Finite Group Databasebeta

← #14645265

Subgroups — #14645265

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2#13068596C211yesmaximal, characteristic, complemented
3C2×#10622185C212yesmaximal, complemented
4C2×#10622182C212yesmaximal, complemented
5C2×C11×#532C211yesmaximal, characteristic
6C22×C11×#41—21no—
7C11×#532—24no—
8C11×#532—24no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C11×#121—21no—
13C2×C11×#121C412yes—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C412yes—
16C22×C42×C11C2211yescharacteristic
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622185—24no—
22#10622182—24no—
23#10622162—21no—
24#10622162—21no—
25C2×C11×#41—28no—
26C2×C11×#41—44no—
27C2×C11×#41—42no—
28C2×C11×#41—42no—
29C22×Q8×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11C2×C412yes—
34C23×C4×C11—22no—
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C11×C4⋊Q8—22no—
39C11×C4⋊Q8D414yes—
40C11×#127—22no—
41C11×#127D414yes—
42C11×#124—28no—
43C11×#121—28no—
44C11×#121—24no—
45C11×#121—24no—
46C4×D4×C11—28no—
47C4×D4×C11—24no—
48C4×D4×C11—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11C2×C411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C22×C11⋊C8—22no—
60C22×C11⋊C8—22no—
61C22⋊(C11⋊C8)—42no—
62C22⋊(C11⋊C8)—42no—
63C4⋊(C11⋊C8)—22no—
64C4⋊(C11⋊C8)—22no—
65C4⋊(C11⋊C8)—22no—
66C4⋊(C11⋊C8)—22no—
67#8341—111nomaximal, Sylow
68C24×C11—22no—
69C24×C11C22⋊C411yescharacteristic
70C11×#41—416no—
71C11×#41—416no—
72C2×Q8×C11—24no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—42no—
76C2×D4×C11—28no—
77C2×D4×C11—22no—
78C2×D4×C11—24no—
79C2×D4×C11—24no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—44no—
83C2×D4×C11—44no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11C22⋊C414yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—28no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—44no—
104C22×C4×C11—44no—
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11D812yes—
109C22×C4×C11SD1612yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4C22⋊C414yes—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—28no—
118C42×C11—21no—
119C42×C11—21no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124C2×C11⋊C8—42no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—42no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8—42no—
130C2×#532D1111yescharacteristic
131#1797—111no—
132#1797—111no—
133C2×#332—112no—
134C2×#331—112no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—24no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11#10212yes—
149C23×C11C2×C22⋊C411yescharacteristic
150Q8×C11—44no—
151Q8×C11—44no—
152D4×C11—44no—
153D4×C11—44no—
154D4×C11—416no—
155D4×C11—44no—
156D4×C11—44no—
157D4×C11—44no—
158D4×C11—44no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—24no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—416no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11#10212yes—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C2×C22⋊C411yescharacteristic
182C2×C4×C11#12012yes—
183C2×C4×C11#12012yes—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×SD1611yescharacteristic
186C2×C4×C11#13512yes—
187C2×C4×C11AGL(1,ℤ/8)12yes—
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C11⋊C8—82no—
191C11⋊C8—82no—
192C22×#41—21no—
193#532—24no—
194#532—24no—
195C2×C4⋊Q8C2×D1111yescharacteristic
196C2×#127C2×D1111yescharacteristic
197C2×#124—21no—
198C2×#121—21no—
199C2×#121Dic1112yes—
200C2×C4×D4—21no—
201C2×C4×D4Dic1112yes—
202C22×C42C2×D1111yescharacteristic
203C2×C4⋊C8—112no—
204C2×C4⋊C8—112no—
205C2×C22⋊C8—221no—
206C2×C22⋊C8—221no—
207#336—221no—
208#336—221no—
209#332—224no—
210#331—224no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—44no—
219C22×C11—44no—
220C22×C11—44no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11#37911yescharacteristic
226C22×C11#41311yescharacteristic
227C22×C11#41311yescharacteristic
228C22×C11C2×#10211yescharacteristic
229C22×C11#41611yescharacteristic
230C22×C11#41711yescharacteristic
231C22×C11#41811yescharacteristic
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—41no—
236C4×C11—44no—
237C4×C11—41no—
238C4×C11#44712yes—
239C4×C11#44912yes—
240C4×C11#45012yes—
241C4×C11#45212yes—
242C2×#41—28no—
243C2×#41—44no—
244C2×#41—42no—
245C2×#41—42no—
246C22×Q8—21no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C2×Dic1112yes—
251C23×C4—22no—
252C23×C4C2×Dic1111yescharacteristic
253C23×C4C22⋊D1111yescharacteristic
254C23×C4C22⋊D1111yescharacteristic
255C22×C8—222no—
256C22×C8—222no—
257C4⋊Q8—22no—
258C4⋊Q8C22⋊D1114yes—
259#127—22no—
260#127C22⋊D1114yes—
261#124—28no—
262#121—28no—
263#121—24no—
264#121—24no—
265C4×D4—28no—
266C4×D4—24no—
267C4×D4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×Dic1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42C2×Dic1111yescharacteristic
275C2×C42C22⋊D1111yescharacteristic
276C2×C42C22⋊D1111yescharacteristic
277C2×C42C22×D1111yescharacteristic
278C4⋊C8—222no—
279C4⋊C8—222no—
280C4⋊C8—222no—
281C4⋊C8—222no—
282C22⋊C8—442no—
283C22⋊C8—442no—
284C2×C11—42no—
285C2×C11—84no—
286C2×C11#154011yescharacteristic
287C2×C11#154711yescharacteristic
288C2×C11#155311yescharacteristic
289C2×C11#155711yescharacteristic
290C2×C11#178511yescharacteristic
291C2×C11#178611yescharacteristic
292C2×C11#178811yescharacteristic
293C24—22no—
294C24C22⋊Dic1111yescharacteristic
295#41—416no—
296#41—416no—
297C2×Q8—24no—
298C2×Q8—41no—
299C2×Q8—42no—
300C2×Q8—41no—
301C2×D4—28no—
302C2×D4—22no—
303C2×D4—24no—
304C2×D4—24no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—44no—
308C2×D4—44no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4C22⋊Dic1114yes—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—28no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—44no—
329C22×C4—44no—
330C22×C4#432312yes—
331C22×C4#432412yes—
332C22×C4C22⋊Dic1111yescharacteristic
333C22×C4C22⋊Dic1111yescharacteristic
334C22×C4C22⋊Dic1111yescharacteristic
335C22×C4C22×Dic1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C2×C8—442no—
339C2×C8—442no—
340C2×C8—442no—
341C2×C8—442no—
342C2×C8—442no—
343C2×C8—442no—
344C4⋊C4—22no—
345C4⋊C4—24no—
346C4⋊C4C22⋊Dic1114yes—
347C22⋊C4—28no—
348C22⋊C4—28no—
349C42—21no—
350C42—21no—
351C42—22no—
352C42—22no—
353C42C2×C22⋊D1112yes—
354C42C2×C22⋊D1112yes—
355C11#834111yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—24no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#6689612yes—
370C23C2×C22⋊Dic1111yescharacteristic
371Q8—44no—
372Q8—44no—
373D4—44no—
374D4—44no—
375D4—416no—
376D4—44no—
377D4—44no—
378D4—44no—
379D4—44no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—24no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—416no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4#6689612yes—
401C2×C4C2×#432311yescharacteristic
402C2×C4#6698512yes—
403C2×C4C2×#432411yescharacteristic
404C2×C4#6700211yescharacteristic
405C2×C4#6700312yes—
406C2×C4#6700411yescharacteristic
407C2×C4C2×C22⋊Dic1111yescharacteristic
408C2×C4C2×C22⋊Dic1111yescharacteristic
409C2×C4#6700612yes—
410C2×C4#6700612yes—
411C8—882no—
412C8—882no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—44no—
421C22—44no—
422C22—44no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22C2×#6689611yescharacteristic
428C22#1062282811yescharacteristic
429C22#1062284511yescharacteristic
430C22#1062284611yescharacteristic
431C22#1062285011yescharacteristic
432C22#1062285011yescharacteristic
433C22#1062286011yescharacteristic
434C4—21no—
435C4—21no—
436C4—22no—
437C4—41no—
438C4—44no—
439C4—41no—
440C4#1062283012yes—
441C4#1062283112yes—
442C4#1062285112yes—
443C4#1062285212yes—
444C2—42no—
445C2—84no—
446C2#1306726511yescharacteristic
447C2#1306729311yescharacteristic
448C2#1306732111yescharacteristic
449C2#1306733811yescharacteristic
450C2#1306854411yescharacteristic
451C2#1306854711yescharacteristic
452C2#1306855611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#532C2
socleC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#532D11
hypocenterC11#8341
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. #13068596C2semidirect
3. C2×#10622185C2semidirect
4. C2×#10622182C2semidirect
355. C11#8341semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221852
C2×#106221822
C2×C11×#5322
#834111