Finite Group Databasebeta

← #11774667

Subgroups — #11774667

Order 1152.

484 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 65 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×#3798C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic, complemented
3#10590340C211yesmaximal, characteristic, complemented
4#10590032C212yesmaximal, complemented
5#10590029C212yesmaximal, complemented
6C2×#3798C411yescharacteristic
7C2×#3788—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C42×D3—21no—
10C4×#627C411yescharacteristic
11C4×#627C2211yescharacteristic
12C4×#626—21no—
13C4×#626—21no—
14C4×#625C411yescharacteristic
15C4×#625C2211yescharacteristic
16#63874C411yescharacteristic
17#63855—21no—
18C2×#3712—21no—
19#63777—21no—
20C4×#622C2212yes—
21C3×C4⋊(C3⋊C8)—21no—
22#63572C2212yes—
23C4×#235—61no—
24#4837—61no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×C4×D3—21no—
29C2×C3×C4×D3—21no—
30C2×C3×C4×D3—21no—
31C2×#627C2×C411yescharacteristic
32C2×#626—21no—
33C2×#625C2×C411yescharacteristic
34#3798—22no—
35#3798—22no—
36C2×#622—22no—
37#3788—24no—
38C32×C42D411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C3×C4×Dic3—21no—
43C3×C4×Dic3—21no—
44C3×C4×Dic3—21no—
45C2×C3×C3⋊C8—22no—
46#3724C2×C411yescharacteristic
47#3724C2×C411yescharacteristic
48Dic3⋊Dic3—21no—
49Dic3⋊Dic3—21no—
50#3722—21no—
51(C2×D3)⋊Dic3—21no—
52(C2×D3)⋊Dic3—21no—
53#3712—42no—
54#1489—91nomaximal, Sylow
55C2×#235—61no—
56C2×C3×C42—61no—
57C4×#67—61no—
58C4×#67—61no—
59C4×#67—61no—
60C4×#67—61no—
61#926—61no—
62C2×ΓL(1,𝔽25)—62no—
63C4×D12—61no—
64C4×D12—61no—
65#872—61no—
66#872—61no—
67C42×D3—21no—
68C42×D3—61no—
69C42×D3—61no—
70C4×Dic6—61no—
71C4×Dic6—61no—
72C3×C4⋊C8—61no—
73Dic3⋊C8—62no—
74C4⋊(C3⋊C8)—21no—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3×D3—21no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C4×C3⋊D3—21no—
84C4×C3⋊D3—21no—
85C4×C3⋊D3—21no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—22no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C3×C4×D3—24no—
92C3×C4×D3—42no—
93C3×C4×D3—41no—
94C3×C4×D3—41no—
95#627—21no—
96#627M1612yescomplemented
97#626—24no—
98#625—21no—
99#625M1612yescomplemented
100#622—24no—
101C3×C3⋊C8—42no—
102C4×#41—91no—
103#423—91no—
104C4×M16—91no—
105Q8⋊C8—92no—
106D4⋊C8—92no—
107C22×C3×C4—61no—
108C22×C3×C4—61no—
109C22×C3×C4—61no—
110C2×#67—61no—
111C2×#67—61no—
112#235—64no—
113#235—64no—
114C2×D12—61no—
115C2×C4×D3—21no—
116C2×C4×D3—21no—
117C2×C4×D3—21no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×Dic6—61no—
125C2×C3×C8—62no—
126C3×C42—21no—
127C3×C42—21no—
128C3×C42—61no—
129C3×C42—61no—
130C3×C42—61no—
131#217—61no—
132#217—61no—
133(C2×D3)⋊C4—61no—
134(C2×D3)⋊C4—61no—
135(C2×D3)⋊C4—61no—
136(C2×D3)⋊C4—61no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139Dic3⋊C4—61no—
140Dic3⋊C4—61no—
141Dic3⋊C4—61no—
142Dic3⋊C4—61no—
143C4×Dic3—21no—
144C4×Dic3—21no—
145C4×Dic3—21no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C2×C3⋊C8—22no—
153ΓL(1,𝔽25)—124no—
154C22×C32C2×C22⋊C411yescharacteristic
155C2×C3⋊D3—21no—
156C2×C3⋊D3—21no—
157C2×C3⋊D3—21no—
158C2×C3×D3—22no—
159C2×C3×D3—41no—
160C2×C3×D3—41no—
161C32×C4—21no—
162C32×C4#10412yes—
163C32×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—21no—
166C3⋊Dic3—21no—
167C3⋊Dic3C2×M1611yescharacteristic
168C3⋊Dic3C2×M1611yescharacteristic
169C3×Dic3—22no—
170C3×Dic3—41no—
171C3×Dic3—41no—
172C2×#41—91no—
173C2×M16—181no—
174C2×M16—181no—
175C4×Q8—91no—
176C4×Q8—91no—
177C4×D4—91no—
178C4×D4—91no—
179C4×D4—181no—
180C4×D4—181no—
181#117—91no—
182#117—181no—
183C2×C42—61no—
184C2×C42—91no—
185C4⋊C8—61no—
186C4⋊C8—92no—
187#97—181no—
188C4×C8—92no—
189C23×C3—61no—
190C22×D3—21no—
191C22×D3—61no—
192C22×D3—61no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—64no—
200C2×C3×C4—61no—
201C2×C3×C4—61no—
202C2×C3×C4—61no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205C2×C3×C4—122no—
206#67—62no—
207#67—64no—
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—
218D12—64no—
219C4×D3—24no—
220C4×D3—41no—
221C4×D3—41no—
222C4×D3—42no—
223C4×D3—62no—
224C4×D3—62no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—121no—
228C4×D3—121no—
229C4×D3—121no—
230C4×D3—121no—
231C4×D3—122no—
232C4×D3—122no—
233Dic6—62no—
234Dic6—62no—
235C3×C8—122no—
236C3⋊C8—42no—
237C2×C32#40711yescharacteristic
238C2×C32#41711yescharacteristic
239C2×C32C2×#10411yescharacteristic
240C3⋊D3—41no—
241C3×D3—42no—
242#41—182no—
243#41—182no—
244C2×Q8—91no—
245C2×D4—91no—
246C2×D4—181no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253M16—184no—
254M16—362no—
255C2×C8—62no—
256C2×C8—182no—
257C4⋊C4—91no—
258C4⋊C4—91no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C22⋊C4—181no—
262C22⋊C4—181no—
263C22⋊C4—181no—
264C42—61no—
265C42—61no—
266C42—61no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42GO+(4,𝔽2)11yescharacteristic
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—62no—
274C22×C3—121no—
275C22×C3—121no—
276C2×D3—22no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—121no—
284C2×D3—121no—
285C3×C4—22no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—62no—
294C3×C4—121no—
295C3×C4—121no—
296Dic3—22no—
297Dic3—41no—
298Dic3—41no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—61no—
303Dic3—62no—
304Dic3—121no—
305Dic3—121no—
306Dic3—121no—
307C32#148911yescharacteristic, complemented, Sylow
308C23—61no—
309C23—91no—
310Q8—92no—
311Q8—181no—
312D4—92no—
313D4—184no—
314D4—181no—
315C2×C4—64no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—122no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—181no—
328C2×C4—181no—
329C2×C4—182no—
330C2×C4D32⋊C411yescharacteristic
331C2×C4D32⋊C411yescharacteristic
332C2×C4C2×GO+(4,𝔽2)11yescharacteristic
333C8—122no—
334C8—184no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—122no—
342D3—42no—
343D3—122no—
344D3—122no—
345C22—62no—
346C22—121no—
347C22—121no—
348C22—181no—
349C22—181no—
350C22—181no—
351C22C2×D32⋊C411yescharacteristic
352C4—21no—
353C4—62no—
354C4—91no—
355C4—91no—
356C4—121no—
357C4—121no—
358C4—181no—
359C4—181no—
360C4#6373112yes—
361C4#6422411yescharacteristic
362C4#6422611yescharacteristic
363C3—21no—
364C3—21no—
365C2—122no—
366C2—361no—
367C2#1059330711yescharacteristic
368C2C2×#6373111yescharacteristic
369C2#1059336011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1489
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3788C2semidirect
3. #10590340C2semidirect
4. #10590032C2semidirect
5. #10590029C2semidirect
96. #627M16semidirect
99. #625M16semidirect
307. C32#1489semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
C4×#37882
#105903402
#105900322
#105900292
#14899