Finite Group Databasebeta

← #14654292

Subgroups — #14654292

Order 2816.

650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079374C211yesmaximal, characteristic
2C2×#10622584C211yesmaximal, characteristic, complemented
3#13073083C211yesmaximal, characteristic
4#13069600C211yesmaximal, characteristic, complemented
5#13067183C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1823C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66982—22no—
11C2×#66977C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622727—22no—
17#10622605—22no—
18#10622601—21no—
19#10622589—21no—
20#10622584—22no—
21#10622584—22no—
22C2×#66874—21no—
23C2×#66872—21no—
24#10622351—21no—
25#10622348—21no—
26#10622344—21no—
27#10622334—21no—
28C11×#340—22no—
29#10622165—22no—
30#10622089—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×D44D411yescharacteristic
35C22×Dic22D411yescharacteristic
36C22×C8×C11D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D412yes—
47#66983—21no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51#66982—44no—
52#66982—44no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4⋊Dic11D411yescharacteristic
57#66977—21no—
58#66977—21no—
59#66977—21no—
60#66977—21no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—21no—
63C2×C4×Dic11—21no—
64C22×C11⋊C8—21no—
65C2×#4314—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)D412yes—
72#66885—22no—
73#66881—22no—
74#66880—22no—
75#66874—24no—
76#66872—24no—
77#9960—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—42no—
96C2×C22⋊D11—42no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—42no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—42no—
107C2×C8×C11—22no—
108C2×C8×C11—42no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—42no—
115C22⋊Dic11—22no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11SD1614yescomplemented
119(C2×D11)⋊C4—48no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126Dic11⋊C4—48no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132#4314—82no—
133#3187—111no—
134C2×#483—111no—
135#2501—111no—
136#1996—111no—
137#1823D1111yescharacteristic, complemented
138#1519—111no—
139#1282—111no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11#12011yescharacteristic
143C23×C11#12111yescharacteristic
144C23×C11#12711yescharacteristic
145C23×C11C2×SD1612yes—
146C23×C11AGL(1,ℤ/8)12yes—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—42no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C22⋊D11—82no—
170C22⋊D11—81no—
171C22⋊D11—81no—
172C2×Dic11—24no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181D44—42no—
182D44—81no—
183Dic22—42no—
184Dic22—42no—
185C8×C11—42no—
186C11⋊C8—42no—
187C2×#123—222no—
188C2×C22⋊Q8—111no—
189C2×#121—111no—
190C22×C4⋊C4C2×D1111yescharacteristic
191#483—221no—
192#483—222no—
193#483—222no—
194#481—221no—
195#465—222no—
196#450—221no—
197#448—221no—
198C2×#106—221no—
199C2×#103—221no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#399—222no—
203#390—221no—
204#384—221no—
205#380C2×D1111yescharacteristic
206C4×C22⋊C4—111no—
207#342—222no—
208#340—22no—
209#327—222no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11#39211yescharacteristic
219C22×C11#45012yes—
220C22×C11#46012yes—
221C22×C11#49211yescharacteristic
222C22×C11#49611yescharacteristic
223C2×D11—84no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—82no—
231C4×C11—161no—
232C4×C11#45812yes—
233Dic11—44no—
234Dic11—81no—
235Dic11—81no—
236Dic11—81no—
237C22×Q8—111no—
238C22×D4—111no—
239C22×D4—221no—
240C23×C4—21no—
241C23×C4C22×D1111yescharacteristic
242C2×SD16—222no—
243C22×C8—221no—
244C22×C8C22⋊D1112yes—
245#123—444no—
246#123—444no—
247C22⋊Q8—221no—
248C22⋊Q8—221no—
249C22⋊Q8—221no—
250C22⋊Q8—221no—
251#121—221no—
252#121—221no—
253#121—221no—
254#121—221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—224no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4D4412yes—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—224no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C42—221no—
272#106—224no—
273#106—222no—
274#103—224no—
275#103—222no—
276#102—222no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—112no—
280C22⋊C8—221no—
281#95—21no—
282#95—221no—
283C2×C11—22no—
284C2×C11—21no—
285C2×C11—22no—
286C2×C11—21no—
287C2×C11#200911yescharacteristic
288C2×C11#201411yescharacteristic
289C2×C11#202211yescharacteristic
290D11—161no—
291C24—221no—
292C24D4×D1111yescharacteristic
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—442no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—441no—
303C22×C4—22no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4C2×D4411yescharacteristic
315C22×C4#433911yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—882no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8—222no—
324C2×C8—442no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—448no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—42no—
338C22⋊C4—114no—
339C22⋊C4—222no—
340C22⋊C4—448no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C42—442no—
346C11#996011yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—442no—
350C23—442no—
351C23—441no—
352C23—442no—
353C23#6693511yescharacteristic
354C23#6693711yescharacteristic
355C23#6696412yes—
356C23SD16×D1112yes—
357C23#6699311yescharacteristic
358Q8—442no—
359Q8—442no—
360D4—442no—
361D4—881no—
362D4—881no—
363D4—881no—
364D4—882no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—224no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4#6693511yescharacteristic
389C2×C4#6693711yescharacteristic
390C2×C4#6698311yescharacteristic
391C2×C4#6699011yescharacteristic
392C8—42no—
393C8—442no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—884no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22#1062237512yes—
407C22#1062238912yes—
408C22#1062257311yescharacteristic
409C22#1062276711yescharacteristic
410C22#1062278811yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—82no—
415C4—161no—
416C4—444no—
417C4—881no—
418C4—881no—
419C4—881no—
420C4#1062266612yes—
421C2—21no—
422C2—22no—
423C2—21no—
424C2—22no—
425C2—1761no—
426C2#1306967811yescharacteristic
427C2#1306970511yescharacteristic
428C2#1306974711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1823C2
socleC22×C11#392
prime radicalC2×#66983C22
hypercenter#1823D11
hypocenterC11#9960
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
4. #13069600C2semidirect
6. #13066463C2semidirect
7. C11×#1823C2semidirect
118. C22⋊Dic11SD16semidirect
137. #1823D11semidirect
346. C11#9960semidirect

Maximal subgroups

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

subgroupindex
#130793742
C2×#106225842
#130730832
#130696002
#130671832
#130664632
C11×#18232
#996011