Finite Group Databasebeta

← #11785333

Subgroups — #11785333

Order 1152.

564 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#3805C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C2×#63741C212yesmaximal
4#10591274C211yesmaximal, characteristic, complemented
5#10590074C212yesmaximal, complemented
6C2×#3805C2211yescharacteristic
7C2×#3792C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10C2×C3×C4⋊Dic3—21no—
11#67⋊Dic3—21no—
12#63957C2211yescharacteristic
13C2×Dic32C2212yes—
14C4×#627C411yescharacteristic, complemented
15#63902C411yescharacteristic, complemented
16C4×#625C411yescharacteristic, complemented
17#63878—21no—
18C4×D3×Dic3—21no—
19#63838C411yescharacteristic, complemented
20#63779—21no—
21C4⋊#622—21no—
22#63741—24no—
23#63579—21no—
24C4×#237—61no—
25Dic3×C4⋊C4—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C3×#67—21no—
30C22×C3×Dic3—22no—
31C2×C3×C4×D3—21no—
32C2×#627C2×C411yescharacteristic
33C2×#625C2×C411yescharacteristic
34#3805—21no—
35#3805—21no—
36#3805D412yes—
37#3805Q812yes—
38C2×D3×Dic3—21no—
39C2×D3×Dic3—21no—
40#3792—22no—
41#3792—22no—
42C2×#622—22no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C3×#217—21no—
48C3×(C2×D3)⋊C4—21no—
49C3×C4⋊Dic3—24no—
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52#3724C2×C411yescharacteristic
53#3724C2×C411yescharacteristic
54Dic3⋊Dic3—21no—
55(C2×D3)⋊Dic3—21no—
56Dic32—21no—
57Dic32—21no—
58Dic32—22no—
59Dic32—22no—
60#1806—91nomaximal, Sylow
61C2×#237—61no—
62C3×C4×D4—61no—
63C2×C3×C4⋊C4—61no—
64D4×Dic3—61no—
65C4×#67—21no—
66C4×#67—61no—
67C2×C4⋊Dic3—21no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—62no—
71C2×C4×Dic3—61no—
72#892—61no—
73#887—61no—
74#67⋊C4—61no—
75#67⋊C4—61no—
76#877—61no—
77#877—61no—
78C42×D3—61no—
79C4×Dic6—61no—
80C3⋊#95—62no—
81C23×C32C2×D411yescharacteristic
82C22×C3×D3—21no—
83C2×C32×C4—22no—
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22×C411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×Q811yescharacteristic
93C2×C3⋊Dic3#4111yescharacteristic
94C2×C3⋊Dic3#4111yescharacteristic
95C3×#67—22no—
96C3×#67—22no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×C4×D3—42no—
104#627—21no—
105#627C4⋊C412yescomplemented
106#625—21no—
107#625C4⋊C412yescomplemented
108D3×Dic3—22no—
109D3×Dic3—22no—
110D3×Dic3—42no—
111#622—42no—
112C4×#41—91no—
113#423—91no—
114C2×#104—92no—
115C4×C4⋊C4—91no—
116#339—92no—
117C2×C3×D4—61no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—61no—
121C22×C3×C4—62no—
122C2×#67—21no—
123C2×#67—61no—
124C22×Dic3—22no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131#237—62no—
132#237—62no—
133#237—62no—
134#237—62no—
135C2×C4×D3—21no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×Dic6—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—64no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—61no—
143C3×C42—61no—
144#217—21no—
145#217—61no—
146(C2×D3)⋊C4—21no—
147(C2×D3)⋊C4—61no—
148C4⋊Dic3—24no—
149C4⋊Dic3—61no—
150Dic3⋊C4—21no—
151Dic3⋊C4—61no—
152Dic3⋊C4—61no—
153Dic3⋊C4—61no—
154C4×Dic3—21no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—122no—
168C4×Dic3—122no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32#12111yescharacteristic
173C22×C32C22⋊Q811yescharacteristic
174C2×C3×D3—22no—
175C2×C3×D3—41no—
176C2×C3×D3—41no—
177C32×C4—21no—
178C32×C4#10412yescomplemented
179C3⋊Dic3—21no—
180C3⋊Dic3—21no—
181C3⋊Dic3C2×C4⋊C411yescharacteristic
182C3⋊Dic3#11711yescharacteristic
183C3⋊Dic3#12111yescharacteristic
184C3⋊Dic3C22⋊Q811yescharacteristic
185C3×Dic3—22no—
186C3×Dic3—44no—
187C3×Dic3—41no—
188C3×Dic3—41no—
189C2×#41—91no—
190C2×M16—92no—
191C4×Q8—91no—
192C4×Q8—91no—
193C4×D4—61no—
194C4×D4—91no—
195C4×D4—91no—
196C4×D4—181no—
197#117—91no—
198#117—181no—
199C2×C4⋊C4—61no—
200C2×C42—91no—
201C2×C42—92no—
202C2×C42—181no—
203C4⋊C8—181no—
204C4⋊C8—181no—
205#104—184no—
206#95—181no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—61no—
210C22×D3—21no—
211C3×D4—62no—
212C3×D4—62no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×C3×C4—61no—
223C2×C3×C4—64no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4—122no—
227#67—22no—
228#67—22no—
229#67—62no—
230#67—62no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—24no—
235C2×Dic3—42no—
236C2×Dic3—42no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C4×D3—42no—
260C4×D3—62no—
261C4×D3—62no—
262C4×D3—122no—
263Dic6—62no—
264Dic6—62no—
265C2×C32—21no—
266C2×C32—21no—
267C2×C32#38011yescharacteristic
268C2×C32C2×#10411yescharacteristic
269C2×C32#42111yescharacteristic
270C3×D3—42no—
271#41—92no—
272#41—92no—
273#41—181no—
274#41—181no—
275C2×Q8—91no—
276C2×D4—61no—
277C2×D4—91no—
278C22×C4—62no—
279C22×C4—61no—
280C22×C4—91no—
281C22×C4—91no—
282C22×C4—181no—
283C22×C4—181no—
284C22×C4GO+(4,𝔽2)11yescharacteristic
285M16—182no—
286M16—182no—
287C2×C8—182no—
288C4⋊C4—64no—
289C4⋊C4—61no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—181no—
293C22⋊C4—61no—
294C22⋊C4—61no—
295C22⋊C4—181no—
296C42—61no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—91no—
301C42—181no—
302C42—181no—
303C42—182no—
304C42—182no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—62no—
318C22×C3—121no—
319C22×C3—121no—
320C2×D3—22no—
321C2×D3—41no—
322C2×D3—41no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—41no—
327C3×C4—62no—
328C3×C4—121no—
329C3×C4—124no—
330C3×C4—121no—
331Dic3—22no—
332Dic3—41no—
333Dic3—44no—
334Dic3—41no—
335Dic3—61no—
336Dic3—61no—
337Dic3—61no—
338Dic3—61no—
339Dic3—61no—
340Dic3—61no—
341Dic3—61no—
342Dic3—61no—
343Dic3—62no—
344Dic3—121no—
345Dic3—121no—
346Dic3—121no—
347C32#180611yescharacteristic, complemented, Sylow
348C23—61no—
349C23C2×GO+(4,𝔽2)11yescharacteristic
350Q8—92no—
351Q8—181no—
352D4—62no—
353D4—62no—
354D4—92no—
355D4—181no—
356C2×C4—22no—
357C2×C4—61no—
358C2×C4—64no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—91no—
364C2×C4—91no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—122no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—362no—
375C2×C4—361no—
376C2×C4D32⋊C411yescharacteristic
377C2×C4D32⋊C411yescharacteristic
378C8—362no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—41no—
390C2×C3—41no—
391C2×C3—122no—
392D3—42no—
393C22—21no—
394C22—21no—
395C22—62no—
396C22—121no—
397C22—121no—
398C22D32⋊Q811yescharacteristic
399C22#6423011yescharacteristic
400C22C2×D32⋊C411yescharacteristic
401C4—21no—
402C4—62no—
403C4—91no—
404C4—91no—
405C4—91no—
406C4—91no—
407C4—124no—
408C4—121no—
409C4—121no—
410C4—181no—
411C4—181no—
412C4#6374112yescomplemented
413C3—21no—
414C3—21no—
415C2—21no—
416C2—21no—
417C2—122no—
418C2#1059338111yescharacteristic
419C2#1059340311yescharacteristic
420C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1806
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
4. #10591274C2semidirect
5. #10590074C2semidirect
14. C4×#627C4semidirect
15. #63902C4semidirect
16. C4×#625C4semidirect
19. #63838C4semidirect
105. #627C4⋊C4semidirect
107. #625C4⋊C4semidirect
178. C32×C4#104semidirect
347. C32#1806semidirect
412. C4#63741semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
#105938052
C2×#637412
#105912742
#105900742
#18069