Finite Group Databasebeta

← #14795259

Subgroups — #14795259

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic
3#13077281C211yesmaximal, characteristic
4#13070062C212yesmaximal
5#13069916C212yesmaximal
6#13069606C211yesmaximal, characteristic, complemented
7#13069394C212yesmaximal, complemented
8#13069392C211yesmaximal, characteristic, complemented
9#13069268C212yesmaximal, complemented
10#13068612C211yesmaximal, characteristic, complemented
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66995C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C11×#475—21no—
17C11×#475—21no—
18C11×#475—22no—
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×#66900C2212yes—
23#10622838C2211yescharacteristic
24#10622723C2212yes—
25C2×#66883C2212yes—
26#10622714C2212yes—
27#10622707—21no—
28#10622704—21no—
29#10622700—21no—
30#10622697—21no—
31#10622643—21no—
32C4×#4326—21no—
33#10622639—21no—
34C4×#4325—21no—
35#10622579C2212yes—
36#10622579C2211yescharacteristic
37#10622577C2211yescharacteristic
38#10622577C2212yes—
39#10622537C2211yescharacteristic
40#10622537C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622453—22no—
43#10622448—21no—
44#10622446—21no—
45#10622190C2212yes—
46#10622168C2212yes—
47#10622168C2212yes—
48#10622168C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11C2311yescharacteristic
51C2×#4339C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4326—21no—
68#66995—22no—
69#66995—22no—
70C2×#4325—21no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73#66979C2311yescharacteristic
74C2×#4318C2312yes—
75C2×#4318C2312yes—
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78C4×D44D411yescharacteristic
79C4×D44D411yescharacteristic
80#66925—21no—
81C42×D11—21no—
82C4×Dic22D411yescharacteristic
83C4×Dic22D411yescharacteristic
84C11×#106—22no—
85C11×#106—22no—
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8D412yes—
89C11×#103—22no—
90C11×#103—22no—
91#66900—24no—
92#66899—21no—
93#66899—21no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—22no—
96#66883—24no—
97#66879—22no—
98C8×Dic11—22no—
99#66874—21no—
100#66874—22no—
101#66873—21no—
102#66873—22no—
103#66872—21no—
104#66872—22no—
105#66871—21no—
106#66871—22no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)—21no—
111#66867—21no—
112C4×C11⋊C8—21no—
113#24723—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—82no—
122C2×Q8×C11#4112yes—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—21no—
130#4339—21no—
131#4339—21no—
132#4339—21no—
133#4339—21no—
134C2×D44C2×D411yescharacteristic
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×Dic22C2×D411yescharacteristic
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C42×C11—41no—
152C42×C11—41no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11—21no—
158#4326—24no—
159#4325—24no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162C4⋊Dic11C2×D411yescharacteristic
163C4⋊Dic11C2×D411yescharacteristic
164Dic11⋊C4—21no—
165Dic11⋊C4—21no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169#4318—21no—
170#4318—22no—
171#4318—22no—
172#4318—22no—
173#4318—21no—
174#4318—22no—
175#4318—21no—
176#4318#4112yes—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181#3079—111no—
182C2×#475D1111yescharacteristic, complemented
183C4×#137—111no—
184#2925—111no—
185#2079—112no—
186#2052—112no—
187#1997—111no—
188#1951—112no—
189#1950—111no—
190#1930—112no—
191#1801—111no—
192C23×C11C2×#4111yescharacteristic
193C22×D11—21no—
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—82no—
199Q8×C11—82no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—81no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C22⋊D11—41no—
220C22⋊D11—41no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224D44—21no—
225D44—21no—
226C4×D11—41no—
227C4×D11—41no—
228C4×D11—42no—
229C4×D11—81no—
230Dic22—21no—
231Dic22—21no—
232C8×C11—22no—
233C8×C11—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C11⋊C8—41no—
237C11⋊C8—42no—
238C2×#137—111no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C4×#41—111no—
241C2×C4×Q8C2×D1111yescharacteristic
242#477—221no—
243#476—221no—
244#475—21no—
245#475—21no—
246#475—22no—
247#475—221no—
248#474—221no—
249#441—221no—
250#440—221no—
251C4×Q16—221no—
252C4×SD16—221no—
253#433—222no—
254#432—221no—
255#431—221no—
256C2×#108—112no—
257#428—112no—
258#428—111no—
259C2×#106C2×D1112yes—
260#423—111no—
261#423—111no—
262C2×C4⋊C8C2×D1111yescharacteristic
263#419—111no—
264#417—112no—
265#417—111no—
266C2×#103C2×D1112yes—
267C2×#101—112no—
268#408—112no—
269#405—112no—
270C4×M16—111no—
271#343—112no—
272#343—112no—
273#343—112no—
274#341—112no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#55211yescharacteristic
279C22×C11#55611yescharacteristic
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11#47112yes—
290C4×C11#52511yescharacteristic
291C4×C11#53611yescharacteristic
292C4×C11#54711yescharacteristic
293C4×C11#54811yescharacteristic
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297C2×#41—111no—
298C22×Q8—21no—
299C22×Q8C22×D1111yescharacteristic
300#137—222no—
301#137—222no—
302C2×Q16—221no—
303C2×SD16—221no—
304C2×M16—111no—
305C2×M16—111no—
306C2×M16—112no—
307C2×M16—112no—
308C22×C8C22×D1112yes—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—111no—
318C4×Q8—111no—
319C4×D4—111no—
320C4×D4—111no—
321C4×D4—221no—
322C4×D4—221no—
323#117—111no—
324#117—221no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1112yes—
329C2×C42—21no—
330C2×C42—221no—
331C2×C42C22×D1111yescharacteristic
332#108—224no—
333#107—221no—
334#107—222no—
335#106—22no—
336#106—22no—
337#106—221no—
338#106—222no—
339C4⋊C8—221no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342C4⋊C8—221no—
343C4⋊C8C22⋊D1111yescharacteristic
344C4⋊C8C22⋊D1111yescharacteristic
345C4⋊C8C22⋊D1112yes—
346#103—22no—
347#103—22no—
348#103—221no—
349#103—222no—
350#103—221no—
351#103—221no—
352#102—221no—
353#102—222no—
354#101—224no—
355C22⋊C8—222no—
356C22⋊C8—222no—
357#97—222no—
358#97—221no—
359C4×C8—222no—
360C4×C8—221no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11#241511yescharacteristic
364C2×C11C2×#47111yescharacteristic
365C2×C11#306911yescharacteristic
366D11—81no—
367#41—221no—
368#41—221no—
369#41—221no—
370#41—221no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—82no—
379C2×Q8—111no—
380C2×Q8#434312yes—
381C2×D4—111no—
382C2×D4—221no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4#434111yescharacteristic
390C22×C4#434111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—224no—
393SD16—224no—
394M16—112no—
395M16—221no—
396M16—222no—
397M16—222no—
398M16—222no—
399M16—221no—
400M16—222no—
401M16—221no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8C2×C22⋊D1112yes—
409C2×C8C2×C22⋊D1112yes—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—111no—
419C4⋊C4—111no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C22⋊C4—221no—
423C22⋊C4—221no—
424C22⋊C4—221no—
425C42—41no—
426C42—41no—
427C42—221no—
428C42—221no—
429C42—221no—
430C42D4×D1111yescharacteristic
431C42D4×D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C42C2×C22⋊D1111yescharacteristic
434C11#2472311yescharacteristic, complemented, Sylow
435C23—221no—
436C23C2×#434111yescharacteristic
437Q8—22no—
438Q8—22no—
439Q8—41no—
440Q8—41no—
441Q8—82no—
442Q8—82no—
443Q8—221no—
444Q8—221no—
445D4—221no—
446D4—221no—
447D4—441no—
448D4—441no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—81no—
457C2×C4—82no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—881no—
465C2×C4#6699111yescharacteristic
466C2×C4#6699111yescharacteristic
467C2×C4#6699111yescharacteristic
468C2×C4#6699111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4C2×#434311yescharacteristic
471C2×C4#6704011yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#6704311yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—22no—
476C8—22no—
477C8—222no—
478C8—442no—
479C8—442no—
480C8—441no—
481C22—21no—
482C22—21no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22#1062317211yescharacteristic
487C22#1062317311yescharacteristic
488C22C2×#6699111yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—441no—
496C4—441no—
497C4—441no—
498C4#1062279012yes—
499C4#1062315811yescharacteristic
500C4#1062315911yescharacteristic
501C4#1062334811yescharacteristic
502C4#1062335511yescharacteristic
503C2—21no—
504C2—21no—
505C2—881no—
506C2#1307204111yescharacteristic
507C2C2×#1062279011yescharacteristic
508C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC22×C11C2×#121
prime radicalC2×#4339C23
hypercenterC2×#475D11
hypocenterC11#24723
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
6. #13069606C2semidirect
7. #13069394C2semidirect
8. #13069392C2semidirect
9. #13069268C2semidirect
10. #13068612C2semidirect
11. C2×C11×#475C2semidirect
182. C2×#475D11semidirect
434. C11#24723semidirect

Maximal subgroups

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

subgroupindex
#130784252
C4×#669952
#130772812
#130700622
#130699162
#130696062
#130693942
#130693922
#130692682
#130686122
C2×C11×#4752
#2472311