Finite Group Databasebeta

← #14654244

Subgroups — #14654244

Order 2816.

594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079369C211yesmaximal, characteristic
2C2×#10622349C211yesmaximal, characteristic
3#13073102C211yesmaximal, characteristic, complemented
4#13069451C211yesmaximal, characteristic
5#13068700C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622843—21no—
14#10622840—21no—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66885—21no—
18C2×#66882—21no—
19#10622661—22no—
20#10622659—21no—
21#10622656—21no—
22#10622599—22no—
23#10622590—21no—
24#10622581—21no—
25C2×#66870—22no—
26#10622556—22no—
27#10622349—22no—
28#10622349—22no—
29C11×#328—22no—
30#10622167—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C23×Dic11—21no—
35C22×D44D411yescharacteristic
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11D412yes—
47C2×#4325—22no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59C2×C4⋊Dic11D411yescharacteristic
60C2×C4×Dic11—21no—
61C22×C11⋊C8D412yes—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64C11×#95—21no—
65#66899—22no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66885—24no—
72#66882—24no—
73#66873—22no—
74#66872—22no—
75#66870—44no—
76#9953—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—42no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C22⋊Dic11—22no—
117C22⋊Dic11—22no—
118#4325—82no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4×Dic11—42no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—42no—
130#3187—111no—
131C2×#480—111no—
132#2503—111no—
133#1964—111no—
134#1823—111no—
135#1520D1111yescharacteristic, complemented
136#1282—111no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#12011yescharacteristic
140C23×C11#12111yescharacteristic
141C23×C11#12711yescharacteristic
142C23×C11#13512yes—
143C23×C11AGL(1,ℤ/8)12yes—
144C22×D11—41no—
145C22×D11—42no—
146C22×D11—81no—
147C22×D11—81no—
148Q8×C11—42no—
149Q8×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C22⋊D11—82no—
168C22⋊D11—81no—
169C22⋊D11—81no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—44no—
176C2×Dic11—42no—
177C2×Dic11—82no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180D44—42no—
181D44—42no—
182C8×C11—42no—
183C11⋊C8—42no—
184C2×C22⋊Q8C2×D1111yescharacteristic
185C2×#121—111no—
186C22×C4⋊C4—111no—
187#483—221no—
188#481—221no—
189#480—222no—
190#480—222no—
191#465—222no—
192#450—221no—
193#448—221no—
194C2×#107—221no—
195C2×#102—221no—
196C2×#99—222no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#400—222no—
200#391—221no—
201#382—221no—
202#381—222no—
203#380C2×D1111yescharacteristic
204C4×C22⋊C4—111no—
205#340—222no—
206#328—22no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11#39211yescharacteristic
216C22×C11#44912yes—
217C22×C11#46312yes—
218C22×C11#49511yescharacteristic
219C22×C11#49611yescharacteristic
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—162no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—161no—
230C4×C11#45812yes—
231Dic11—82no—
232Dic11—82no—
233Dic11—81no—
234C22×Q8D4411yescharacteristic
235C22×D4—111no—
236C22×D4—221no—
237C23×C4—221no—
238C23×C4C22×D1111yescharacteristic
239C2×SD16—222no—
240C22×C8—21no—
241C22×C8—112no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246#121—221no—
247#121—221no—
248#121—221no—
249#121—221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—112no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4D4411yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—112no—
263C2×C22⋊C4—221no—
264C2×C42—221no—
265#107—224no—
266#106—222no—
267#103—222no—
268#102—222no—
269#102—224no—
270#99—444no—
271C22⋊C8—21no—
272C22⋊C8—221no—
273C22⋊C8—221no—
274C22⋊C8C22⋊D1112yes—
275#95—21no—
276#95—224no—
277#95—224no—
278#95—221no—
279C2×C11—22no—
280C2×C11—21no—
281C2×C11—22no—
282C2×C11—21no—
283C2×C11#200911yescharacteristic
284C2×C11#201211yescharacteristic
285C2×C11#202211yescharacteristic
286D11—161no—
287C24—221no—
288C24D4×D1111yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—42no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—442no—
295C2×D4—441no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—441no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—221no—
306C22×C4—441no—
307C22×C4—442no—
308C22×C4—442no—
309C22×C4—441no—
310C22×C4C2×D4411yescharacteristic
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316SD16—882no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—222no—
320C2×C8—442no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—222no—
336C22⋊C4—222no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C42—442no—
340C11#995311yescharacteristic, complemented, Sylow
341C23—41no—
342C23—41no—
343C23—441no—
344C23—442no—
345C23—881no—
346C23—881no—
347C23#6693511yescharacteristic
348C23#6693711yescharacteristic
349C23#6696712yes—
350C23#6697212yes—
351C23#6699311yescharacteristic
352Q8—42no—
353Q8—81no—
354D4—442no—
355D4—442no—
356D4—881no—
357D4—881no—
358D4—882no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—441no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—444no—
378C2×C4—442no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4—882no—
382C2×C4#6693511yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6699011yescharacteristic
386C8—42no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—881no—
397C22—881no—
398C22—881no—
399C22—1762no—
400C22#1062242412yes—
401C22#1062243212yes—
402C22#1062257311yescharacteristic
403C22#1062278911yescharacteristic
404C22#1062280411yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—161no—
411C4—882no—
412C4—882no—
413C4—881no—
414C4#1062235512yes—
415C2—21no—
416C2—22no—
417C2—22no—
418C2—21no—
419C2—1761no—
420C2#1306967711yescharacteristic
421C2#1306969411yescharacteristic
422C2#1306974611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#392
prime radicalC2×#66983C22
hypercenter#1520D11
hypocenterC11#9953
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
3. #13073102C2semidirect
5. #13068700C2semidirect
6. #13066462C2semidirect
7. C11×#1520C2semidirect
135. #1520D11semidirect
340. C11#9953semidirect

Maximal subgroups

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

subgroupindex
#130793692
C2×#106223492
#130731022
#130694512
#130687002
#130664622
C11×#15202
#995311