Finite Group Databasebeta

← C2×#10592522 #11861032

Subgroups — C2×#10592522 #11861032

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C2×#64157C211yesmaximal, characteristic, complemented
3C2×#64116C211yesmaximal, characteristic, complemented
4C2×C32×#104C211yesmaximal, characteristic, complemented
5C2×#63649C211yesmaximal, characteristic, complemented
6C2×#63632C211yesmaximal, characteristic, complemented
7C2×#63630C211yesmaximal, characteristic, complemented
8#10592522C218yesmaximal, direct product factor
9C2×#4823—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14#64159C414yescomplemented
15#64159C2214yes—
16#64157—22no—
17#64157C2214yescomplemented
18C2×#3756C411yescharacteristic, complemented
19C2×#3755C411yescharacteristic, complemented
20C2×#3754C411yescharacteristic, complemented
21C2×#3753C411yescharacteristic, complemented
22C2×#3748—21no—
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)—21no—
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C22×C3⋊(C3⋊C8)C2211yescharacteristic
27#64116—22no—
28#64116C2214yescomplemented
29C2×#3743—21no—
30C2×C8×C3⋊D3—21no—
31C32×#104C2214yescomplemented
32#63649C2214yescomplemented
33#63632C2214yescomplemented
34#63630C2214yescomplemented
35C2×#950—34no—
36C2×#948—34no—
37C2×#907—34no—
38C2×C3×#104D314yescomplemented
39C2×#822—34no—
40C2×#805—34no—
41C2×#803—34no—
42#4823—332no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41C2×C412yes—
46C32×#41C2312yes—
47C2×C32×Q8C2×C411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4C2×C411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828C2×C412yes—
57#3828C2312yes—
58C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634C2×C411yescharacteristic
61C32×M16—21no—
62C32×M16C2312yes—
63C2×C32×C8—21no—
64C32×C42—21no—
65C32×C42C2312yes—
66#3756C2×C414yescomplemented
67#3755C2×C414yescomplemented
68#3754C2×C414yescomplemented
69#3753C2×C414yescomplemented
70#3748—21no—
71#3748—24no—
72#3748C2312yes—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)—24no—
75C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
76C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
77C2×C3⋊(C3⋊C8)C2×C412yes—
78C2×C3⋊(C3⋊C8)D411yescharacteristic
79C2×C3⋊(C3⋊C8)D411yescharacteristic
80C2×C3⋊(C3⋊C8)D412yes—
81C2×C3⋊(C3⋊C8)C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83#3743—24no—
84C8×C3⋊D3—24no—
85C2×#444—91noSylow
86C2×C3×#41C2×D314yes—
87C2×#235—34no—
88C2×C3×M16C2×D314yes—
89C2×C3×C42C2×D314yes—
90#950—316no—
91#950—316no—
92#948—316no—
93#948—68no—
94C2×#216—34no—
95C2×#215—34no—
96C2×#214—34no—
97C2×#213—34no—
98C2×#208—34no—
99C2×#208—64no—
100C22×C3⋊C8—34no—
101C22×C3⋊C8—34no—
102C22×C3⋊C8—64no—
103#907—316no—
104#907—68no—
105C2×ΓL(1,𝔽25)—64no—
106C2×D3×C8—64no—
107C3×#104C2×D3116yescomplemented
108#822—316no—
109#805—316no—
110#803—316no—
111C23×C32—21no—
112C23×C32#4111yescharacteristic
113C22×C3⋊D3—21no—
114C32×Q8—21no—
115C32×Q8C22×C412yes—
116C32×D4—22no—
117C32×D4—22no—
118C32×D4—21no—
119C32×D4C22×C412yes—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—42no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4C2411yescharacteristic
131#638—22no—
132#638—22no—
133C2×C3⋊Dic3—21no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)C22×C412yes—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138#634—21no—
139#634C22×C412yes—
140C32×C8—22no—
141C3⋊(C3⋊C8)—22no—
142C3⋊(C3⋊C8)C22×C412yes—
143C3⋊(C3⋊C8)C22×C412yes—
144C3⋊(C3⋊C8)C2×D412yes—
145C3⋊(C3⋊C8)C2×D412yes—
146C2×#135—91no—
147C2×#131—91no—
148C2×#131—91no—
149#444—98no—
150C2×#108—91no—
151C2×#104—91no—
152C2×#104C3⋊D311yescharacteristic, complemented
153C2×#97—91no—
154C3×#41—24no—
155C3×#41—24no—
156C3×#41C4×D318yes—
157C3×#41C22×D318yes—
158C2×C3×Q8C4×D314yes—
159C2×C3×D4—24no—
160C2×C3×D4C4×D314yes—
161C22×C3×C4—24no—
162C22×C3×C4—24no—
163C22×C3×C4C22×D314yes—
164C2×#67—64no—
165#235—38no—
166#235—38no—
167#235—64no—
168#235—64no—
169C2×D12—34no—
170C2×C4×D3—64no—
171C2×Dic6—34no—
172C3×M16—24no—
173C3×M16C22×D318yes—
174C2×C3×C8—24no—
175C3×C42—24no—
176C3×C42C22×D318yes—
177#216—316no—
178#215—316no—
179#214—316no—
180#213—316no—
181#208—38no—
182#208—616no—
183#208—64no—
184C2×C3⋊C8—34no—
185C2×C3⋊C8—34no—
186C2×C3⋊C8—38no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C2×C3⋊C8—38no—
191C2×C3⋊C8—38no—
192C2×C3⋊C8—616no—
193C2×C3⋊C8—64no—
194ΓL(1,𝔽25)—616no—
195D3×C8—616no—
196C22×C32—22no—
197C22×C32—22no—
198C22×C32—42no—
199C22×C32C4×D411yescharacteristic
200C22×C32C4×D411yescharacteristic
201C22×C32C2×#4111yescharacteristic
202C2×C3⋊D3—22no—
203C2×C3⋊D3—42no—
204C32×C4—22no—
205C32×C4—42no—
206C32×C4C4×D411yescharacteristic
207C32×C4C4×D411yescharacteristic
208C32×C4C23×C411yescharacteristic
209C32×C4C22×D411yescharacteristic
210C3⋊Dic3—22no—
211C2×#41—91no—
212C2×#41C2×C3⋊D311yescharacteristic
213#135—94no—
214#135—94no—
215C2×Q16—91no—
216C2×SD16—91no—
217C2×SD16—91no—
218C2×D8—91no—
219#131—94no—
220#131—94no—
221#131—182no—
222#131—182no—
223C2×M16—91no—
224C2×M16—181no—
225C2×M16—181no—
226C2×M16C2×C3⋊D311yescharacteristic
227C22×C8—91no—
228C22×C8—91no—
229C22×C8—181no—
230C22×C8—181no—
231C2×C42C2×C3⋊D311yescharacteristic
232#108—94no—
233#104—94no—
234#104C2×C3⋊D314yescomplemented
235#97—94no—
236C23×C3—24no—
237C23×C3#23714yes—
238C22×D3—64no—
239C3×Q8—24no—
240C3×Q8C2×C4×D318yes—
241C3×D4—28no—
242C3×D4—28no—
243C3×D4—24no—
244C3×D4C2×C4×D318yes—
245C2×C3×C4—24no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4—48no—
250C2×C3×C4C2×C4×D314yes—
251C2×C3×C4C2×C4×D314yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4D3×D414yes—
254C2×C3×C4#23714yes—
255C2×C3×C4C23×D314yes—
256#67—68no—
257#67—68no—
258C2×Dic3—64no—
259D12—38no—
260D12—64no—
261C4×D3—68no—
262C4×D3—68no—
263Dic6—38no—
264Dic6—64no—
265C3×C8—28no—
266C3⋊C8—38no—
267C3⋊C8—38no—
268C3⋊C8—38no—
269C3⋊C8—38no—
270C3⋊C8—68no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—42no—
274C2×C32#44412yescomplemented
275C2×C32C2×C4×D411yescharacteristic
276C3⋊D3—42no—
277#41—21no—
278#41—21no—
279#41—92no—
280#41—92no—
281#41—181no—
282#41—181no—
283#41C4×C3⋊D312yes—
284#41C22×C3⋊D312yes—
285C2×Q8—91no—
286C2×Q8C4×C3⋊D311yescharacteristic
287C2×D4—21no—
288C2×D4—91no—
289C2×D4—181no—
290C2×D4C4×C3⋊D311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—181no—
294C22×C4C22×C3⋊D311yescharacteristic
295Q16—94no—
296SD16—94no—
297SD16—94no—
298D8—94no—
299M16—21no—
300M16—92no—
301M16—184no—
302M16—184no—
303M16—181no—
304M16C22×C3⋊D312yes—
305C2×C8—21no—
306C2×C8—92no—
307C2×C8—92no—
308C2×C8—91no—
309C2×C8—91no—
310C2×C8—92no—
311C2×C8—92no—
312C2×C8—91no—
313C2×C8—91no—
314C2×C8—184no—
315C2×C8—184no—
316C2×C8—181no—
317C42—21no—
318C42C22×C3⋊D312yes—
319C22×C3—28no—
320C22×C3—28no—
321C22×C3—48no—
322C22×C3#67⋊C414yes—
323C22×C3#67⋊C414yes—
324C22×C3C2×#23714yes—
325C2×D3—68no—
326C2×D3—128no—
327C3×C4—28no—
328C3×C4—48no—
329C3×C4#67⋊C414yes—
330C3×C4#67⋊C414yes—
331C3×C4C22×C4×D314yes—
332C3×C4C2×D3×D414yes—
333Dic3—68no—
334C32C2×#44411yescharacteristic, complemented, Sylow
335C23—21no—
336C23—181no—
337C23#383011yescharacteristic
338Q8—21no—
339Q8—92no—
340Q8—181no—
341Q8C2×C4×C3⋊D312yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4—92no—
346D4—182no—
347D4—182no—
348D4—181no—
349D4C2×C4×C3⋊D312yes—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4C2×C4×C3⋊D311yescharacteristic
359C2×C4C2×C4×C3⋊D311yescharacteristic
360C2×C4D4×C3⋊D311yescharacteristic
361C2×C4D4×C3⋊D311yescharacteristic
362C2×C4#383011yescharacteristic
363C2×C4C23×C3⋊D311yescharacteristic
364C8—22no—
365C8—92no—
366C8—92no—
367C8—92no—
368C8—92no—
369C8—182no—
370C2×C3—24no—
371C2×C3—24no—
372C2×C3—48no—
373C2×C3#482318yescomplemented
374C2×C3C2×#67⋊C414yes—
375D3—128no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—182no—
380C22—362no—
381C22#6409011yescharacteristic
382C22#6409011yescharacteristic
383C22C2×#383011yescharacteristic
384C4—22no—
385C4—42no—
386C4—182no—
387C4#6409011yescharacteristic
388C4#6409011yescharacteristic
389C4C22×C4×C3⋊D311yescharacteristic
390C4C2×D4×C3⋊D311yescharacteristic
391C3C2×#482314yescomplemented
392C2—21no—
393C2—21no—
394C2—42no—
395C2—362no—
396C2#1059252212yesdirect product factor
397C2C2×#6409011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C4×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenterC2×#104C3⋊D3
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#64157C2semidirect
3. C2×#64116C2semidirect
4. C2×C32×#104C2semidirect
5. C2×#63649C2semidirect
6. C2×#63632C2semidirect
7. C2×#63630C2semidirect
8. #10592522C2direct (N × H)
14. #64159C4semidirect
17. #64157C22semidirect
18. C2×#3756C4semidirect
19. C2×#3755C4semidirect
20. C2×#3754C4semidirect
21. C2×#3753C4semidirect
28. #64116C22semidirect
31. C32×#104C22semidirect
32. #63649C22semidirect
33. #63632C22semidirect
34. #63630C22semidirect
38. C2×C3×#104D3semidirect
66. #3756C2×C4semidirect
67. #3755C2×C4semidirect
68. #3754C2×C4semidirect
69. #3753C2×C4semidirect
107. C3×#104C2×D3semidirect
152. C2×#104C3⋊D3semidirect
234. #104C2×C3⋊D3semidirect
274. C2×C32#444semidirect
334. C32C2×#444semidirect
373. C2×C3#4823semidirect
391. C3C2×#4823semidirect
396. C2#10592522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641592
C2×#641572
C2×#641162
C2×C32×#1042
C2×#636492
C2×#636322
C2×#636302
#105925222
C2×#48233