Finite Group Databasebeta

← #14654276

Subgroups — #14654276

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×#10622657C211yesmaximal, characteristic, complemented
3#13073108C211yesmaximal, characteristic
4#13068704C211yesmaximal, characteristic, complemented
5#13067183C211yesmaximal, characteristic
6#13066464C211yesmaximal, characteristic, complemented
7C11×#1996C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622840—21no—
14C2×#66899—21no—
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622661—22no—
18#10622659—21no—
19#10622657—22no—
20#10622657—22no—
21#10622656—21no—
22#10622581—21no—
23C2×#66871—21no—
24#10622571—22no—
25#10622552—21no—
26#10622549—21no—
27#10622287—22no—
28C11×#342—22no—
29#10622167—22no—
30#10622089—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C23×Dic11—21no—
35C22×D44D411yescharacteristic
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4D412yes—
46C2×C42×C11—21no—
47C2×#4325—22no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—24no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D412yes—
60C2×C4⋊Dic11D411yescharacteristic
61C22×C11⋊C8—21no—
62C22×C11⋊C8D412yes—
63C11×#95—21no—
64C11×#95—21no—
65#66899—24no—
66#66899—22no—
67C11⋊#95—24no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)D412yes—
72#66873—22no—
73#66872—22no—
74#66871—24no—
75#9958—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C23×D11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—42no—
81C22×C4×C11—22no—
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—21no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—82no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—42no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—42no—
114C42×C11—42no—
115#4325—82no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—84no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C2×C11⋊C8—42no—
129#3187—111no—
130C2×#484—111no—
131#2504—111no—
132#1996D1111yescharacteristic, complemented
133#1824—111no—
134#1519—111no—
135#1282—111no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139C23×C11#12111yescharacteristic
140C23×C11#12711yescharacteristic
141C23×C11#13512yes—
142C23×C11#13712yes—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—42no—
147Q8×C11—42no—
148Q8×C11—42no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
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—44no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—82no—
177C2×Dic11—82no—
178D44—42no—
179D44—81no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C2×C22⋊Q8C2×D1111yescharacteristic
183C2×#121—111no—
184C22×C4⋊C4—111no—
185#484—222no—
186#484—222no—
187#483—221no—
188#481—221no—
189#465—222no—
190#450—221no—
191#448—221no—
192C2×#107—221no—
193C2×#103—221no—
194C2×C22⋊C8—111no—
195C2×C22⋊C8—111no—
196#397—222no—
197#390—221no—
198#386—222no—
199#382—221no—
200#380C2×D1111yescharacteristic
201C4×C22⋊C4C2×D1111yescharacteristic
202#342—22no—
203#340—222no—
204#327—222no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11#39211yescharacteristic
214C22×C11#45212yes—
215C22×C11#46412yes—
216C22×C11#49511yescharacteristic
217C22×C11#49711yescharacteristic
218C2×D11—84no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—161no—
229C4×C11#45812yes—
230Dic11—82no—
231Dic11—81no—
232C22×Q8D4411yescharacteristic
233C22×D4—111no—
234C22×D4—221no—
235C23×C4—221no—
236C23×C4C22×D1111yescharacteristic
237C2×SD16—222no—
238C22×C8—112no—
239C22×C8—221no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244#121—221no—
245#121—221no—
246#121—221no—
247#121—221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4D4411yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—224no—
262C2×C22⋊C4C22⋊D1112yes—
263C2×C42—21no—
264#107—224no—
265#106—222no—
266#103—224no—
267#103—222no—
268#102—222no—
269C22⋊C8—112no—
270C22⋊C8—221no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273#95—21no—
274#95—21no—
275#95—224no—
276C2×C11—22no—
277C2×C11—21no—
278C2×C11—22no—
279C2×C11—21no—
280C2×C11#200811yescharacteristic
281C2×C11#201511yescharacteristic
282C2×C11#202211yescharacteristic
283D11—161no—
284C24—221no—
285C24C2×C22⋊D1111yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—42no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—442no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—442no—
295C2×D4—442no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4—882no—
306C22×C4C2×D4411yescharacteristic
307C22×C4#433911yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312SD16—882no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—442no—
316C2×C8—442no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—221no—
323C4⋊C4—222no—
324C4⋊C4—222no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—42no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—884no—
336C42—42no—
337C11#995811yescharacteristic, complemented, Sylow
338C23—41no—
339C23—41no—
340C23—442no—
341C23—442no—
342C23—441no—
343C23—442no—
344C23#6698311yescharacteristic
345C23#6699011yescharacteristic
346C23#6699311yescharacteristic
347C23#6699512yes—
348C23#6700312yes—
349Q8—42no—
350Q8—42no—
351D4—442no—
352D4—881no—
353D4—882no—
354D4—881no—
355D4—881no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—444no—
373C2×C4—441no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4#6693511yescharacteristic
379C2×C4#6693511yescharacteristic
380C2×C4#6693711yescharacteristic
381C2×C4#6693711yescharacteristic
382C8—442no—
383C8—442no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—884no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22#1062257311yescharacteristic
397C22#1062264112yes—
398C22#1062266012yes—
399C22#1062267211yescharacteristic
400C22#1062269911yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—161no—
408C4—882no—
409C4—881no—
410C4#1062235512yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—1761no—
416C2#1306966811yescharacteristic
417C2#1306970911yescharacteristic
418C2#1306974611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1996C2
socleC22×C11#392
prime radicalC2×#66983C22
hypercenter#1996D11
hypocenterC11#9958
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. C2×#10622657C2semidirect
4. #13068704C2semidirect
6. #13066464C2semidirect
7. C11×#1996C2semidirect
132. #1996D11semidirect
337. C11#9958semidirect

Maximal subgroups

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

subgroupindex
#130793692
C2×#106226572
#130731082
#130687042
#130671832
#130664642
C11×#19962
#995811