Finite Group Databasebeta

← #14719865

Subgroups — #14719865

Order 2816.

1386 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×#10622820C212yesmaximal
2#13066980C218yesmaximal, complemented
3#13066946C214yesmaximal, complemented
4C22×C11×C22⋊Q8C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—22no—
8C2×C11×C22⋊Q8—22no—
9C2×C11×C22⋊Q8—22no—
10C2×C11×C22⋊Q8—22no—
11C2×C11×C22⋊Q8C414yes—
12C2×C11×C22⋊Q8C2214yes—
13C22×C11×C4⋊C4C411yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C22⋊C4C412yes—
16C22×#4318—22no—
17#10622820—22no—
18#10622820—22no—
19#10622820C2214yes—
20#10622820C2214yes—
21C2×C22⋊(C11⋊C8)—22no—
22C2×C22⋊(C11⋊C8)C2214yes—
23#10622166C22116yescomplemented
24C25×C11C2×C411yescharacteristic
25C22×Q8×C11—22no—
26C22×Q8×C11—21no—
27C22×Q8×C11—21no—
28C22×Q8×C11—44no—
29C22×Q8×C11C2×C414yes—
30C23×C4×C11—44no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C412yes—
35C23×C4×C11D412yes—
36C23×C4×C11D412yes—
37C23×C4×C11D412yes—
38C23×C4×C11D412yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4C2×C418yes—
61C2×#4318—24no—
62C2×#4318—24no—
63C2×#4318—48no—
64C22×C11⋊C8—24no—
65C22⋊(C11⋊C8)—24no—
66C22⋊(C11⋊C8)—24no—
67C22⋊(C11⋊C8)—24no—
68C22⋊(C11⋊C8)C2318yes—
69#17397—111nomaximal, Sylow
70C24×C11—24no—
71C24×C11—42no—
72C24×C11—42no—
73C24×C11C22⋊C412yes—
74C24×C11C22⋊C411yescharacteristic
75C24×C11C22⋊C411yescharacteristic
76C24×C11C22×C411yescharacteristic
77C24×C11C22×C412yes—
78C2×Q8×C11—24no—
79C2×Q8×C11—24no—
80C2×Q8×C11—44no—
81C2×Q8×C11—48no—
82C2×Q8×C11—48no—
83C2×Q8×C11—44no—
84C22×C4×C11—28no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11—44no—
95C22×C4×C11—42no—
96C22×C4×C11—44no—
97C22×C4×C11—44no—
98C22×C4×C11C22⋊C411yescharacteristic
99C22×C4×C11C22⋊C412yes—
100C22×C4×C11C22⋊C412yes—
101C22×C4×C11C22⋊C412yes—
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C412yes—
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C414yes—
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2411yescharacteristic
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—28no—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—28no—
122#4318—48no—
123#4318—48no—
124C2×C11⋊C8—28no—
125C2×C11⋊C8—48no—
126C22×C22⋊Q8D1111yescharacteristic
127C2×#407—112no—
128#1472—118no—
129#1463—114no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—24no—
134C23×C11—24no—
135C23×C11—24no—
136C23×C11—22no—
137C23×C11—24no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—42no—
143C23×C11—41no—
144C23×C11—416no—
145C23×C11#10114yes—
146C23×C11C2×C22⋊C412yes—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11C2×C22⋊C412yes—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11C23×C411yescharacteristic
151Q8×C11—48no—
152Q8×C11—48no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—28no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11#9914yes—
177C2×C4×C11C2×C22⋊C412yes—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C22×D412yes—
181C11⋊C8—48no—
182C23×Q8Dic1111yescharacteristic
183C24×C4C2×D1111yescharacteristic
184C22×M16—222no—
185C2×C22⋊Q8—22no—
186C2×C22⋊Q8—22no—
187C2×C22⋊Q8—22no—
188C2×C22⋊Q8—22no—
189C2×C22⋊Q8Dic1114yes—
190C2×C22⋊Q8C2×D1114yes—
191C22×C4⋊C4Dic1111yescharacteristic
192C22×C4⋊C4C2×D1112yes—
193C22×C22⋊C4Dic1112yes—
194#407—114no—
195#407—114no—
196#407—222no—
197#407—222no—
198C2×C22⋊C8—114no—
199C2×C22⋊C8—222no—
200#324—1116no—
201C22×C11—28no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—44no—
214C22×C11—48no—
215C22×C11—48no—
216C22×C11—44no—
217C22×C11C2×#9912yes—
218C22×C11C2×#10112yes—
219C22×C11C2×#10114yes—
220C22×C11C22×C22⋊C411yescharacteristic
221C22×C11#56812yes—
222C4×C11—22no—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—44no—
226C4×C11—44no—
227C4×C11C2×#9914yes—
228C25C2×Dic1111yescharacteristic
229C22×Q8—22no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—44no—
233C22×Q8C2×Dic1114yes—
234C23×C4—44no—
235C23×C4C2×Dic1111yescharacteristic
236C23×C4C2×Dic1112yes—
237C23×C4C2×Dic1112yes—
238C23×C4C2×Dic1112yes—
239C23×C4C22⋊D1112yes—
240C23×C4C22⋊D1112yes—
241C23×C4C22⋊D1112yes—
242C23×C4C22⋊D1112yes—
243C23×C4C22×D1111yescharacteristic
244C23×C4C22×D1112yes—
245C2×M16—224no—
246C2×M16—224no—
247C2×M16—448no—
248C22×C8—224no—
249C22⋊Q8—24no—
250C22⋊Q8—24no—
251C22⋊Q8—24no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—24no—
255C22⋊Q8—24no—
256C22⋊Q8—24no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4C2×Dic1114yes—
263C2×C4⋊C4C2×Dic1114yes—
264C2×C4⋊C4C22×D1114yes—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4C2×Dic1118yes—
269C22⋊C8—118no—
270C22⋊C8—224no—
271C22⋊C8—224no—
272C22⋊C8—224no—
273C2×C11—22no—
274C2×C11—22no—
275C2×C11—22no—
276C2×C11—24no—
277C2×C11—42no—
278C2×C11#287911yescharacteristic
279C2×C11C22×#9911yescharacteristic
280C2×C11C22×#10111yescharacteristic
281C24—24no—
282C24—42no—
283C24—42no—
284C24C22⋊Dic1112yes—
285C24C22⋊Dic1111yescharacteristic
286C24C22⋊Dic1111yescharacteristic
287C24C22×Dic1111yescharacteristic
288C24C22×Dic1112yes—
289C2×Q8—24no—
290C2×Q8—24no—
291C2×Q8—48no—
292C2×Q8—44no—
293C2×Q8—48no—
294C2×Q8—44no—
295C22×C4—28no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—44no—
302C22×C4—44no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—42no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4C22⋊Dic1111yescharacteristic
310C22×C4C22⋊Dic1112yes—
311C22×C4C22⋊Dic1112yes—
312C22×C4C22⋊Dic1112yes—
313C22×C4C22⋊Dic1112yes—
314C22×C4C22⋊Dic1112yes—
315C22×C4C22⋊Dic1111yescharacteristic
316C22×C4C22×Dic1114yes—
317C22×C4C22×Dic1112yes—
318C22×C4C22×Dic1114yes—
319C22×C4C22×Dic1111yescharacteristic
320C22×C4C2×C22⋊D1112yes—
321C22×C4C2×C22⋊D1112yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C2×C22⋊D1112yes—
325C22×C4C2×C22⋊D1112yes—
326C22×C4C23×D1111yescharacteristic
327M16—448no—
328M16—448no—
329C2×C8—228no—
330C2×C8—448no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C22⋊C4—28no—
336C22⋊C4—28no—
337C11#1739711yescharacteristic, complemented, Sylow
338C23—22no—
339C23—22no—
340C23—22no—
341C23—24no—
342C23—24no—
343C23—24no—
344C23—22no—
345C23—24no—
346C23—41no—
347C23—41no—
348C23—42no—
349C23—41no—
350C23—42no—
351C23—41no—
352C23—416no—
353C23#6690014yes—
354C23C2×C22⋊Dic1112yes—
355C23C2×C22⋊Dic1111yescharacteristic
356C23C2×C22⋊Dic1112yes—
357C23C2×C22⋊Dic1111yescharacteristic
358C23C23×Dic1111yescharacteristic
359Q8—48no—
360Q8—48no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—28no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4#6689814yes—
385C2×C4C2×C22⋊Dic1112yes—
386C2×C4C2×C22⋊Dic1112yes—
387C2×C4C2×C22⋊Dic1112yes—
388C2×C4C22×C22⋊D1112yes—
389C8—448no—
390C22—28no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—44no—
403C22—48no—
404C22—48no—
405C22—44no—
406C22C2×#6689812yes—
407C22C2×#6690012yes—
408C22C2×#6690014yes—
409C22#1062335012yes—
410C22C22×C22⋊Dic1111yescharacteristic
411C4—22no—
412C4—22no—
413C4—22no—
414C4—44no—
415C4—44no—
416C4C2×#6689814yes—
417C2—22no—
418C2—22no—
419C2—22no—
420C2—24no—
421C2—42no—
422C2#1307706111yescharacteristic
423C2C22×#6689811yescharacteristic
424C2C22×#6690011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11#17397
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13066980C2semidirect
3. #13066946C2semidirect
23. #10622166C22semidirect
337. C11#17397semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130669802
#130669462
C22×C11×C22⋊Q82
#1739711