Finite Group Databasebeta

← #11783406

Subgroups — #11783406

Order 1152.

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

normal subgroups only

This group has 790 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×#64283C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590052C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C412yes—
7C2×#3792—21no—
8#64283—22no—
9#64283C414yescomplemented
10C2×#3788C2212yes—
11C2×#3787—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×#208—21no—
14C2×#3724—21no—
15#63900—21no—
16#63900—21no—
17#63900C412yes—
18#63900C2212yes—
19C2×#3712C2212yes—
20#63818—22no—
21#63818C414yescomplemented
22C2×#3710—21no—
23C2×D3×M16—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3Q812yes—
35C2×C4×C3⋊D3C2311yescharacteristic
36C22×C3×Dic3—22no—
37C2×#624—22no—
38C2×#624—44no—
39C2×#624C2×C414yes—
40#3792—24no—
41C2×#622—22no—
42#3788—22no—
43#3788C2×C414yescomplemented
44#3787—24no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×#208—24no—
48C2×C3×C3⋊C8—22no—
49#3724—22no—
50#3724—22no—
51#3712—22no—
52#3712C2×C414yescomplemented
53#3710—24no—
54C2×#343—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⋊D3C4212yes—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C4⋊C412yes—
77C22×C3⋊D3C22×C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C412yes—
80C2×C32×C4C4⋊C412yes—
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C412yes—
84C2×C3⋊Dic3C4⋊C412yes—
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4×C3⋊D3C4212yes—
87C4×C3⋊D3C22⋊C412yes—
88C4×C3⋊D3C22⋊C412yes—
89C4×C3⋊D3C4⋊C412yes—
90C4×C3⋊D3C4⋊C412yes—
91C4×C3⋊D3C4⋊C412yes—
92C4×C3⋊D3C22×C411yescharacteristic
93C4×C3⋊D3C22×C411yescharacteristic
94C4×C3⋊D3C2×D411yescharacteristic
95C4×C3⋊D3C2×Q811yescharacteristic
96C2×C3×Dic3—24no—
97C2×C3×Dic3—44no—
98#624—44no—
99#624—44no—
100#622—24no—
101C3×C3⋊C8—24no—
102C22×M16—91no—
103C22×M16—91no—
104C22×C4⋊C4—91no—
105#343—94no—
106C23×D3—61no—
107C23×D3—61no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—62no—
111C22×Dic3—22no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—61no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—61no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—64no—
131C2×C4×D3—64no—
132C2×C4×D3—128no—
133C3×M16—64no—
134C2×C3×C8—62no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4—62no—
137C4⋊Dic3—22no—
138C4⋊Dic3—22no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141#208—24no—
142C2×C3⋊C8—22no—
143ΓL(1,𝔽25)—64no—
144ΓL(1,𝔽25)—64no—
145D3×C8—68no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32#9512yes—
149C22×C32C2×C22⋊C411yescharacteristic
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3⋊D3—24no—
153C2×C3⋊D3—24no—
154C2×C3⋊D3#9512yes—
155C2×C3⋊D3#10012yes—
156C2×C3⋊D3#10112yes—
157C2×C3⋊D3C2×C4211yescharacteristic
158C2×C3⋊D3C2×C4⋊C411yescharacteristic
159C32×C4#9512yes—
160C32×C4C2×C22⋊C411yescharacteristic
161C32×C4C2×C4⋊C411yescharacteristic
162C3⋊Dic3#9512yes—
163C3⋊Dic3C2×C22⋊C411yescharacteristic
164C3⋊Dic3C2×C4⋊C411yescharacteristic
165C3×Dic3—44no—
166C23×C4—92no—
167C23×C4—91no—
168C2×M16—61no—
169C2×M16—92no—
170C2×M16—94no—
171C2×M16—92no—
172C2×M16—94no—
173C2×M16—182no—
174C2×M16—182no—
175C2×M16—181no—
176C22×C8—181no—
177C22×C8—181no—
178C2×C4⋊C4—61no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4—181no—
183C2×C4⋊C4—181no—
184C23×C3—21no—
185C23×C3—21no—
186C22×D3—62no—
187C22×D3—61no—
188C22×D3—61no—
189C22×D3—62no—
190C22×D3—61no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—61no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—122no—
197C22×D3—122no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—64no—
207C2×C3×C4—124no—
208C2×Dic3—24no—
209C2×Dic3—44no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
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—61no—
231C4×D3—61no—
232C4×D3—61no—
233C4×D3—61no—
234C4×D3—61no—
235C4×D3—61no—
236C4×D3—61no—
237C4×D3—61no—
238C4×D3—128no—
239C4×D3—128no—
240C3×C8—64no—
241C3⋊C8—24no—
242C2×C32—22no—
243C2×C32C2×#9511yescharacteristic
244C2×C32C2×#10011yescharacteristic
245C2×C32C2×#10111yescharacteristic
246C3⋊D3—21no—
247C3⋊D3—21no—
248C3⋊D3#34314yescomplemented
249C24—91no—
250C22×C4—62no—
251C22×C4—94no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—92no—
258C22×C4—92no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—182no—
262C22×C4—364no—
263C22×C4GO+(4,𝔽2)11yescharacteristic
264M16—64no—
265M16—94no—
266M16—94no—
267M16—182no—
268M16—182no—
269M16—184no—
270C2×C8—62no—
271C2×C8—184no—
272C2×C8—184no—
273C2×C8—182no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—182no—
277C4⋊C4—182no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—41no—
285C22×C3—41no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—61no—
289C2×D3—61no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—61no—
295C2×D3—61no—
296C2×D3—62no—
297C2×D3—68no—
298C2×D3—68no—
299C2×D3—62no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—121no—
303C2×D3—121no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—124no—
311Dic3—44no—
312Dic3—62no—
313Dic3—62no—
314Dic3—61no—
315Dic3—61no—
316Dic3—61no—
317Dic3—61no—
318C32C2×#34311yescharacteristic, complemented, Sylow
319C23—91no—
320C23—91no—
321C23—92no—
322C23—92no—
323C23—182no—
324C23—182no—
325C23D32⋊C411yescharacteristic
326C2×C4—64no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—92no—
336C2×C4—91no—
337C2×C4—92no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—124no—
342C2×C4—364no—
343C2×C4—364no—
344C2×C4D32⋊C412yes—
345C2×C4D32⋊C411yescharacteristic
346C2×C4#377312yes—
347C2×C4C2×GO+(4,𝔽2)11yescharacteristic
348C8—64no—
349C8—184no—
350C2×C3—24no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—42no—
358D3—64no—
359D3—64no—
360D3—62no—
361D3—62no—
362D3—121no—
363D3—121no—
364C22—21no—
365C22—21no—
366C22—92no—
367C22—92no—
368C22—92no—
369C22—91no—
370C22—91no—
371C22—184no—
372C22—184no—
373C22—181no—
374C22—181no—
375C22#6373712yes—
376C22C2×D32⋊C411yescharacteristic
377C4—91no—
378C4—91no—
379C4—92no—
380C4—124no—
381C4#6373712yes—
382C4C2×D32⋊C411yescharacteristic
383C4C2×#377311yescharacteristic
384C3—21no—
385C3—21no—
386C2—22no—
387C2—94no—
388C2—181no—
389C2—181no—
390C2#1059331211yescharacteristic
391C2#1059331511yescharacteristic
392C2C2×#6373711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#343
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590052C2semidirect
9. #64283C4semidirect
21. #63818C4semidirect
43. #3788C2×C4semidirect
52. #3712C2×C4semidirect
248. C3⋊D3#343semidirect
318. C32C2×#343semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×#639002
C2×#638182
#105900522
C2×#3439