Finite Group Databasebeta

← #11774727

Subgroups — #11774727

Order 1152.

828 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 151 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
1#10596019C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589349C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68176—34nomaximal
9C2×#3828—21no—
10C32×C4×D4C2211yescharacteristic
11#64149C411yescharacteristic
12#64147C411yescharacteristic
13C4×#638—21no—
14C2×#3743—21no—
15C2×C8×C3⋊D3—21no—
16#64104C411yescharacteristic
17#64097C411yescharacteristic
18#64094—21no—
19#64093—21no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C42×C3⋊D3C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24#63641—21no—
25C8×C3⋊Dic3—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28#5548—34no—
29#4837—34no—
30C4×D3×C8—34no—
31C3×D4⋊C8D314yescomplemented
32D4⋊(C3⋊C8)—34no—
33#4483—34no—
34#4459—34no—
35C2×C32×D4C2×C411yescharacteristic
36C22×C32×C4—21no—
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40#3828—42no—
41#3828—42no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3C2×C411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×#634—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#3743—42no—
65C8×C3⋊D3—24no—
66#1492—91noSylow
67C2×#235—64no—
68C3×C4×D4C2×D314yes—
69#940—34no—
70#938—34no—
71C4×#67—64no—
72C2×ΓL(1,𝔽25)—64no—
73C2×D3×C8—64no—
74#895—34no—
75#888—34no—
76#885—64no—
77#884—64no—
78C4×D12—34no—
79C42×D3—34no—
80C3×C4⋊C8C2×D314yes—
81C3×C4×C8C2×D314yes—
82Dic3⋊C8—64no—
83C8×Dic3—64no—
84C4⋊(C3⋊C8)—34no—
85C4×C3⋊C8—34no—
86C23×C32—21no—
87C22×C3⋊D3—21no—
88C22×C3⋊D3C22⋊C411yescharacteristic
89C32×D4—21no—
90C32×D4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97#638—42no—
98#638—42no—
99#638—42no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4⋊(C3⋊D3)—21no—
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)—42no—
107C4×C3⋊D3—21no—
108C4×C3⋊D3—21no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—41no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3D812yes—
113C4×C3⋊D3SD1612yes—
114#634—42no—
115C32×C8—22no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—22no—
118C3⋊(C3⋊C8)—41no—
119#532—91no—
120#423—91no—
121C2×C4×C8—91no—
122D4⋊C8—91no—
123D4⋊C8—91no—
124D4⋊C8—91no—
125D4⋊C8C3⋊D311yescharacteristic, complemented
126C2×C3×D4C4×D314yes—
127C22×C3×C4—24no—
128C2×#67—64no—
129C2×#67—64no—
130C2×#67—64no—
131#235—128no—
132#235—128no—
133C2×D12—34no—
134C2×D12—64no—
135C2×C4×D3—34no—
136C2×C4×D3—34no—
137C2×C4×D3—34no—
138C2×C4×D3—64no—
139C2×Dic6—64no—
140C2×C3×C8—24no—
141C2×C3×C8—24no—
142C3×C4⋊C4C4×D314yes—
143C3×C22⋊C4—24no—
144C3×C42C22×D314yes—
145#217—64no—
146(C2×D3)⋊C4—64no—
147(C2×D3)⋊C4—64no—
148C4⋊Dic3—34no—
149Dic3⋊C4—64no—
150C4×Dic3—34no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C2×C3⋊C8—64no—
154C2×C3⋊C8—64no—
155ΓL(1,𝔽25)—128no—
156D3×C8—616no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32—41no—
160C22×C32C2×C22⋊C411yescharacteristic
161C2×C3⋊D3—21no—
162C2×C3⋊D3—21no—
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—41no—
166C2×C3⋊D3#10212yes—
167C32×C4—21no—
168C32×C4—41no—
169C32×C4#13111yescharacteristic
170C32×C4#13111yescharacteristic
171C32×C4C2×D811yescharacteristic
172C32×C4C2×SD1611yescharacteristic
173C3⋊Dic3—21no—
174C3⋊Dic3—41no—
175C3⋊Dic3#10212yes—
176C3⋊Dic3#10412yes—
177C2×#41—181no—
178C2×M16—181no—
179C22×C8—181no—
180C4⋊Q8—91no—
181#127—91no—
182#124—181no—
183#121—91no—
184#121—91no—
185#121—181no—
186C4×D4—91no—
187C4×D4—181no—
188C4×D4C2×C3⋊D311yescharacteristic
189C2×C42—91no—
190C4⋊C8—91no—
191C4⋊C8—181no—
192C4⋊C8C2×C3⋊D311yescharacteristic
193C4×C8—91no—
194C4×C8—181no—
195C4×C8C2×C3⋊D311yescharacteristic
196C23×C3—24no—
197C22×D3—34no—
198C22×D3—64no—
199C3×D4—24no—
200C3×D4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4D3×D414yes—
206C2×C3×C4D3×D414yes—
207#67—128no—
208#67—128no—
209#67—128no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—34no—
213C2×Dic3—64no—
214D12—64no—
215D12—64no—
216D12—128no—
217C4×D3—38no—
218C4×D3—38no—
219C4×D3—68no—
220C4×D3—64no—
221C4×D3—64no—
222C4×D3—124no—
223C4×D3—124no—
224Dic6—128no—
225C3×C8—28no—
226C3×C8—44no—
227C3⋊C8—68no—
228C3⋊C8—124no—
229C2×C32—81no—
230C2×C32#40811yescharacteristic
231C2×C32C2×#10211yescharacteristic
232C2×C32C2×#10411yescharacteristic
233C3⋊D3—22no—
234C3⋊D3—81no—
235#41—362no—
236#41—362no—
237C2×Q8—181no—
238C2×D4—91no—
239C2×D4—181no—
240C2×D4—181no—
241C2×D4—181no—
242C2×D4—181no—
243C2×D4C4×C3⋊D311yescharacteristic
244C22×C4—21no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—181no—
249M16—362no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—184no—
253C2×C8—181no—
254C2×C8—181no—
255C4⋊C4—91no—
256C4⋊C4—181no—
257C4⋊C4C4×C3⋊D311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—181no—
260C22⋊C4—181no—
261C22⋊C4—181no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42C22×C3⋊D311yescharacteristic
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3D3×C22⋊C414yes—
270C2×D3—38no—
271C2×D3—64no—
272C2×D3—64no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—124no—
276C3×C4—24no—
277C3×C4—44no—
278C3×C4#90114yes—
279C3×C4#90714yes—
280C3×C4D3×D814yes—
281C3×C4D3×SD1614yes—
282Dic3—38no—
283Dic3—38no—
284Dic3—64no—
285Dic3—124no—
286C32#149211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—91no—
289C23—181no—
290Q8—362no—
291D4—21no—
292D4—21no—
293D4—181no—
294D4—181no—
295D4—362no—
296D4—362no—
297D4—362no—
298D4—362no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—91no—
307C2×C4—182no—
308C2×C4—181no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4C2×C4×C3⋊D311yescharacteristic
314C2×C4D4×C3⋊D311yescharacteristic
315C2×C4D4×C3⋊D311yescharacteristic
316C8—22no—
317C8—41no—
318C8—182no—
319C8—361no—
320C2×C3—84no—
321C2×C3#472714yes—
322C2×C3D3×#10214yes—
323C2×C3D3×#10414yes—
324D3—68no—
325D3—244no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—92no—
330C22—181no—
331C22—181no—
332C22—361no—
333C22—361no—
334C22—361no—
335C22C22⋊C4×C3⋊D311yescharacteristic
336C4—21no—
337C4—41no—
338C4—92no—
339C4—92no—
340C4—181no—
341C4—361no—
342C4#6411011yescharacteristic
343C4#6411611yescharacteristic
344C4D8×C3⋊D311yescharacteristic
345C4SD16×C3⋊D311yescharacteristic
346C3#6817614yescomplemented
347C2—81no—
348C2—182no—
349C2—721no—
350C2#1059242611yescharacteristic
351C2C3⋊D3×#10211yescharacteristic
352C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radical#10596019C2
cosocleC32×C42C23
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1492
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. C4×C8×C3⋊D3C2semidirect
4. C32×D4⋊C8C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589349C2semidirect
7. #10589325C2semidirect
31. C3×D4⋊C8D3semidirect
125. D4⋊C8C3⋊D3semidirect
286. C32#1492semidirect
346. C3#68176semidirect

Maximal subgroups

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

subgroupindex
#105960192
#105925362
C4×C8×C3⋊D32
C32×D4⋊C82
D4⋊(C3⋊(C3⋊C8))2
#105893492
#105893252
#681763