Finite Group Databasebeta

← #14654287

Subgroups — #14654287

Order 2816.

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

normal subgroups only

This group has 568 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#13079391C211yesmaximal, characteristic
2C2×#10622335C211yesmaximal, characteristic
3#13073094C211yesmaximal, characteristic
4#13069601C211yesmaximal, characteristic
5#13068707C211yesmaximal, characteristic
6#13067189C211yesmaximal, characteristic
7C11×#1282C211yesmaximal, characteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622729—22no—
16C2×#66882—21no—
17C2×#66880—21no—
18#10622563—22no—
19#10622548—21no—
20#10622542—21no—
21#10622352—21no—
22#10622352—21no—
23#10622335—21no—
24#10622335—21no—
25#10622335—22no—
26#10622335—22no—
27#10622274—22no—
28#10622189—22no—
29#10622165—22no—
30#10622105—22no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C22×Dic22D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11D412yes—
37C2×C11×C22⋊C4D412yes—
38C2×C42×C11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—24no—
49C2×C4⋊Dic11D412yes—
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56#66977—21no—
57#66977—21no—
58#66977—21no—
59#66977—21no—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—21no—
62C2×Dic44—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8D412yes—
67C11×#95—21no—
68C11⋊#95—24no—
69C11⋊#95—21no—
70#66882—22no—
71#66882—24no—
72#66880—22no—
73#66880—22no—
74#66880—24no—
75#9959—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—42no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—22no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—82no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4Q1614yescomplemented
106C42×C11—42no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—42no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—42no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—84no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic44—82no—
127#3189—111no—
128C2×#484—111no—
129#2502—111no—
130#1996—111no—
131#1824—111no—
132#1520—111no—
133#1282D1111yescharacteristic
134C23×C11—41no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137C23×C11#12111yescharacteristic
138C23×C11#12711yescharacteristic
139C23×C11C2×Q1612yes—
140C23×C11#13712yes—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×Dic11—42no—
155C2×Dic11—44no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163C2×Dic11—82no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169Dic22—42no—
170Dic22—42no—
171Dic22—42no—
172Dic22—81no—
173C8×C11—42no—
174C8×C11—42no—
175C2×C22⋊Q8—111no—
176C2×C22⋊Q8—111no—
177C22×C4⋊C4—111no—
178#484—222no—
179#484—221no—
180#484—221no—
181#484—222no—
182#467—222no—
183#451—221no—
184#451—221no—
185C2×#107—221no—
186C2×#103—221no—
187C2×C22⋊C8C2×D1111yescharacteristic
188C2×C22⋊C8C2×D1111yescharacteristic
189#398—222no—
190#391—221no—
191#385—222no—
192#384—221no—
193#380—111no—
194C4×C22⋊C4C2×D1111yescharacteristic
195#342—222no—
196#340—222no—
197#328—222no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11#39211yescharacteristic
207C22×C11#45112yes—
208C22×C11#46212yes—
209C22×C11#49411yescharacteristic
210C22×C11#49711yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—44no—
215C4×C11#45812yes—
216Dic11—81no—
217Dic11—82no—
218Dic11—81no—
219Dic11—81no—
220Dic11—81no—
221Dic11—161no—
222C22×Q8—111no—
223C22×Q8—111no—
224C23×C4—221no—
225C23×C4C22×D1111yescharacteristic
226C2×Q16—222no—
227C22×C8—21no—
228C22×C8D4412yes—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232C22⋊Q8—221no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—224no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4D4412yes—
253C2×C42—21no—
254#107—224no—
255#107—222no—
256#103—224no—
257#103—222no—
258#103—222no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8D4412yes—
263#95—21no—
264#95—224no—
265#95—221no—
266C2×C11—21no—
267C2×C11—22no—
268C2×C11—22no—
269C2×C11—21no—
270C2×C11#200811yescharacteristic
271C2×C11#201611yescharacteristic
272C2×C11#202211yescharacteristic
273C24C2×D4411yescharacteristic
274C2×Q8—221no—
275C2×Q8—221no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—442no—
279C2×Q8—442no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—221no—
283C22×C4—222no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4—882no—
291C22×C4C2×D4411yescharacteristic
292C22×C4C2×D4411yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C22×C4#434311yescharacteristic
297Q16—882no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—222no—
307C4⋊C4—221no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—884no—
316C22⋊C4—22no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—442no—
322C22⋊C4Dic4414yescomplemented
323C42—42no—
324C11#995911yescharacteristic, complemented, Sylow
325C23—41no—
326C23—41no—
327C23#6692711yescharacteristic
328C23#6693511yescharacteristic
329C23#6694811yescharacteristic
330C23C2×Dic4412yes—
331C23#6696212yes—
332Q8—442no—
333Q8—442no—
334Q8—442no—
335Q8—881no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—442no—
346C2×C4—444no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—882no—
354C2×C4—882no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4#6693511yescharacteristic
361C2×C4#6693511yescharacteristic
362C2×C4#6694811yescharacteristic
363C2×C4#6694811yescharacteristic
364C8—42no—
365C8—42no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1062228411yescharacteristic
375C22#1062231211yescharacteristic
376C22#1062232811yescharacteristic
377C22#1062235212yes—
378C22#1062246212yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—882no—
384C4—881no—
385C4—881no—
386C4—881no—
387C4—881no—
388C4—1761no—
389C4#1062235512yes—
390C2—22no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2#1306967211yescharacteristic
395C2#1306971811yescharacteristic
396C2#1306974811yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1282C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#1282D11
hypocenterC11#9959
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
105. C11×C22⋊C4Q16semidirect
322. C22⋊C4Dic44semidirect
324. C11#9959semidirect

Maximal subgroups

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

subgroupindex
#130793912
C2×#106223352
#130730942
#130696012
#130687072
#130671892
C11×#12822
#995911