Finite Group Databasebeta

← #14775590

Subgroups — #14775590

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic
2C4⋊C4×Dic22C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic
4#13069379C211yesmaximal, characteristic
5#13069341C212yesmaximal
6#13069201C212yesmaximal
7#13068883C212yesmaximal
8C4⋊C4×C11⋊C8C211yesmaximal, characteristic
9C4×#66874C212yesmaximal
10C4×#66874C211yesmaximal, characteristic
11C11×#2365C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×Dic22C2212yes—
15C2×C4×Dic22C2211yescharacteristic
16C11×#391—21no—
17C11×#389C2212yes—
18C11×#387—22no—
19C4×C11×C4⋊C4C2211yescharacteristic
20C4×C11×C4⋊C4C2212yes—
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622707C418yescomplemented
23#10622589—21no—
24C4⋊C4×Dic11—21no—
25C2×#66874C2211yescharacteristic
26C2×#66874C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66872C2212yes—
29C2×#66872C2212yes—
30#10622548C2211yescharacteristic
31#10622541C2212yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34C2×C4×C11⋊C8C2212yes—
35#10622260—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622162C2212yes—
42C22×Q8×C11—21no—
43C22×Dic22C2311yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C4×Q8×C11—44no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—22no—
55C2×C42×C11—21no—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69C22×C11⋊C8C2311yescharacteristic
70C4×Dic22—22no—
71C4×Dic22—24no—
72C4×Dic22—42no—
73C4×Dic22C2×C414yes—
74C11×#95—21no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95D412yes—
78C11⋊#95—22no—
79#66874—22no—
80#66874C2×C418yes—
81#66874Q814yescomplemented
82#66872—42no—
83#66872C2×C418yes—
84C4⋊(C11⋊C8)C2×C414yes—
85C4×C11⋊C8—22no—
86C4×C11⋊C8—42no—
87#22964—111nomaximal, Sylow
88C2×Q8×C11—24no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—22no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22C22×C412yes—
106C2×Dic22C2×Q812yes—
107C2×Dic22#4112yes—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4SD1614yes—
116C11×C4⋊C4C22×C414yes—
117C11×C4⋊C4C2×Q812yes—
118C42×C11—22no—
119C42×C11—22no—
120C42×C11—44no—
121C42×C11—42no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—42no—
128C4⋊Dic11—81no—
129C4⋊Dic11C22×C412yes—
130Dic11⋊C4—24no—
131Dic11⋊C4—44no—
132Dic11⋊C4—82no—
133C4×Dic11—24no—
134C4×Dic11—44no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8C22×C414yes—
143C2×C11⋊C8C2×Q812yes—
144C2×#475—111no—
145#2365D1111yescharacteristic
146Q8×C4⋊C4—111no—
147#1990—111no—
148#1948—111no—
149#1941—112no—
150#1920—112no—
151#1865—112no—
152C8×C4⋊C4—111no—
153C4×#103—111no—
154C4×#103—112no—
155C23×C11C22×D411yescharacteristic
156Q8×C11—48no—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11C4×D412yes—
174C2×C4×C11C4×D412yes—
175C2×C4×C11C2×SD1614yes—
176C2×C4×C11C2×SD1612yes—
177C2×C4×C11#13512yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193Dic22—22no—
194Dic22—22no—
195Dic22—22no—
196Dic22C4×Q814yescomplemented
197C11⋊C8—24no—
198C11⋊C8—22no—
199C11⋊C8—41no—
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×C4×Q8—21no—
202C2×C4×Q8—111no—
203C2×C4×Q8—112no—
204#475—118no—
205C2×#106—112no—
206C2×#106—112no—
207C2×C4⋊C8—111no—
208C2×#103—112no—
209C2×#103—111no—
210C2×#103—111no—
211C2×C4×C8—111no—
212C2×C4×C8—112no—
213#391—21no—
214#389—112no—
215#389—222no—
216#389C2×D1112yes—
217#387—22no—
218#384—111no—
219#384—221no—
220C4×C4⋊C4—221no—
221C4×C4⋊C4C2×D1112yes—
222C4×C4⋊C4C2×D1111yescharacteristic
223C4×C4⋊C4C2×D1111yescharacteristic
224#340—112no—
225#340—111no—
226#340—112no—
227#340—111no—
228#340—112no—
229#336—112no—
230C22×C11C2×C4×D411yescharacteristic
231C22×C11#54611yescharacteristic
232C22×C11D4×Q811yescharacteristic
233C22×C11C22×SD1611yescharacteristic
234C22×C11C2×#13511yescharacteristic
235C22×C11#57711yescharacteristic
236C22×C11#57811yescharacteristic
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—42no—
242C4×C11—81no—
243C4×C11C4×SD1614yes—
244C4×C11C2×C4×Q811yescharacteristic
245C4×C11#52011yescharacteristic
246C4×C11#55211yescharacteristic
247C4×C11#55411yescharacteristic
248Dic11—24no—
249Dic11—42no—
250Dic11—82no—
251C22×Q8—21no—
252C22×Q8—111no—
253C22×C8—112no—
254C22×C8—111no—
255C22×C8—111no—
256C4⋊Q8—22no—
257C4⋊Q8C4×D1114yes—
258C4×Q8—44no—
259C4×Q8—114no—
260C4×Q8—224no—
261C4×Q8—222no—
262C4×Q8—442no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C4⋊C4C22×D1112yes—
276C2×C4⋊C4C22×D1111yescharacteristic
277C2×C42—22no—
278C2×C42—21no—
279C2×C42—221no—
280C2×C42—222no—
281C2×C42C22×D1112yes—
282C2×C42C22×D1111yescharacteristic
283#106—118no—
284#106—442no—
285C4⋊C8—114no—
286#103—118no—
287#103—114no—
288#103—222no—
289C4×C8—222no—
290C4×C8—442no—
291#95—21no—
292#95—22no—
293#95—22no—
294#95—222no—
295#95C22⋊D1112yes—
296C2×C11#236011yescharacteristic
297C2×C11C2×C4×SD1611yescharacteristic
298C2×C11#294711yescharacteristic
299C2×C11#329811yescharacteristic
300C2×C11#330411yescharacteristic
301C2×C11Q8×SD1611yescharacteristic
302C2×C11#338311yescharacteristic
303C2×Q8—24no—
304C2×Q8—42no—
305C2×Q8—42no—
306C2×Q8—112no—
307C2×Q8—112no—
308C2×Q8—112no—
309C2×Q8—221no—
310C2×Q8—221no—
311C2×Q8—221no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—222no—
318C22×C4C2×C22⋊D1112yes—
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1111yescharacteristic
322C22×C4C23×D1111yescharacteristic
323C2×C8—114no—
324C2×C8—112no—
325C2×C8—221no—
326C2×C8—222no—
327C2×C8—221no—
328C2×C8—222no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—221no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—44no—
339C4⋊C4—112no—
340C4⋊C4—224no—
341C4⋊C4—221no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—444no—
345C4⋊C4—442no—
346C4⋊C4—882no—
347C4⋊C4—881no—
348C4⋊C4#432414yes—
349C4⋊C4C2×C4×D1114yes—
350C4⋊C4Q8×D1112yes—
351C42—22no—
352C42—22no—
353C42—44no—
354C42—42no—
355C42—224no—
356C42—444no—
357C42C2×C4×D1112yes—
358C42#433912yes—
359C11#2296411yescharacteristic, complemented, Sylow
360C23C22×C22⋊D1111yescharacteristic
361Q8—48no—
362Q8—114no—
363Q8—222no—
364Q8—222no—
365Q8—222no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4C4×C22⋊D1112yes—
392C2×C4C4×C22⋊D1112yes—
393C2×C4C2×#432414yes—
394C2×C4C2×#432412yes—
395C2×C4#6700312yes—
396C2×C4C22×C4×D1111yescharacteristic
397C2×C4C2×#433911yescharacteristic
398C2×C4C2×Q8×D1111yescharacteristic
399C2×C4#6704011yescharacteristic
400C2×C4#41×D1111yescharacteristic
401C2×C4#6704211yescharacteristic
402C8—224no—
403C8—222no—
404C8—441no—
405C22C2×C4×C22⋊D1111yescharacteristic
406C22C22×#432411yescharacteristic
407C22Q8×C22⋊D1111yescharacteristic
408C22C2×#6700311yescharacteristic
409C22#1062336011yescharacteristic
410C22#1062336811yescharacteristic
411C22#1062336911yescharacteristic
412C4—24no—
413C4—22no—
414C4—44no—
415C4—42no—
416C4—42no—
417C4—81no—
418C4—224no—
419C4—442no—
420C4—882no—
421C4C4×#432414yes—
422C4C4×Q8×D1111yescharacteristic
423C4#1062310511yescharacteristic
424C4#1062311011yescharacteristic
425C4#1062311211yescharacteristic
426C2#1307161711yescharacteristic
427C2C2×C4×#432411yescharacteristic
428C2#1307745911yescharacteristic
429C2#1308047511yescharacteristic
430C2#1308054911yescharacteristic
431C2Q8×#432411yescharacteristic
432C2#1308150311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2365D11
hypocenterC11#22964
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
22. #10622707C4semidirect
81. #66874Q8semidirect
196. Dic22C4×Q8semidirect
359. C11#22964semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C4⋊C4×Dic222
#130695782
#130693792
#130693412
#130692012
#130688832
C4⋊C4×C11⋊C82
C4×#668742
C11×#23652
#2296411