Finite Group Databasebeta

← #14772210

Subgroups — #14772210

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4326C212yesmaximal
2C2×C4×#4326C211yesmaximal, characteristic
3#13071536C211yesmaximal, characteristic
4#13069346C212yesmaximal
5#13068884C212yesmaximal
6#13068883C212yesmaximal
7#13068778C211yesmaximal, characteristic
8#13068631C211yesmaximal, characteristic
9#13068628C211yesmaximal, characteristic
10C4⋊C4×C11⋊C8C211yesmaximal, characteristic
11C11×#2351C211yesmaximal, characteristic
12C2×C4×Q8×C11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4326C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C11×#389—22no—
18C11×#389C2212yes—
19C11×#382—21no—
20C11×#382C2211yescharacteristic
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C4×#4326—28no—
26C4×#4326C418yescomplemented
27#10622585—22no—
28C2×#66874C2212yes—
29C2×#66874C2211yescharacteristic
30C2×#66872C2212yes—
31C2×#66871C2212yes—
32C2×#66871C2211yescharacteristic
33#10622549C2211yescharacteristic
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2212yes—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622263—21no—
39#10622262—21no—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×Dic22C2311yescharacteristic
45C4×Q8×C11—22no—
46C4×Q8×C11—24no—
47C4×Q8×C11—42no—
48C4×Q8×C11C2×C414yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11—22no—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×#4326C2×C414yes—
60C2×#4326D414yes—
61C2×#4326Q814yes—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C4×Dic22—22no—
73C4×Dic22—24no—
74C4×Dic22—42no—
75C4×Dic22C2×C414yes—
76C11×#95—21no—
77C11×#95—22no—
78C11×#95—21no—
79C11×#95D411yescharacteristic
80C11×#95D411yescharacteristic
81#66899—24no—
82#66899C2×C414yes—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—21no—
86#66874—24no—
87#66874C2×C414yes—
88#66872—42no—
89#66871—24no—
90#66871C2×C414yes—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—24no—
93C4×C11⋊C8C2×C414yes—
94#22685—111nomaximal, Sylow
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22×C412yes—
99C2×Q8×C11C2×D412yes—
100C2×Q8×C11C2×Q812yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—21no—
115C2×Dic22C22×C412yes—
116C2×Dic22C2×D412yes—
117C2×Dic22C2×Q812yes—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4C22×C412yes—
126C42×C11—24no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—44no—
130C42×C11C22×C412yes—
131C42×C11#4112yes—
132#4326C4⋊C4116yescomplemented
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—22no—
136C4⋊Dic11C22×C412yes—
137Dic11⋊C4—24no—
138Dic11⋊C4—44no—
139Dic11⋊C4—44no—
140C4×Dic11—24no—
141C4×Dic11—44no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C22×C412yes—
148C2×C11⋊C8C22×C412yes—
149C2×C11⋊C8C2×D412yes—
150C2×C11⋊C8C2×Q812yes—
151C2×C4×Q16—111no—
152C2×C4×Q16—112no—
153#2351—111no—
154#2351D1111yescharacteristic
155#1942—112no—
156#1865—112no—
157#1865—112no—
158#1846—111no—
159#1805—111no—
160#1805—111no—
161C8×C4⋊C4—111no—
162C23×C11C22×D411yescharacteristic
163Q8×C11—22no—
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11C2×C4⋊C414yes—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C4×D412yes—
184C2×C4×C11#13514yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199Dic22—22no—
200Dic22—22no—
201Dic22—22no—
202Dic22C2×C4⋊C414yes—
203C11⋊C8—22no—
204C11⋊C8—42no—
205C11⋊C8C2×C4⋊C414yes—
206C22×Q16—111no—
207C2×C4×Q8—111no—
208C2×C4×Q8—112no—
209C2×C4×Q8C2×D1112yes—
210C2×C4×Q8C2×D1111yescharacteristic
211C4×Q16—118no—
212C4×Q16—228no—
213C2×#107—111no—
214C2×#107—112no—
215C2×#106—112no—
216C2×C4⋊C8—111no—
217C2×#103—111no—
218C2×#103—111no—
219C2×#103—112no—
220C2×#103—112no—
221C2×C4×C8—111no—
222C2×C4×C8—112no—
223#389—22no—
224#389—112no—
225#389—222no—
226#389C2×D1112yes—
227#382—21no—
228#382—111no—
229#382—221no—
230#382C2×D1111yescharacteristic
231C4×C4⋊C4—21no—
232C4×C4⋊C4—221no—
233C4×C4⋊C4C2×D1111yescharacteristic
234#340—112no—
235#340—112no—
236#336—112no—
237C22×C11C2×C4×D411yescharacteristic
238C22×C11D4211yescharacteristic
239C22×C11D4×Q811yescharacteristic
240C22×C11C2×#13512yes—
241C22×C11#57812yes—
242C4×C11—24no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—24no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—82no—
249C4×C11C22×C4⋊C411yescharacteristic
250C4×C11#52011yescharacteristic
251C4×C11#54711yescharacteristic
252C4×C11#55411yescharacteristic
253Dic11—24no—
254Dic11—42no—
255Dic11—82no—
256C22×Q8—111no—
257C22×Q8C22×D1111yescharacteristic
258C2×Q16—114no—
259C2×Q16—114no—
260C2×Q16—114no—
261C22×C8—111no—
262C22×C8—111no—
263C22×C8—112no—
264C4×Q8—22no—
265C4×Q8—24no—
266C4×Q8—42no—
267C4×Q8—114no—
268C4×Q8—224no—
269C4×Q8—222no—
270C4×Q8—442no—
271C4×Q8C4×D1114yes—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4C22⋊D1112yes—
281C2×C4⋊C4C22×D1112yes—
282C2×C4⋊C4C22×D1111yescharacteristic
283C2×C42—21no—
284C2×C42—22no—
285C2×C42—221no—
286C2×C42—222no—
287C2×C42C22×D1112yes—
288C2×C42C22×D1111yescharacteristic
289#107—114no—
290#107—224no—
291#106—442no—
292C4⋊C8—222no—
293#103—114no—
294#103—114no—
295#103—224no—
296#103—224no—
297C4×C8—114no—
298C4×C8—224no—
299#95—21no—
300#95—22no—
301#95—21no—
302#95—221no—
303#95—221no—
304#95—222no—
305#95C22⋊D1111yescharacteristic
306#95C22⋊D1111yescharacteristic
307C2×C11D4×C4⋊C411yescharacteristic
308C2×C11C4×#13511yescharacteristic
309C2×C11#295011yescharacteristic
310C2×C11#328512yes—
311C2×C11#338312yes—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—112no—
316C2×Q8—112no—
317C2×Q8—112no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×Q8—221no—
321C2×Q8C2×C4×D1112yes—
322C2×Q8D4×D1112yes—
323C2×Q8Q8×D1112yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—222no—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1112yes—
334C22×C4C23×D1111yescharacteristic
335Q16—1116no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—112no—
353C4⋊C4—224no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C4⋊C4—444no—
358C4⋊C4—444no—
359C4⋊C4C2×C4×D1112yes—
360C42—24no—
361C42—22no—
362C42—22no—
363C42—44no—
364C42—224no—
365C42—444no—
366C42C2×C4×D1112yes—
367C42#433912yes—
368C11#2268511yescharacteristic, complemented, Sylow
369C23C22×C22⋊D1111yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—22no—
373Q8—114no—
374Q8—222no—
375Q8—222no—
376Q8—222no—
377Q8C4⋊C4×D1114yes—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4C4×C22⋊D1112yes—
402C2×C4C4×C22⋊D1112yes—
403C2×C4#6700314yes—
404C2×C4C22×C4×D1111yescharacteristic
405C2×C4C2×#433911yescharacteristic
406C2×C4C2×D4×D1111yescharacteristic
407C2×C4#6703711yescharacteristic
408C2×C4C2×Q8×D1111yescharacteristic
409C2×C4#6704011yescharacteristic
410C8—114no—
411C8—222no—
412C8—442no—
413C22C2×C4×C22⋊D1111yescharacteristic
414C22D4×C22⋊D1111yescharacteristic
415C22Q8×C22⋊D1111yescharacteristic
416C22C2×#6700312yes—
417C22#1062336912yes—
418C4—24no—
419C4—22no—
420C4—24no—
421C4—22no—
422C4—42no—
423C4—42no—
424C4—82no—
425C4—224no—
426C4—442no—
427C4—882no—
428C4C2×C4⋊C4×D1111yescharacteristic
429C4#1062303511yescharacteristic
430C4#1062303811yescharacteristic
431C4#1062304211yescharacteristic
432C2C4⋊C4×C22⋊D1111yescharacteristic
433C2C4×#6700311yescharacteristic
434C2#1307748211yescharacteristic
435C2#1308035312yes—
436C2#1308150312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2351D11
hypocenterC11#22685
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
26. C4×#4326C4semidirect
132. #4326C4⋊C4semidirect
368. C11#22685semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43262
#130715362
#130693462
#130688842
#130688832
#130687782
#130686312
#130686282
C4⋊C4×C11⋊C82
C11×#23512
#2268511