Finite Group Databasebeta

← #14756493

Subgroups — #14756493

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622838C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic
3C2×C4×#4318C211yesmaximal, characteristic
4#13071099C211yesmaximal, characteristic
5#13069309C214yesmaximal, complemented
6#13069295C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic
8#13068335C211yesmaximal, characteristic
9C2×C11×#391C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#391—22no—
18C11×#391C2212yes—
19C11×#391C2212yes—
20C2×C11×#95—22no—
21#10622838—24no—
22#10622838C418yescomplemented
23C2×#66899C2214yes—
24C2×#66899C2214yes—
25#10622823—22no—
26C4×Dic11⋊C4—22no—
27#10622541C2212yes—
28#10622541C2212yes—
29C4×#4318—24no—
30C2×#66867C2212yes—
31C2×C4×C11⋊C8C2212yes—
32#10622167C2214yes—
33#10622167C2214yes—
34C22×Q8×C11—21no—
35C22×Q8×C11—22no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11C2×C414yes—
41C22×Q8×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11—21no—
57#66979—22no—
58#66979—22no—
59#66979—22no—
60#66979C2×C414yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318—22no—
71C2×#4318C2×C414yes—
72C2×#4318D414yes—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2312yes—
75C11×#95—24no—
76C11×#95—24no—
77#66899—28no—
78#66899C2×C4116yescomplemented
79C11⋊#95—22no—
80C11⋊#95—22no—
81#66867—24no—
82C4×C11⋊C8—24no—
83#21094—111nomaximal, Sylow
84C24×C11C2×D411yescharacteristic
85C2×Q8×C11—24no—
86C2×Q8×C11—22no—
87C2×Q8×C11—28no—
88C2×Q8×C11—28no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—42no—
94C2×Q8×C11—44no—
95C2×Q8×C11—42no—
96C2×Q8×C11—44no—
97C2×Q8×C11C22×C414yes—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—44no—
107C22×C4×C11—42no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C42×C11—24no—
124C42×C11—21no—
125C42×C11—21no—
126C42×C11—21no—
127C42×C11—21no—
128C22⋊Dic11—24no—
129C22⋊Dic11—42no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C22×C414yes—
134Dic11⋊C4—44no—
135Dic11⋊C4—44no—
136C4×Dic11—24no—
137C4×Dic11—42no—
138#4318—28no—
139#4318—28no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C22×C414yes—
145C2×C11⋊C8C2×D414yes—
146C2×#419—111no—
147C2×#419—111no—
148C2×C4×M16—111no—
149#2296—111no—
150C2×#391D1111yescharacteristic
151#1935—114no—
152#1933—114no—
153#1736—111no—
154#1736—111no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11C4×D412yes—
158C23×C11#12112yes—
159C23×C11#12412yes—
160C23×C11C22×D411yescharacteristic
161Q8×C11—24no—
162Q8×C11—24no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11—48no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—48no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—48no—
176C2×C4×C11—42no—
177C2×C4×C11—44no—
178C2×C4×C11—84no—
179C2×C4×C11#11714yes—
180C2×C4×C11C4×D414yes—
181C2×C4×C11C4×D412yes—
182C2×C4×C11#12112yes—
183C2×C4×C11#12314yes—
184C2×C4×C11#12412yes—
185C2×C4×C11#12614yes—
186C2×C4×C11#13714yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×Dic11—24no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C11⋊C8—24no—
200C11⋊C8—24no—
201C23×Q8C2×D1111yescharacteristic
202C22×M16—111no—
203C22×M16—111no—
204C2×#117—111no—
205C2×#117—111no—
206C22×C4⋊C4C2×D1111yescharacteristic
207C22×C42C2×D1111yescharacteristic
208#419—118no—
209#419—224no—
210C2×#103—114no—
211C2×#103—114no—
212C4×M16—224no—
213C2×#97—112no—
214C2×C4×C8—112no—
215#391—22no—
216#391C2×D1112yes—
217#391C2×D1112yes—
218#389—112no—
219#389—112no—
220#385—222no—
221C4×C4⋊C4—222no—
222C2×#95—22no—
223#340—114no—
224#340—114no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—24no—
228C22×C11—24no—
229C22×C11#38814yes—
230C22×C11C2×C4×D411yescharacteristic
231C22×C11C2×#12111yescharacteristic
232C22×C11C2×#12411yescharacteristic
233C22×C11C2×#13712yes—
234C22×C11#57512yes—
235C4×C11—24no—
236C4×C11—42no—
237C4×C11—44no—
238C4×C11—82no—
239C4×C11#38814yes—
240C4×C11C2×#11711yescharacteristic
241C4×C11C2×C4×D411yescharacteristic
242C4×C11C2×#12311yescharacteristic
243C4×C11C2×#12611yescharacteristic
244Dic11—44no—
245Dic11—82no—
246C22×Q8—22no—
247C22×Q8—21no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8C4×D1114yes—
253C22×Q8C22×D1112yes—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4C22⋊D1112yes—
257C23×C4C22×D1111yescharacteristic
258C2×M16—114no—
259C2×M16—114no—
260C2×M16—222no—
261C2×M16—222no—
262C2×M16—222no—
263C2×M16—222no—
264C22×C8—112no—
265C22×C8—112no—
266#117—114no—
267#117—222no—
268#117—222no—
269#117—222no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4C22×D1112yes—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C42—22no—
281C2×C42—22no—
282C2×C42—221no—
283C2×C42—221no—
284C2×C42C22⋊D1112yes—
285C2×C42C22×D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
287#103—1116no—
288#103—228no—
289#97—224no—
290C4×C8—224no—
291#95—24no—
292#95—24no—
293#95—222no—
294#95—222no—
295C2×C11—24no—
296C2×C11C2×#38811yescharacteristic
297C2×C11C4×#13712yes—
298C2×C11#305612yes—
299C2×C11#313911yescharacteristic
300C2×C11#314011yescharacteristic
301C24C2×C22⋊D1111yescharacteristic
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—28no—
305C2×Q8—28no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8C2×C4×D1114yes—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—44no—
324C22×C4—42no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4C2×C4×D1112yes—
328C22×C4#433912yes—
329C22×C4D4×D1112yes—
330C22×C4#434112yes—
331C22×C4#434112yes—
332C22×C4#434112yes—
333C22×C4C2×C22⋊D1112yes—
334C22×C4C2×C22⋊D1112yes—
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C23×D1111yescharacteristic
337M16—228no—
338M16—228no—
339C2×C8—114no—
340C2×C8—114no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—114no—
349C4⋊C4—222no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—444no—
353C4⋊C4—444no—
354C22⋊C4—224no—
355C22⋊C4—442no—
356C42—24no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—224no—
362C42—442no—
363C11#2109411yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23C4×C22⋊D1112yes—
367C23#6698912yes—
368C23#6699212yes—
369C23C22×C22⋊D1111yescharacteristic
370Q8—24no—
371Q8—24no—
372Q8—42no—
373Q8—42no—
374Q8—48no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—48no—
382C2×C4—48no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—84no—
388C2×C4—224no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4#6693014yes—
395C2×C4#6693214yes—
396C2×C4(C22⋊D11)⋊C414yes—
397C2×C4#6693614yes—
398C2×C4C4×C22⋊D1112yes—
399C2×C4#6698912yes—
400C2×C4#6699212yes—
401C2×C4#6699514yes—
402C2×C4C22×C4×D1111yescharacteristic
403C2×C4C2×#433911yescharacteristic
404C2×C4C2×D4×D1111yescharacteristic
405C2×C4C2×#434111yescharacteristic
406C2×C4C2×#434111yescharacteristic
407C2×C4C2×#434111yescharacteristic
408C8—224no—
409C8—224no—
410C22—24no—
411C22—22no—
412C22—22no—
413C22—24no—
414C22#1062255814yes—
415C22C2×C4×C22⋊D1111yescharacteristic
416C22C2×#6698911yescharacteristic
417C22C2×#6699211yescharacteristic
418C22C2×#6699512yes—
419C22#1062335312yes—
420C4—24no—
421C4—44no—
422C4—42no—
423C4—82no—
424C4—444no—
425C4—882no—
426C4#1062255814yes—
427C4C2×#6693011yescharacteristic
428C4C2×#6693211yescharacteristic
429C4C2×(C22⋊D11)⋊C411yescharacteristic
430C4C2×#6693611yescharacteristic
431C2—24no—
432C2C2×#1062255811yescharacteristic
433C2C4×#6699512yes—
434C2#1307824212yes—
435C2#1307899611yescharacteristic
436C2#1307900211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#391D11
hypocenterC11#21094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
5. #13069309C2semidirect
6. #13069295C2semidirect
22. #10622838C4semidirect
78. #66899C2×C4semidirect
363. C11#21094semidirect

Maximal subgroups

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

subgroupindex
C2×#106228382
C2×C4×#43182
#130710992
#130693092
#130692952
#130683352
C2×C11×#3912
#2109411