Finite Group Databasebeta

← #14654291

Subgroups — #14654291

Order 2816.

650 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079373C211yesmaximal, characteristic
2C2×#10622584C211yesmaximal, characteristic, complemented
3#13069601C211yesmaximal, characteristic, complemented
4#13068702C211yesmaximal, characteristic, complemented
5#13067184C211yesmaximal, characteristic
6#13066464C211yesmaximal, characteristic, complemented
7C11×#2501C211yesmaximal, characteristic
8C2×C11×#123—22no—
9C2×C11×#121C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66977C2211yescharacteristic
12C11×#399—22no—
13C11×#390—21no—
14C11×#384—21no—
15C4×C11×C22⋊C4C2211yescharacteristic
16#10622831—21no—
17#10622825C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622654—22no—
21#10622653—21no—
22#10622647—21no—
23#10622584—21no—
24#10622584—22no—
25#10622584—22no—
26C2×#66874—21no—
27C2×#66872—21no—
28#10622175—22no—
29#10622167—22no—
30#10622165—22no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×Dic22D411yescharacteristic
36C11×#123—44no—
37C11×#123—44no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56C2×#4324—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D411yescharacteristic
59#66977—21no—
60#66977—21no—
61#66977—21no—
62#66977—21no—
63C2×Dic11⋊C4—21no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8D412yes—
66C11×#95—21no—
67#66896—22no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66874—24no—
74#66874—22no—
75#66872—24no—
76#66872—22no—
77#9960—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11C2×D411yescharacteristic
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—41no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—42no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—48no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4SD1614yescomplemented
119C42×C11—42no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C22⋊Dic11—42no—
123#4324—82no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—42no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133#3187—111no—
134C2×#483—111no—
135#2501D1111yescharacteristic
136#1996—111no—
137#1823—111no—
138#1519—111no—
139#1282—111no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11#12011yescharacteristic
147C23×C11#12111yescharacteristic
148C23×C11#12711yescharacteristic
149C23×C11C2×SD1612yes—
150C23×C11AGL(1,ℤ/8)12yes—
151D4×C11—42no—
152D4×C11—81no—
153D4×C11—82no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183Dic22—42no—
184Dic22—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×#123—22no—
188C2×C22⋊Q8—111no—
189C2×#121C2×D1111yescharacteristic
190C22×C4⋊C4C2×D1111yescharacteristic
191#483—222no—
192#483—222no—
193#483—221no—
194#481—221no—
195#465—222no—
196#450—221no—
197#448—221no—
198C2×#106—221no—
199C2×#103—221no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8—111no—
202#399—22no—
203#390—21no—
204#384—21no—
205#380—111no—
206C4×C22⋊C4C2×D1111yescharacteristic
207#342—222no—
208#340—222no—
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—84no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39211yescharacteristic
223C22×C11#45012yes—
224C22×C11#46012yes—
225C22×C11#49211yescharacteristic
226C22×C11#49611yescharacteristic
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11—81no—
233C4×C11#45812yes—
234Dic11—81no—
235Dic11—81no—
236Dic11—161no—
237C22×Q8—111no—
238C22×D4—21no—
239C22×D4C22⋊D1111yescharacteristic
240C23×C4—21no—
241C23×C4C22×D1111yescharacteristic
242C2×SD16—222no—
243C22×C8—112no—
244C22×C8—221no—
245#123—44no—
246#123—44no—
247C22⋊Q8—221no—
248C22⋊Q8—221no—
249C22⋊Q8—221no—
250C22⋊Q8—221no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4C22⋊D1112yes—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C22⋊C4—24no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4C22⋊D1112yes—
271C2×C42—21no—
272#106—224no—
273#106—222no—
274#103—224no—
275#103—222no—
276#102—222no—
277C22⋊C8—112no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C22⋊C8—221no—
281#95—21no—
282#95—221no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—22no—
286C2×C11—21no—
287C2×C11—161no—
288C2×C11#200911yescharacteristic
289C2×C11#201411yescharacteristic
290C2×C11#202211yescharacteristic
291C24—21no—
292C24C2×C22⋊D1111yescharacteristic
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—442no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—441no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4#434111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—882no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—442no—
324C2×C8—442no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—48no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—442no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—22no—
338C22⋊C4—48no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—442no—
344C22⋊C4#432414yescomplemented
345C42—42no—
346C11#996011yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23#6698512yes—
354C23C2×#432412yes—
355C23#6699111yescharacteristic
356C23#6699311yescharacteristic
357C23#6700611yescharacteristic
358Q8—442no—
359Q8—442no—
360D4—42no—
361D4—81no—
362D4—81no—
363D4—82no—
364D4—81no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—82no—
380C2×C4—81no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4#6699011yescharacteristic
389C2×C4#6699011yescharacteristic
390C2×C4#6699211yescharacteristic
391C2×C4#6699211yescharacteristic
392C8—442no—
393C8—442no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1062268711yescharacteristic
407C22#1062268812yes—
408C22#1062268911yescharacteristic
409C22#1062283112yes—
410C22#1062283611yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—44no—
415C4—82no—
416C4—81no—
417C4—881no—
418C4—881no—
419C4—1761no—
420C4#1062266612yes—
421C2—22no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—161no—
426C2#1306967611yescharacteristic
427C2#1306970411yescharacteristic
428C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2501C2
socleC22×C11#392
prime radicalC2×C11×#121C22
hypercenter#2501D11
hypocenterC11#9960
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
3. #13069601C2semidirect
4. #13068702C2semidirect
6. #13066464C2semidirect
118. C11×C22⋊C4SD16semidirect
344. C22⋊C4#4324semidirect
346. C11#9960semidirect

Maximal subgroups

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

subgroupindex
#130793732
C2×#106225842
#130696012
#130687022
#130671842
#130664642
C11×#25012
#996011