Finite Group Databasebeta

← #14657645

Subgroups — #14657645

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic
2#13069419C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic
4#13068617C211yesmaximal, characteristic
5C2×#10622118C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#332C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66899—21no—
13C2×#66899—21no—
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17#10622700—22no—
18#10622700—22no—
19C2×#66873—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24C11×#332—22no—
25#10622189—21no—
26#10622118—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⋊Q8D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8D411yescharacteristic
46C22×C11⋊C8D411yescharacteristic
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55#66899—42no—
56#66899—42no—
57#66885—42no—
58(C2×D11)⋊C8—42no—
59(C2×D11)⋊C8—42no—
60#66873—24no—
61#66871—24no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10484—111nomaximal, Sylow
67C23×D11—21no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44SD1612yes—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—81no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8D812yes—
124C2×#474—111no—
125#1956—111no—
126#1954—111no—
127#1802—111no—
128C2×#334—111no—
129C2×#332D1111yescharacteristic, complemented
130#1296—111no—
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—81no—
142Q8×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11#12411yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168D44—22no—
169D44—22no—
170D44—41no—
171D44—41no—
172C4×D11—81no—
173C4×D11—81no—
174C4×D11—81no—
175C4×D11—81no—
176C8×C11—81no—
177C8×C11—81no—
178C11⋊C8—22no—
179C11⋊C8—42no—
180C11⋊C8—41no—
181C2×C4⋊Q8C2×D1111yescharacteristic
182C2×C4×D4—111no—
183#474—222no—
184#474—222no—
185C2×#107—221no—
186C2×C4⋊C8—111no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×C4⋊C8C2×D1111yescharacteristic
189C2×#103—221no—
190C2×#103—221no—
191C2×#102—221no—
192C2×#102—221no—
193C2×C22⋊C8—221no—
194C2×C22⋊C8—221no—
195C2×C4×C8—111no—
196#384—111no—
197#340—221no—
198#334—222no—
199#332—22no—
200C22×C11#39411yescharacteristic
201C22×C11#45911yescharacteristic
202C22×C11#46311yescharacteristic
203C22×C11#46511yescharacteristic
204C22×C11#47011yescharacteristic
205C22×C11#47111yescharacteristic
206C22×C11#47311yescharacteristic
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—82no—
217C4×C11#44811yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#45911yescharacteristic
220C4×C11#46311yescharacteristic
221C4×C11#46611yescharacteristic
222C4×C11#46911yescharacteristic
223C4×C11#48311yescharacteristic
224C4×C11#48511yescharacteristic
225Dic11—81no—
226Dic11—161no—
227C22×Q8—21no—
228C22×D4—111no—
229C23×C4—221no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—111no—
233C22×C8—111no—
234C22×C8—221no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C22⋊D1112yes—
239C4×D4—221no—
240C4×D4—221no—
241C4×D4—221no—
242C4×D4—221no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258#103—442no—
259#103—442no—
260#102—224no—
261#102—442no—
262C22⋊C8—442no—
263C22⋊C8—442no—
264C4×C8—221no—
265C4×C8—221no—
266C2×C11#166511yescharacteristic
267C2×C11#167911yescharacteristic
268C2×C11#168911yescharacteristic
269C2×C11#170311yescharacteristic
270C2×C11#203511yescharacteristic
271C2×C11#205211yescharacteristic
272C2×C11#205411yescharacteristic
273D11—82no—
274C24—221no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—112no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C22×C4—41no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4#433911yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—112no—
306C2×C8—221no—
307C2×C8—221no—
308C2×C8—221no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8—222no—
312C2×C8—441no—
313C2×C8—441no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—881no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C42#433911yescharacteristic
328C42D4×D1111yescharacteristic
329C42#434111yescharacteristic
330C42C2×C22⋊D1111yescharacteristic
331C11#1048411yescharacteristic, complemented, Sylow
332C23—222no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23#6693711yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—222no—
345D4—222no—
346D4—441no—
347D4—441no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4—881no—
363C2×C4#6693611yescharacteristic
364C2×C4#6693711yescharacteristic
365C2×C4#6693811yescharacteristic
366C2×C4D8×D1111yescharacteristic
367C2×C4#6696411yescharacteristic
368C2×C4SD16×D1111yescharacteristic
369C2×C4#6696711yescharacteristic
370C2×C4#6696811yescharacteristic
371C2×C4#6696911yescharacteristic
372C2×C4#6697111yescharacteristic
373C2×C4#6697211yescharacteristic
374C2×C4#6698211yescharacteristic
375C2×C4#6699011yescharacteristic
376C2×C4#6699211yescharacteristic
377C8—81no—
378C8—81no—
379C8—222no—
380C8—442no—
381C8—441no—
382C22—442no—
383C22—442no—
384C22—442no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22—881no—
389C22#1062236711yescharacteristic
390C22#1062236811yescharacteristic
391C22#1062239911yescharacteristic
392C22#1062240011yescharacteristic
393C22#1062242011yescharacteristic
394C22#1062242911yescharacteristic
395C22#1062257211yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—881no—
400C4—1761no—
401C4#1062238811yescharacteristic
402C4#1062239511yescharacteristic
403C4#1062241811yescharacteristic
404C4#1062242711yescharacteristic
405C4#1062276311yescharacteristic
406C4#1062277811yescharacteristic
407C4#1062278311yescharacteristic
408C4#1062280011yescharacteristic
409C2—882no—
410C2#1306796011yescharacteristic
411C2#1306803811yescharacteristic
412C2#1306810411yescharacteristic
413C2#1306819011yescharacteristic
414C2#1306981011yescharacteristic
415C2#1306991511yescharacteristic
416C2#1306992511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#332C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11#10484
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. #13069419C2semidirect
5. C2×#10622118C2semidirect
6. #13066500C2semidirect
7. C2×C11×#332C2semidirect
129. C2×#332D11semidirect
331. C11#10484semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130694192
#130694092
#130686172
C2×#106221182
#130665002
C2×C11×#3322
#1048411