Finite Group Databasebeta

← #14657186

Subgroups — #14657186

Order 2816.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073612C211yesmaximal, characteristic
2#13069578C211yesmaximal, characteristic, complemented
3#13069375C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622121C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#67000—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622843—21no—
14C2×#66885—21no—
15C2×#66882—21no—
16#10622606—22no—
17#10622600—21no—
18#10622600—21no—
19#10622548C2211yescharacteristic
20C4×C4⋊Dic11C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#332—22no—
23#10622189—21no—
24#10622189—21no—
25#10622167—22no—
26#10622121—22no—
27C22×Q8×C11—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D412yes—
38C2×C42×C11C2311yescharacteristic
39#67000—42no—
40#67000—42no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95—21no—
63#66885—42no—
64#66882—42no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67#10416—111nomaximal, Sylow
68C23×D11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44D812yes—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109(C2×D11)⋊C4—44no—
110(C2×D11)⋊C4—44no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#2547—111no—
130#1990—111no—
131#1947—111no—
132#1802—111no—
133C2×#332D1111yescharacteristic, complemented
134C2×D4⋊C8—111no—
135#1279—111no—
136C23×C11#12011yescharacteristic
137C22×D11—22no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144Q8×C11—81no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12311yescharacteristic
158C2×C4×C11#12411yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×C4×C11#13711yescharacteristic
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—22no—
180D44—22no—
181D44—41no—
182D44—41no—
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—81no—
186C4×D11—81no—
187C8×C11—42no—
188C8×C11—81no—
189C11⋊C8—42no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191C2×#124—221no—
192C2×C4×D4—111no—
193C2×#107—221no—
194C2×C4⋊C8C2×D1111yescharacteristic
195C2×C4⋊C8C2×D1111yescharacteristic
196C2×#102—221no—
197C2×C4×C8—111no—
198#397—222no—
199#391—221no—
200#384—111no—
201#380—221no—
202#380—221no—
203C4×C4⋊C4—111no—
204#340—221no—
205#340—221no—
206#340—222no—
207#332—22no—
208D4⋊C8—222no—
209C22×C11#39411yescharacteristic
210C22×C11#44711yescharacteristic
211C22×C11#44911yescharacteristic
212C22×C11#45211yescharacteristic
213C22×C11#45211yescharacteristic
214C22×C11#45411yescharacteristic
215C22×C11#45611yescharacteristic
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11#46311yescharacteristic
227C4×C11#46411yescharacteristic
228C4×C11#46611yescharacteristic
229C4×C11#46811yescharacteristic
230C4×C11#48011yescharacteristic
231C4×C11#48211yescharacteristic
232C4×C11#48811yescharacteristic
233C4×C11#48911yescharacteristic
234Dic11—81no—
235Dic11—81no—
236Dic11—81no—
237Dic11—161no—
238C22×Q8—21no—
239C22×D4—111no—
240C23×C4—221no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—221no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248#124—442no—
249#124—442no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4D4412yes—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—222no—
264C2×C22⋊C4—221no—
265C2×C42—221no—
266C2×C42C22×D1111yescharacteristic
267#107—442no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8C22⋊D1112yes—
272#102—442no—
273C4×C8—221no—
274C4×C8—221no—
275#95—222no—
276#95—222no—
277#95—221no—
278C2×C11#162511yescharacteristic
279C2×C11#163811yescharacteristic
280C2×C11#164711yescharacteristic
281C2×C11#165211yescharacteristic
282C2×C11#203311yescharacteristic
283C2×C11#203811yescharacteristic
284C2×C11#204211yescharacteristic
285D11—82no—
286C24—221no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—112no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C22×C4—22no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4C2×D4411yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—222no—
320C2×C8—441no—
321C2×C8—441no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—442no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C22⋊C4—444no—
338C22⋊C4—444no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C42—441no—
342C42—441no—
343C42#433911yescharacteristic
344C42#434111yescharacteristic
345C42#434111yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C11#1041611yescharacteristic, complemented, Sylow
348C23—222no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23#6693511yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—222no—
361D4—222no—
362D4—441no—
363D4—441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—881no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4#6693611yescharacteristic
386C2×C4#6693811yescharacteristic
387C2×C4#6693911yescharacteristic
388C2×C4D8×D1111yescharacteristic
389C2×C4#6696511yescharacteristic
390C2×C4#6696711yescharacteristic
391C2×C4#6696711yescharacteristic
392C2×C4#6696811yescharacteristic
393C2×C4#6696911yescharacteristic
394C2×C4#6697111yescharacteristic
395C2×C4#6697211yescharacteristic
396C2×C4#6698311yescharacteristic
397C2×C4#6699111yescharacteristic
398C2×C4#6699211yescharacteristic
399C8—42no—
400C8—81no—
401C8—442no—
402C22—442no—
403C22—442no—
404C22—442no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22#1062236511yescharacteristic
410C22#1062236611yescharacteristic
411C22#1062238611yescharacteristic
412C22#1062239611yescharacteristic
413C22#1062242311yescharacteristic
414C22#1062242411yescharacteristic
415C22#1062257411yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—881no—
420C4—881no—
421C4—881no—
422C4—1761no—
423C4#1062238711yescharacteristic
424C4#1062239711yescharacteristic
425C4#1062240811yescharacteristic
426C4#1062241311yescharacteristic
427C4#1062277011yescharacteristic
428C4#1062277811yescharacteristic
429C4#1062278711yescharacteristic
430C4#1062279811yescharacteristic
431C2—882no—
432C2#1306770611yescharacteristic
433C2#1306778911yescharacteristic
434C2#1306785211yescharacteristic
435C2#1306788711yescharacteristic
436C2#1306979711yescharacteristic
437C2#1306983411yescharacteristic
438C2#1306985411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11#10416
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13069578C2semidirect
3. #13069375C2semidirect
6. #13066455C2semidirect
7. C2×C11×#332C2semidirect
133. C2×#332D11semidirect
347. C11#10416semidirect

Maximal subgroups

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

subgroupindex
#130736122
#130695782
#130693752
#130686172
C2×#106221212
#130664552
C2×C11×#3322
#1041611