Finite Group Databasebeta

← #11783295

Subgroups — #11783295

Order 1152.

806 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64286C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590049C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—21no—
7C2×C22⋊#157—21no—
8#64286—22no—
9#64286C414yescomplemented
10C2×C4⋊#157C2212yes—
11C2×C4×#157—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×#208—21no—
14C2×#3724C412yescomplemented
15#63900—21no—
16#63900—21no—
17#63900C412yescomplemented
18#63900C2212yes—
19C2×#3712—21no—
20#63818—22no—
21#63818C414yescomplemented
22C2×#3710C2212yes—
23C2×D3×M16—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2×C412yes—
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3Q812yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C22×C3×Dic3—22no—
38C2×#624—22no—
39C2×#624—22no—
40C2×#624—44no—
41C22⋊#157—24no—
42C4⋊#157—22no—
43C4⋊#157C2×C414yescomplemented
44C4×#157—24no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×#208—24no—
48C2×C3×C3⋊C8—22no—
49#3724—22no—
50#3724C2×C414yes—
51#3712—24no—
52#3710—22no—
53#3710C2×C414yescomplemented
54#1736—91nomaximal, Sylow
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C22×C4×D3—62no—
58C2×C3×M16—61no—
59C2×C3×C4⋊C4—61no—
60C2×C4⋊Dic3—21no—
61C2×Dic3⋊C4—62no—
62C2×#208—21no—
63D3×M16—64no—
64D3×M16—64no—
65C2×ΓL(1,𝔽25)—62no—
66C2×D3×C8—62no—
67D3×C4⋊C4—62no—
68D3×C4⋊C4—62no—
69D3×C4⋊C4—62no—
70D3×C4⋊C4—62no—
71C23×C32C22⋊C411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3⋊D3C22⋊C412yes—
76C22×C3⋊D3C4⋊C412yes—
77C22×C3⋊D3C2×D411yescharacteristic
78C2×#157—24no—
79C2×#157—42no—
80C2×#157—42no—
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C412yes—
83C2×C32×C4C4⋊C412yes—
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3C4212yes—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C4⋊C412yes—
88C2×C3⋊Dic3C22×C411yescharacteristic
89C4×C3⋊D3C4212yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C22⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C22×C411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3C2×Q811yescharacteristic
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101#624—44no—
102#624—44no—
103C3×C3⋊C8—24no—
104C22×M16—91no—
105C2×#117—91no—
106C22×C4⋊C4—91no—
107#340—94no—
108C23×D3—61no—
109C23×D3—61no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—62no—
113C22×Dic3—22no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—61no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—128no—
135C3×M16—64no—
136C2×C3×C8—62no—
137C3×C4⋊C4—62no—
138C3×C4⋊C4—62no—
139C4⋊Dic3—22no—
140C4⋊Dic3—22no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143#208—24no—
144C2×C3⋊C8—22no—
145ΓL(1,𝔽25)—68no—
146D3×C8—64no—
147D3×C8—64no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32#9512yes—
151C22×C32C2×C22⋊C411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3—24no—
155C2×C3⋊D3—24no—
156C2×C3⋊D3#9512yes—
157C2×C3⋊D3C2×C22⋊C411yescharacteristic
158C2×C3⋊D3C2×C4⋊C411yescharacteristic
159C2×C3⋊D3AGL(1,ℤ/8)12yes—
160C2×C3⋊D3#13712yes—
161#157—44no—
162C32×C4#9512yes—
163C32×C4C2×C22⋊C411yescharacteristic
164C32×C4C2×C4⋊C411yescharacteristic
165C3⋊Dic3#9512yes—
166C3⋊Dic3C2×C4211yescharacteristic
167C3⋊Dic3C2×C4⋊C411yescharacteristic
168C3×Dic3—44no—
169C23×C4—91no—
170C23×C4—181no—
171C2×M16—61no—
172C2×M16—94no—
173C2×M16—181no—
174C2×M16—182no—
175C22×C8—92no—
176#117—94no—
177#117—182no—
178C2×C4⋊C4—61no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—92no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—181no—
184C2×C4⋊C4—181no—
185C2×C22⋊C4—181no—
186C2×C42—181no—
187C23×C3—21no—
188C23×C3—21no—
189C22×D3—61no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—61no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—62no—
196C22×D3—62no—
197C22×D3—64no—
198C22×D3—64no—
199C22×D3—122no—
200C22×D3—122no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—64no—
210C2×C3×C4—124no—
211C2×Dic3—24no—
212C2×Dic3—44no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C4×D3—62no—
222C4×D3—62no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—62no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—62no—
232C4×D3—62no—
233C4×D3—61no—
234C4×D3—61no—
235C4×D3—61no—
236C4×D3—61no—
237C4×D3—61no—
238C4×D3—61no—
239C4×D3—61no—
240C4×D3—61no—
241C4×D3—128no—
242C4×D3—128no—
243C3×C8—64no—
244C3⋊C8—24no—
245C2×C32—22no—
246C2×C32C2×#9511yescharacteristic
247C2×C32#41811yescharacteristic
248C2×C32#41911yescharacteristic
249C3⋊D3—22no—
250C3⋊D3#41712yes—
251C3⋊D3#42812yes—
252C24—91no—
253C22×C4—62no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—92no—
262C22×C4—92no—
263C22×C4—182no—
264C22×C4—182no—
265C22×C4—182no—
266C22×C4—364no—
267C22×C4GO+(4,𝔽2)11yescharacteristic
268M16—64no—
269M16—184no—
270C2×C8—62no—
271C2×C8—94no—
272C2×C8—182no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—94no—
276C4⋊C4—94no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C22⋊C4—184no—
280C42—184no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—41no—
288C22×C3—41no—
289C2×D3—62no—
290C2×D3—61no—
291C2×D3—61no—
292C2×D3—61no—
293C2×D3—61no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—62no—
303C2×D3—124no—
304C2×D3—124no—
305C2×D3—121no—
306C2×D3—121no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—124no—
314Dic3—44no—
315Dic3—62no—
316Dic3—62no—
317Dic3—61no—
318Dic3—61no—
319Dic3—61no—
320Dic3—61no—
321C32#173611yescharacteristic, complemented, Sylow
322C23—91no—
323C23—91no—
324C23—92no—
325C23—92no—
326C23—182no—
327C23—182no—
328C23D32⋊C411yescharacteristic
329C2×C4—64no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—92no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—92no—
344C2×C4—124no—
345C2×C4—184no—
346C2×C4—364no—
347C2×C4—364no—
348C2×C4—362no—
349C2×C4—362no—
350C2×C4D32⋊C412yes—
351C2×C4D32⋊C411yescharacteristic
352C2×C4#377312yes—
353C2×C4C2×GO+(4,𝔽2)11yescharacteristic
354C8—64no—
355C2×C3—24no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363D3—62no—
364D3—62no—
365D3—62no—
366D3—62no—
367D3—64no—
368D3—122no—
369C22—21no—
370C22—21no—
371C22—92no—
372C22—92no—
373C22—91no—
374C22—91no—
375C22—92no—
376C22—184no—
377C22—184no—
378C22—181no—
379C22—181no—
380C22#6373712yes—
381C22C2×D32⋊C411yescharacteristic
382C4—91no—
383C4—91no—
384C4—92no—
385C4—124no—
386C4—364no—
387C4#6373712yes—
388C4C2×D32⋊C411yescharacteristic
389C4C2×#377311yescharacteristic
390C3—21no—
391C3—21no—
392C2—22no—
393C2—92no—
394C2—92no—
395C2—182no—
396C2#1059331811yescharacteristic
397C2#1059332111yescharacteristic
398C2C2×#6373711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1736
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590049C2semidirect
9. #64286C4semidirect
14. C2×#3724C4semidirect
17. #63900C4semidirect
21. #63818C4semidirect
43. C4⋊#157C2×C4semidirect
53. #3710C2×C4semidirect
321. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#639002
C2×#638182
#105900492
#17369