Finite Group Databasebeta

← #11774295

Subgroups — #11774295

Order 1152.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#10593966C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C2×#3798C411yescharacteristic
7C2×#3787—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#872—21no—
10#63902C411yescharacteristic
11#63902C2211yescharacteristic
12#63881—21no—
13#63881—21no—
14C4×D3×Dic3—21no—
15#63874C411yescharacteristic
16#63838C411yescharacteristic
17#63838C2211yescharacteristic
18#63779C2212yes—
19C4⋊#622—21no—
20C3×C4⋊(C3⋊C8)—21no—
21#63557—21no—
22#63553C2212yes—
23#5522—61no—
24#4833—61no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×C4×D3—21no—
29C2×#627C2×C411yescharacteristic
30C2×#626—21no—
31C2×#625C2×C411yescharacteristic
32C2×D3×Dic3—21no—
33C2×D3×Dic3—21no—
34#3798—22no—
35#3798C814yescomplemented
36C2×#622—22no—
37#3787—42no—
38C32×C42D411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C3×(C2×D3)⋊C4—21no—
43C3×(C2×D3)⋊C4—21no—
44C3×Dic3⋊C4—21no—
45C3×Dic3⋊C4—21no—
46C3×C4×Dic3—21no—
47C2×C3×C3⋊C8—22no—
48#3724C2×C411yescharacteristic
49#3724C2×C411yescharacteristic
50#3722—21no—
51Dic32—21no—
52Dic32—21no—
53#1477—91nomaximal, Sylow
54C2×#235—61no—
55C3×#117—61no—
56C2×C4×Dic3—61no—
57#893—61no—
58#893—61no—
59#887—61no—
60#887—61no—
61#67⋊C4—61no—
62#67⋊C4—61no—
63#67⋊C4—61no—
64#67⋊C4—61no—
65#872—21no—
66#872—61no—
67C42×D3—61no—
68C42×D3—61no—
69C42×D3—61no—
70C3×C4⋊C8—61no—
71(C2×D3)⋊C8—62no—
72C8×Dic3—62no—
73C4⋊(C3⋊C8)—21no—
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3×D3—21no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22×C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3C2×C812yes—
86C4×C3⋊D3M1612yes—
87C2×C3×Dic3—21no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C3×C4×D3—24no—
91#627—21no—
92#627C2×C812yescomplemented
93#626—24no—
94#625—21no—
95#625C2×C812yescomplemented
96D3×Dic3—42no—
97D3×Dic3—41no—
98D3×Dic3—41no—
99#622—42no—
100C3×C3⋊C8—42no—
101C4×#41—91no—
102#431—91no—
103C2×C4⋊C8—91no—
104Q8⋊C8—92no—
105D4⋊C8—92no—
106C22×C3×C4—61no—
107C2×#67—61no—
108C2×#67—61no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111#235—64no—
112#235—64no—
113C2×D12—61no—
114C2×C4×D3—21no—
115C2×C4×D3—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—61no—
123C2×Dic6—61no—
124C2×C3×C8—62no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C22⋊C4—61no—
128C3×C22⋊C4—61no—
129C3×C42—21no—
130C3×C42—21no—
131C3×C42—61no—
132(C2×D3)⋊C4—21no—
133(C2×D3)⋊C4—21no—
134(C2×D3)⋊C4—61no—
135(C2×D3)⋊C4—61no—
136Dic3⋊C4—21no—
137Dic3⋊C4—21no—
138Dic3⋊C4—61no—
139Dic3⋊C4—61no—
140C4×Dic3—21no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—22no—
152C22×C32C2×C22⋊C411yescharacteristic
153C2×C3⋊D3—21no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3C22⋊C812yes—
156C2×C3×D3—22no—
157C2×C3×D3—41no—
158C2×C3×D3—41no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4C22⋊C812yes—
162C3⋊Dic3—21no—
163C3⋊Dic3C22×C811yescharacteristic
164C3⋊Dic3C2×M1611yescharacteristic
165C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
166C3⋊Dic3#13711yescharacteristic
167C3×Dic3—22no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C2×#41—91no—
171C22×C8—181no—
172C4×Q8—91no—
173C4×Q8—91no—
174C4×D4—91no—
175C4×D4—91no—
176C4×D4—181no—
177C4×D4—181no—
178#117—61no—
179#117—91no—
180C2×C42—91no—
181C2×C42—181no—
182C4⋊C8—61no—
183C4⋊C8—92no—
184C4⋊C8—181no—
185C22⋊C8—181no—
186C4×C8—92no—
187C23×C3—61no—
188C22×D3—21no—
189C22×D3—61no—
190C22×D3—61no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—64no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201#67—62no—
202#67—64no—
203#67—62no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215C2×Dic3—122no—
216D12—64no—
217C4×D3—24no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—62no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—121no—
225C4×D3—121no—
226C4×D3—122no—
227C4×D3—121no—
228C4×D3—121no—
229C4×D3—122no—
230C4×D3—121no—
231C4×D3—121no—
232Dic6—62no—
233Dic6—62no—
234C3×C8—122no—
235C3⋊C8—42no—
236C2×C32C2×C22⋊C811yescharacteristic
237C2×C32#41711yescharacteristic
238C2×C32#42111yescharacteristic
239C3⋊D3—22no—
240C3×D3—42no—
241#41—94no—
242#41—182no—
243C2×Q8—91no—
244C2×D4—91no—
245C2×D4—181no—
246C22×C4—61no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—181no—
251C22×C4—181no—
252C2×C8—62no—
253C2×C8—182no—
254C2×C8—362no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—91no—
258C4⋊C4—91no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—181no—
262C42—61no—
263C42—91no—
264C42—91no—
265C42—91no—
266C42—181no—
267C42—181no—
268C42GO+(4,𝔽2)11yescharacteristic
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—62no—
272C22×C3—121no—
273C22×C3—121no—
274C2×D3—22no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—62no—
291C3×C4—121no—
292C3×C4—121no—
293Dic3—22no—
294Dic3—41no—
295Dic3—41no—
296Dic3—61no—
297Dic3—61no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—61no—
304Dic3—62no—
305Dic3—121no—
306C32#147711yescharacteristic, complemented, Sylow
307C23—61no—
308C23—91no—
309Q8—92no—
310Q8—181no—
311D4—92no—
312D4—184no—
313D4—181no—
314C2×C4—61no—
315C2×C4—64no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—91no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—361no—
326C2×C4—361no—
327C2×C4—361no—
328C2×C4—362no—
329C2×C4D32⋊C411yescharacteristic
330C2×C4D32⋊C411yescharacteristic
331C2×C4C2×GO+(4,𝔽2)11yescharacteristic
332C8—122no—
333C8—362no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—122no—
341D3—42no—
342D3—122no—
343D3—122no—
344C22—62no—
345C22—92no—
346C22—121no—
347C22—121no—
348C22—181no—
349C22—181no—
350C22C2×D32⋊C411yescharacteristic
351C4—21no—
352C4—21no—
353C4—62no—
354C4—91no—
355C4—91no—
356C4—91no—
357C4—91no—
358C4—121no—
359C4—121no—
360C4—181no—
361C4D32⋊C812yes—
362C3—21no—
363C3—21no—
364C2—122no—
365C2—182no—
366C2C2×D32⋊C811yescharacteristic
367C2#1059331911yescharacteristic
368C2#1059338111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1477
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593726C2semidirect
3. #10590256C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
35. #3798C8semidirect
92. #627C2×C8semidirect
95. #625C2×C8semidirect
306. C32#1477semidirect

Maximal subgroups

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

subgroupindex
#105939662
#105937262
#105902562
#105900312
#105900302
#14779