Finite Group Databasebeta

← #11774666

Subgroups — #11774666

Order 1152.

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

normal subgroups only

This group has 484 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
2C4×#3792C211yesmaximal, characteristic, complemented
3#10591120C211yesmaximal, characteristic, complemented
4#10590032C212yesmaximal, complemented
5#10590029C212yesmaximal, 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×#627C2211yescharacteristic
14#63902C411yescharacteristic
15C4×#625C2211yescharacteristic
16#63878—21no—
17C4×D3×Dic3—21no—
18#63838C411yescharacteristic
19#63777—21no—
20C4×#622C2212yes—
21#63572—21no—
22#63572C2212yes—
23C4×#237—61no—
24#5118—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—24no—
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—42no—
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—
73Dic3⋊C8—62no—
74Dic3⋊C8—62no—
75C23×C32C22⋊C411yescharacteristic
76C22×C3×D3—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—22no—
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—41no—
93C3×C4×D3—41no—
94#627—21no—
95#627M1612yescomplemented
96#625—21no—
97#625M1612yescomplemented
98D3×Dic3—24no—
99D3×Dic3—42no—
100#622—24no—
101C3×C3⋊C8—42no—
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—122no—
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—42no—
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×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—21no—
166C3⋊Dic3—21no—
167C3⋊Dic3#10412yes—
168C3⋊Dic3C2×M1611yescharacteristic
169C3⋊Dic3C2×M1611yescharacteristic
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—41no—
202C2×C3×C4—41no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4—61no—
206C2×C3×C4—121no—
207C2×C3×C4—121no—
208#67—24no—
209#67—62no—
210#67—62no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229C2×Dic3—122no—
230C4×D3—41no—
231C4×D3—41no—
232C4×D3—64no—
233C4×D3—122no—
234Dic6—62no—
235Dic6—62no—
236C3×C8—122no—
237C3⋊C8—42no—
238C2×C32—41no—
239C2×C32#40711yescharacteristic
240C2×C32#41711yescharacteristic
241C2×C32C2×#10411yescharacteristic
242C3×D3—42no—
243#41—182no—
244#41—182no—
245C2×Q8—91no—
246C2×D4—61no—
247C2×D4—91no—
248C22×C4—61no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—181no—
252C22×C4—181no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254M16—122no—
255M16—184no—
256C2×C8—62no—
257C2×C8—182no—
258C4⋊C4—61no—
259C4⋊C4—91no—
260C4⋊C4—91no—
261C4⋊C4—181no—
262C22⋊C4—61no—
263C22⋊C4—61no—
264C22⋊C4—181no—
265C42—61no—
266C42—91no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42—181no—
271C42—181no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—62no—
281C22×C3—121no—
282C22×C3—121no—
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—62no—
293C3×C4—121no—
294C3×C4—121no—
295Dic3—22no—
296Dic3—41no—
297Dic3—41no—
298Dic3—61no—
299Dic3—61no—
300Dic3—62no—
301Dic3—62no—
302Dic3—61no—
303Dic3—61no—
304Dic3—62no—
305Dic3—121no—
306Dic3—121no—
307Dic3—121no—
308C32#148911yescharacteristic, complemented, Sylow
309C23—61no—
310C23D32⋊C411yescharacteristic
311Q8—92no—
312Q8—181no—
313D4—64no—
314D4—92no—
315D4—181no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—121no—
326C2×C4—121no—
327C2×C4—184no—
328C2×C4—182no—
329C2×C4—181no—
330C2×C4—181no—
331C2×C4—362no—
332C2×C4D32⋊C411yescharacteristic
333C2×C4C2×GO+(4,𝔽2)11yescharacteristic
334C8—122no—
335C8—184no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—42no—
343C2×C3—42no—
344C2×C3—122no—
345D3—42no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—62no—
350C22—121no—
351C22—121no—
352C22C2×D32⋊C411yescharacteristic
353C4—21no—
354C4—62no—
355C4—91no—
356C4—91no—
357C4—92no—
358C4—121no—
359C4—121no—
360C4—181no—
361C4—181no—
362C4#6423611yescharacteristic
363C4#6423911yescharacteristic
364C3—21no—
365C3—21no—
366C2—41no—
367C2—122no—
368C2#1059330711yescharacteristic
369C2#1059332511yescharacteristic
370C2#1059349611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
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 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
3. #10591120C2semidirect
4. #10590032C2semidirect
5. #10590029C2semidirect
95. #627M16semidirect
97. #625M16semidirect
308. C32#1489semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
C4×#37922
#105911202
#105900322
#105900292
#14899