Finite Group Databasebeta

← #14650249

Subgroups — #14650249

Order 2816.

478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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#13079399C211yesmaximal, characteristic
2#13077670C211yesmaximal, characteristic
3#13067121C211yesmaximal, characteristic
4C2×#10622105C211yesmaximal, characteristic, complemented
5#13066981C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1298C211yesmaximal, characteristic, complemented
8#10623322C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11⋊#95C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15#10622729—21no—
16#10622727—21no—
17#10622724—21no—
18C8×C22⋊D11—21no—
19#10622352C411yescharacteristic, complemented
20#10622351C411yescharacteristic, complemented
21#10622349C411yescharacteristic, complemented
22#10622346—21no—
23#10622343—21no—
24#10622340—21no—
25(C22⋊D11)⋊C8—21no—
26#10622336—21no—
27#10622334C411yescharacteristic, complemented
28#10622333—21no—
29#10622108—21no—
30#10622107—21no—
31#10622107—21no—
32#10622105—21no—
33#10622105—21no—
34#10622105—21no—
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C2×#4339D411yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42#67006—21no—
43C2×C22⋊Dic11—21no—
44#66983C2×C411yescharacteristic
45#66983D411yescharacteristic
46#66982—21no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49#66979D411yescharacteristic
50C2×C4⋊Dic11C2×C411yescharacteristic
51#66977—21no—
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977C2×C411yescharacteristic
56#66977D411yescharacteristic
57C2×Dic11⋊C4—21no—
58C22×C11⋊C8—21no—
59C2×Dic44—21no—
60C2×#4314—21no—
61C2×#4313—21no—
62C2×C8×D11—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8C2×C411yescharacteristic
68C11×C22⋊C8C2×C411yescharacteristic
69C11×C22⋊C8D411yescharacteristic
70C11×C22⋊C8D411yescharacteristic
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D411yescharacteristic
75C22⋊(C11⋊C8)D411yescharacteristic
76#66885—21no—
77(C2×D11)⋊C8—21no—
78(C2×D11)⋊C8—21no—
79#66882—21no—
80#66881—21no—
81#66880—21no—
82#66880—21no—
83#66880—21no—
84#66879—21no—
85Dic11⋊C8—21no—
86Dic11⋊C8—21no—
87C8×Dic11—21no—
88#9263—111nomaximal, Sylow
89C24×C11#4111yescharacteristic
90C22×C4×C11—81no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—21no—
98C2×C22⋊D11—21no—
99C2×C22⋊D11—21no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—81no—
106C22×Dic11—81no—
107#4339—81no—
108C2×D44C22⋊C411yescharacteristic
109C2×C4×D11—21no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22—81no—
113C2×Dic22C22⋊C411yescharacteristic
114C11×M16—81no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—41no—
120C2×C8×C11—81no—
121C2×C8×C11—81no—
122C22⋊Dic11—21no—
123C22⋊Dic11—21no—
124C22⋊Dic11—21no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127(C2×D11)⋊C4—21no—
128(C2×D11)⋊C4—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11C22⋊C411yescharacteristic
132C4⋊Dic11C22⋊C411yescharacteristic
133Dic11⋊C4—21no—
134Dic11⋊C4—21no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—81no—
141Dic44—81no—
142#4314—81no—
143#4313—81no—
144C8×D11—81no—
145#3190—111no—
146#2977—111no—
147#1504—111no—
148C2×#328—111no—
149#1472—111no—
150#1298D1111yescharacteristic, complemented
151#1280—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—41no—
157C23×C11C4×D411yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12311yescharacteristic
160C22×D11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C22⋊D11—41no—
172C22⋊D11—41no—
173C22⋊D11—41no—
174C22⋊D11—41no—
175C22⋊D11—81no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—81no—
185C2×Dic11—82no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—82no—
189D44—41no—
190C4×D11—41no—
191C4×D11—41no—
192Dic22—41no—
193Dic22—41no—
194Dic22—41no—
195Dic22—81no—
196C8×C11—41no—
197C8×C11—41no—
198C8×C11—41no—
199C8×C11—41no—
200C8×C11—81no—
201C11⋊C8—41no—
202C11⋊C8—41no—
203#525—111no—
204C2×C22⋊Q8—111no—
205#485—221no—
206#483—111no—
207#480—111no—
208#467—221no—
209#465—221no—
210#452—221no—
211#451—111no—
212#448—111no—
213#435—221no—
214#435—221no—
215C8×D4—221no—
216C8×D4—221no—
217#433—221no—
218#408—221no—
219#407C2×D1111yescharacteristic
220C2×C22⋊C8—111no—
221C2×C22⋊C8C2×D1111yescharacteristic
222C2×C22⋊C8C2×D1111yescharacteristic
223C2×#95—111no—
224#328—221no—
225#328—221no—
226#328—221no—
227#327—221no—
228#324—221no—
229#324—221no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11#38611yescharacteristic
242C22×C11#44311yescharacteristic
243C22×C11#44411yescharacteristic
244C22×C11#47111yescharacteristic
245C22×C11#47311yescharacteristic
246C2×D11—41no—
247C2×D11—41no—
248C2×D11—41no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256Dic11—82no—
257Dic11—81no—
258Dic11—81no—
259C2×#41—111no—
260C22×Q8—111no—
261C23×C4—221no—
262C23×C4C22×D1111yescharacteristic
263C2×Q16—221no—
264C2×SD16—221no—
265C2×M16—21no—
266C2×M16—221no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—221no—
270C22×C8—221no—
271#123—221no—
272C22⋊Q8—111no—
273C22⋊Q8—111no—
274C22⋊Q8—221no—
275C22⋊Q8—221no—
276C22⋊Q8—221no—
277C22⋊Q8—221no—
278#121—111no—
279#121—111no—
280#120—221no—
281C4×D4—221no—
282C4×D4—221no—
283#117—111no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—221no—
286C2×C22⋊C4—221no—
287#107—221no—
288#106—221no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291#103—221no—
292#103—221no—
293#103—221no—
294#102—221no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—111no—
300C22⋊C8—111no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303C22⋊C8—221no—
304C22⋊C8C4×D1111yescharacteristic
305C22⋊C8C4×D1111yescharacteristic
306C22⋊C8D4411yescharacteristic
307C22⋊C8D4411yescharacteristic
308#97—221no—
309C4×C8—221no—
310#95—221no—
311#95—221no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—41no—
317C2×C11#187611yescharacteristic
318C2×C11#190811yescharacteristic
319C2×C11#191311yescharacteristic
320D11—81no—
321C24#434311yescharacteristic
322#41—881no—
323C2×Q8—111no—
324C2×Q8—221no—
325C2×Q8—221no—
326C2×Q8—881no—
327C2×D4—111no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C22×C4—81no—
332C22×C4—221no—
333C22×C4—221no—
334C22×C4—222no—
335C22×C4—221no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4—881no—
339C22×C4—881no—
340C22×C4C2×C4×D1111yescharacteristic
341C22×C4C2×D4411yescharacteristic
342C22×C4#433911yescharacteristic
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346Q16—881no—
347SD16—881no—
348M16—81no—
349M16—881no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—41no—
355C2×C8—81no—
356C2×C8—81no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—881no—
360C2×C8—881no—
361C4⋊C4—111no—
362C4⋊C4—111no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C22⋊C4—221no—
370C22⋊C4—221no—
371C22⋊C4—221no—
372C22⋊C4—221no—
373C22⋊C4—221no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C42—221no—
377C11#926311yescharacteristic, complemented, Sylow
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—41no—
383C23—221no—
384C23#6694611yescharacteristic
385C23#6694711yescharacteristic
386C23#6694811yescharacteristic
387Q8—441no—
388Q8—441no—
389Q8—441no—
390Q8—881no—
391D4—441no—
392D4—441no—
393D4—441no—
394D4—441no—
395D4—441no—
396D4—881no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—881no—
414C2×C4—882no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4—882no—
418C2×C4C4×D4411yescharacteristic
419C2×C4C22⋊C4×D1111yescharacteristic
420C2×C4#6693511yescharacteristic
421C2×C4#6693711yescharacteristic
422C8—41no—
423C8—41no—
424C8—41no—
425C8—41no—
426C8—81no—
427C8—441no—
428C8—441no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—441no—
441C22—441no—
442C22—441no—
443C22#1062227811yescharacteristic
444C22#1062250711yescharacteristic
445C22#1062250811yescharacteristic
446C22#1062250911yescharacteristic
447C22#1062251111yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—441no—
453C4—441no—
454C4—441no—
455C4—882no—
456C4—881no—
457C4—881no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—881no—
464C2#1306894411yescharacteristic
465C2#1306913011yescharacteristic
466C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1298C2
socleC22×C11#386
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1298D11
hypocenterC11#9263
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1298

Complements

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

NH ≅ G/Ntype
4. C2×#10622105C2semidirect
5. #13066981C2semidirect
6. #13066458C2semidirect
7. C11×#1298C2semidirect
19. #10622352C4semidirect
20. #10622351C4semidirect
21. #10622349C4semidirect
27. #10622334C4semidirect
150. #1298D11semidirect
377. C11#9263semidirect

Maximal subgroups

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

subgroupindex
#130793992
#130776702
#130671212
C2×#106221052
#130669812
#130664582
C11×#12982
#926311