Finite Group Databasebeta

← #14656319

Subgroups — #14656319

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622697C211yesmaximal, characteristic, complemented
3C2×#10622456C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×D88—21no—
10C2×#66927C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—22no—
16#10622701—22no—
17#10622701—22no—
18#10622697—22no—
19#10622697—22no—
20C2×#66873—21no—
21C2×#66873—22no—
22C2×#66872—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622456—22no—
26#10622456—22no—
27C11×#333—22no—
28#10622123—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8D412yes—
48C2×D88—24no—
49C2×D88—42no—
50C2×D88—42no—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66927D412yes—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63#66885—24no—
64(C2×D11)⋊C8—44no—
65#66873—24no—
66#66873—28no—
67#66872—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10267—111nomaximal, Sylow
73C23×D11—21no—
74C23×D11—41no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—42no—
97C2×D44—41no—
98C2×D44—42no—
99C2×D44—41no—
100C2×D44—82no—
101C2×D44SD1612yes—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—42no—
105C2×C4×D11—42no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—42no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129D88—48no—
130C2×#486—111no—
131C2×#476—111no—
132C2×#459—111no—
133#1954—111no—
134C2×#333D1111yescharacteristic, complemented
135C2×#331—111no—
136#1277—111no—
137C23×C11#12111yescharacteristic
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—42no—
141C22×D11—41no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—81no—
146C22×D11—81no—
147C22×D11—82no—
148Q8×C11—82no—
149Q8×C11—82no—
150C2×C4×C11—22no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11#13512yes—
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11#13711yescharacteristic
165C2×Dic11—41no—
166C2×Dic11—42no—
167D44—22no—
168D44—22no—
169D44—41no—
170D44—44no—
171D44—42no—
172D44—41no—
173D44—42no—
174D44—82no—
175D44—82no—
176D44—81no—
177D44—81no—
178D44—81no—
179D44—81no—
180C4×D11—82no—
181C4×D11—81no—
182C4×D11—81no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C22×D8—221no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×#127—111no—
190C2×C4×D4—111no—
191#486—222no—
192#486—222no—
193#476—222no—
194#476—222no—
195#459—222no—
196#459—222no—
197C2×#106—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—222no—
202C2×#102—221no—
203C2×#102—221no—
204C2×C22⋊C8—222no—
205C2×C4×C8—111no—
206#333—22no—
207#331—222no—
208C22×C11#39211yescharacteristic
209C22×C11#46312yes—
210C22×C11#46511yescharacteristic
211C22×C11#46811yescharacteristic
212C22×C11#47212yes—
213C2×D11—44no—
214C2×D11—42no—
215C2×D11—82no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—162no—
222C2×D11—162no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#44912yes—
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#49511yescharacteristic
232C4×C11#49611yescharacteristic
233Dic11—81no—
234C22×Q8—21no—
235C22×D4—111no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4—221no—
239C23×C4—221no—
240C2×D8—224no—
241C2×D8—442no—
242C2×D8—442no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—112no—
246C22×C8—221no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8D4412yes—
251#127—112no—
252#127—221no—
253#127—221no—
254#127—221no—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#102—224no—
272#102—228no—
273#102—224no—
274C22⋊C8—444no—
275C4×C8—221no—
276C4×C8—221no—
277C2×C11#167712yes—
278C2×C11#169712yes—
279C2×C11#200011yescharacteristic
280C2×C11#201211yescharacteristic
281C2×C11#201811yescharacteristic
282D11—82no—
283D11—162no—
284C24—221no—
285C24—441no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×D4—112no—
290C2×D4—221no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—222no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—442no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—442no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—882no—
308C22×C4—41no—
309C22×C4—221no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—441no—
314C22×C4#433911yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317D8—448no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—441no—
328C2×C8—441no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42C2×D4411yescharacteristic
338C42D4×D1111yescharacteristic
339C42D4×D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1026711yescharacteristic, complemented, Sylow
342C23—222no—
343C23—441no—
344C23—442no—
345C23—441no—
346C23—442no—
347C23—442no—
348C23—882no—
349C23—881no—
350C23—881no—
351C23—882no—
352C23#6693711yescharacteristic
353Q8—82no—
354Q8—82no—
355D4—222no—
356D4—222no—
357D4—442no—
358D4—441no—
359D4—442no—
360D4—441no—
361D4—444no—
362D4—882no—
363D4—882no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—82no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—882no—
376C2×C4#6693511yescharacteristic
377C2×C4#6693511yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4SD16×D1111yescharacteristic
380C2×C4#6696711yescharacteristic
381C2×C4#6696712yes—
382C2×C4#6697111yescharacteristic
383C2×C4#6697211yescharacteristic
384C2×C4#6697212yes—
385C2×C4#6698311yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699311yescharacteristic
388C8—42no—
389C8—81no—
390C8—442no—
391C8—442no—
392C22—442no—
393C22—444no—
394C22—882no—
395C22—881no—
396C22—881no—
397C22—882no—
398C22—882no—
399C22—882no—
400C22—1762no—
401C22—1762no—
402C22#1062236212yes—
403C22#1062242011yescharacteristic
404C22#1062242511yescharacteristic
405C22#1062243212yes—
406C22#1062257311yescharacteristic
407C4—21no—
408C4—21no—
409C4—82no—
410C4—881no—
411C4#1062241911yescharacteristic
412C4#1062242411yescharacteristic
413C4#1062242412yes—
414C4#1062278211yescharacteristic
415C4#1062278911yescharacteristic
416C4#1062280011yescharacteristic
417C4#1062280411yescharacteristic
418C2—882no—
419C2—1762no—
420C2#1306802812yes—
421C2#1306815212yes—
422C2#1306961811yescharacteristic
423C2#1306969411yescharacteristic
424C2#1306972411yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC23×C11#121
prime radicalC2×#10622456C2
hypercenterC2×#333D11
hypocenterC11#10267
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
2. C2×#10622697C2semidirect
4. #13069409C2semidirect
5. C2×#10622123C2semidirect
6. #13066450C2semidirect
7. C2×C11×#333C2semidirect
134. C2×#333D11semidirect
341. C11#10267semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226972
C2×#106224562
#130694092
C2×#106221232
#130664502
C2×C11×#3332
#1026711