Finite Group Databasebeta

← #14656299

Subgroups — #14656299

Order 2816.

626 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×#10622307C211yesmaximal, characteristic
2C2×#10622462C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4#13069552C211yesmaximal, characteristic, complemented
5C2×#10622120C211yesmaximal, characteristic, complemented
6C2×#10622123C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×Dic44—21no—
9C22×#4314—21no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66885—22no—
17C2×#66885—21no—
18C2×#66880—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20#10622462—22no—
21#10622462—22no—
22#10622461—22no—
23#10622461—22no—
24#10622307—22no—
25#10622307—22no—
26#10622188—22no—
27#10622123—22no—
28#10622120—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×Dic22—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44C2×Dic44—24no—
45C2×Dic44—42no—
46C2×Dic44—42no—
47C2×#4314—24no—
48C2×#4314—42no—
49C2×#4314—42no—
50#66927—21no—
51#66927—21no—
52#66927—21no—
53#66927D412yes—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D412yes—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68#66885—28no—
69#66885—24no—
70#66880—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73#10263—111nomaximal, Sylow
74C23×D11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—41no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—42no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—42no—
93C2×D44—82no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—22no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22D812yes—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—42no—
131Dic44—48no—
132#4314—48no—
133C2×#486—111no—
134C2×#462—111no—
135C2×#460—111no—
136#1984—111no—
137C2×#332—111no—
138C2×#331—111no—
139#1277D1111yescharacteristic, complemented
140C23×C11#12111yescharacteristic
141C22×D11—42no—
142C22×D11—82no—
143C22×D11—81no—
144C22×D11—81no—
145C22×D11—82no—
146C2×C4×C11—22no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13712yes—
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167D44—42no—
168D44—42no—
169D44—44no—
170D44—82no—
171D44—82no—
172D44—81no—
173D44—81no—
174D44—81no—
175D44—81no—
176Dic22—22no—
177Dic22—22no—
178Dic22—41no—
179Dic22—41no—
180Dic22—42no—
181Dic22—42no—
182Dic22—81no—
183Dic22—81no—
184C8×C11—42no—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—81no—
188C22×Q16—221no—
189C22×SD16—221no—
190C2×C4⋊Q8—111no—
191C2×#127—111no—
192C2×C4×Q8—111no—
193#486—222no—
194#486—222no—
195#462—222no—
196#462—222no—
197#460—222no—
198#460—222no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×C4⋊C8C2×D1111yescharacteristic
202C2×#103—221no—
203C2×#102—221no—
204C2×#102—222no—
205C2×C4×C8C2×D1111yescharacteristic
206#336—222no—
207#332—222no—
208#331—222no—
209C22×C11#39211yescharacteristic
210C22×C11#46412yes—
211C22×C11#46611yescharacteristic
212C22×C11#46911yescharacteristic
213C22×C11#47112yes—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—82no—
217C2×D11—162no—
218C2×D11—162no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11#44711yescharacteristic
222C4×C11#44711yescharacteristic
223C4×C11#44911yescharacteristic
224C4×C11#44911yescharacteristic
225C4×C11#45212yes—
226C4×C11#49511yescharacteristic
227C4×C11#49711yescharacteristic
228Dic11—42no—
229Dic11—82no—
230Dic11—81no—
231C22×Q8—111no—
232C22×Q8—221no—
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×Q16—224no—
237C2×Q16—442no—
238C2×Q16—442no—
239C2×SD16—224no—
240C2×SD16—442no—
241C2×SD16—442no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—221no—
245C22×C8D4412yes—
246C4⋊Q8—112no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250#127—112no—
251#127—221no—
252#127—221no—
253#127—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×Q8—221no—
257C4×Q8—221no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C42—221no—
263C2×C42C22×D1111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8D4412yes—
269C4⋊C8D4412yes—
270#103—224no—
271#102—224no—
272#102—228no—
273C4×C8—21no—
274C4×C8—21no—
275C2×C11#168212yes—
276C2×C11#170212yes—
277C2×C11#199911yescharacteristic
278C2×C11#201511yescharacteristic
279C2×C11#201911yescharacteristic
280D11—162no—
281C24—441no—
282C2×Q8—112no—
283C2×Q8—221no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×Q8—222no—
287C2×Q8—221no—
288C2×Q8—221no—
289C2×Q8—441no—
290C2×Q8—441no—
291C2×Q8—441no—
292C2×Q8—441no—
293C2×Q8—441no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—882no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4C2×D4411yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4#434311yescharacteristic
313Q16—448no—
314SD16—448no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—441no—
325C2×C8—442no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—221no—
329C4⋊C4—222no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C42—441no—
335C42—441no—
336C42C2×D4411yescharacteristic
337C42C2×D4411yescharacteristic
338C42D4×D1111yescharacteristic
339C42D4×D1111yescharacteristic
340C11#1026311yescharacteristic, complemented, Sylow
341C23—442no—
342C23—881no—
343C23—881no—
344C23—882no—
345C23—882no—
346C23#6694811yescharacteristic
347Q8—222no—
348Q8—222no—
349Q8—441no—
350Q8—441no—
351Q8—442no—
352Q8—442no—
353Q8—881no—
354Q8—881no—
355D4—444no—
356D4—442no—
357D4—442no—
358D4—882no—
359D4—882no—
360D4—881no—
361D4—881no—
362D4—881no—
363D4—881no—
364C2×C4—22no—
365C2×C4—222no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—442no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6692711yescharacteristic
374C2×C4#6693511yescharacteristic
375C2×C4#6693511yescharacteristic
376C2×C4#6693511yescharacteristic
377C2×C4#6694811yescharacteristic
378C2×C4#6694811yescharacteristic
379C2×C4#6695712yes—
380C2×C4#6696212yes—
381C2×C4D8×D1111yescharacteristic
382C2×C4#6696711yescharacteristic
383C2×C4#6696711yescharacteristic
384C2×C4#6697211yescharacteristic
385C8—42no—
386C8—42no—
387C8—42no—
388C8—881no—
389C22—882no—
390C22—882no—
391C22—882no—
392C22—1762no—
393C22—1762no—
394C22#1062228411yescharacteristic
395C22#1062245812yes—
396C22#1062247811yescharacteristic
397C22#1062249611yescharacteristic
398C22#1062251112yes—
399C4—21no—
400C4—21no—
401C4—442no—
402C4—882no—
403C4—881no—
404C4#1062230911yescharacteristic
405C4#1062232811yescharacteristic
406C4#1062234612yes—
407C4#1062238611yescharacteristic
408C4#1062238611yescharacteristic
409C4#1062242411yescharacteristic
410C4#1062242411yescharacteristic
411C2—1762no—
412C2#1306806112yes—
413C2#1306818512yes—
414C2#1306961511yescharacteristic
415C2#1306971311yescharacteristic
416C2#1306973311yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenter#1277D11
hypocenterC11#10263
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. C2×#10622462C2semidirect
4. #13069552C2semidirect
5. C2×#10622120C2semidirect
7. C11×#1277C2semidirect
139. #1277D11semidirect
340. C11#10263semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106224622
C2×#106224612
#130695522
C2×#106221202
C2×#106221232
C11×#12772
#1026311