Finite Group Databasebeta

← #14654530

Subgroups — #14654530

Order 2816.

632 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078620C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic, complemented
3#13073518C211yesmaximal, characteristic
4#13067042C211yesmaximal, characteristic, complemented
5#13067006C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66948—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#382C2211yescharacteristic
14#10622700—21no—
15#10622697—21no—
16#10622697—21no—
17#10622696—21no—
18#10622679—22no—
19#10622659—21no—
20#10622656—21no—
21C4×#4325—22no—
22#10622614—21no—
23#10622608—21no—
24#10622600—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622287—21no—
28#10622284—21no—
29#10622278—22no—
30C11×#328—22no—
31#10622121—22no—
32#10622097—22no—
33C22×D44—22no—
34C22×D44D411yescharacteristic
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C22×C4×D11—21no—
38C11×C4⋊Q8D411yescharacteristic, complemented
39C11×C4⋊Q8D411yescharacteristic, complemented
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×#4318—21no—
56#66948—42no—
57#66948—42no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C11×C4⋊C8—21no—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69C11×#95—21no—
70C11×#95D412yes—
71#66899—22no—
72C11⋊#95—22no—
73C22⋊(C11⋊C8)—21no—
74#66873—22no—
75#66873—22no—
76#66873—22no—
77#66872—22no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yescomplemented
83C4×C11⋊C8D412yescomplemented
84#10000—111nomaximal, Sylow
85C23×D11—21no—
86C23×D11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—42no—
103C2×D44—44no—
104C2×D44—44no—
105C2×D44—82no—
106C2×D44SD1612yescomplemented
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—82no—
116C2×C8×C11—41no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#4325—44no—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—82no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142#4318—41no—
143#4318—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146#3101—111no—
147#3077—111no—
148#2535—111no—
149#1518D1111yescharacteristic, complemented
150#1486—111no—
151#1478—111no—
152#1286—111no—
153C23×C11#12011yescharacteristic
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—41no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166Q8×C11—42no—
167Q8×C11—81no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12711yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11#13711yescharacteristic
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190D44—22no—
191D44—22no—
192D44—22no—
193D44—22no—
194D44—41no—
195D44—41no—
196D44—41no—
197D44—41no—
198D44—88no—
199C4×D11—82no—
200C4×D11—82no—
201C4×D11—81no—
202C4×D11—81no—
203C4×D11—81no—
204C4×D11—81no—
205C8×C11—81no—
206C11⋊C8—42no—
207C11⋊C8—42no—
208#533C2×D1111yescharacteristic
209C2×#121—221no—
210C2×C4×D4—111no—
211C2×C4×D4—111no—
212#483—221no—
213#478—222no—
214#476—221no—
215#476—221no—
216#474—221no—
217#461—221no—
218#450—221no—
219C4×SD16—222no—
220#431—111no—
221#431C2×D1111yescharacteristic
222#428—221no—
223#423—111no—
224#418—221no—
225#397—221no—
226#392—221no—
227#386—222no—
228#382C2×D1111yescharacteristic
229#380—221no—
230#328—22no—
231D4⋊C8—222no—
232D4⋊C8—222no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11#39211yescharacteristic
236C22×C11#45011yescharacteristic
237C22×C11#45211yescharacteristic
238C2×D11—42no—
239C2×D11—44no—
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—81no—
244C2×D11—82no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#44811yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#46511yescharacteristic
260C4×C11#46811yescharacteristic
261Dic11—81no—
262Dic11—81no—
263C22×D4—111no—
264C22×D4—111no—
265C22×D4—222no—
266C23×C4—221no—
267C23×C4—221no—
268C2×SD16—222no—
269C2×M16—221no—
270C4⋊Q8D4411yescharacteristic, complemented
271C4⋊Q8D4411yescharacteristic, complemented
272#125—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—442no—
276#121—442no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—221no—
280C4×D4—221no—
281C4×D4—221no—
282C4×D4—221no—
283C4×D4—221no—
284C4×D4—221no—
285C4×D4—221no—
286C4×D4—221no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C42C22×D1111yescharacteristic
296#107—222no—
297#106—222no—
298#106—222no—
299C4⋊C8—21no—
300C4⋊C8—112no—
301C4⋊C8—221no—
302C4⋊C8—221no—
303#103—222no—
304#102—222no—
305#102—222no—
306#102—222no—
307C22⋊C8—21no—
308C22⋊C8—221no—
309C4×C8—21no—
310C4×C8—112no—
311#95—21no—
312#95—222no—
313#95C22⋊D1112yes—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11#200011yescharacteristic
317C2×C11#200811yescharacteristic
318C2×C11#201011yescharacteristic
319D11—82no—
320D11—82no—
321C24—221no—
322C24—221no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×D4—112no—
326C2×D4—221no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—221no—
333C2×D4—442no—
334C2×D4—444no—
335C2×D4—444no—
336C2×D4—882no—
337C22×C4—22no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352SD16—444no—
353M16—441no—
354M16—441no—
355C2×C8—41no—
356C2×C8—222no—
357C2×C8—222no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C22⋊C4—41no—
371C22⋊C4—444no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—882no—
377C42—41no—
378C42C2×D4411yescharacteristic
379C42#433911yescharacteristic
380C42D4×D1111yescharacteristic
381C42D4×D1111yescharacteristic
382C11#1000011yescharacteristic, complemented, Sylow
383C23—222no—
384C23—222no—
385C23—441no—
386C23—442no—
387C23—442no—
388C23—441no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23#6699011yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—222no—
399D4—222no—
400D4—222no—
401D4—222no—
402D4—441no—
403D4—441no—
404D4—441no—
405D4—441no—
406D4—888no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—882no—
420C2×C4—882no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4#6693511yescharacteristic
426C2×C4#6693511yescharacteristic
427C2×C4#6693711yescharacteristic
428C2×C4#6693711yescharacteristic
429C2×C4SD16×D1111yescharacteristic
430C2×C4#6696711yescharacteristic
431C2×C4#6697111yescharacteristic
432C2×C4#6697211yescharacteristic
433C2×C4#6698311yescharacteristic
434C2×C4#6699311yescharacteristic
435C8—81no—
436C8—442no—
437C8—442no—
438C22—21no—
439C22—21no—
440C22—442no—
441C22—444no—
442C22—442no—
443C22—442no—
444C22—442no—
445C22—881no—
446C22—882no—
447C22—881no—
448C22—881no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062257311yescharacteristic
453C22#1062278211yescharacteristic
454C22#1062280011yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—881no—
463C4—881no—
464C4#1062241911yescharacteristic
465C4#1062242011yescharacteristic
466C4#1062242411yescharacteristic
467C4#1062242511yescharacteristic
468C2—21no—
469C2—21no—
470C2—882no—
471C2—882no—
472C2#1306961811yescharacteristic
473C2#1306966811yescharacteristic
474C2#1306968211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#392
prime radical#13073518C2
hypercenter#1518D11
hypocenterC11#10000
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
1. #13078620C2semidirect
2. #13078409C2semidirect
4. #13067042C2semidirect
5. #13067006C2semidirect
6. #13066474C2semidirect
7. C11×#1518C2semidirect
38. C11×C4⋊Q8D4semidirect
39. C11×C4⋊Q8D4semidirect
82. C4⋊(C11⋊C8)D4semidirect
83. C4×C11⋊C8D4semidirect
106. C2×D44SD16semidirect
149. #1518D11semidirect
270. C4⋊Q8D44semidirect
271. C4⋊Q8D44semidirect
382. C11#10000semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130784092
#130735182
#130670422
#130670062
#130664742
C11×#15182
#1000011