Finite Group Databasebeta

← #14672132

Subgroups — #14672132

Order 2816.

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

normal subgroups only

This group has 432 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#13070310C211yesmaximal, characteristic
3#13070271C211yesmaximal, characteristic
4#13070270C211yesmaximal, characteristic
5#13068664C211yesmaximal, characteristic
6#13068419C211yesmaximal, characteristic
7C11×#2135C211yesmaximal, characteristic
8C11×#536C2211yescharacteristic
9#10623356C2211yescharacteristic
10C2×#67001C2211yescharacteristic
11C22×#4326C411yescharacteristic, complemented
12C11×#413C2211yescharacteristic
13C11×#413C2211yescharacteristic
14#10622853C2211yescharacteristic
15#10622850C2211yescharacteristic
16#10622838C411yescharacteristic, complemented
17C2×#66886—21no—
18#10622735—21no—
19#10622665—21no—
20#10622665—21no—
21#10622664—21no—
22#10622664—21no—
23#10622617C411yescharacteristic, complemented
24#10622611C411yescharacteristic, complemented
25C11×#356—22no—
26C11⋊#338—21no—
27#10622197—21no—
28#10622177—22no—
29#10622116—22no—
30#10622114—22no—
31C2×C11×#41C2311yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×#124—21no—
38C11×#123—21no—
39C11×#123—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—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#66979C2×C411yescharacteristic
55#66977—21no—
56#66977—21no—
57C2×#4318—21no—
58C2×#4318C2×C411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×#4318D411yescharacteristic
61C22×C11⋊C8C2×C411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C11×#101—21no—
65C11×#101D412yes—
66C11×#100—21no—
67C11×#100—21no—
68#66900—21no—
69#66899—21no—
70#66899—21no—
71#66898—21no—
72#66898D412yes—
73#66897—21no—
74#66886—41no—
75#66886—41no—
76#66879—41no—
77C8×Dic11—41no—
78#66874—21no—
79#66874—21no—
80#66872—21no—
81#66871—21no—
82#13233—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×C11C2×D411yescharacteristic
90C2×D4×C11C2×D411yescharacteristic
91C2×D4×C11#4111yescharacteristic
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—
104C11×M16—41no—
105C11×M16—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—21no—
115C22⋊Dic11—21no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119#4326—42no—
120#4326—41no—
121#4326—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—21no—
127C4×Dic11—41no—
128#4318—41no—
129#4318—41no—
130#4318—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8C22⋊C411yescharacteristic
141C2×C11⋊C8C22⋊C411yescharacteristic
142C2×C11⋊C8C22⋊C411yescharacteristic
143C2×C11⋊C8C22⋊C411yescharacteristic
144#3059—111no—
145#2135—111no—
146#2135D1111yescharacteristic
147#2123—111no—
148#2123—111no—
149#1813—111no—
150#1757—111no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12411yescharacteristic
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×C11C2×C22⋊C411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—81no—
178Dic22—41no—
179Dic22—41no—
180Dic22—81no—
181C8×C11—42no—
182C8×C11—81no—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C11⋊C8—21no—
186C11⋊C8—81no—
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—
197C2×#108—221no—
198#427—111no—
199#419—111no—
200#419—111no—
201#413—111no—
202#413C2×D1111yescharacteristic
203#413C2×D1111yescharacteristic
204#410—111no—
205#405—221no—
206#356—22no—
207#356—222no—
208#352—222no—
209#352—222no—
210#344—221no—
211#338—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×C11C2×#9911yescharacteristic
225C4×C11#41011yescharacteristic
226Dic11—81no—
227Dic11—82no—
228Dic11—81no—
229C2×#41C22×D1111yescharacteristic
230C22×Q8—111no—
231C22×Q8C4×D1111yescharacteristic
232C2×Q16—221no—
233C2×Q16—221no—
234C2×Q16—441no—
235C2×Q16—441no—
236#131—441no—
237#131—441no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—111no—
241C2×M16—111no—
242C2×M16—111no—
243C2×M16—221no—
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—111no—
260#117—221no—
261#117C4×D1111yescharacteristic
262#108—441no—
263#108—441no—
264#107—221no—
265#106—221no—
266#103—221no—
267#103—221no—
268#103—221no—
269#103—221no—
270#101—21no—
271#101—221no—
272#101C22⋊D1112yes—
273#100—21no—
274#100—21no—
275#100—221no—
276#99—112no—
277#99—221no—
278#97—441no—
279C4×C8—441no—
280C2×C11—21no—
281C2×C11—41no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11#196411yescharacteristic
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×Q8—441no—
294C2×Q8—441no—
295C2×Q8C2×C22⋊D1111yescharacteristic
296C2×D4#433911yescharacteristic
297C2×D4D4×D1111yescharacteristic
298C2×D4#434111yescharacteristic
299C22×C4—21no—
300C22×C4—221no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304Q16—441no—
305Q16—441no—
306Q16—442no—
307M16—22no—
308M16—41no—
309M16—41no—
310M16—41no—
311M16—441no—
312M16—441no—
313M16—441no—
314M16—441no—
315M16—441no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—111no—
321C2×C8—111no—
322C2×C8—221no—
323C2×C8—221no—
324C2×C8—221no—
325C2×C8—221no—
326C2×C8—221no—
327C2×C8—221no—
328C2×C8—441no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C22⋊C4—21no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—221no—
340C22⋊C4—222no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C42—21no—
344C42—221no—
345C42—441no—
346C11#1323311yescharacteristic, complemented, Sylow
347C23(C22⋊D11)⋊C411yescharacteristic
348C23#6693711yescharacteristic
349C23#6693811yescharacteristic
350Q8—41no—
351Q8—41no—
352Q8—41no—
353Q8—81no—
354Q8—441no—
355Q8—441no—
356Q8—881no—
357D4—41no—
358D4—41no—
359D4—41no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—881no—
373C2×C4C22⋊C4×D1111yescharacteristic
374C2×C4C4×C22⋊D1111yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6699311yescharacteristic
377C8—42no—
378C8—81no—
379C8—111no—
380C8—111no—
381C8—221no—
382C8—221no—
383C8—221no—
384C8—881no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22#1062257011yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—81no—
397C4—881no—
398C4—882no—
399C4—881no—
400C4#1062235311yescharacteristic
401C4D11×#9911yescharacteristic
402C2—21no—
403C2—41no—
404C2—41no—
405C2—41no—
406C2#1306945011yescharacteristic
subgroupG/H
centerC2#13069450
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2135C2
socleC2×C11#1964
prime radical, cosocleC2×C11×#41C23
hypercenter#2135D11
hypocenterC11#13233
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2135

Complements

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

NH ≅ G/Ntype
11. C22×#4326C4semidirect
16. #10622838C4semidirect
23. #10622617C4semidirect
24. #10622611C4semidirect
346. C11#13233semidirect

Maximal subgroups

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

subgroupindex
#130782682
#130703102
#130702712
#130702702
#130686642
#130684192
C11×#21352
#1323311