Finite Group Databasebeta

← #14658125

Subgroups — #14658125

Order 2816.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#13069085C211yesmaximal, characteristic
3#13069082C211yesmaximal, characteristic
4#13068801C211yesmaximal, characteristic
5#13067135C211yesmaximal, characteristic
6#13066492C211yesmaximal, characteristic
7C11×#1508C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622841—21no—
14C2×#66900—21no—
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66888—21no—
18#10622664—21no—
19#10622664—21no—
20#10622663—21no—
21#10622657—21no—
22#10622583—21no—
23C2×C4⋊(C11⋊C8)—21no—
24C11×#328—21no—
25C11×#328—21no—
26#10622192—21no—
27#10622168—21no—
28#10622162—21no—
29#10622090—21no—
30#10622090—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×Dic22D411yescharacteristic
34C2×C11×M16—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×C22⋊Dic11—21no—
45C2×#4326—21no—
46C2×#4326—21no—
47C2×C4⋊Dic11D411yescharacteristic
48#66977—21no—
49#66977—21no—
50#66977—21no—
51#66977—21no—
52C2×Dic11⋊C4—21no—
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×#4318—42no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#66900—42no—
65#66899—21no—
66#66899—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66888—42no—
72#66874—21no—
73#66874—21no—
74#66871—21no—
75#66871—21no—
76C4⋊(C11⋊C8)—42no—
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—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C11×M16—41no—
102C11×M16—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115#4326—81no—
116#4326—81no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121#4318—22no—
122#4318—22no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#3189—111no—
136#1901—111no—
137#1901—111no—
138#1851—111no—
139#1508—111no—
140#1508D1111yescharacteristic
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—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12411yescharacteristic
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179Dic22—41no—
180Dic22—41no—
181Dic22—81no—
182C8×C11—81no—
183C11⋊C8—42no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186C11⋊C8—81no—
187C22×M16—111no—
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—221no—
198C2×#101—221no—
199#407—111no—
200#407C2×D1111yescharacteristic
201C2×C22⋊C8—111no—
202C4×C22⋊C4C2×D1111yescharacteristic
203#343—221no—
204#343—221no—
205#336—221no—
206#328—21no—
207#328—21no—
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—42no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11B(4,𝔽2)11yescharacteristic
231C4×C11#45811yescharacteristic
232Dic11—81no—
233Dic11—81no—
234C22×Q8—111no—
235C22×Q8D4411yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C2×Q16—221no—
238C2×Q16—221no—
239C2×M16—21no—
240C2×M16—221no—
241C2×M16—221no—
242C2×M16—221no—
243C2×M16—442no—
244C22×C8—111no—
245C22×C8—111no—
246C22×C8—221no—
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⋊C4D4411yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—221no—
262C2×C42—21no—
263#107—221no—
264#107—221no—
265C4⋊C8—442no—
266#103—221no—
267#103—221no—
268#103—221no—
269#103—221no—
270#101—442no—
271#101—442no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278#95C22⋊D1111yescharacteristic
279#95C22⋊D1111yescharacteristic
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11#204411yescharacteristic
285C2×C11#204711yescharacteristic
286C2×C11#205011yescharacteristic
287C24#434111yescharacteristic
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—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4C2×D4411yescharacteristic
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310Q16—881no—
311Q16—881no—
312M16—41no—
313M16—41no—
314M16—222no—
315M16—222no—
316M16—441no—
317M16—441no—
318M16—441no—
319M16—441no—
320C2×C8—41no—
321C2×C8—222no—
322C2×C8—221no—
323C2×C8—221no—
324C2×C8—441no—
325C2×C8—441no—
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—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C42—41no—
343C42—41no—
344C11#1055911yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23#6693611yescharacteristic
350C23#6693911yescharacteristic
351C23#6699211yescharacteristic
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—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4#6693511yescharacteristic
382C2×C4#6693811yescharacteristic
383C2×C4#6698311yescharacteristic
384C2×C4#6699111yescharacteristic
385C8—81no—
386C8—442no—
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#1062257411yescharacteristic
401C22#1062281711yescharacteristic
402C22#1062281711yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—881no—
411C4—881no—
412C4#1062235411yescharacteristic
413C4#1062235511yescharacteristic
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2#1306986611yescharacteristic
419C2#1306988311yescharacteristic
420C2#1306990211yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1508C2
socleC22×C11#394
prime radicalC24×C11#41
hypercenter#1508D11
hypocenterC11#10559
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

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
#130690852
#130690822
#130688012
#130671352
#130664922
C11×#15082
#1055911