Finite Group Databasebeta

← #14657242

Subgroups — #14657242

Order 2816.

534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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#13076661C211yesmaximal, characteristic
2#13069433C211yesmaximal, characteristic, complemented
3#13069432C211yesmaximal, characteristic, complemented
4#13068784C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic, complemented
6#13066498C211yesmaximal, characteristic, complemented
7C2×C11×#329C211yesmaximal, characteristic, complemented
8C2×C11×#124C2211yescharacteristic
9C2×#66928C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12#10622844—21no—
13C2×#66899—21no—
14#10622836—21no—
15C2×#66896—21no—
16C2×#66885—21no—
17C2×#66882—21no—
18C2×#66881—21no—
19C2×#66880—21no—
20#10622574—21no—
21#10622574—21no—
22#10622573—21no—
23#10622560—21no—
24#10622549C2211yescharacteristic
25#10622548C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C11×#329—22no—
28#10622102—22no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C22×C22⋊D11—21no—
32C22×C22⋊D11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×#124—21no—
38C11×#124—21no—
39C11×#124—21no—
40C11×#124—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C22×C11⋊C8—21no—
56#66928—21no—
57#66928—21no—
58#66928—21no—
59#66928—21no—
60C11×#97—21no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97D412yescomplemented
64#66899—42no—
65#66896—42no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70#66885—42no—
71#66882—42no—
72#66881—42no—
73#66880—42no—
74#66867—21no—
75#66867—21no—
76#10424—111nomaximal, Sylow
77C24×C11—21no—
78C23×D11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C22×C4×C11—21no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—81no—
92C2×C22⋊D11—81no—
93C2×C22⋊D11—81no—
94C2×C22⋊D11—81no—
95C2×C22⋊D11—81no—
96C2×C22⋊D11—81no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—41no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—41no—
104C2×D44—41no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11#4111yescharacteristic
123C22⋊Dic11—81no—
124C22⋊Dic11—81no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—81no—
130(C2×D11)⋊C4—81no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142#2819—111no—
143#1959—111no—
144#1959—111no—
145#1847—111no—
146C2×#329—111no—
147C2×#329D1111yescharacteristic, complemented
148#1295—111no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11#12011yescharacteristic
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164Q8×C11—42no—
165Q8×C11—81no—
166D4×C11—42no—
167D4×C11—81no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12311yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C2×C4×C11#12411yescharacteristic
183C22⋊D11—84no—
184C22⋊D11—84no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—81no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197D44—42no—
198D44—81no—
199Dic22—42no—
200Dic22—81no—
201C8×C11—24no—
202C8×C11—42no—
203C11⋊C8—42no—
204C2×#124—111no—
205C2×#124C2×D1111yescharacteristic
206C2×#107—221no—
207C2×#106—221no—
208C2×#103—221no—
209C2×#103—221no—
210C2×#102—221no—
211C2×#102—221no—
212C2×#97—111no—
213C2×#97C2×D1111yescharacteristic
214C2×#97C2×D1111yescharacteristic
215#394—221no—
216#394—221no—
217#393—221no—
218#393—221no—
219#392—221no—
220#392—221no—
221#384—111no—
222#382—111no—
223#329—22no—
224#329—222no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11#39411yescharacteristic
233C22×C11#45311yescharacteristic
234C22×C11#45311yescharacteristic
235C22×C11#45311yescharacteristic
236C22×C11#45511yescharacteristic
237C22×C11#45511yescharacteristic
238C22×C11#45611yescharacteristic
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C2×D11—81no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—81no—
253Dic11—81no—
254Dic11—81no—
255Dic11—81no—
256Dic11—161no—
257C22×Q8—111no—
258C22×Q8D4411yescharacteristic
259C22×D4—111no—
260C22×D4—221no—
261C22×D4—221no—
262C22×D4D4411yescharacteristic
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—221no—
266#124—21no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—221no—
271#124—221no—
272#124—221no—
273#124—221no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4—221no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C42C22×D1111yescharacteristic
288#107—442no—
289#106—442no—
290#103—442no—
291#103—442no—
292#102—442no—
293#102—442no—
294#97—21no—
295#97—21no—
296#97—21no—
297#97—221no—
298#97—221no—
299#97C22⋊D1112yescomplemented
300#95—221no—
301#95—221no—
302#95—221no—
303#95—221no—
304C2×C11—161no—
305C2×C11#165511yescharacteristic
306C2×C11#165911yescharacteristic
307C2×C11#166111yescharacteristic
308C2×C11#166111yescharacteristic
309C2×C11#203711yescharacteristic
310C2×C11#203711yescharacteristic
311C2×C11#203911yescharacteristic
312D11—161no—
313C24—21no—
314C24—221no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×Q8—221no—
320C2×Q8—221no—
321C2×Q8—441no—
322C2×Q8—441no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—881no—
332C2×D4—881no—
333C2×D4—881no—
334C2×D4—881no—
335C2×D4—881no—
336C2×D4—881no—
337C22×C4—21no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—441no—
342C22×C4C2×D4411yescharacteristic
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—222no—
352C2×C8—441no—
353C2×C8—441no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C22⋊C4—881no—
371C22⋊C4—881no—
372C22⋊C4—881no—
373C22⋊C4—881no—
374C42#433911yescharacteristic
375C42#434111yescharacteristic
376C42#434111yescharacteristic
377C42C2×C22⋊D1111yescharacteristic
378C11#1042411yescharacteristic, complemented, Sylow
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23#6693511yescharacteristic
394Q8—42no—
395Q8—81no—
396Q8—442no—
397Q8—881no—
398D4—42no—
399D4—81no—
400D4—442no—
401D4—881no—
402D4—884no—
403D4—884no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4#6693611yescharacteristic
426C2×C4#6693811yescharacteristic
427C2×C4#6693911yescharacteristic
428C2×C4#6698311yescharacteristic
429C2×C4#6699111yescharacteristic
430C2×C4#6699211yescharacteristic
431C8—24no—
432C8—42no—
433C8—442no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22—881no—
448C22#1062235911yescharacteristic
449C22#1062236011yescharacteristic
450C22#1062243511yescharacteristic
451C22#1062243511yescharacteristic
452C22#1062243811yescharacteristic
453C22#1062243911yescharacteristic
454C22#1062257411yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—81no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4—1761no—
466C2—161no—
467C2—1761no—
468C2#1306790611yescharacteristic
469C2#1306792411yescharacteristic
470C2#1306793411yescharacteristic
471C2#1306793611yescharacteristic
472C2#1306982511yescharacteristic
473C2#1306982711yescharacteristic
474C2#1306983911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#329C2
socleC23×C11#120
prime radical#13076661C2
hypercenterC2×#329D11
hypocenterC11#10424
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #13069433C2semidirect
3. #13069432C2semidirect
4. #13068784C2semidirect
5. C2×#10622102C2semidirect
6. #13066498C2semidirect
7. C2×C11×#329C2semidirect
63. C11×#97D4semidirect
147. C2×#329D11semidirect
299. #97C22⋊D11semidirect
378. C11#10424semidirect

Maximal subgroups

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

subgroupindex
#130766612
#130694332
#130694322
#130687842
C2×#106221022
#130664982
C2×C11×#3292
#1042411