Finite Group Databasebeta

← #14672113

Subgroups — #14672113

Order 2816.

436 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 87 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#13078268C211yesmaximal, characteristic
2#13070291C211yesmaximal, characteristic
3#13070290C211yesmaximal, characteristic
4#13070271C211yesmaximal, characteristic
5#13068660C211yesmaximal, characteristic
6#13068419C211yesmaximal, characteristic
7C11×#2123C211yesmaximal, characteristic
8C11×#536C2211yescharacteristic
9#10623356C2211yescharacteristic
10C2×#67001C2211yescharacteristic
11C22×#4326C411yescharacteristic, complemented
12C11×#413C2211yescharacteristic
13C11×#410C2211yescharacteristic
14#10622853C2211yescharacteristic
15#10622853C2211yescharacteristic
16#10622838C411yescharacteristic, complemented
17#10622735—21no—
18#10622665—21no—
19#10622665—21no—
20#10622664—21no—
21#10622664—21no—
22#10622617C411yescharacteristic, complemented
23#10622611—21no—
24#10622611C411yescharacteristic, complemented
25C11×#352—22no—
26#10622197—21no—
27#10622179—22no—
28#10622169—21no—
29#10622114—22no—
30#10622111—22no—
31C2×C11×#41C2311yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×#124—21no—
37C11×#123—21no—
38C11×#123—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×#117—21no—
42C11×#117C2×C411yescharacteristic
43#67001—41no—
44#67001—41no—
45#66997—21no—
46C2×#4326—21no—
47C2×#4326—21no—
48C2×#4326—41no—
49C2×#4326—41no—
50#66989—21no—
51#66988—21no—
52#66988—21no—
53#66979—21no—
54#66979—21no—
55#66979C2×C411yescharacteristic
56#66977—21no—
57#66977—21no—
58C2×#4318C2×C411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×#4318D411yescharacteristic
61C22×C11⋊C8C2×C411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C11×#101—21no—
65C11×#100D412yes—
66C11×#99—21no—
67C11×#99—21no—
68#66899—21no—
69#66899—21no—
70#66898—21no—
71#66898—21no—
72#66898—21no—
73#66898D412yes—
74#66879—41no—
75C8×Dic11—41no—
76#66874—21no—
77#66874—21no—
78#66872—21no—
79#66872—41no—
80#66871—21no—
81#66871—41no—
82#13230—111nomaximal, Sylow
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11#4111yescharacteristic
90C2×D4×C11C2×D411yescharacteristic
91C2×D4×C11C2×D411yescharacteristic
92C2×D4×C11#4111yescharacteristic
93C22×C4×C11—21no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C11×M16—22no—
103C11×M16—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—21no—
114C42×C11—41no—
115C22⋊Dic11—21no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120#4326—42no—
121#4326—41no—
122#4326—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—21no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131#4318—41no—
132#4318—41no—
133#4318—41no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8C22⋊C411yescharacteristic
141C2×C11⋊C8C22⋊C411yescharacteristic
142C2×C11⋊C8C22⋊C411yescharacteristic
143C2×C11⋊C8C22⋊C411yescharacteristic
144#3059—111no—
145#2129—111no—
146#2129—111no—
147#2123—111no—
148#2123D1111yescharacteristic
149#1812—111no—
150#1757—111no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12711yescharacteristic
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—81no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11C2×C22⋊C411yescharacteristic
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12411yescharacteristic
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180Dic22—41no—
181Dic22—41no—
182Dic22—81no—
183C8×C11—42no—
184C11⋊C8—21no—
185C11⋊C8—21no—
186C11⋊C8—21no—
187C11⋊C8#9911yescharacteristic
188C11⋊C8#9911yescharacteristic
189C22×Q16—111no—
190C2×#131—111no—
191#536—111no—
192#536C2×D1111yescharacteristic
193#470—221no—
194#470—221no—
195#467—221no—
196#467—221no—
197#427—111no—
198#427—221no—
199#419—111no—
200#419—111no—
201#413C2×D1111yescharacteristic
202#410—111no—
203#410—111no—
204#410C2×D1111yescharacteristic
205#405—221no—
206#354—222no—
207#354—222no—
208#352—22no—
209#352—222no—
210#344—221no—
211H(3,ℤ/4)—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11#39011yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—161no—
225C4×C11C2×#9911yescharacteristic
226C4×C11#41011yescharacteristic
227Dic11—81no—
228Dic11—82no—
229Dic11—81no—
230Dic11—161no—
231C2×#41C22×D1111yescharacteristic
232C22×Q8—111no—
233C22×Q8C4×D1111yescharacteristic
234C2×Q16—221no—
235C2×Q16—221no—
236C2×Q16—441no—
237C2×Q16—441no—
238#131—441no—
239#131—441no—
240C2×M16—21no—
241C2×M16—111no—
242C2×M16—111no—
243C2×M16—111no—
244C22×C8—111no—
245C22×C8—111no—
246C22×C8—111no—
247C4⋊Q8—21no—
248C4⋊Q8—221no—
249#124—21no—
250#124—221no—
251#123—21no—
252#123—21no—
253#123—221no—
254#123—221no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—221no—
258C22⋊Q8—221no—
259#117—21no—
260#117—111no—
261#117—221no—
262#117—221no—
263#117C4×D1111yescharacteristic
264#107—221no—
265#107—441no—
266#106—221no—
267#106—441no—
268#103—221no—
269#103—221no—
270#103—221no—
271#103—221no—
272#101—21no—
273#100C22⋊D1112yes—
274#99—21no—
275#99—21no—
276#99—112no—
277#99—221no—
278#99—221no—
279#99—221no—
280#97—441no—
281C4×C8—441no—
282C2×C11—21no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11—41no—
286C2×C11#196411yescharacteristic
287#41—41no—
288#41—41no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×Q8#434111yescharacteristic
298C2×D4#433911yescharacteristic
299C2×D4D4×D1111yescharacteristic
300C2×D4C2×C22⋊D1111yescharacteristic
301C22×C4—21no—
302C22×C4—221no—
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306Q16—441no—
307Q16—441no—
308Q16—442no—
309M16—22no—
310M16—41no—
311M16—441no—
312M16—441no—
313M16—441no—
314C2×C8—41no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—221no—
320C2×C8—221no—
321C2×C8—221no—
322C2×C8—221no—
323C2×C8—221no—
324C2×C8—221no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—21no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—222no—
339C22⋊C4—221no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C42—21no—
344C42—41no—
345C42—221no—
346C42—441no—
347C42—441no—
348C11#1323011yescharacteristic, complemented, Sylow
349C23#6693711yescharacteristic
350C23C4×C22⋊D1111yescharacteristic
351C23#6699311yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—41no—
355Q8—81no—
356Q8—441no—
357Q8—441no—
358Q8—881no—
359D4—41no—
360D4—41no—
361D4—41no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—442no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—881no—
376C2×C4—881no—
377C2×C4C22⋊C4×D1111yescharacteristic
378C2×C4(C22⋊D11)⋊C411yescharacteristic
379C2×C4#6693811yescharacteristic
380C2×C4#6699211yescharacteristic
381C8—42no—
382C8—111no—
383C8—111no—
384C8—221no—
385C8—221no—
386C8—221no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1062257011yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—81no—
398C4—81no—
399C4—161no—
400C4—881no—
401C4—882no—
402C4—881no—
403C4—1761no—
404C4#1062235311yescharacteristic
405C4D11×#9911yescharacteristic
406C2—21no—
407C2—41no—
408C2—41no—
409C2—41no—
410C2#1306945011yescharacteristic
subgroupG/H
centerC2#13069450
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2123C2
socleC2×C11#1964
prime radical, cosocleC2×C11×#41C23
hypercenter#2123D11
hypocenterC11#13230
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
11. C22×#4326C4semidirect
16. #10622838C4semidirect
22. #10622617C4semidirect
24. #10622611C4semidirect
348. C11#13230semidirect

Maximal subgroups

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

subgroupindex
#130782682
#130702912
#130702902
#130702712
#130686602
#130684192
C11×#21232
#1323011