Finite Group Databasebeta

← #11774629

Subgroups — #11774629

Order 1152.

647 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 647 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3832C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4C3×#4535C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#68237—32nomaximal
7C2×#3832C411yescharacteristic
8C32×C4×Q8C2211yescharacteristic
9Q8×C3⋊Dic3C411yescharacteristic
10#64102—21no—
11#64102C411yescharacteristic
12#64101—21no—
13#64101C411yescharacteristic
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C42×C3⋊D3—21no—
17C42×C3⋊D3C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×C4×C3⋊C8C2212yes—
20#63572—21no—
21#63557—21no—
22#63557—21no—
23#63555—21no—
24C4×#239—32no—
25C4×#239—61no—
26#4835—32no—
27#4685—32no—
28C3×Q8⋊C8—32no—
29#4535D312yescomplemented
30#4483—32no—
31#4459—32no—
32C2×C32×Q8C2×C411yescharacteristic
33#3832—22no—
34#3832—22no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47#3752—21no—
48#3752—21no—
49#3752—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#1488—91noSylow
60C2×#239—32no—
61C2×#239—61no—
62C3×C4×Q8—21no—
63C3×C4×Q8C2×D312yes—
64Q8×Dic3—32no—
65Q8×Dic3—61no—
66#893—32no—
67#893—61no—
68#893—62no—
69#893—62no—
70#892—32no—
71#892—61no—
72#892—62no—
73#892—62no—
74C4×D12—32no—
75C4×D12—61no—
76C4×D12—62no—
77C4×D12—62no—
78C42×D3—32no—
79C42×D3—61no—
80C42×D3—62no—
81C42×D3—62no—
82C3×C4⋊C8—32no—
83C3×C4×C8—32no—
84(C2×D3)⋊C8—62no—
85(C2×D3)⋊C8—62no—
86#815—62no—
87Dic3⋊C8—62no—
88C4⋊(C3⋊C8)C2×D312yes—
89C4×C3⋊C8C2×D312yes—
90C22×C3⋊D3—21no—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C32×Q8—21no—
93C32×Q8M1612yes—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C4⋊(C3⋊D3)—24no—
104C4⋊(C3⋊D3)—21no—
105C4⋊(C3⋊D3)M1612yes—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—21no—
108C4×C3⋊D3—21no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—41no—
111C4×C3⋊D3—42no—
112C4×C3⋊D3—42no—
113C3×C3⋊C8—42no—
114C3×C3⋊C8—42no—
115C4×#41—91no—
116#432—91no—
117#431—91no—
118Q8⋊C8—32no—
119D4⋊C8—92no—
120C2×C3×Q8—21no—
121C2×C3×Q8C4×D312yes—
122#239—64no—
123#239—64no—
124#239—64no—
125#239—64no—
126C2×D12—32no—
127C2×D12—61no—
128C2×D12—62no—
129C2×D12—62no—
130C2×C4×D3—32no—
131C2×C4×D3—32no—
132C2×C4×D3—32no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C3×C8—62no—
143C2×C3×C8—62no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4C4×D312yes—
148C3×C42—22no—
149C3×C42—22no—
150C3×C42—21no—
151C3×C42C22×D312yes—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154(C2×D3)⋊C4—62no—
155(C2×D3)⋊C4—62no—
156(C2×D3)⋊C4—62no—
157(C2×D3)⋊C4—62no—
158C4⋊Dic3—32no—
159C4⋊Dic3—61no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4×Dic3—32no—
163C4×Dic3—32no—
164C4×Dic3—32no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C2×C3⋊C8—22no—
173C2×C3⋊C8—22no—
174C22×C32C2×C22⋊C411yescharacteristic
175C2×C3⋊D3—21no—
176C2×C3⋊D3—22no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3—21no—
179C2×C3⋊D3—41no—
180C2×C3⋊D3—41no—
181C32×C4—22no—
182C32×C4—21no—
183C32×C4—41no—
184C32×C4C2×M1611yescharacteristic
185C32×C4C2×M1611yescharacteristic
186C32×C4#13512yes—
187C3⋊Dic3—21no—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—41no—
191C2×#41—91no—
192C4×Q8—91no—
193C4×Q8D3211yescharacteristic
194C4×D4—91no—
195C4×D4—91no—
196C4×D4—181no—
197C4×D4—181no—
198#117—91no—
199#117—181no—
200C2×C42—91no—
201C2×C42—181no—
202C4⋊C8—32no—
203C4⋊C8—181no—
204C22⋊C8—181no—
205C22⋊C8—181no—
206#97—181no—
207C4×C8—32no—
208C22×D3—32no—
209C22×D3—61no—
210C22×D3—62no—
211C22×D3—62no—
212C3×Q8—22no—
213C3×Q8—22no—
214C3×Q8—22no—
215C3×Q8ΓL(1,𝔽25)14yes—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4C2×C4×D312yes—
224C2×C3×C4D3×D412yes—
225C2×C3×C4D3×D412yes—
226C2×Dic3—32no—
227C2×Dic3—32no—
228C2×Dic3—32no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234D12—34no—
235D12—62no—
236D12—68no—
237D12—68no—
238D12—62no—
239D12—62no—
240C4×D3—68no—
241C4×D3—68no—
242C4×D3—62no—
243C4×D3—62no—
244C4×D3—62no—
245C4×D3—62no—
246C4×D3—62no—
247C4×D3—62no—
248C4×D3—122no—
249C4×D3—122no—
250C4×D3—122no—
251C4×D3—124no—
252C4×D3—124no—
253C4×D3—124no—
254C4×D3—122no—
255C4×D3—122no—
256C3×C8—122no—
257C3×C8—122no—
258C3⋊C8—42no—
259C3⋊C8—42no—
260C2×C32#40711yescharacteristic
261C2×C32#41611yescharacteristic
262C2×C32#42111yescharacteristic
263C3⋊D3—41no—
264C3⋊D3—42no—
265#41—182no—
266#41—182no—
267C2×Q8#62411yescharacteristic
268C2×D4—91no—
269C2×D4—181no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—181no—
274C22×C4—181no—
275C22×C4—181no—
276C2×C8—62no—
277C2×C8—62no—
278C4⋊C4—21no—
279C4⋊C4—91no—
280C4⋊C4—181no—
281C4⋊C4#62411yescharacteristic
282C22⋊C4—181no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C42—21no—
286C42—91no—
287C42—91no—
288C42—91no—
289C42—181no—
290C42—181no—
291C42C2×D3211yescharacteristic
292C22×C3—21no—
293C22×C3D3×C22⋊C412yes—
294C2×D3—64no—
295C2×D3—62no—
296C2×D3—64no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—121no—
301C2×D3—121no—
302C2×D3—122no—
303C2×D3—122no—
304C2×D3—122no—
305C2×D3—122no—
306C3×C4—24no—
307C3×C4—24no—
308C3×C4—22no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—22no—
312C3×C4—41no—
313C3×C4—42no—
314C3×C4—42no—
315C3×C4C2×ΓL(1,𝔽25)12yes—
316C3×C4D3×M1612yes—
317C3×C4#91612yes—
318C3×C4#91912yes—
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—62no—
323Dic3—62no—
324Dic3—121no—
325Dic3—122no—
326Dic3—122no—
327C32#148811yescharacteristic, complemented, Sylow
328C23—91no—
329C23—181no—
330Q8—21no—
331Q8#371212yes—
332D4—92no—
333D4—184no—
334D4—181no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—184no—
341C2×C4—181no—
342C2×C4—181no—
343C2×C4—182no—
344C2×C4—181no—
345C2×C4—361no—
346C2×C4—362no—
347C2×C4—362no—
348C2×C4C2×#62411yescharacteristic
349C2×C4#381111yescharacteristic
350C2×C4#381111yescharacteristic
351C8—122no—
352C8—122no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3#472612yes—
357C2×C3#480412yes—
358C2×C3#482112yes—
359D3—122no—
360D3—124no—
361D3—122no—
362D3—124no—
363C22—181no—
364C22—182no—
365C22—181no—
366C22—181no—
367C22—361no—
368C22—361no—
369C22#6397411yescharacteristic
370C4—22no—
371C4—21no—
372C4—41no—
373C4—181no—
374C4—181no—
375C4—181no—
376C4—361no—
377C4#6381811yescharacteristic
378C4C2×#371211yescharacteristic
379C4#6395012yes—
380C3—21no—
381C3#6823712yescomplemented
382C2—361no—
383C2—362no—
384C2#1059115911yescharacteristic
385C2#1059156011yescharacteristic
386C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10590297C2semidirect
3. #10590260C2semidirect
4. C3×#4535C2semidirect
5. #10589082C2semidirect
29. #4535D3semidirect
327. C32#1488semidirect
381. C3#68237semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105902972
#105902602
C3×#45352
#105890822
#682373