D11semidirect
486. C11#17998semidirect

Maximal subgroups

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

subgroupindex
#130786532
Q8×#43132
#130775582
#130675142
#130675102
#130674672
#130674662
#130674652
#130674202
#130673892
#130670692
D11×Q8⋊C82
C8×#43132
C8×C11×Q162
#1799811