Finite Group Databasebeta

← #11774541

Subgroups — #11774541

Order 1152.

936 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 163 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×D4×C3⋊D3C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589349C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68172—34nomaximal
9C2×D4×C3⋊D3C411yescharacteristic
10C22×C4×C3⋊D3—21no—
11C32×C4×D4C2211yescharacteristic
12D4×C3⋊Dic3C411yescharacteristic
13C4×#638—21no—
14C2×#3743—21no—
15#64102C411yescharacteristic
16C4⋊C4×C3⋊D3C411yescharacteristic
17#64090—21no—
18C22⋊C4×C3⋊D3—21no—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C42×C3⋊D3C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic, complemented
22C32×C4×C8C2211yescharacteristic, complemented
23#63647—21no—
24#63641—21no—
25#63641—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
27C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C4×D3×D4—34no—
29#4837—34no—
30#4685—34no—
31C3×D4⋊C8D314yescomplemented
32D4⋊(C3⋊C8)—34no—
33#4483—34no—
34#4459—34no—
35C23×C3⋊D3—21no—
36C2×C32×D4C2×C411yescharacteristic
37C22×C32×C4—21no—
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40D4×C3⋊D3—22no—
41D4×C3⋊D3—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—42no—
47C2×C4×C3⋊D3—42no—
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56#3757—21no—
57#3752—21no—
58#3752—21no—
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60#3750—21no—
61C4×C3⋊Dic3C2×C411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66#3743—42no—
67#1486—91noSylow
68C2×D3×D4—34no—
69C22×C4×D3—64no—
70C3×C4×D4C2×D314yes—
71D4×Dic3—34no—
72C4×#67—64no—
73C2×ΓL(1,𝔽25)—64no—
74#893—34no—
75D3×C4⋊C4—34no—
76#67⋊C4—64no—
77D3×C22⋊C4—64no—
78C4×D12—34no—
79C42×D3—34no—
80C3×C4⋊C8C2×D314yescomplemented
81C3×C4×C8C2×D314yescomplemented
82(C2×D3)⋊C8—64no—
83Dic3⋊C8—64no—
84Dic3⋊C8—64no—
85C4⋊(C3⋊C8)—34no—
86C4×C3⋊C8—34no—
87C23×C32—21no—
88C22×C3⋊D3—24no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3—42no—
92C22×C3⋊D3C22⋊C411yescharacteristic
93C32×D4—21no—
94C32×D4M1612yescomplemented
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101#638—24no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—42no—
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C4⋊(C3⋊D3)—21no—
108C4⋊(C3⋊D3)M1612yescomplemented
109C4×C3⋊D3—21no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—42no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—42no—
116C4×C3⋊D3D812yes—
117C4×C3⋊D3SD1612yes—
118C32×C8—41no—
119C32×C8—41no—
120C3⋊(C3⋊C8)—41no—
121C3⋊(C3⋊C8)—41no—
122C2×C4×D4—91no—
123#431—91no—
124#423—91no—
125D4⋊C8—91no—
126D4⋊C8—91no—
127D4⋊C8—91no—
128D4⋊C8C3⋊D311yescharacteristic, complemented
129C23×D3—64no—
130C2×C3×D4C4×D314yes—
131C22×C3×C4—24no—
132C2×#67—64no—
133C22×Dic3—64no—
134D3×D4—68no—
135D3×D4—68no—
136C2×D12—34no—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—34no—
140C2×C4×D3—64no—
141C2×C4×D3—64no—
142C2×C4×D3—64no—
143C2×C4×D3—128no—
144C2×C4×D3—128no—
145C2×C3×C8—24no—
146C2×C3×C8—24no—
147C3×C4⋊C4C4×D314yes—
148C3×C22⋊C4—24no—
149C3×C42C22×D314yes—
150#217—64no—
151(C2×D3)⋊C4—64no—
152(C2×D3)⋊C4—64no—
153C4⋊Dic3—34no—
154Dic3⋊C4—64no—
155C4×Dic3—34no—
156C4×Dic3—34no—
157C4×Dic3—34no—
158C2×C3⋊C8—64no—
159C2×C3⋊C8—64no—
160ΓL(1,𝔽25)—128no—
161C22×C32—22no—
162C22×C32—41no—
163C22×C32—41no—
164C22×C32C2×C22⋊C411yescharacteristic
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3—22no—
168C2×C3⋊D3—48no—
169C2×C3⋊D3—41no—
170C2×C3⋊D3—41no—
171C2×C3⋊D3#10212yes—
172C32×C4—21no—
173C32×C4—41no—
174C32×C4C2×M1611yescharacteristic
175C32×C4C2×M1611yescharacteristic
176C32×C4C2×D811yescharacteristic
177C32×C4C2×SD1611yescharacteristic
178C3⋊Dic3—21no—
179C3⋊Dic3—21no—
180C3⋊Dic3—41no—
181C3⋊Dic3#10212yes—
182C22×D4—91no—
183C23×C4—181no—
184C2×M16—181no—
185C4×D4—91no—
186C4×D4—91no—
187C4×D4—91no—
188C4×D4—181no—
189C4×D4—181no—
190C4×D4C2×C3⋊D311yescharacteristic
191C2×C4⋊C4—91no—
192C2×C22⋊C4—181no—
193C2×C42—91no—
194C4⋊C8—91no—
195C4⋊C8—181no—
196C4⋊C8—181no—
197C4⋊C8C2×C3⋊D311yescharacteristic, complemented
198C22⋊C8—181no—
199C4×C8—91no—
200C4×C8C2×C3⋊D311yescharacteristic, complemented
201C23×C3—24no—
202C22×D3—34no—
203C22×D3—616no—
204C22×D3—64no—
205C22×D3—128no—
206C22×D3—128no—
207C3×D4—24no—
208C3×D4ΓL(1,𝔽25)18yescomplemented
209C2×C3×C4—24no—
210C2×C3×C4—44no—
211C2×C3×C4—44no—
212C2×C3×C4C2×C4×D314yes—
213C2×C3×C4D3×D414yes—
214C2×C3×C4D3×D414yes—
215#67—616no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—34no—
219C2×Dic3—64no—
220C2×Dic3—128no—
221D12—38no—
222D12—64no—
223C4×D3—38no—
224C4×D3—38no—
225C4×D3—64no—
226C4×D3—64no—
227C4×D3—128no—
228C4×D3—124no—
229C4×D3—128no—
230C4×D3—124no—
231C4×D3—124no—
232C3×C8—44no—
233C3×C8—44no—
234C3⋊C8—124no—
235C3⋊C8—124no—
236C2×C32—42no—
237C2×C32#40711yescharacteristic
238C2×C32C2×#10211yescharacteristic
239C2×C32#42111yescharacteristic
240C3⋊D3—22no—
241C3⋊D3—42no—
242C24—181no—
243C2×D4—91no—
244C2×D4—181no—
245C2×D4—182no—
246C2×D4—182no—
247C2×D4C4×C3⋊D311yescharacteristic
248C22×C4—21no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4—181no—
256C22×C4—362no—
257C22×C4—362no—
258M16—362no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—181no—
262C2×C8—181no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4C4×C3⋊D311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—181no—
268C22⋊C4—181no—
269C22⋊C4—181no—
270C42—91no—
271C42—91no—
272C42—91no—
273C42C22×C3⋊D311yescharacteristic
274C22×C3—28no—
275C22×C3—44no—
276C22×C3—44no—
277C22×C3D3×C22⋊C414yes—
278C2×D3—38no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—68no—
282C2×D3—1232no—
283C2×D3—124no—
284C2×D3—124no—
285C3×C4—24no—
286C3×C4—44no—
287C3×C4C2×ΓL(1,𝔽25)14yes—
288C3×C4D3×M1614yes—
289C3×C4D3×D814yes—
290C3×C4D3×SD1614yes—
291Dic3—38no—
292Dic3—64no—
293Dic3—64no—
294Dic3—124no—
295C32#148611yescharacteristic, complemented, Sylow
296C23—21no—
297C23—91no—
298C23—184no—
299C23—181no—
300C23—362no—
301C23—362no—
302D4—21no—
303D4—92no—
304D4—184no—
305D4—181no—
306D4#374312yescomplemented
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—91no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—361no—
319C2×C4—362no—
320C2×C4—362no—
321C2×C4—362no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4C2×C4×C3⋊D311yescharacteristic
325C2×C4D4×C3⋊D311yescharacteristic
326C2×C4D4×C3⋊D311yescharacteristic
327C8—41no—
328C8—41no—
329C8—361no—
330C8—361no—
331C2×C3—48no—
332C2×C3#472614yes—
333C2×C3D3×#10214yes—
334C2×C3#482114yes—
335D3—68no—
336D3—128no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—92no—
341C22—181no—
342C22—181no—
343C22—182no—
344C22—368no—
345C22—361no—
346C22—361no—
347C22C22⋊C4×C3⋊D311yescharacteristic
348C4—21no—
349C4—41no—
350C4—92no—
351C4—181no—
352C4—181no—
353C4—361no—
354C4C2×#374311yescharacteristic
355C4M16×C3⋊D311yescharacteristic
356C4D8×C3⋊D311yescharacteristic
357C4SD16×C3⋊D311yescharacteristic
358C3#6817214yescomplemented
359C2—42no—
360C2—182no—
361C2—362no—
362C2#1059242511yescharacteristic
363C2C3⋊D3×#10211yescharacteristic
364C2#1059252011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC32×C42C23
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592536C2semidirect
3. #10592384C2semidirect
4. C32×D4⋊C8C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589349C2semidirect
7. #10589325C2semidirect
21. C32×C4⋊C8C22semidirect
22. C32×C4×C8C22semidirect
26. C4⋊(C3⋊(C3⋊C8))C22semidirect
27. C4×C3⋊(C3⋊C8)C22semidirect
31. C3×D4⋊C8D3semidirect
80. C3×C4⋊C8C2×D3semidirect
81. C3×C4×C8C2×D3semidirect
94. C32×D4M16semidirect
108. C4⋊(C3⋊D3)M16semidirect
128. D4⋊C8C3⋊D3semidirect
197. C4⋊C8C2×C3⋊D3semidirect
200. C4×C8C2×C3⋊D3semidirect
208. C3×D4ΓL(1,𝔽25)semidirect
295. C32#1486semidirect
306. D4#3743semidirect
358. C3#68172semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105925362
#105923842
C32×D4⋊C82
D4⋊(C3⋊(C3⋊C8))2
#105893492
#105893252
#681723