Finite Group Databasebeta

← #11857310

Subgroups — #11857310

Order 1152.

1267 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C2×#63817C212yesmaximal
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C2×C3×#803C211yesmaximal, characteristic, complemented
5#10591059C212yesmaximal, complemented
6#10590322C212yesmaximal, complemented
7#10590321C214yesmaximal, complemented
8#10590247C212yesmaximal, complemented
9#78516—31nomaximal
10#78486—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C4×#638C414yes—
14#64135C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C412yes—
16#64081C2212yes—
17C42×C3⋊D3C2212yes—
18C4×#634C412yes—
19C2×C3×#208C2212yes—
20C22×C3×C3⋊C8C2212yes—
21C2×#3712C2214yes—
22#63817C4116yescomplemented
23C2×#3710C2214yes—
24C3×#803C2211yescharacteristic
25C3×#803C2212yes—
26C3×#803C2211yescharacteristic
27C3×#803C2212yes—
28C3×C4×C3⋊C8C2212yes—
29#63555C2214yes—
30#63553C2214yes—
31C2×#907—32no—
32C2×#901—32no—
33C4×#235—31no—
34C4×#235—31no—
35C4×#235—61no—
36C3×C4×M16—31no—
37C2×C3×#97—31no—
38#5122—32no—
39#5101—32no—
40C4×#208D311yescharacteristic, complemented
41C2×#803D311yescharacteristic, complemented
42#4708—34no—
43#4707—32no—
44#4707—32no—
45D3×#97—32no—
46D3×#97—32no—
47#4689—34no—
48C22×C32×C4C2×C412yes—
49C22×C32×C4C2311yescharacteristic
50C2×#638C2×C412yes—
51#3828C2×C418yes—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
53C2×C4×C3⋊D3C2×C414yes—
54C2×C4×C3⋊D3C2312yes—
55C2×#634C2×C411yescharacteristic
56C32×C42C2×C412yes—
57C32×C42C2311yescharacteristic
58C32×C42C2311yescharacteristic
59#3757C2×C412yes—
60#3752C2×C414yes—
61C4⋊(C3⋊Dic3)C2×C412yes—
62#3750C2×C414yes—
63C4×C3⋊Dic3C2×C414yes—
64C4×C3⋊Dic3C2312yes—
65C3×#208C2×C418yescomplemented
66C2×C3×C3⋊C8C2×C418yescomplemented
67C2×C3×C3⋊C8C2312yes—
68C2×C3×C3⋊C8C2312yes—
69C2×C3×C3⋊C8C2314yes—
70#3712C2×C4116yescomplemented
71#3710C2×C4116yescomplemented
72#2875—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—32no—
77C22×C3×C8—32no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C2×D311yescharacteristic
81C4×#67—34no—
82C4×#67—34no—
83C4×#67—64no—
84#926—31no—
85#926—31no—
86#926—61no—
87C2×#208C2×D312yes—
88C22×C3⋊C8C2×D312yes—
89#907—316no—
90#901—316no—
91C2×ΓL(1,𝔽25)—34no—
92C2×ΓL(1,𝔽25)—34no—
93C2×D3×C8—34no—
94C2×D3×C8—34no—
95C4×D12—32no—
96C4×D12—32no—
97C4×D12—62no—
98#872—32no—
99#872—32no—
100#872—62no—
101C42×D3—32no—
102C42×D3—32no—
103C42×D3—62no—
104C4×Dic6—32no—
105C4×Dic6—32no—
106C4×Dic6—62no—
107C3×#97—31no—
108C3×#97—32no—
109C3×#97—31no—
110C3×#97—32no—
111C3×C4×C8—32no—
112#815—34no—
113#815—34no—
114C8×Dic3—34no—
115C8×Dic3—34no—
116#803C2×D312yes—
117#803C2×D311yescharacteristic
118#803C2×D311yescharacteristic
119#803C2×D312yes—
120C4×C3⋊C8C2×D312yes—
121C23×C32C22×C411yescharacteristic
122C22×C3⋊D3C22×C412yes—
123C2×C32×C4—42no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C22×C414yes—
128C2×C32×C4C2411yescharacteristic
129#638C4218yes—
130C2×C3⋊Dic3C22×C414yes—
131C2×C3⋊Dic3C22×C412yes—
132C4⋊(C3⋊D3)C4214yes—
133C4×C3⋊D3—44no—
134C4×C3⋊D3C22×C418yes—
135#634C4214yes—
136C3×C3⋊C8C22×C414yes—
137C3×C3⋊C8C22×C418yes—
138C3×C3⋊C8C22×C414yes—
139C2×#131—92no—
140C4×#41—91no—
141#405—94no—
142#405—92no—
143C4×M16—31no—
144C4×M16—92no—
145C2×#97—31no—
146C2×#97—92no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4C4×D312yes—
150C22×C3×C4C4×D312yes—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—32no—
154C2×#67—32no—
155C2×#67—62no—
156#235—38no—
157#235—38no—
158#235—68no—
159C2×D12—31no—
160C2×D12—31no—
161C2×D12—61no—
162C2×C4×D3—32no—
163C2×C4×D3—32no—
164C2×C4×D3—34no—
165C2×C4×D3—34no—
166C2×C4×D3—62no—
167C2×C4×D3—64no—
168C2×Dic6—31no—
169C2×Dic6—31no—
170C2×Dic6—61no—
171C3×M16—38no—
172C2×C3×C8—38no—
173C2×C3×C8—32no—
174C2×C3×C8—34no—
175C2×C3×C8—32no—
176C3×C42—22no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42C4×D312yes—
180C3×C42C4×D312yes—
181C3×C42C22×D311yescharacteristic
182C3×C42C22×D311yescharacteristic
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185#217—32no—
186#217—32no—
187#217—62no—
188(C2×D3)⋊C4—34no—
189(C2×D3)⋊C4—34no—
190(C2×D3)⋊C4—64no—
191C4⋊Dic3—32no—
192C4⋊Dic3—32no—
193C4⋊Dic3—62no—
194Dic3⋊C4—34no—
195Dic3⋊C4—34no—
196Dic3⋊C4—64no—
197C4×Dic3—34no—
198C4×Dic3—34no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—64no—
202C4×Dic3—62no—
203#208C4×D318yescomplemented
204C2×C3⋊C8C4×D318yescomplemented
205C2×C3⋊C8C22×D314yes—
206C2×C3⋊C8C22×D312yes—
207C2×C3⋊C8C22×D312yes—
208ΓL(1,𝔽25)—316no—
209ΓL(1,𝔽25)—316no—
210D3×C8—316no—
211D3×C8—316no—
212C22×C32—22no—
213C22×C32C2×C4212yes—
214C22×C32C23×C411yescharacteristic
215C2×C3⋊D3—24no—
216C2×C3⋊D3C2×C4214yes—
217C32×C4—22no—
218C32×C4—22no—
219C32×C4C2×C4212yes—
220C32×C4C23×C412yes—
221C3⋊Dic3—24no—
222C3⋊Dic3C2×C4214yes—
223C2×#41—91no—
224#131—916no—
225C2×M16—32no—
226C2×M16—94no—
227C22×C8—32no—
228C22×C8—94no—
229C4×Q8—92no—
230C4×D4—94no—
231C4×D4—92no—
232#117—91no—
233#117—92no—
234C2×C42—92no—
235C2×C42D3211yescharacteristic
236#97—31no—
237#97—31no—
238#97—32no—
239#97—32no—
240#97—94no—
241C4×C8—32no—
242C4×C8—94no—
243C23×C3—21no—
244C23×C3C2×C4×D311yescharacteristic
245C23×C3C2×C4×D311yescharacteristic
246C22×D3—32no—
247C22×D3—32no—
248C22×D3—62no—
249C2×C3×C4—21no—
250C2×C3×C4—24no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—44no—
257C2×C3×C4C2×C4×D314yes—
258C2×C3×C4C2×C4×D314yes—
259C2×C3×C4C2×C4×D312yes—
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C23×D311yescharacteristic
266C2×C3×C4C23×D311yescharacteristic
267#67—38no—
268#67—38no—
269#67—68no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—62no—
275C2×Dic3—64no—
276D12—34no—
277D12—34no—
278D12—64no—
279C4×D3—38no—
280C4×D3—38no—
281C4×D3—68no—
282C4×D3—124no—
283C4×D3—124no—
284C4×D3—128no—
285Dic6—34no—
286Dic6—34no—
287Dic6—64no—
288C3×C8—34no—
289C3×C8—38no—
290C3×C8—34no—
291C3⋊C8C2×C4×D314yes—
292C3⋊C8C2×C4×D318yes—
293C3⋊C8C2×C4×D314yes—
294C2×C32—22no—
295C2×C32C22×C4211yescharacteristic
296C2×C32#56812yes—
297C3⋊D3—24no—
298#41—98no—
299C2×Q8—91no—
300C2×D4—92no—
301C2×D4—91no—
302C22×C4—92no—
303C22×C4—94no—
304C22×C4#62412yes—
305C22×C4C2×D3211yescharacteristic
306M16—38no—
307M16—916no—
308C2×C8—34no—
309C2×C8—32no—
310C2×C8—32no—
311C2×C8—38no—
312C2×C8—916no—
313C4⋊C4—94no—
314C4⋊C4—92no—
315C22⋊C4—92no—
316C22⋊C4—94no—
317C42—92no—
318C42—94no—
319C42#62412yes—
320C42C2×D3211yescharacteristic
321C42C2×D3211yescharacteristic
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—22no—
326C22×C3—42no—
327C22×C3C42×D312yes—
328C22×C3C42×D312yes—
329C22×C3C22×C4×D311yescharacteristic
330C22×C3C22×C4×D311yescharacteristic
331C2×D3—34no—
332C2×D3—34no—
333C2×D3—64no—
334C2×D3—64no—
335C2×D3—64no—
336C2×D3—124no—
337C3×C4—24no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—42no—
345C3×C4C42×D312yes—
346C3×C4C42×D312yes—
347C3×C4C22×C4×D312yes—
348C3×C4C22×C4×D312yes—
349Dic3—34no—
350Dic3—34no—
351Dic3—64no—
352Dic3—64no—
353Dic3—64no—
354Dic3—124no—
355C32#287511yescharacteristic, complemented, Sylow
356C23—92no—
357C23C2×#62411yescharacteristic
358Q8—94no—
359D4—98no—
360D4—94no—
361C2×C4—42no—
362C2×C4—92no—
363C2×C4—98no—
364C2×C4—94no—
365C2×C4—364no—
366C2×C4C4×D3214yes—
367C2×C4C2×#62412yes—
368C2×C4C2×#62412yes—
369C2×C4C2×#62411yescharacteristic
370C2×C4C22×D3211yescharacteristic
371C8—34no—
372C8—34no—
373C8—38no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—22no—
378C2×C3—42no—
379C2×C3C2×C42×D311yescharacteristic
380C2×C3C2×C42×D311yescharacteristic
381C2×C3#574512yes—
382C2×C3#574512yes—
383D3—64no—
384D3—64no—
385D3—124no—
386C22—22no—
387C22—94no—
388C22—184no—
389C22C4×#62412yes—
390C22C22×#62411yescharacteristic
391C4—22no—
392C4—22no—
393C4—94no—
394C4—184no—
395C4C4×#62412yes—
396C4C2×C4×D3212yes—
397C3—21no—
398C3#7848611yescharacteristic, complemented
399C3#7851611yescharacteristic, complemented
400C2—22no—
401C2—184no—
402C2#1059478012yes—
403C2C2×C4×#62411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socleC22×C32C23×C4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2875
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×#208C2semidirect
4. C2×C3×#803C2semidirect
5. #10591059C2semidirect
6. #10590322C2semidirect
7. #10590321C2semidirect
8. #10590247C2semidirect
22. #63817C4semidirect
40. C4×#208D3semidirect
41. C2×#803D3semidirect
65. C3×#208C2×C4semidirect
66. C2×C3×C3⋊C8C2×C4semidirect
70. #3712C2×C4semidirect
71. #3710C2×C4semidirect
203. #208C4×D3semidirect
204. C2×C3⋊C8C4×D3semidirect
355. C32#2875semidirect
398. C3#78486semidirect
399. C3#78516semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C2×#638172
C3×C4×#2082
C2×C3×#8032
#105910592
#105903222
#105903212
#105902472
#785163
#784863