Finite Group Databasebeta

← C2×#10588503 #11861031

Subgroups — C2×#10588503 #11861031

Order 1152.

696 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×#63513C211yesmaximal, characteristic
2C2×#63510C211yesmaximal, characteristic, complemented
3C2×#63469C211yesmaximal, characteristic, complemented
4C2×C9×#104C211yesmaximal, characteristic, complemented
5C2×#63381C211yesmaximal, characteristic, complemented
6C2×#63364C211yesmaximal, characteristic, complemented
7C2×#63362C211yesmaximal, characteristic, complemented
8#10588503C218yesmaximal, direct product factor
9C2×#4823—31nomaximal
10C2×C9×#41C2211yescharacteristic
11C2×#3697C2211yescharacteristic
12C2×C9×M16C2211yescharacteristic
13C2×C42×C9C2211yescharacteristic
14#63513C414yescomplemented
15#63513C2214yes—
16#63510—22no—
17#63510C2214yescomplemented
18C2×#3675C411yescharacteristic, complemented
19C2×#3674C411yescharacteristic, complemented
20C2×#3673C411yescharacteristic, complemented
21C2×#3672C411yescharacteristic, complemented
22C2×#3667—21no—
23C2×#3667C2211yescharacteristic
24C22×C9⋊C8—21no—
25C22×C9⋊C8C2211yescharacteristic
26C22×C9⋊C8C2211yescharacteristic
27#63469—22no—
28#63469C2214yescomplemented
29C2×#3663—21no—
30C2×C8×D9—21no—
31C9×#104C2214yescomplemented
32#63381C2214yescomplemented
33#63364C2214yescomplemented
34#63362C2214yescomplemented
35C2×#950—31no—
36C2×#948—31no—
37C2×#907—31no—
38C2×C3×#104D311yescharacteristic
39C2×#822—31no—
40C2×#805—31no—
41C2×#803—31no—
42#4823—38no—
43C9×#41—21no—
44C9×#41—21no—
45C9×#41C2×C412yes—
46C9×#41C2312yes—
47C2×Q8×C9C2×C411yescharacteristic
48C2×D4×C9—21no—
49C2×D4×C9C2×C411yescharacteristic
50C22×C4×C9—21no—
51C22×C4×C9—21no—
52C22×C4×C9C2311yescharacteristic
53C2×#611—21no—
54#3697—21no—
55#3697—21no—
56#3697C2×C412yes—
57#3697C2312yes—
58C2×D36C2×C411yescharacteristic
59C2×C4×D9—21no—
60C2×Dic18C2×C411yescharacteristic
61C9×M16—21no—
62C9×M16C2312yes—
63C2×C8×C9—21no—
64C42×C9—21no—
65C42×C9C2312yes—
66#3675C2×C414yescomplemented
67#3674C2×C414yescomplemented
68#3673C2×C414yescomplemented
69#3672C2×C414yescomplemented
70#3667—21no—
71#3667—24no—
72#3667C2312yes—
73C2×C9⋊C8—21no—
74C2×C9⋊C8—24no—
75C2×C9⋊C8C2×C411yescharacteristic
76C2×C9⋊C8C2×C411yescharacteristic
77C2×C9⋊C8C2×C412yes—
78C2×C9⋊C8D412yes—
79C2×C9⋊C8D411yescharacteristic
80C2×C9⋊C8D411yescharacteristic
81C2×C9⋊C8C2312yes—
82C2×C9⋊C8C2312yes—
83#3663—24no—
84C8×D9—24no—
85C2×#444—91noSylow
86C2×C3×#41C2×D311yescharacteristic
87C2×#235—31no—
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×C42C2×D311yescharacteristic
90#950—34no—
91#950—34no—
92#948—34no—
93#948—62no—
94C2×#216—31no—
95C2×#215—31no—
96C2×#214—31no—
97C2×#213—31no—
98C2×#208—31no—
99C2×#208—61no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103#907—34no—
104#907—62no—
105C2×ΓL(1,𝔽25)—61no—
106C2×D3×C8—61no—
107C3×#104C2×D314yes—
108#822—34no—
109#805—34no—
110#803—34no—
111C23×C9—21no—
112C23×C9#4111yescharacteristic
113C22×D9—21no—
114Q8×C9—21no—
115Q8×C9C22×C412yes—
116D4×C9—22no—
117D4×C9—22no—
118D4×C9—21no—
119D4×C9C22×C412yes—
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9—22no—
123C2×C4×C9—22no—
124C2×C4×C9—42no—
125C2×C4×C9C22×C411yescharacteristic
126C2×C4×C9C22×C411yescharacteristic
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2×D411yescharacteristic
129C2×C4×C9#4111yescharacteristic
130C2×C4×C9C2411yescharacteristic
131#611—22no—
132#611—22no—
133C2×Dic9—21no—
134D36—21no—
135D36C22×C412yes—
136C4×D9—22no—
137C4×D9—22no—
138Dic18—21no—
139Dic18C22×C412yes—
140C8×C9—22no—
141C9⋊C8—22no—
142C9⋊C8C22×C412yes—
143C9⋊C8C22×C412yes—
144C9⋊C8C2×D412yes—
145C9⋊C8C2×D412yes—
146C2×#135—91no—
147C2×#131—91no—
148C2×#131—91no—
149#444—98no—
150C2×#108—91no—
151C2×#104—91no—
152C2×#104D911yescharacteristic, complemented
153C2×#97—91no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41C4×D312yes—
157C3×#41C22×D312yes—
158C2×C3×Q8C4×D311yescharacteristic
159C2×C3×D4—21no—
160C2×C3×D4C4×D311yescharacteristic
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—61no—
165#235—32no—
166#235—32no—
167#235—61no—
168#235—61no—
169C2×D12—31no—
170C2×C4×D3—61no—
171C2×Dic6—31no—
172C3×M16—21no—
173C3×M16C22×D312yes—
174C2×C3×C8—21no—
175C3×C42—21no—
176C3×C42C22×D312yes—
177#216—34no—
178#215—34no—
179#214—34no—
180#213—34no—
181#208—32no—
182#208—64no—
183#208—61no—
184C2×C3⋊C8—31no—
185C2×C3⋊C8—31no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—31no—
188C2×C3⋊C8—31no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—32no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—64no—
193C2×C3⋊C8—61no—
194ΓL(1,𝔽25)—64no—
195D3×C8—64no—
196C22×C9—22no—
197C22×C9—22no—
198C22×C9—42no—
199C22×C9C4×D411yescharacteristic
200C22×C9C4×D411yescharacteristic
201C22×C9C2×#4111yescharacteristic
202C2×D9—22no—
203C2×D9—42no—
204C4×C9—22no—
205C4×C9—42no—
206C4×C9C4×D411yescharacteristic
207C4×C9C4×D411yescharacteristic
208C4×C9C23×C411yescharacteristic
209C4×C9C22×D411yescharacteristic
210Dic9—22no—
211C2×#41—91no—
212C2×#41C2×D911yescharacteristic
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×D911yescharacteristic
227C22×C8—91no—
228C22×C8—91no—
229C22×C8—181no—
230C22×C8—181no—
231C2×C42C2×D911yescharacteristic
232#108—94no—
233#104—94no—
234#104C2×D914yescomplemented
235#97—94no—
236C23×C3—21no—
237C23×C3#23711yescharacteristic
238C22×D3—61no—
239C3×Q8—21no—
240C3×Q8C2×C4×D312yes—
241C3×D4—22no—
242C3×D4—22no—
243C3×D4—21no—
244C3×D4C2×C4×D312yes—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—42no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4C23×D311yescharacteristic
256#67—62no—
257#67—62no—
258C2×Dic3—61no—
259D12—32no—
260D12—61no—
261C4×D3—62no—
262C4×D3—62no—
263Dic6—32no—
264Dic6—61no—
265C3×C8—22no—
266C3⋊C8—32no—
267C3⋊C8—32no—
268C3⋊C8—32no—
269C3⋊C8—32no—
270C3⋊C8—62no—
271C2×C9—21no—
272C2×C9—21no—
273C2×C9—42no—
274C2×C9#44412yescomplemented
275C2×C9C2×C4×D411yescharacteristic
276D9—42no—
277#41—21no—
278#41—21no—
279#41—92no—
280#41—92no—
281#41—181no—
282#41—181no—
283#41C4×D912yes—
284#41C22×D912yes—
285C2×Q8—91no—
286C2×Q8C4×D911yescharacteristic
287C2×D4—21no—
288C2×D4—91no—
289C2×D4—181no—
290C2×D4C4×D911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—181no—
294C22×C4C22×D911yescharacteristic
295Q16—94no—
296SD16—94no—
297SD16—94no—
298D8—94no—
299M16—21no—
300M16—92no—
301M16—184no—
302M16—184no—
303M16—181no—
304M16C22×D912yes—
305C2×C8—21no—
306C2×C8—91no—
307C2×C8—91no—
308C2×C8—92no—
309C2×C8—92no—
310C2×C8—91no—
311C2×C8—91no—
312C2×C8—92no—
313C2×C8—92no—
314C2×C8—184no—
315C2×C8—184no—
316C2×C8—181no—
317C42—21no—
318C42C22×D912yes—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—42no—
322C22×C3#67⋊C411yescharacteristic
323C22×C3#67⋊C411yescharacteristic
324C22×C3C2×#23711yescharacteristic
325C2×D3—62no—
326C2×D3—122no—
327C3×C4—22no—
328C3×C4—42no—
329C3×C4#67⋊C411yescharacteristic
330C3×C4#67⋊C411yescharacteristic
331C3×C4C22×C4×D311yescharacteristic
332C3×C4C2×D3×D411yescharacteristic
333Dic3—62no—
334C9C2×#44411yescharacteristic, complemented, Sylow
335C23—21no—
336C23—181no—
337C23#369911yescharacteristic
338Q8—21no—
339Q8—92no—
340Q8—181no—
341Q8C2×C4×D912yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4—92no—
346D4—182no—
347D4—182no—
348D4—181no—
349D4C2×C4×D912yes—
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×D911yescharacteristic
359C2×C4C2×C4×D911yescharacteristic
360C2×C4D4×D911yescharacteristic
361C2×C4D4×D911yescharacteristic
362C2×C4#369911yescharacteristic
363C2×C4C23×D911yescharacteristic
364C8—22no—
365C8—92no—
366C8—92no—
367C8—92no—
368C8—92no—
369C8—182no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—42no—
373C2×C3#482312yes—
374C2×C3C2×#67⋊C411yescharacteristic
375D3—122no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—182no—
380C22—362no—
381C22#611⋊C411yescharacteristic
382C22#611⋊C411yescharacteristic
383C22C2×#369911yescharacteristic
384C4—22no—
385C4—42no—
386C4—182no—
387C4#611⋊C411yescharacteristic
388C4#611⋊C411yescharacteristic
389C4C22×C4×D911yescharacteristic
390C4C2×D4×D911yescharacteristic
391C3C2×#482311yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2—362no—
396C2#1058850312yesdirect product factor
397C2C2×#611⋊C411yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#104C2
socleC22×C3#67⋊C4
prime radicalC2×#63513C2
cosocleC2×C4×C9C24
hypercenterC2×#104D9
hypocenterC9C2×#444
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#63510C2semidirect
3. C2×#63469C2semidirect
4. C2×C9×#104C2semidirect
5. C2×#63381C2semidirect
6. C2×#63364C2semidirect
7. C2×#63362C2semidirect
8. #10588503C2direct (N × H)
14. #63513C4semidirect
17. #63510C22semidirect
18. C2×#3675C4semidirect
19. C2×#3674C4semidirect
20. C2×#3673C4semidirect
21. C2×#3672C4semidirect
28. #63469C22semidirect
31. C9×#104C22semidirect
32. #63381C22semidirect
33. #63364C22semidirect
34. #63362C22semidirect
66. #3675C2×C4semidirect
67. #3674C2×C4semidirect
68. #3673C2×C4semidirect
69. #3672C2×C4semidirect
152. C2×#104D9semidirect
234. #104C2×D9semidirect
274. C2×C9#444semidirect
334. C9C2×#444semidirect
396. C2#10588503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#635132
C2×#635102
C2×#634692
C2×C9×#1042
C2×#633812
C2×#633642
C2×#633622
#105885032
C2×#48233