Finite Group Databasebeta

← C2×#10589121 #11796770

Subgroups — C2×#10589121 #11796770

Order 1152.

501 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×#63646C211yesmaximal, characteristic, complemented
3C22×C3×C3⋊C16C211yesmaximal, characteristic, complemented
4#10589121C214yesmaximal, direct product factor
5C2×#4567—31nomaximal
6C2×#4510—31nomaximal
7C2×C3×#235—21no—
8C22×C32×C8C2211yescharacteristic
9C2×#3748—21no—
10C2×C3×Dic12C411yescharacteristic
11C3×#904—21no—
12C3×#904—21no—
13C3×#904C412yes—
14C3×#904C2212yes—
15C2×C3×D24C411yescharacteristic
16C2×C3×#204—21no—
17#63646—21no—
18#63646C2212yescomplemented
19C2×C3×C3⋊C16—21no—
20C2×C3×C3⋊C16—21no—
21C2×C3×C3⋊C16C2212yescomplemented
22C2×C3×#135—31no—
23C2×#904D311yescharacteristic
24C22×C3×C16—31no—
25C2×#819—31no—
26C2×#819—31no—
27C2×#819—61no—
28C22×C3⋊C16D311yescharacteristic, complemented
29#4567—34no—
30#4510—34no—
31C22×C32×C4D411yescharacteristic
32C2×C3×#67—41no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—41no—
36C3×#235—41no—
37C2×C3×D12—21no—
38C2×C3×C4×D3—41no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42C2×C32×C8D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46#3748—22no—
47#3748—41no—
48C2×C3⋊(C3⋊C8)—41no—
49C3×Dic12—21no—
50C3×Dic12C2×C412yes—
51C3×D24—21no—
52C3×D24C2×C412yes—
53C3×#204—22no—
54C3×#204—22no—
55C3×C3⋊C16—22no—
56C2×#359—91noSylow
57C2×C3×#41—61no—
58C2×#235—21no—
59C3×#135—32no—
60C3×#135—32no—
61C3×#135—61no—
62C3×#135—61no—
63C2×C3×Q16—31no—
64C2×C3×SD16—61no—
65C2×C3×D8—31no—
66C22×C3×C8—21no—
67C22×C3×C8C2×D311yescharacteristic
68C22×C3×C8C2×D311yescharacteristic
69C2×#208—62no—
70C2×#208—61no—
71C2×#208—61no—
72C2×Dic12Dic311yescharacteristic
73#904—21no—
74#904—21no—
75#904Dic312yes—
76#904C2×D312yes—
77C2×D24Dic311yescharacteristic
78C2×#204—21no—
79C2×C3×C16—32no—
80C2×C3×C16—61no—
81C2×C3×C16—61no—
82#819—32no—
83#819—32no—
84#819—62no—
85#819—62no—
86#819—61no—
87#819—61no—
88C2×C3⋊C16—21no—
89C2×C3⋊C16—21no—
90C2×C3⋊C16C2×D312yescomplemented
91C23×C32SD1611yescharacteristic
92C22×C3×D3—41no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4D811yescharacteristic
96C2×C32×C4D811yescharacteristic
97C2×C32×C4SD1611yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C3×#67—42no—
100C3×#67—42no—
101C2×C3×Dic3—41no—
102C3×D12—22no—
103C3×D12—41no—
104C3×C4×D3—42no—
105C3×C4×D3—42no—
106C3×Dic6—22no—
107C3×Dic6—41no—
108C32×C8C22⋊C411yescharacteristic
109C32×C8C22⋊C411yescharacteristic
110C32×C8C22×C411yescharacteristic
111C32×C8C2×D411yescharacteristic
112C3⋊(C3⋊C8)—42no—
113C2×#135—31no—
114C22×C16—31no—
115C2×#108—91no—
116#359—94no—
117C3×#41—62no—
118C3×#41—62no—
119C3×#41—121no—
120C3×#41—121no—
121C2×C3×Q8—61no—
122C2×C3×D4—61no—
123C2×C3×D4—121no—
124C22×C3×C4—21no—
125C22×C3×C4—121no—
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C2×#67—41no—
129#235—22no—
130#235—22no—
131#235—41no—
132#235—41no—
133C2×D12—21no—
134C2×C4×D3—41no—
135C2×Dic6—21no—
136C3×Q16—32no—
137C3×Q16—61no—
138C3×SD16—62no—
139C3×SD16—62no—
140C3×D8—32no—
141C3×D8—61no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8C4×D311yescharacteristic
149C2×C3×C8C4×D311yescharacteristic
150C2×C3×C8D1211yescharacteristic
151C2×C3×C8C2×Dic311yescharacteristic
152C2×C3×C8C2×Dic311yescharacteristic
153C2×C3×C8#6711yescharacteristic
154C2×C3×C8#6711yescharacteristic
155C2×C3×C8#6711yescharacteristic
156C2×C3×C8#6711yescharacteristic
157C2×C3×C8#6711yescharacteristic
158C2×C3×C8C22×D311yescharacteristic
159C2×C3×C8C22×D311yescharacteristic
160#208—64no—
161#208—62no—
162#208—62no—
163#208—122no—
164#208—121no—
165#208—121no—
166C2×C3⋊C8—122no—
167C2×C3⋊C8—121no—
168C2×C3⋊C8—121no—
169Dic12—21no—
170Dic12C2×Dic312yes—
171D24—21no—
172D24C2×Dic312yes—
173#204—22no—
174#204—22no—
175C3×C16—62no—
176C3⋊C16—22no—
177C22×C32—22no—
178C22×C32#10211yescharacteristic
179C22×C32#10211yescharacteristic
180C22×C32C2×SD1611yescharacteristic
181C2×C3×D3—42no—
182C2×C3×D3—82no—
183C32×C4#10211yescharacteristic
184C32×C4#10211yescharacteristic
185C32×C4C2×C22⋊C411yescharacteristic
186C32×C4C2×D811yescharacteristic
187C3×Dic3—42no—
188C2×#41—61no—
189#135—32no—
190#135—32no—
191#135—61no—
192#135—61no—
193C2×Q16—31no—
194C2×SD16—61no—
195C2×D8—31no—
196C2×M16—181no—
197C22×C8D3211yescharacteristic
198C2×C16—32no—
199C2×C16—61no—
200C2×C16—61no—
201#108—92no—
202#108—181no—
203C23×C3—21no—
204C23×C3—121no—
205C23×C3#20411yescharacteristic
206C23×C3#21411yescharacteristic
207C22×D3—41no—
208C3×Q8—62no—
209C3×Q8—121no—
210C3×D4—62no—
211C3×D4—122no—
212C3×D4—122no—
213C3×D4—121no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—121no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4#20411yescharacteristic
224C2×C3×C4D2411yescharacteristic
225C2×C3×C4D2411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4(C2×D3)⋊C411yescharacteristic
228C2×C3×C4#21311yescharacteristic
229C2×C3×C4#21311yescharacteristic
230C2×C3×C4#21411yescharacteristic
231C2×C3×C4#21711yescharacteristic
232C2×C3×C4#21711yescharacteristic
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235#67—42no—
236#67—42no—
237C2×Dic3—41no—
238D12—22no—
239D12—41no—
240C4×D3—42no—
241C4×D3—42no—
242Dic6—22no—
243Dic6—41no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—21no—
247C3×C8—21no—
248C3×C8(C2×D3)⋊C411yescharacteristic
249C3×C8(C2×D3)⋊C411yescharacteristic
250C3×C8#21711yescharacteristic
251C3×C8#21711yescharacteristic
252C3×C8C2×C4×D311yescharacteristic
253C3×C8C22×Dic311yescharacteristic
254C3×C8C2×#6711yescharacteristic
255C3×C8C2×#6711yescharacteristic
256C3⋊C8—124no—
257C3⋊C8—122no—
258C3⋊C8—122no—
259C2×C32—21no—
260C2×C32—21no—
261C2×C32#35912yescomplemented
262C2×C32C2×#10211yescharacteristic
263C3×D3—82no—
264#41—62no—
265#41—62no—
266#41—121no—
267#41—121no—
268C2×Q8—61no—
269C2×D4—61no—
270C2×D4—121no—
271C22×C4—121no—
272C22×C4#62611yescharacteristic
273Q16—32no—
274Q16—61no—
275SD16—62no—
276SD16—62no—
277D8—32no—
278D8—61no—
279M16—182no—
280M16—361no—
281C2×C8—361no—
282C2×C8D3×Dic311yescharacteristic
283C2×C8D3×Dic311yescharacteristic
284C2×C8#62511yescharacteristic
285C2×C8#62511yescharacteristic
286C2×C8#62611yescharacteristic
287C2×C8C2×D3211yescharacteristic
288C16—62no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—42no—
295C22×C3—122no—
296C22×C3—242no—
297C22×C3#82111yescharacteristic
298C22×C3#82111yescharacteristic
299C22×C3#83211yescharacteristic
300C22×C3#83211yescharacteristic
301C22×C3C2×#20411yescharacteristic
302C22×C3C2×#21411yescharacteristic
303C2×D3—42no—
304C2×D3—82no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—122no—
310C3×C4#82111yescharacteristic
311C3×C4#82111yescharacteristic
312C3×C4#83211yescharacteristic
313C3×C4#83211yescharacteristic
314C3×C4C2×D2411yescharacteristic
315C3×C4C2×(C2×D3)⋊C411yescharacteristic
316C3×C4C2×#21311yescharacteristic
317C3×C4C2×#21711yescharacteristic
318Dic3—42no—
319C32C2×#35911yescharacteristic, complemented, Sylow
320C23—121no—
321C23#371611yescharacteristic
322Q8—62no—
323Q8—121no—
324D4—62no—
325D4—122no—
326D4—122no—
327D4—121no—
328C2×C4—121no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4#371411yescharacteristic
332C2×C4#371411yescharacteristic
333C2×C4#371611yescharacteristic
334C2×C4(C2×D3)⋊Dic311yescharacteristic
335C2×C4(C2×D3)⋊Dic311yescharacteristic
336C2×C4C2×#62611yescharacteristic
337C8—362no—
338C8(C2×D3)⋊Dic311yescharacteristic
339C8(C2×D3)⋊Dic311yescharacteristic
340C8C2×D3×Dic311yescharacteristic
341C8C2×#62511yescharacteristic
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—22no—
348C2×C3—41no—
349C2×C3—41no—
350C2×C3—242no—
351C2×C3#451012yescomplemented
352C2×C3#456712yescomplemented
353C2×C3C2×#82111yescharacteristic
354C2×C3C2×#83211yescharacteristic
355D3—82no—
356C22—22no—
357C22—122no—
358C22—242no—
359C22#6356311yescharacteristic
360C22#6356311yescharacteristic
361C22C2×#371611yescharacteristic
362C4—122no—
363C4#6356311yescharacteristic
364C4#6356311yescharacteristic
365C4C2×#371411yescharacteristic
366C4C2×(C2×D3)⋊Dic311yescharacteristic
367C3—21no—
368C3C2×#451011yescharacteristic, complemented
369C3C2×#456711yescharacteristic, complemented
370C2—21no—
371C2—21no—
372C2—242no—
373C2#1058912112yesdirect product factor
374C2C2×#6356311yescharacteristic
subgroupG/H
centerC2×C4#3714
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32#102
prime radicalC2×C3×#904C2
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32C2×#359
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63646C2semidirect
3. C22×C3×C3⋊C16C2semidirect
4. #10589121C2direct (N × H)
18. #63646C22semidirect
21. C2×C3×C3⋊C16C22semidirect
28. C22×C3⋊C16D3semidirect
90. C2×C3⋊C16C2×D3semidirect
261. C2×C32#359semidirect
319. C32C2×#359semidirect
351. C2×C3#4510semidirect
352. C2×C3#4567semidirect
368. C3C2×#4510semidirect
369. C3C2×#4567semidirect
373. C2#10589121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×#636462
C22×C3×C3⋊C162
#105891212
C2×#45673
C2×#45103