Finite Group Databasebeta

← C2×#10591038 #11899571

Subgroups — C2×#10591038 #11899571

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2C2×D3×D24C211yesmaximal, characteristic, complemented
3C2×#63655C211yesmaximal, characteristic, complemented
4C2×C3×#828C211yesmaximal, characteristic, complemented
5#10591038C218yesmaximal, direct product factor
6C2×#63546C211yesmaximal, characteristic, complemented
7C2×#63545C211yesmaximal, characteristic, complemented
8C2×#63543C211yesmaximal, characteristic, complemented
9C2×#5193—31nomaximal
10C2×#4914—31nomaximal
11C2×C3×#239—21no—
12C2×D3×D12—21no—
13C2×C32×Q16C2211yescharacteristic, complemented
14C2×#3745C2211yescharacteristic
15C2×C3×#215—21no—
16C3×#919—22no—
17C3×#919C2214yescomplemented
18C2×C3×D24C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic, complemented
20C2×C3×D3×C8C2211yescharacteristic
21C2×#3714—21no—
22D3×D24—22no—
23D3×D24C2214yescomplemented
24#63655C2214yescomplemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
26C3×#828C2214yescomplemented
27C2×C3×C3⋊C16C2211yescharacteristic, complemented
28#63546C2214yescomplemented
29#63545C2214yescomplemented
30#63543C2214yescomplemented
31C2×C3×#135—31no—
32C2×#919D311yescharacteristic, complemented
33C2×D3×D8—31no—
34C22×D24—31no—
35C2×C3×SD32—31no—
36#5193—38no—
37C2×#828—31no—
38C2×#828—31no—
39C2×#828—61no—
40C2×#828D311yescharacteristic, complemented
41C2×#826—31no—
42C2×#826—31no—
43C2×#826—31no—
44C2×#812—31no—
45#4914—38no—
46C2×D48—31no—
47C2×#798—31no—
48C22×D32—41no—
49C2×C32×Q8—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C3×#239—24no—
52C3×#239—42no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—41no—
56C2×C3×C4×D3—41no—
57C2×C3×C4×D3D411yescharacteristic
58C2×#626—41no—
59D3×D12—24no—
60D3×D12—42no—
61C32×Q16—21no—
62C32×Q16C2312yescomplemented
63C2×C32×C8C2311yescharacteristic
64#3745—21no—
65#3745C2312yes—
66C3×#215—24no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×D24—21no—
69C3×D24—21no—
70C3×D24C2312yes—
71C3×D24C2312yescomplemented
72C3×D3×C8D412yes—
73C3×D3×C8C2312yes—
74#3714—24no—
75C3⋊(C3⋊C16)C2312yescomplemented
76C3×C3⋊C16C2312yescomplemented
77C2×#509—91noSylow
78C2×C3×#41—61no—
79C2×#239—21no—
80C2×D3×D4—61no—
81C22×D12—61no—
82C3×#135—34no—
83C3×#135—62no—
84C2×C3×Q16—21no—
85C2×C3×Q16C2×D311yescharacteristic, complemented
86C2×C3×Q16C2×D311yescharacteristic, complemented
87C2×C3×SD16—61no—
88C2×C3×D8—31no—
89C2×C3×D8—31no—
90C22×C3×C8—31no—
91C2×#215—21no—
92C2×#213—61no—
93#919—22no—
94#919C2×D314yescomplemented
95D3×D8—34no—
96D3×D8—62no—
97C2×D24—31no—
98C2×D24—31no—
99C2×D24—34no—
100C2×D24—61no—
101C2×D24—62no—
102C2×D24—61no—
103C2×D24C2×D311yescharacteristic
104C2×D24C2×D311yescharacteristic, complemented
105C2×D3×C8C2×D311yescharacteristic
106C3×SD32—34no—
107C2×C3×C16—31no—
108#828—34no—
109#828—34no—
110#828—64no—
111#828C2×D314yescomplemented
112#826—34no—
113#826—34no—
114#826—34no—
115#812—34no—
116C2×C3⋊C16—31no—
117C2×C3⋊C16—31no—
118C2×C3⋊C16—61no—
119C2×C3⋊C16C2×D311yescharacteristic, complemented
120D48—34no—
121#798—34no—
122C22×C3⋊D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3D811yescharacteristic
126C2×D32—44no—
127C2×D32—84no—
128C32×Q8—22no—
129C32×Q8—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—41no—
134C2×C3×Dic3D811yescharacteristic
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—44no—
138C3×D12—41no—
139C3×D12—41no—
140C3×C4×D3—44no—
141C3×C4×D3D812yes—
142C3×C4×D3C2×D412yes—
143#626—44no—
144C32×C8C2×D411yescharacteristic
145C32×C8C2411yescharacteristic
146C3×C3⋊C8C2×D412yes—
147C2×#135—31no—
148C22×D8—91no—
149#509—98no—
150C2×SD32—31no—
151C2×SD32—91no—
152C2×D16—91no—
153C2×D16—91no—
154C2×M32—91no—
155C23×D3—121no—
156C23×D3—121no—
157C3×#41—64no—
158C3×#41—122no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—41no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—121no—
165C22×C3×C4—31no—
166C22×C3×C4—121no—
167C2×#67—121no—
168#239—24no—
169#239—42no—
170D3×D4—64no—
171D3×D4—122no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—41no—
175C2×D12—64no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—121no—
179C2×D12—122no—
180C2×D12—121no—
181C2×C4×D3—41no—
182C2×C4×D3#6711yescharacteristic
183C3×Q16—21no—
184C3×Q16—21no—
185C3×Q16—22no—
186C3×Q16—41no—
187C3×Q16C22×D312yescomplemented
188C3×Q16C22×D312yescomplemented
189C3×SD16—64no—
190C3×D8—32no—
191C3×D8—32no—
192C3×D8—61no—
193C3×D8—61no—
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—32no—
197C2×C3×C8—32no—
198C2×C3×C8C22×D311yescharacteristic
199C2×C3×C8C22×D311yescharacteristic
200#215—24no—
201#213—64no—
202C2×C3⋊C8#6711yescharacteristic
203D24—21no—
204D24—21no—
205D24—32no—
206D24—32no—
207D24—62no—
208D24—64no—
209D24—61no—
210D24—61no—
211D24—121no—
212D24C22×D312yes—
213D24C22×D312yescomplemented
214D3×C8#6712yes—
215D3×C8C22×D312yes—
216C3×C16—32no—
217C3⋊C16—32no—
218C3⋊C16—32no—
219C3⋊C16—62no—
220C3⋊C16C22×D312yescomplemented
221C22×C32C2×D811yescharacteristic
222C2×C3⋊D3—42no—
223C2×C3⋊D3—82no—
224C2×C3×D3—22no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—82no—
228C2×C3×D3—82no—
229C2×C3×D3C2×D812yes—
230D32—88no—
231C32×C4—42no—
232C32×C4C2×D811yescharacteristic
233C32×C4C22×D411yescharacteristic
234C3×Dic3C2×D812yes—
235C2×#41—61no—
236C22×D4—181no—
237#135—34no—
238#135—62no—
239C2×Q16D3211yescharacteristic, complemented
240C2×SD16—61no—
241C2×D8—31no—
242C2×D8—31no—
243C2×D8—94no—
244C2×D8—91no—
245C2×D8—182no—
246C2×D8—181no—
247C22×C8—31no—
248SD32—34no—
249SD32—94no—
250D16—94no—
251D16—94no—
252M32—94no—
253C2×C16—31no—
254C2×C16—91no—
255C23×C3—31no—
256C23×C3—121no—
257C23×C3—121no—
258C22×D3—41no—
259C22×D3—41no—
260C22×D3—124no—
261C22×D3—121no—
262C22×D3—121no—
263C22×D3—124no—
264C22×D3—241no—
265C22×D3—244no—
266C22×D3—244no—
267C22×D3#21311yescharacteristic
268C3×Q8—22no—
269C3×Q8—22no—
270C3×Q8—42no—
271C3×Q8—41no—
272C3×Q8—41no—
273C3×Q8—81no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—124no—
277C3×D4—121no—
278C3×D4—121no—
279C2×C3×C4—21no—
280C2×C3×C4—31no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—81no—
286C2×C3×C4—124no—
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289#67—124no—
290C2×Dic3#21311yescharacteristic
291D12—22no—
292D12—22no—
293D12—44no—
294D12—41no—
295D12—41no—
296D12—62no—
297D12—62no—
298D12—122no—
299D12—124no—
300D12—121no—
301D12—121no—
302D12—241no—
303C4×D3—44no—
304C4×D3#21312yes—
305C4×D3C2×#6712yes—
306C3×C8—21no—
307C3×C8—21no—
308C3×C8—32no—
309C3×C8D3×D411yescharacteristic
310C3×C8C2×#6711yescharacteristic
311C3×C8C23×D311yescharacteristic
312C3×C8C23×D311yescharacteristic
313C3⋊C8C2×#6712yes—
314C2×C32#50912yescomplemented
315C2×C32C22×D811yescharacteristic
316C3⋊D3—82no—
317C3×D3—22no—
318C3×D3—82no—
319C3×D3—82no—
320C24—361no—
321#41—64no—
322#41—122no—
323C2×Q8—21no—
324C2×D4—61no—
325C2×D4—61no—
326C2×D4—121no—
327C2×D4—184no—
328C2×D4—181no—
329C2×D4—362no—
330C2×D4—361no—
331C22×C4—31no—
332C22×C4—121no—
333Q16—21no—
334Q16C2×D3212yescomplemented
335SD16—64no—
336D8—32no—
337D8—32no—
338D8—61no—
339D8—61no—
340D8—92no—
341D8—184no—
342D8—181no—
343C2×C8—31no—
344C2×C8—32no—
345C2×C8—32no—
346C2×C8C2×D3211yescharacteristic
347C16—32no—
348C16—92no—
349C22×C3—21no—
350C22×C3—32no—
351C22×C3—62no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3—242no—
355C22×C3—242no—
356C22×C3D3×D811yescharacteristic
357C22×C3C2×#21311yescharacteristic
358C2×D3—22no—
359C2×D3—42no—
360C2×D3—42no—
361C2×D3—82no—
362C2×D3—82no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—242no—
366C2×D3—248no—
367C2×D3—248no—
368C2×D3—242no—
369C2×D3—242no—
370C2×D3—482no—
371C2×D3C2×#21312yes—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—32no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—82no—
378C3×C4D3×D811yescharacteristic
379C3×C4C2×#21311yescharacteristic
380C3×C4C2×D3×D411yescharacteristic
381C3×C4C22×#6711yescharacteristic
382Dic3C2×#21312yes—
383C32C2×#50911yescharacteristic, complemented, Sylow
384C23—31no—
385C23—121no—
386C23—121no—
387C23—364no—
388C23—361no—
389C23—724no—
390Q8—22no—
391Q8—41no—
392D4—62no—
393D4—62no—
394D4—124no—
395D4—121no—
396D4—121no—
397D4—182no—
398D4—364no—
399D4—361no—
400C2×C4—31no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—41no—
404C2×C4—124no—
405C2×C4D3×#6711yescharacteristic
406C8—32no—
407C8D3×#6711yescharacteristic
408C8C22×D3211yescharacteristic
409C2×C3—21no—
410C2×C3—22no—
411C2×C3—62no—
412C2×C3—242no—
413C2×C3—242no—
414C2×C3#491412yescomplemented
415C2×C3#519312yescomplemented
416C2×C3C2×D3×D811yescharacteristic
417C2×C3C22×#21311yescharacteristic
418D3—22no—
419D3—82no—
420D3—82no—
421D3—242no—
422D3—242no—
423D3—482no—
424C22—32no—
425C22—62no—
426C22—122no—
427C22—122no—
428C22—242no—
429C22—242no—
430C22—362no—
431C22—728no—
432C22—722no—
433C22D3×#21311yescharacteristic
434C4—32no—
435C4—42no—
436C4D3×#21311yescharacteristic
437C4C2×D3×#6711yescharacteristic
438C3—21no—
439C3C2×#491411yescharacteristic, complemented
440C3C2×#519311yescharacteristic, complemented
441C2—62no—
442C2—242no—
443C2—242no—
444C2—722no—
445C2#1059103812yesdirect product factor
446C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. C2×D3×D24C2semidirect
3. C2×#63655C2semidirect
4. C2×C3×#828C2semidirect
5. #10591038C2direct (N × H)
6. C2×#63546C2semidirect
7. C2×#63545C2semidirect
8. C2×#63543C2semidirect
13. C2×C32×Q16C22semidirect
17. C3×#919C22semidirect
19. C2×C3×D24C22semidirect
23. D3×D24C22semidirect
24. #63655C22semidirect
25. C2×C3⋊(C3⋊C16)C22semidirect
26. C3×#828C22semidirect
27. C2×C3×C3⋊C16C22semidirect
28. #63546C22semidirect
29. #63545C22semidirect
30. #63543C22semidirect
32. C2×#919D3semidirect
40. C2×#828D3semidirect
62. C32×Q16C23semidirect
71. C3×D24C23semidirect
75. C3⋊(C3⋊C16)C23semidirect
76. C3×C3⋊C16C23semidirect
85. C2×C3×Q16C2×D3semidirect
86. C2×C3×Q16C2×D3semidirect
94. #919C2×D3semidirect
104. C2×D24C2×D3semidirect
111. #828C2×D3semidirect
119. C2×C3⋊C16C2×D3semidirect
187. C3×Q16C22×D3semidirect
188. C3×Q16C22×D3semidirect
213. D24C22×D3semidirect
220. C3⋊C16C22×D3semidirect
239. C2×Q16D32semidirect
314. C2×C32#509semidirect
334. Q16C2×D32semidirect
383. C32C2×#509semidirect
414. C2×C3#4914semidirect
415. C2×C3#5193semidirect
439. C3C2×#4914semidirect
440. C3C2×#5193semidirect
445. C2#10591038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×D3×D242
C2×#636552
C2×C3×#8282
#105910382
C2×#635462
C2×#635452
C2×#635432
C2×#51933
C2×#49143