Finite Group Databasebeta

← #14812685

Subgroups — #14812685

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079152C211yesmaximal, characteristic, complemented
2#13078483C212yesmaximal
3#13077212C211yesmaximal, characteristic
4#13070127C212yesmaximal, complemented
5#13069966C212yesmaximal, complemented
6#13069399C211yesmaximal, characteristic, complemented
7#13069364C211yesmaximal, characteristic, complemented
8#13068848C212yesmaximal
9#13068681C211yesmaximal, characteristic
10#13068453C211yesmaximal, characteristic
11C11×#1846C211yesmaximal, characteristic, complemented
12C2×#66954C2211yescharacteristic
13#10623035C2212yes—
14#10623031C2212yes—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#107C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C11×#382C2212yes—
20#10622726C2211yescharacteristic
21C2×#66883C2211yescharacteristic
22#10622719C2211yescharacteristic
23#10622715C2212yes—
24#10622714C2211yescharacteristic
25#10622579C2212yes—
26#10622577C2212yes—
27#10622577C2212yes—
28#10622577C2212yes—
29C2×#66869C2211yescharacteristic
30#10622494—22no—
31#10622493—21no—
32D11×#107—21no—
33#10622491—21no—
34#10622489—22no—
35#10622487—21no—
36#10622484—22no—
37#10622483—22no—
38#10622470—22no—
39#10622467—22no—
40#10622190C2211yescharacteristic
41#10622168C2212yes—
42#10622168C2212yes—
43#10622161C2212yes—
44#10622161C2211yescharacteristic
45C2×#4339C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51C4×C22⋊D11—42no—
52#66979C2311yescharacteristic
53#66979C2312yes—
54#66977—42no—
55C2×#4318C2312yes—
56C2×#4318C2311yescharacteristic
57C2×#4318C2311yescharacteristic
58#66954—22no—
59#66954Q814yescomplemented
60C2×#4313—21no—
61C2×C8×D11—21no—
62#66946—22no—
63#66945—22no—
64C4⋊C4×D11—22no—
65#66943—22no—
66#66943—22no—
67#66941—22no—
68#66941—22no—
69#66940—22no—
70C11×#107—21no—
71C11×#107—21no—
72C11×#107—21no—
73C11×#107—21no—
74C11×#106—22no—
75C11×#106—22no—
76C4×C8×C11—22no—
77C11×#95—42no—
78#66885D411yescharacteristic
79#66885D411yescharacteristic
80#66883—22no—
81#66882D411yescharacteristic
82#66882D411yescharacteristic
83#66881D412yes—
84#66880D411yescharacteristic
85#66880D411yescharacteristic
86#66879—21no—
87Dic11⋊C8—22no—
88Dic11⋊C8—22no—
89C8×Dic11—21no—
90#66874—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66872—22no—
95#66871—22no—
96#66871—22no—
97#66871—22no—
98#66869Q814yescomplemented
99#26082—111nomaximal, Sylow
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C2411yescharacteristic
104C2×C22⋊D11—21no—
105#4339—21no—
106#4339—21no—
107#4339C2×Q812yes—
108#4339C2×Q812yes—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×C4×D11—42no—
112C2×Dic22—42no—
113C2×Dic22C2×D411yescharacteristic
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×Q812yes—
121C2×C8×C11#4112yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C42×C11—21no—
127C42×C11C2×Q812yes—
128C22⋊Dic11—21no—
129C22⋊Dic11—22no—
130(C2×D11)⋊C4—42no—
131C4⋊Dic11—42no—
132C4⋊Dic11C2×D411yescharacteristic
133C4⋊Dic11C2×D412yes—
134C4⋊Dic11C2×D412yes—
135C4⋊Dic11C2×D411yescharacteristic
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139C4×Dic11—21no—
140C4×Dic11—22no—
141C4×Dic11—42no—
142#4318—21no—
143#4318—22no—
144#4318—21no—
145#4318—22no—
146#4318C2×Q812yes—
147#4318C2×Q812yes—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151#4313—24no—
152C8×D11—24no—
153#3164—111no—
154#3084—112no—
155#2913—111no—
156#2090—112no—
157#2061—112no—
158#1952—111no—
159#1945—111no—
160#1860—112no—
161#1846D1111yescharacteristic, complemented
162#1816—111no—
163#1764—111no—
164C23×C11H(5,𝔽2)11yescharacteristic
165C22×D11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11—82no—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C22⋊D11—22no—
180C22⋊D11—22no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—21no—
184C2×Dic11—22no—
185C2×Dic11—21no—
186D44—21no—
187D44C4⋊Q812yes—
188C4×D11—22no—
189C4×D11—22no—
190C4×D11—162no—
191Dic22—21no—
192Dic22—162no—
193Dic22C4⋊Q812yes—
194C8×C11—21no—
195C8×C11—21no—
196C8×C11C22⋊Q812yes—
197C8×C11C22⋊Q812yes—
198C11⋊C8—22no—
199C11⋊C8—22no—
200C11⋊C8—42no—
201C2×#131—111no—
202#544—112no—
203#520—112no—
204#501—222no—
205#500—221no—
206#499—221no—
207#479—222no—
208#478—222no—
209#476—222no—
210#475—222no—
211C2×#108—111no—
212#428—112no—
213#428—112no—
214#428—112no—
215#428—222no—
216#427—111no—
217#427—221no—
218C2×#107—221no—
219C2×#107C2×D1111yescharacteristic
220C2×#107C2×D1111yescharacteristic
221C2×#106C2×D1112yes—
222#424—112no—
223C2×#104—111no—
224#417—112no—
225#416—111no—
226#405—111no—
227C2×C4×C8C2×D1111yescharacteristic
228#382C2×D1112yes—
229#343—112no—
230#343—112no—
231#341—111no—
232#339—111no—
233#339—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11#54411yescharacteristic
237C22×C11D4211yescharacteristic
238C22×C11#55411yescharacteristic
239C2×D11—22no—
240C2×D11—41no—
241C2×D11—41no—
242C4×C11—42no—
243C4×C11—82no—
244C4×C11—82no—
245C4×C11C2×C22⋊Q811yescharacteristic
246C4×C11C2×C4⋊Q811yescharacteristic
247C4×C11#54711yescharacteristic
248C4×C11D4×Q811yescharacteristic
249Dic11—22no—
250Dic11—41no—
251Dic11—42no—
252Dic11—42no—
253Dic11—41no—
254C2×#41—111no—
255#131—114no—
256#131—222no—
257C2×M16—111no—
258C2×M16—111no—
259C2×M16—112no—
260C2×M16—221no—
261C22×C8—221no—
262C22×C8C22×D1111yescharacteristic
263C22×C8C22×D1111yescharacteristic
264C4⋊Q8—222no—
265C4⋊Q8—222no—
266#125—222no—
267#125—222no—
268C22⋊Q8—442no—
269C4×Q8—222no—
270C4×D4—222no—
271C4×D4—442no—
272#117—112no—
273#117—111no—
274#117—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22×D1112yes—
277C2×C4⋊C4C22×D1112yes—
278C2×C42C22×D1111yescharacteristic
279#108—222no—
280#107—21no—
281#107—21no—
282#107—21no—
283#107—21no—
284#107—111no—
285#107—111no—
286#107—222no—
287#107—222no—
288#107—222no—
289#106—22no—
290#106—22no—
291#106—112no—
292#106—222no—
293#106—222no—
294#106—222no—
295C4⋊C8—222no—
296C4⋊C8—222no—
297#104—114no—
298#103—111no—
299#103—111no—
300#103—222no—
301#102—111no—
302#102—111no—
303#102—222no—
304#97—221no—
305C4×C8—22no—
306C4×C8—221no—
307#95—42no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11#244011yescharacteristic
311C2×C11#329011yescharacteristic
312C2×C11#329011yescharacteristic
313D11—42no—
314#41—112no—
315#41—112no—
316#41—221no—
317#41—221no—
318C2×Q8—111no—
319C2×Q8—442no—
320C2×D4—111no—
321C2×D4—221no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—221no—
326C22×C4—442no—
327C22×C4C23×D1111yescharacteristic
328M16—112no—
329M16—112no—
330M16—221no—
331M16—221no—
332M16—224no—
333M16—222no—
334M16—222no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—224no—
340C2×C8—222no—
341C2×C8#433912yes—
342C2×C8D4×D1111yescharacteristic
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8D4×D1111yescharacteristic
346C2×C8Q8×D1112yes—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—111no—
352C4⋊C4—111no—
353C4⋊C4—112no—
354C4⋊C4—112no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C22⋊C4—222no—
360C22⋊C4—221no—
361C22⋊C4—442no—
362C42—21no—
363C42—221no—
364C42—222no—
365C42—442no—
366C42Q8×D1112yes—
367C11#2608211yescharacteristic, complemented, Sylow
368C23—221no—
369C23#6703711yescharacteristic
370Q8—112no—
371Q8—221no—
372Q8—1762no—
373D4—112no—
374D4—222no—
375D4—222no—
376D4—221no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—221no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—221no—
389C2×C4—222no—
390C2×C4—221no—
391C2×C4—1762no—
392C2×C4C2×#433911yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4C2×Q8×D1111yescharacteristic
396C2×C4C2×Q8×D1111yescharacteristic
397C2×C4#6704011yescharacteristic
398C8—21no—
399C8—21no—
400C8—222no—
401C8—222no—
402C8—442no—
403C8#6694912yes—
404C8#6694912yes—
405C22—21no—
406C22—21no—
407C22—222no—
408C22—441no—
409C22—441no—
410C22#1062304211yescharacteristic
411C22#1062324811yescharacteristic
412C22#1062326011yescharacteristic
413C4—42no—
414C4—82no—
415C4—82no—
416C4—222no—
417C4—442no—
418C4—441no—
419C4—442no—
420C4—441no—
421C4#1062303811yescharacteristic
422C4C2×#6694911yescharacteristic
423C4D11×C4⋊Q811yescharacteristic
424C4#1062325811yescharacteristic
425C2—21no—
426C2—21no—
427C2—442no—
428C2#1307232111yescharacteristic
429C2#1308040111yescharacteristic
430C2#1308040111yescharacteristic
subgroupG/H
centerC22#10623248
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1846C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#1846D11
hypocenterC11#26082
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1846

Complements

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

NH ≅ G/Ntype
1. #13079152C2semidirect
4. #13070127C2semidirect
5. #13069966C2semidirect
6. #13069399C2semidirect
7. #13069364C2semidirect
11. C11×#1846C2semidirect
59. #66954Q8semidirect
98. #66869Q8semidirect
161. #1846D11semidirect
367. C11#26082semidirect

Maximal subgroups

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

subgroupindex
#130791522
#130784832
#130772122
#130701272
#130699662
#130693992
#130693642
#130688482
#130686812
#130684532
C11×#18462
#2608211