Finite Group Databasebeta

← #14645294

Subgroups — #14645294

Order 2816.

726 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068382C211yesmaximal, characteristic, complemented
2#13067236C212yesmaximal, complemented
3#13067076C212yesmaximal, complemented
4#13066950C211yesmaximal, characteristic, complemented
5C11×#3491C211yesmaximal, characteristic
6C11×#552—22no—
7C11×#552—22no—
8C11×#551—22no—
9C11×#551—22no—
10C11×#543C411yescharacteristic
11C11×#539—21no—
12C11×#539C412yes—
13C11×#534C411yescharacteristic
14C11×#529—21no—
15C11×#529C2212yes—
16C2×C11×#123—21no—
17C11×#518—21no—
18C2×C11×#117C2211yescharacteristic
19C2×C22⋊(C11⋊C8)—21no—
20#10622539C2212yescomplemented
21C2×#66867C2211yescharacteristic, complemented
22C2×C4×C11⋊C8C2211yescharacteristic, complemented
23#10622181—22no—
24#10622178—22no—
25Q8⋊(C11⋊C8)—22no—
26D4⋊(C11⋊C8)—22no—
27#10622166—21no—
28#10622163—21no—
29#10622162—21no—
30C22×D4×C11—21no—
31C23×C4×C11D411yescharacteristic
32C11×#126—22no—
33C11×#126—22no—
34C11×#126—22no—
35C11×#126—22no—
36C11×#125—21no—
37C11×#125—22no—
38C11×#125—22no—
39C11×#125D412yes—
40C11×#124—21no—
41C11×#124D412yes—
42C11×#123—22no—
43C11×#123—22no—
44C11×#123—22no—
45C11×#123—22no—
46C11×#123—22no—
47C11×#123—22no—
48C11×#123—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8C2×C412yes—
55C11×#121—21no—
56C11×#121C2×C412yes—
57C11×#120—22no—
58C4×Q8×C11—21no—
59C4×Q8×C11D412yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—21no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11D412yes—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85C22⋊(C11⋊C8)—24no—
86C22⋊(C11⋊C8)—22no—
87C4⋊(C11⋊C8)—22no—
88#66867—22no—
89#66867—22no—
90C4×C11⋊C8—22no—
91#8348—111nomaximal, Sylow
92C24×C11—21no—
93C24×C11C22⋊C411yescharacteristic
94C2×Q8×C11—21no—
95C2×Q8×C11C22⋊C412yes—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11C22⋊C412yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
111C22×C4×C11C22⋊C411yescharacteristic
112C22×C4×C11C22⋊C411yescharacteristic
113C22×C4×C11C22⋊C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C22⋊C412yes—
130C11×C4⋊C4C22⋊C412yes—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C42×C11—22no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11—22no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—42no—
156#3491D1111yescharacteristic
157#1750—111no—
158#1532—112no—
159#1494—112no—
160#1464—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11#10412yes—
170C23×C11C2×C22⋊C411yescharacteristic
171Q8×C11—42no—
172Q8×C11—81no—
173D4×C11—42no—
174D4×C11—44no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—81no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11—81no—
197C2×C4×C11—82no—
198C2×C4×C11—81no—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11#12012yes—
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12011yescharacteristic
203C11⋊C8—42no—
204C11⋊C8—42no—
205C11⋊C8—82no—
206#552—22no—
207#552—22no—
208#551—22no—
209#551—22no—
210#543Dic1111yescharacteristic
211#539—21no—
212#539Dic1112yes—
213#534Dic1111yescharacteristic
214#529—21no—
215#529C2×D1112yes—
216C2×#123—21no—
217#518—21no—
218C2×#117C2×D1111yescharacteristic
219#432—112no—
220C2×C22⋊C8—221no—
221C2×#97—111no—
222C2×C4×C8—111no—
223#336—221no—
224#330—222no—
225#329—222no—
226Q8⋊C8—222no—
227D4⋊C8—222no—
228#324—221no—
229#323—221no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—22no—
233C22×C11—42no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—162no—
241C22×C11#37911yescharacteristic
242C22×C11C2×#10411yescharacteristic
243C22×C11#42111yescharacteristic
244C4×C11—22no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—42no—
250C4×C11—41no—
251C4×C11—42no—
252C4×C11—41no—
253C4×C11—42no—
254C22×D4—21no—
255C23×C4C22⋊D1111yescharacteristic
256C22×C8—221no—
257C22×C8—221no—
258#126—22no—
259#126—22no—
260#126—22no—
261#126—22no—
262#125—21no—
263#125—22no—
264#125—22no—
265#125C22⋊D1112yes—
266#124—21no—
267#124C22⋊D1112yes—
268#123—22no—
269#123—22no—
270#123—22no—
271#123—22no—
272#123—22no—
273#123—22no—
274#123—22no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—21no—
279C22⋊Q8—22no—
280C22⋊Q8C2×Dic1112yes—
281#121—21no—
282#121C2×Dic1112yes—
283#120—22no—
284C4×Q8—21no—
285C4×Q8C22⋊D1112yes—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—21no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4C22⋊D1112yes—
292#117—22no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4C2×Dic1111yescharacteristic
300C2×C4⋊C4C22⋊D1111yescharacteristic
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4C2×Dic1111yescharacteristic
306C2×C22⋊C4C22⋊D1111yescharacteristic
307C2×C42C22⋊D1111yescharacteristic
308C2×C42C22×D1111yescharacteristic
309C4⋊C8—222no—
310C22⋊C8—224no—
311C22⋊C8—222no—
312#97—222no—
313#97—222no—
314C4×C8—222no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—42no—
318C2×C11—82no—
319C2×C11#178911yescharacteristic
320C2×C11#179111yescharacteristic
321C2×C11#179411yescharacteristic
322C24—21no—
323C24C22⋊Dic1111yescharacteristic
324C2×Q8—21no—
325C2×Q8C22⋊Dic1112yes—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4C22⋊Dic1112yes—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—41no—
341C22×C4C22⋊Dic1111yescharacteristic
342C22×C4C22⋊Dic1111yescharacteristic
343C22×C4C22⋊Dic1111yescharacteristic
344C22×C4C22×Dic1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8—441no—
352C2×C8—441no—
353C2×C8—442no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4C22⋊Dic1112yes—
367C4⋊C4C22⋊Dic1112yes—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C42—22no—
381C42—21no—
382C42—21no—
383C42—22no—
384C42C2×C22⋊D1112yes—
385C42C2×C22⋊D1112yes—
386C11#834811yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—22no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—81no—
394C23—81no—
395C23#6690112yes—
396C23C2×C22⋊Dic1111yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—42no—
400D4—44no—
401D4—42no—
402D4—42no—
403D4—81no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4C2×C22⋊Dic1112yes—
426C2×C4#6700611yescharacteristic
427C2×C4#6700611yescharacteristic
428C2×C4#6700612yes—
429C8—442no—
430C8—442no—
431C8—882no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—162no—
443C22C2×#6690111yescharacteristic
444C22#1062284911yescharacteristic
445C22#1062286011yescharacteristic
446C4—21no—
447C4—21no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—42no—
452C4—41no—
453C4—42no—
454C4—41no—
455C4—42no—
456C2—21no—
457C2—21no—
458C2—42no—
459C2—82no—
460C2#1306856011yescharacteristic
461C2#1306856711yescharacteristic
462C2#1306858011yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3491C2
socleC22×C11#379
prime radicalC11×#534C4
cosocleC2×C42×C11C23
hypercenter#3491D11
hypocenterC11#8348
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #13068382C2semidirect
2. #13067236C2semidirect
3. #13067076C2semidirect
4. #13066950C2semidirect
20. #10622539C22semidirect
21. C2×#66867C22semidirect
22. C2×C4×C11⋊C8C22semidirect
386. C11#8348semidirect

Maximal subgroups

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

subgroupindex
#130683822
#130672362
#130670762
#130669502
C11×#34912
#834811