Finite Group Databasebeta

← #14657247

Subgroups — #14657247

Order 2816.

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

normal subgroups only

This group has 518 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#13068750C211yesmaximal, 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×#66880—21no—
18#10622574—21no—
19#10622574—21no—
20#10622573—21no—
21#10622560—21no—
22#10622549C2211yescharacteristic
23#10622548C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25C11×#329—22no—
26#10622189—21no—
27#10622189—21no—
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#66880—42no—
72#66867—21no—
73#66867—21no—
74#10425—111nomaximal, Sylow
75C24×C11—21no—
76C23×D11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—81no—
90C2×C22⋊D11—81no—
91C2×C22⋊D11—81no—
92C2×C22⋊D11—81no—
93C2×C22⋊D11—81no—
94C2×C22⋊D11—81no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—41no—
102C2×D44—41no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11#4111yescharacteristic
121C22⋊Dic11—81no—
122C22⋊Dic11—81no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—81no—
128(C2×D11)⋊C4—81no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#2819—111no—
140#1959—111no—
141#1959—111no—
142#1836—111no—
143C2×#329—111no—
144C2×#329D1111yescharacteristic, complemented
145#1295—111no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11#12011yescharacteristic
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161Q8×C11—42no—
162Q8×C11—81no—
163D4×C11—42no—
164D4×C11—81no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12311yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11#12411yescharacteristic
180C22⋊D11—84no—
181C22⋊D11—84no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194D44—42no—
195D44—81no—
196Dic22—42no—
197Dic22—81no—
198C8×C11—42no—
199C8×C11—42no—
200C11⋊C8—42no—
201C2×#124—111no—
202C2×#124C2×D1111yescharacteristic
203C2×#103—221no—
204C2×#103—221no—
205C2×#102—221no—
206C2×#102—221no—
207C2×#97—111no—
208C2×#97C2×D1111yescharacteristic
209C2×#97C2×D1111yescharacteristic
210#394—221no—
211#394—221no—
212#393—221no—
213#393—221no—
214#392—221no—
215#392—221no—
216#384—111no—
217#382—111no—
218#340—221no—
219#340—221no—
220#329—22no—
221#329—222no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11#39411yescharacteristic
230C22×C11#45311yescharacteristic
231C22×C11#45311yescharacteristic
232C22×C11#45411yescharacteristic
233C22×C11#45511yescharacteristic
234C22×C11#45511yescharacteristic
235C22×C11#45511yescharacteristic
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250Dic11—81no—
251Dic11—81no—
252Dic11—81no—
253Dic11—161no—
254C22×Q8—111no—
255C22×Q8D4411yescharacteristic
256C22×D4—111no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4D4411yescharacteristic
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—221no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#124—221no—
268#124—221no—
269#124—221no—
270#124—221no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C42C22×D1111yescharacteristic
285#103—442no—
286#103—442no—
287#102—442no—
288#102—442no—
289#97—21no—
290#97—21no—
291#97—21no—
292#97—221no—
293#97—221no—
294#97C22⋊D1112yescomplemented
295#95—221no—
296#95—221no—
297#95—221no—
298#95—221no—
299C2×C11—161no—
300C2×C11#165611yescharacteristic
301C2×C11#165911yescharacteristic
302C2×C11#165911yescharacteristic
303C2×C11#166211yescharacteristic
304C2×C11#203711yescharacteristic
305C2×C11#203711yescharacteristic
306C2×C11#204011yescharacteristic
307D11—161no—
308C24—21no—
309C24—221no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—221no—
315C2×Q8—221no—
316C2×Q8—441no—
317C2×Q8—441no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—881no—
327C2×D4—881no—
328C2×D4—881no—
329C2×D4—881no—
330C2×D4—881no—
331C2×D4—881no—
332C22×C4—21no—
333C22×C4—221no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—441no—
337C22×C4C2×D4411yescharacteristic
338C22×C4D4×D1111yescharacteristic
339C22×C4D4×D1111yescharacteristic
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—222no—
347C2×C8—441no—
348C2×C8—441no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4—442no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—881no—
365C22⋊C4—881no—
366C22⋊C4—881no—
367C22⋊C4—881no—
368C42#433911yescharacteristic
369C42#434111yescharacteristic
370C42#434111yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C11#1042511yescharacteristic, complemented, Sylow
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—441no—
381C23—441no—
382C23—441no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23—441no—
387C23#6693511yescharacteristic
388Q8—42no—
389Q8—81no—
390Q8—442no—
391Q8—881no—
392D4—42no—
393D4—81no—
394D4—442no—
395D4—881no—
396D4—884no—
397D4—884no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—881no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4#6693611yescharacteristic
420C2×C4#6693811yescharacteristic
421C2×C4#6693911yescharacteristic
422C2×C4#6698311yescharacteristic
423C2×C4#6699111yescharacteristic
424C2×C4#6699211yescharacteristic
425C8—42no—
426C8—42no—
427C8—442no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—881no—
436C22—881no—
437C22—881no—
438C22—881no—
439C22—881no—
440C22—881no—
441C22—881no—
442C22#1062235911yescharacteristic
443C22#1062236011yescharacteristic
444C22#1062243511yescharacteristic
445C22#1062243811yescharacteristic
446C22#1062243811yescharacteristic
447C22#1062244011yescharacteristic
448C22#1062257411yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—81no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4—1761no—
460C2—161no—
461C2—1761no—
462C2#1306791011yescharacteristic
463C2#1306792311yescharacteristic
464C2#1306792411yescharacteristic
465C2#1306794111yescharacteristic
466C2#1306982511yescharacteristic
467C2#1306982711yescharacteristic
468C2#1306984411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#329C2
socleC23×C11#120
prime radical#13076661C2
hypercenterC2×#329D11
hypocenterC11#10425
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. #13068750C2semidirect
5. C2×#10622102C2semidirect
6. #13066498C2semidirect
7. C2×C11×#329C2semidirect
63. C11×#97D4semidirect
144. C2×#329D11semidirect
294. #97C22⋊D11semidirect
372. C11#10425semidirect

Maximal subgroups

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

subgroupindex
#130766612
#130694332
#130694322
#130687502
C2×#106221022
#130664982
C2×C11×#3292
#1042511