Finite Group Databasebeta

← C2×#10591048 #11899522

Subgroups — C2×#10591048 #11899522

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2C2×#63808C211yesmaximal, characteristic, complemented
3C2×#63655C211yesmaximal, characteristic, complemented
4C2×C3×#829C211yesmaximal, characteristic, complemented
5#10591048C218yesmaximal, direct product factor
6C2×#63547C211yesmaximal, characteristic, complemented
7C2×#63546C211yesmaximal, characteristic, complemented
8C2×D3×C3⋊C16C211yesmaximal, characteristic, complemented
9C2×#5194—31nomaximal
10C2×#4919—31nomaximal
11C2×C3×#239—21no—
12C2×#3799—21no—
13C2×C32×Q16C2211yescharacteristic
14C2×#3745C2211yescharacteristic
15C2×C3×#215—21no—
16C3×#919—22no—
17C3×#919C2214yescomplemented
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C2×#3717—21no—
22#63808—22no—
23#63808C2214yescomplemented
24#63655C2214yescomplemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic
26C3×#829C2214yescomplemented
27C2×C3×C3⋊C16C2211yescharacteristic
28#63547C2214yescomplemented
29#63546C2214yescomplemented
30D3×C3⋊C16C2214yescomplemented
31C2×C3×#135—31no—
32C2×#919—31no—
33C2×#919D311yescharacteristic, complemented
34C2×#904—31no—
35C2×C3×Q32—31no—
36#5194—38no—
37C2×#829D311yescharacteristic, complemented
38C2×#828—31no—
39C2×#828—31no—
40C2×#828—31no—
41C2×#828—61no—
42C2×#827—31no—
43C2×#826—31no—
44C22×C3⋊C16—31no—
45#4919—38no—
46C2×D48—31no—
47C2×D3×C16—31no—
48C2×C32×Q8—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C3×#239—24no—
51C3×#239—42no—
52C2×C3×D12—21no—
53C2×C3×D12—41no—
54C2×C3×C4×D3—41no—
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×Dic6—21no—
57C2×#626—41no—
58C2×#624—41no—
59#3799—24no—
60#3799—42no—
61C32×Q16—21no—
62C32×Q16C2312yes—
63C2×C32×C8C2311yescharacteristic
64#3745—21no—
65#3745C2312yes—
66C3×#215—24no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×Dic12—21no—
69C3×Dic12C2312yes—
70C3×D24—21no—
71C3×D24C2312yes—
72C3×D3×C8D412yes—
73C3×D3×C8C2312yes—
74#3717—24no—
75C3⋊(C3⋊C16)C2312yes—
76C3×C3⋊C16C2312yes—
77C2×#508—91noSylow
78C2×C3×#41—61no—
79C2×#239—21no—
80C2×#239—61no—
81C2×#235—61no—
82C3×#135—34no—
83C3×#135—62no—
84C2×C3×Q16—21no—
85C2×C3×Q16—31no—
86C2×C3×Q16C2×D311yescharacteristic
87C2×C3×Q16C2×D311yescharacteristic
88C2×C3×SD16—61no—
89C2×C3×D8—31no—
90C22×C3×C8—31no—
91C2×#215—21no—
92C2×#215—61no—
93#919—22no—
94#919—34no—
95#919—62no—
96#919C2×D314yescomplemented
97C2×Dic12C2×D311yescharacteristic
98#904—34no—
99#904—62no—
100C2×D24—31no—
101C2×D24—31no—
102C2×D24—61no—
103C2×D24C2×D311yescharacteristic
104C2×#204—61no—
105C2×D3×C8C2×D311yescharacteristic
106C3×Q32—34no—
107C2×C3×C16—31no—
108#829C2×D314yescomplemented
109#828—34no—
110#828—34no—
111#828—34no—
112#828—64no—
113#827—34no—
114#826—34no—
115C2×C3⋊C16—31no—
116C2×C3⋊C16—31no—
117C2×C3⋊C16—34no—
118C2×C3⋊C16—61no—
119C2×C3⋊C16C2×D311yescharacteristic
120D48—34no—
121D3×C16—34no—
122C22×C3⋊D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3D811yescharacteristic
125C32×Q8—22no—
126C32×Q8—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—22no—
134C3×D12—44no—
135C3×D12—41no—
136C3×C4×D3—44no—
137C3×C4×D3D812yes—
138C3×C4×D3C2×D412yes—
139C3×Dic6—22no—
140C3×Dic6—41no—
141#626—44no—
142#624—44no—
143C32×C8C2×D411yescharacteristic
144C32×C8C2411yescharacteristic
145C3×C3⋊C8C2×D412yes—
146C2×#135—31no—
147C2×#135—91no—
148#508—98no—
149C2×Q32—31no—
150C2×SD32—91no—
151C2×SD32—91no—
152C2×D16—91no—
153C22×C16—91no—
154C3×#41—64no—
155C3×#41—122no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—41no—
159C2×C3×Q8—61no—
160C2×C3×D4—61no—
161C2×C3×D4—121no—
162C22×C3×C4—31no—
163C22×C3×C4—121no—
164C2×#67—121no—
165#239—24no—
166#239—42no—
167#239—64no—
168#239—122no—
169#235—64no—
170#235—122no—
171C2×D12—21no—
172C2×D12—41no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—121no—
176C2×D12—121no—
177C2×C4×D3—41no—
178C2×C4×D3—121no—
179C2×C4×D3—121no—
180C2×C4×D3#6711yescharacteristic
181C2×Dic6—21no—
182C3×Q16—21no—
183C3×Q16—21no—
184C3×Q16—22no—
185C3×Q16—32no—
186C3×Q16—41no—
187C3×Q16—61no—
188C3×Q16C22×D312yes—
189C3×Q16C22×D312yes—
190C3×SD16—64no—
191C3×D8—32no—
192C3×D8—61no—
193C2×C3×C8—21no—
194C2×C3×C8—31no—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C2×C3×C8C22×D311yescharacteristic
198C2×C3×C8C22×D311yescharacteristic
199#215—24no—
200#215—64no—
201C2×C3⋊C8#6711yescharacteristic
202Dic12—21no—
203Dic12C22×D312yes—
204D24—21no—
205D24—32no—
206D24—32no—
207D24—62no—
208D24—61no—
209D24—61no—
210D24—121no—
211D24C22×D312yes—
212#204—64no—
213D3×C8#6712yes—
214D3×C8C22×D312yes—
215C3×C16—32no—
216C3⋊C16—32no—
217C3⋊C16—32no—
218C3⋊C16—62no—
219C3⋊C16C22×D312yes—
220C22×C32C2×D811yescharacteristic
221C2×C3⋊D3—42no—
222C2×C3⋊D3—82no—
223C2×C3×D3—22no—
224C2×C3×D3—42no—
225C2×C3×D3—82no—
226C2×C3×D3C2×D812yes—
227C32×C4—42no—
228C32×C4C2×D811yescharacteristic
229C32×C4C22×D411yescharacteristic
230C3×Dic3—42no—
231C3×Dic3C2×D812yes—
232C2×#41—61no—
233C2×#41—181no—
234#135—34no—
235#135—62no—
236#135—94no—
237#135—182no—
238C2×Q16—31no—
239C2×Q16D3211yescharacteristic
240C2×SD16—61no—
241C2×SD16—181no—
242C2×D8—31no—
243C2×D8—91no—
244C22×C8—31no—
245Q32—34no—
246SD32—94no—
247SD32—94no—
248D16—94no—
249C2×C16—31no—
250C2×C16—94no—
251C2×C16—91no—
252C23×C3—31no—
253C23×C3—121no—
254C22×D3—41no—
255C22×D3—121no—
256C22×D3—121no—
257C22×D3—241no—
258C22×D3#21311yescharacteristic
259C3×Q8—22no—
260C3×Q8—22no—
261C3×Q8—42no—
262C3×Q8—41no—
263C3×Q8—41no—
264C3×Q8—62no—
265C3×Q8—81no—
266C3×Q8—121no—
267C3×D4—62no—
268C3×D4—124no—
269C3×D4—121no—
270C2×C3×C4—21no—
271C2×C3×C4—31no—
272C2×C3×C4—32no—
273C2×C3×C4—32no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—81no—
277C2×C3×C4—124no—
278C2×C3×C4—121no—
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281#67—124no—
282C2×Dic3—41no—
283C2×Dic3#21311yescharacteristic
284D12—22no—
285D12—44no—
286D12—41no—
287D12—62no—
288D12—62no—
289D12—122no—
290D12—124no—
291D12—121no—
292D12—121no—
293D12—241no—
294C4×D3—44no—
295C4×D3—124no—
296C4×D3—124no—
297C4×D3#21312yes—
298C4×D3C2×#6712yes—
299Dic6—22no—
300Dic6—41no—
301C3×C8—21no—
302C3×C8—21no—
303C3×C8—32no—
304C3×C8D3×D411yescharacteristic
305C3×C8C2×#6711yescharacteristic
306C3×C8C23×D311yescharacteristic
307C3×C8C23×D311yescharacteristic
308C3⋊C8C2×#6712yes—
309C2×C32#50812yescomplemented
310C2×C32C22×D811yescharacteristic
311C3⋊D3—82no—
312C3×D3—22no—
313C3×D3—82no—
314#41—64no—
315#41—122no—
316#41—184no—
317#41—362no—
318C2×Q8—21no—
319C2×Q8—61no—
320C2×D4—61no—
321C2×D4—121no—
322C2×D4—181no—
323C2×D4—361no—
324C22×C4—31no—
325C22×C4—121no—
326C22×C4—361no—
327Q16—21no—
328Q16—32no—
329Q16—61no—
330Q16C2×D3212yes—
331SD16—64no—
332SD16—184no—
333D8—32no—
334D8—61no—
335D8—92no—
336D8—181no—
337C2×C8—31no—
338C2×C8—32no—
339C2×C8—32no—
340C2×C8C2×D3211yescharacteristic
341C16—32no—
342C16—92no—
343C22×C3—21no—
344C22×C3—32no—
345C22×C3—62no—
346C22×C3—122no—
347C22×C3—242no—
348C22×C3D3×D811yescharacteristic
349C22×C3C2×#21311yescharacteristic
350C2×D3—22no—
351C2×D3—42no—
352C2×D3—82no—
353C2×D3—122no—
354C2×D3—122no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—242no—
358C2×D3—482no—
359C2×D3C2×#21312yes—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—32no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—82no—
366C3×C4—122no—
367C3×C4D3×D811yescharacteristic
368C3×C4C2×#21311yescharacteristic
369C3×C4C2×D3×D411yescharacteristic
370C3×C4C22×#6711yescharacteristic
371Dic3—42no—
372Dic3C2×#21312yes—
373C32C2×#50811yescharacteristic, complemented, Sylow
374C23—31no—
375C23—121no—
376C23—361no—
377Q8—22no—
378Q8—41no—
379Q8—62no—
380Q8—121no—
381D4—62no—
382D4—124no—
383D4—121no—
384D4—182no—
385D4—364no—
386D4—361no—
387C2×C4—31no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—41no—
391C2×C4—124no—
392C2×C4—121no—
393C2×C4—364no—
394C2×C4D3×#6711yescharacteristic
395C8—32no—
396C8D3×#6711yescharacteristic
397C8C22×D3211yescharacteristic
398C2×C3—21no—
399C2×C3—22no—
400C2×C3—62no—
401C2×C3—242no—
402C2×C3#491912yescomplemented
403C2×C3#519412yescomplemented
404C2×C3C2×D3×D811yescharacteristic
405C2×C3C22×#21311yescharacteristic
406D3—22no—
407D3—82no—
408D3—242no—
409D3—242no—
410D3—482no—
411C22—32no—
412C22—62no—
413C22—122no—
414C22—242no—
415C22—362no—
416C22—722no—
417C22D3×#21311yescharacteristic
418C4—32no—
419C4—42no—
420C4—122no—
421C4D3×#21311yescharacteristic
422C4C2×D3×#6711yescharacteristic
423C3—21no—
424C3C2×#491911yescharacteristic, complemented
425C3C2×#519411yescharacteristic, complemented
426C2—62no—
427C2—242no—
428C2—722no—
429C2#1059104812yesdirect product factor
430C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32C2×#508
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×#63808C2semidirect
3. C2×#63655C2semidirect
4. C2×C3×#829C2semidirect
5. #10591048C2direct (N × H)
6. C2×#63547C2semidirect
7. C2×#63546C2semidirect
8. C2×D3×C3⋊C16C2semidirect
17. C3×#919C22semidirect
23. #63808C22semidirect
24. #63655C22semidirect
26. C3×#829C22semidirect
28. #63547C22semidirect
29. #63546C22semidirect
30. D3×C3⋊C16C22semidirect
33. C2×#919D3semidirect
37. C2×#829D3semidirect
96. #919C2×D3semidirect
108. #829C2×D3semidirect
309. C2×C32#508semidirect
373. C32C2×#508semidirect
402. C2×C3#4919semidirect
403. C2×C3#5194semidirect
424. C3C2×#4919semidirect
425. C3C2×#5194semidirect
429. C2#10591048direct (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×#638082
C2×#636552
C2×C3×#8292
#105910482
C2×#635472
C2×#635462
C2×D3×C3⋊C162
C2×#51943
C2×#49193