Finite Group Databasebeta

← #14658124

Subgroups — #14658124

Order 2816.

448 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 77 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#13079388C211yesmaximal, characteristic
2#13069084C211yesmaximal, characteristic
3#13068799C211yesmaximal, characteristic
4#13067137C211yesmaximal, characteristic
5#13067136C211yesmaximal, characteristic
6#13066492C211yesmaximal, characteristic
7C11×#1901C211yesmaximal, characteristic
8C22×C11×M16C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×#101—21no—
12C11×#407C2211yescharacteristic
13#10622841—21no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66888—21no—
18C2×Dic11⋊C8—21no—
19#10622664—21no—
20#10622664—21no—
21#10622663—21no—
22#10622657—21no—
23#10622583—21no—
24C11×#343—21no—
25#10622192—21no—
26#10622188—21no—
27#10622176—21no—
28#10622176—21no—
29#10622105—21no—
30#10622105—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×Dic22D411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—42no—
38C22×C8×C11—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×#4326—21no—
49C2×#4326—21no—
50C2×C4⋊Dic11D411yescharacteristic
51#66977—21no—
52#66977—21no—
53#66977—21no—
54#66977—21no—
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C2×#4318—21no—
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×#101—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63#66899—21no—
64#66899—21no—
65C11⋊#95D411yescharacteristic
66C11⋊#95D411yescharacteristic
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66888—42no—
72Dic11⋊C8—42no—
73#66874—21no—
74#66874—21no—
75#66871—21no—
76#66871—21no—
77#10559—111nomaximal, Sylow
78C24×C11#4111yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C11×M16—22no—
102C11×M16—22no—
103C11×M16—41no—
104C11×M16—41no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—42no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120#4326—81no—
121#4326—81no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128#4318—41no—
129#4318—41no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#3189—111no—
136#1901—111no—
137#1901D1111yescharacteristic
138#1851—111no—
139#1508—111no—
140#1508—111no—
141#1293—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11#12111yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11#12311yescharacteristic
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—81no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—81no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12411yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179Dic22—41no—
180Dic22—41no—
181Dic22—81no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186C11⋊C8—81no—
187C22×M16C2×D1111yescharacteristic
188C2×C22⋊Q8—111no—
189C2×C22⋊Q8C2×D1111yescharacteristic
190#484—221no—
191#484—221no—
192#467—221no—
193#467—221no—
194#451—221no—
195#451—221no—
196C2×C4⋊C8—221no—
197C2×#101—21no—
198C2×#101—221no—
199#407—111no—
200#407C2×D1111yescharacteristic
201C2×C22⋊C8—111no—
202C4×C22⋊C4—111no—
203#343—21no—
204#343—221no—
205#336—221no—
206#328—221no—
207#328—221no—
208#328—221no—
209#328—221no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39411yescharacteristic
221C22×C11#47311yescharacteristic
222C22×C11#47311yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11B(4,𝔽2)11yescharacteristic
229C4×C11#45811yescharacteristic
230Dic11—42no—
231Dic11—81no—
232Dic11—81no—
233Dic11—81no—
234C22×Q8—111no—
235C22×Q8C22⋊D1111yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C2×Q16—221no—
238C2×Q16—221no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—42no—
243C2×M16—221no—
244C22×C8—21no—
245C22×C8—111no—
246C22×C8—111no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—221no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254C22⋊Q8—221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42—221no—
263#107—221no—
264#107—221no—
265C4⋊C8—442no—
266#103—221no—
267#103—221no—
268#103—221no—
269#103—221no—
270#101—42no—
271#101—442no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278#95—111no—
279#95—111no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11#204411yescharacteristic
285C2×C11#204711yescharacteristic
286C2×C11#205011yescharacteristic
287C24#433911yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×Q8—441no—
295C2×Q8—441no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4#433911yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310Q16—881no—
311Q16—881no—
312M16—22no—
313M16—22no—
314M16—41no—
315M16—41no—
316M16—41no—
317M16—41no—
318M16—441no—
319M16—441no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—221no—
325C2×C8—221no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—441no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C42—441no—
343C42—441no—
344C11#1055911yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23#6693611yescharacteristic
350C23#6693711yescharacteristic
351C23#6698211yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—81no—
355Q8—441no—
356Q8—441no—
357Q8—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4#6693711yescharacteristic
382C2×C4#6693811yescharacteristic
383C2×C4#6699011yescharacteristic
384C2×C4#6699211yescharacteristic
385C8—42no—
386C8—81no—
387C8—441no—
388C8—441no—
389C8—881no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1062236811yescharacteristic
401C22#1062236811yescharacteristic
402C22#1062257211yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—81no—
407C4—81no—
408C4—442no—
409C4—881no—
410C4—881no—
411C4—881no—
412C4#1062264511yescharacteristic
413C4#1062266611yescharacteristic
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2#1306986511yescharacteristic
419C2#1306988211yescharacteristic
420C2#1306990111yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1901C2
socleC22×C11#394
prime radicalC24×C11#41
hypercenter#1901D11
hypocenterC11#10559
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
344. C11#10559semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130690842
#130687992
#130671372
#130671362
#130664922
C11×#19012
#1055911