Finite Group Databasebeta

← #14664121

Subgroups — #14664121

Order 2816.

500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074474C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic, complemented
3#13066931C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622844C411yescharacteristic, complemented
12#10622573—21no—
13#10622573C2211yescharacteristic
14#10622571—21no—
15C2×#66870—21no—
16C22⋊C4×Dic11—21no—
17D11×C22⋊C8—21no—
18#10622288—21no—
19#10622284C411yescharacteristic, complemented
20#10622278—21no—
21#10622264C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×D44—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38#67000—41no—
39#67000—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—41no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C8×D11—41no—
50(C22⋊D11)⋊C4—41no—
51(C22⋊D11)⋊C4—41no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62#66870—24no—
63#11730—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C22×Dic11—81no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×D44—41no—
91C2×D44—42no—
92C2×D44—81no—
93C2×D44—81no—
94C2×D44—81no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—81no—
98C2×C8×C11—41no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—81no—
103C22⋊Dic11—22no—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112Dic11⋊C4—41no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—82no—
116C2×C11⋊C8—41no—
117C8×D11—82no—
118#2631—111no—
119C4×#99—111no—
120#1459—111no—
121#1351—111no—
122#1351D1111yescharacteristic, complemented
123#1343—111no—
124#1343—111no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#13511yescharacteristic
131C23×C11#13511yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11#10412yes—
144Q8×C11—82no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C22⋊D11—42no—
159C22⋊D11—42no—
160C22⋊D11—82no—
161C22⋊D11—82no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11#9911yescharacteristic
177C2×Dic11#9911yescharacteristic
178D44—82no—
179D44—84no—
180C4×D11—42no—
181C4×D11—81no—
182C8×C11—81no—
183C11⋊C8—81no—
184C2×#124—111no—
185C2×C4×D4—111no—
186C2×#99—221no—
187C2×C22⋊C8—221no—
188#397—221no—
189#393—111no—
190#393C2×D1111yescharacteristic
191#392—111no—
192#392—111no—
193#392—221no—
194#386—221no—
195#386—221no—
196#383—111no—
197C4×C22⋊C4—221no—
198#342—111no—
199#342C2×D1111yescharacteristic
200#324—221no—
201#323—111no—
202#323C2×D1111yescharacteristic
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—81no—
212C22×C11C2×#9911yescharacteristic
213C22×C11#41611yescharacteristic
214C22×C11C2×#10411yescharacteristic
215C2×D11—22no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—81no—
230C4×C11—82no—
231C4×C11—81no—
232Dic11—21no—
233Dic11—21no—
234Dic11—41no—
235Dic11—41no—
236Dic11—81no—
237Dic11—82no—
238C22×Q8C4×D1111yescharacteristic
239C22×D4—111no—
240C22×D4—111no—
241C22×D4—221no—
242C22×D4—221no—
243C23×C4—111no—
244C23×C4—111no—
245C22×C8—441no—
246#124—441no—
247#124—441no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—111no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4C22×D1111yescharacteristic
261C2×C42—111no—
262C2×C42—441no—
263#99—224no—
264C22⋊C8—21no—
265C22⋊C8—221no—
266C22⋊C8—441no—
267#95—21no—
268#95—111no—
269#95—221no—
270#95—221no—
271#95—221no—
272#95—441no—
273#95C4×D1111yescharacteristic
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—41no—
277C2×C11—41no—
278C2×C11#150111yescharacteristic
279C2×C11#212211yescharacteristic
280C2×C11#212711yescharacteristic
281D11—42no—
282D11—161no—
283C24—111no—
284C24—221no—
285C24D4×D1111yescharacteristic
286C2×Q8—41no—
287C2×Q8—81no—
288C2×D4—222no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—441no—
292C2×D4—442no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—881no—
297C2×D4—881no—
298C2×D4—881no—
299C2×D4—881no—
300C2×D4—881no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—441no—
313C22×C4—881no—
314C22×C4—881no—
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C2×C8—41no—
318C2×C8—441no—
319C2×C8—882no—
320C4⋊C4—441no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—81no—
325C22⋊C4—222no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—442no—
330C22⋊C4—441no—
331C22⋊C4—881no—
332C22⋊C4—881no—
333C22⋊C4—881no—
334C42—221no—
335C42—221no—
336C42—882no—
337C11#1173011yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—112no—
343C23—221no—
344C23—221no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23C22⋊C4×D1111yescharacteristic
355C23#6696911yescharacteristic
356C23#6697211yescharacteristic
357Q8—82no—
358D4—442no—
359D4—442no—
360D4—882no—
361D4—884no—
362D4—882no—
363D4—882no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—111no—
378C2×C4—111no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4—881no—
395C8—81no—
396C8—881no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—222no—
407C22—442no—
408C22—441no—
409C22—441no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22D11×#9911yescharacteristic
419C22#1062241711yescharacteristic
420C22D11×#10411yescharacteristic
421C4—41no—
422C4—41no—
423C4—81no—
424C4—82no—
425C4—81no—
426C4—221no—
427C4—221no—
428C4—441no—
429C4—441no—
430C4—881no—
431C4—882no—
432C2—21no—
433C2—21no—
434C2—41no—
435C2—41no—
436C2—442no—
437C2—1761no—
438C2#1306710611yescharacteristic
439C2#1307026411yescharacteristic
440C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radical#13074474C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11730
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #13068403C2semidirect
3. #13066931C2semidirect
4. #13066637C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1351C2semidirect
8. C2×#67000C4semidirect
11. #10622844C4semidirect
19. #10622284C4semidirect
21. #10622264C4semidirect
122. #1351D11semidirect
337. C11#11730semidirect

Maximal subgroups

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

subgroupindex
#130744742
#130684032
#130669312
#130666372
#130666142
#130666122
C11×#13512
#1173011