Finite Group Databasebeta

← #11774668

Subgroups — #11774668

Order 1152.

492 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 63 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
3#10591060C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C2×#3805C411yescharacteristic
7C2×#3792—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10C2×C3×#208—21no—
11#67⋊Dic3—21no—
12#63957C411yescharacteristic
13C4×#627C411yescharacteristic
14#63902C2211yescharacteristic
15C4×#625C411yescharacteristic
16#63878—21no—
17C4×D3×Dic3—21no—
18#63838C2211yescharacteristic
19#63779C2212yes—
20C4⋊#622—21no—
21#63555—21no—
22#63553C2212yes—
23C4×#237—61no—
24Dic3×M16—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C3×#67—21no—
29C2×C3×C4×D3—21no—
30C2×#627C2×C411yescharacteristic
31C2×#625C2×C411yescharacteristic
32#3805—22no—
33#3805—22no—
34C2×D3×Dic3—21no—
35C2×D3×Dic3—21no—
36#3792—42no—
37C2×#622—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C3×#217—21no—
43C3×(C2×D3)⋊C4—21no—
44C3×Dic3⋊C4—21no—
45C3×C4×Dic3—21no—
46C3×#208—24no—
47C2×C3×C3⋊C8—22no—
48#3724C2×C411yescharacteristic
49#3724C2×C411yescharacteristic
50Dic3⋊Dic3—21no—
51(C2×D3)⋊Dic3—21no—
52Dic32—21no—
53Dic32—21no—
54#1489—91nomaximal, Sylow
55C2×#237—61no—
56C2×C3×M16—61no—
57C3×C4×D4—61no—
58D4×Dic3—61no—
59C4×#67—21no—
60C4×#67—61no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—61no—
64C2×#208—21no—
65#892—61no—
66#887—61no—
67#67⋊C4—61no—
68#67⋊C4—61no—
69#877—61no—
70#877—61no—
71C42×D3—61no—
72C4×Dic6—61no—
73#815—62no—
74C8×Dic3—62no—
75C23×C32C22⋊C411yescharacteristic
76C22×C3×D3—21no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22×C411yescharacteristic
87C2×C3⋊Dic3C2×D411yescharacteristic
88C3×#67—24no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—21no—
92C3×C4×D3—42no—
93#627—21no—
94#627M1612yescomplemented
95#625—21no—
96#625M1612yescomplemented
97D3×Dic3—24no—
98D3×Dic3—41no—
99D3×Dic3—41no—
100#622—42no—
101C3×C3⋊C8—24no—
102C4×#41—91no—
103#423—91no—
104C4×M16—91no—
105Q8⋊C8—92no—
106D4⋊C8—92no—
107C2×C3×D4—61no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—61no—
111C2×#67—21no—
112C2×#67—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119#237—64no—
120#237—64no—
121C2×C4×D3—21no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×Dic6—61no—
125C3×M16—64no—
126C2×C3×C8—62no—
127C3×C4⋊C4—61no—
128C3×C22⋊C4—61no—
129C3×C22⋊C4—61no—
130C3×C42—61no—
131#217—21no—
132#217—61no—
133(C2×D3)⋊C4—21no—
134(C2×D3)⋊C4—61no—
135C4⋊Dic3—61no—
136Dic3⋊C4—21no—
137Dic3⋊C4—61no—
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—
151C4×Dic3—61no—
152C4×Dic3—61no—
153#208—24no—
154C2×C3⋊C8—22no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32C2×C22⋊C411yescharacteristic
159C2×C3×D3—22no—
160C2×C3×D3—41no—
161C2×C3×D3—41no—
162C32×C4—21no—
163C32×C4#10412yes—
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3C2×M1611yescharacteristic
167C3⋊Dic3C2×M1611yescharacteristic
168C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
169C3⋊Dic3#13711yescharacteristic
170C3×Dic3—22no—
171C3×Dic3—41no—
172C3×Dic3—41no—
173C2×#41—91no—
174C2×M16—61no—
175C2×M16—181no—
176C4×Q8—91no—
177C4×Q8—91no—
178C4×D4—61no—
179C4×D4—91no—
180C4×D4—91no—
181C4×D4—181no—
182#117—91no—
183#117—181no—
184C2×C42—91no—
185C2×C42—181no—
186C4⋊C8—92no—
187C4⋊C8—181no—
188#97—181no—
189C4×C8—92no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—61no—
193C22×D3—21no—
194C3×D4—64no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—42no—
202C2×C3×C4—61no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4—122no—
206#67—24no—
207#67—62no—
208#67—62no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—64no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226C2×Dic3—121no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231C4×D3—42no—
232C4×D3—64no—
233C4×D3—121no—
234C4×D3—121no—
235Dic6—62no—
236Dic6—62no—
237C3×C8—64no—
238C3⋊C8—24no—
239C2×C32—41no—
240C2×C32#40711yescharacteristic
241C2×C32#41711yescharacteristic
242C2×C32C2×#10411yescharacteristic
243C3×D3—42no—
244#41—182no—
245#41—182no—
246C2×Q8—91no—
247C2×D4—61no—
248C2×D4—91no—
249C22×C4—61no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254C22×C4GO+(4,𝔽2)11yescharacteristic
255M16—64no—
256M16—362no—
257C2×C8—62no—
258C2×C8—182no—
259C4⋊C4—61no—
260C4⋊C4—91no—
261C4⋊C4—91no—
262C4⋊C4—181no—
263C22⋊C4—61no—
264C22⋊C4—61no—
265C22⋊C4—181no—
266C42—61no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42—91no—
271C42—181no—
272C42—181no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—62no—
282C22×C3—121no—
283C22×C3—121no—
284C2×D3—22no—
285C2×D3—41no—
286C2×D3—41no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—41no—
292C3×C4—62no—
293C3×C4—121no—
294C3×C4—121no—
295Dic3—22no—
296Dic3—41no—
297Dic3—41no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—61no—
304Dic3—61no—
305Dic3—61no—
306Dic3—62no—
307Dic3—121no—
308Dic3—121no—
309Dic3—121no—
310C32#148911yescharacteristic, complemented, Sylow
311C23—61no—
312C23D32⋊C411yescharacteristic
313Q8—92no—
314Q8—181no—
315D4—64no—
316D4—92no—
317D4—181no—
318C2×C4—22no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—122no—
327C2×C4—184no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—181no—
332C2×C4—361no—
333C2×C4—361no—
334C2×C4D32⋊C411yescharacteristic
335C2×C4C2×GO+(4,𝔽2)11yescharacteristic
336C8—64no—
337C8—362no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—42no—
345C2×C3—42no—
346C2×C3—122no—
347D3—42no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—62no—
352C22—121no—
353C22—121no—
354C22C2×D32⋊C411yescharacteristic
355C4—21no—
356C4—62no—
357C4—91no—
358C4—91no—
359C4—91no—
360C4—91no—
361C4—121no—
362C4—121no—
363C4—181no—
364C4—181no—
365C4#6374112yes—
366C3—21no—
367C3—21no—
368C2—41no—
369C2—122no—
370C2#1059330711yescharacteristic
371C2#1059331911yescharacteristic
372C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1489
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
3. #10591060C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
94. #627M16semidirect
96. #625M16semidirect
310. C32#1489semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
#105938052
#105910602
#105900312
#105900302
#14899