Finite Group Databasebeta

← C2×#10589120 #11796772

Subgroups — C2×#10589120 #11796772

Order 1152.

497 conjugacy classes of subgroups.

The subgroup lattice has 373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C22×C3⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
3C2×C3×#819C211yesmaximal, characteristic, complemented
4#10589120C214yesmaximal, direct product factor
5C2×#4567—31nomaximal
6C2×#4497—31nomaximal
7C2×C3×#235—21no—
8C22×C32×C8C2211yescharacteristic
9C2×C3×#208—21no—
10C2×C3×Dic12C411yescharacteristic
11C3×#904—21no—
12C3×#904—21no—
13C3×#904C412yes—
14C3×#904C2212yes—
15C2×C3×D24C411yescharacteristic
16C2×C3×#204—21no—
17C2×C3⋊(C3⋊C16)—21no—
18C2×C3⋊(C3⋊C16)—21no—
19C2×C3⋊(C3⋊C16)C2212yescomplemented
20C3×#819—21no—
21C3×#819C2212yescomplemented
22C2×C3×#135—31no—
23C2×#904D311yescharacteristic
24C2×C3×#108—31no—
25C2×#819D311yescharacteristic, complemented
26C22×C3⋊C16—31no—
27C22×C3⋊C16—31no—
28C22×C3⋊C16—61no—
29#4567—34no—
30#4497—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
46C3×#208—22no—
47C3×#208—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—
66C2×C3×M16—61no—
67C22×C3×C8—21no—
68C22×C3×C8C2×D311yescharacteristic
69C22×C3×C8C2×D311yescharacteristic
70C2×#208—21no—
71C2×Dic12Dic311yescharacteristic
72#904—21no—
73#904—21no—
74#904Dic312yes—
75#904C2×D312yes—
76C2×D24Dic311yescharacteristic
77C2×#204—21no—
78C3×#108—32no—
79C3×#108—61no—
80#819—21no—
81#819C2×D312yescomplemented
82C2×C3⋊C16—32no—
83C2×C3⋊C16—32no—
84C2×C3⋊C16—62no—
85C2×C3⋊C16—62no—
86C2×C3⋊C16—62no—
87C2×C3⋊C16—61no—
88C2×C3⋊C16—61no—
89C2×C3⋊C16—61no—
90C2×C3⋊C16—61no—
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—91no—
115C2×#108—31no—
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×C4#6711yescharacteristic
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—
142C3×M16—62no—
143C3×M16—121no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—121no—
151C2×C3×C8C4×D311yescharacteristic
152C2×C3×C8C4×D311yescharacteristic
153C2×C3×C8D1211yescharacteristic
154C2×C3×C8D1211yescharacteristic
155C2×C3×C8C2×Dic311yescharacteristic
156C2×C3×C8C2×Dic311yescharacteristic
157C2×C3×C8#6711yescharacteristic
158C2×C3×C8#6711yescharacteristic
159C2×C3×C8#6711yescharacteristic
160C2×C3×C8#6711yescharacteristic
161C2×C3×C8C22×D311yescharacteristic
162C2×C3×C8C22×D311yescharacteristic
163#208—22no—
164#208—41no—
165C2×C3⋊C8—41no—
166Dic12—21no—
167Dic12C2×Dic312yes—
168D24—21no—
169D24C2×Dic312yes—
170#204—22no—
171#204—22no—
172C3⋊C16—64no—
173C3⋊C16—62no—
174C3⋊C16—62no—
175C22×C32—22no—
176C22×C32#10211yescharacteristic
177C22×C32#10211yescharacteristic
178C22×C32C2×SD1611yescharacteristic
179C2×C3×D3—42no—
180C2×C3×D3—82no—
181C32×C4#10211yescharacteristic
182C32×C4#10211yescharacteristic
183C32×C4C2×C22⋊C411yescharacteristic
184C32×C4C2×D811yescharacteristic
185C3×Dic3—42no—
186C2×#41—61no—
187#135—32no—
188#135—32no—
189#135—61no—
190#135—61no—
191C2×Q16—31no—
192C2×SD16—61no—
193C2×D8—31no—
194C2×M16—61no—
195C22×C8D3211yescharacteristic
196C2×C16—92no—
197C2×C16—181no—
198C2×C16—181no—
199#108—32no—
200#108—61no—
201C23×C3—21no—
202C23×C3—121no—
203C23×C3#21411yescharacteristic
204C23×C3#21511yescharacteristic
205C22×D3—41no—
206C3×Q8—62no—
207C3×Q8—121no—
208C3×D4—62no—
209C3×D4—122no—
210C3×D4—122no—
211C3×D4—121no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—121no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4#21311yescharacteristic
224C2×C3×C4#21311yescharacteristic
225C2×C3×C4#21311yescharacteristic
226C2×C3×C4#21311yescharacteristic
227C2×C3×C4#21411yescharacteristic
228C2×C3×C4#21511yescharacteristic
229C2×C3×C4#21711yescharacteristic
230C2×C3×C4#21711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233#67—42no—
234#67—42no—
235C2×Dic3—41no—
236D12—22no—
237D12—41no—
238C4×D3—42no—
239C4×D3—42no—
240Dic6—22no—
241Dic6—41no—
242C3×C8—21no—
243C3×C8—21no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—122no—
247C3×C8(C2×D3)⋊C411yescharacteristic
248C3×C8(C2×D3)⋊C411yescharacteristic
249C3×C8#21711yescharacteristic
250C3×C8#21711yescharacteristic
251C3×C8C2×C4×D311yescharacteristic
252C3×C8C2×D1211yescharacteristic
253C3×C8C22×Dic311yescharacteristic
254C3×C8C2×#6711yescharacteristic
255C3⋊C8—42no—
256C2×C32—21no—
257C2×C32—21no—
258C2×C32#35912yescomplemented
259C2×C32C2×#10211yescharacteristic
260C3×D3—82no—
261#41—62no—
262#41—62no—
263#41—121no—
264#41—121no—
265C2×Q8—61no—
266C2×D4—61no—
267C2×D4—121no—
268C22×C4—121no—
269C22×C4#62511yescharacteristic
270Q16—32no—
271Q16—61no—
272SD16—62no—
273SD16—62no—
274D8—32no—
275D8—61no—
276M16—62no—
277M16—121no—
278C2×C8—121no—
279C2×C8D3×Dic311yescharacteristic
280C2×C8D3×Dic311yescharacteristic
281C2×C8#62511yescharacteristic
282C2×C8#62611yescharacteristic
283C2×C8#62611yescharacteristic
284C2×C8C2×D3211yescharacteristic
285C16—182no—
286C22×C3—24no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—122no—
293C22×C3—242no—
294C22×C3#80911yescharacteristic
295C22×C3#80911yescharacteristic
296C22×C3#83211yescharacteristic
297C22×C3#83211yescharacteristic
298C22×C3C2×#21411yescharacteristic
299C22×C3C2×#21511yescharacteristic
300C2×D3—42no—
301C2×D3—82no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—122no—
307C3×C4#80911yescharacteristic
308C3×C4#80911yescharacteristic
309C3×C4#83211yescharacteristic
310C3×C4#83211yescharacteristic
311C3×C4C2×(C2×D3)⋊C411yescharacteristic
312C3×C4C2×#21311yescharacteristic
313C3×C4C2×#21311yescharacteristic
314C3×C4C2×#21711yescharacteristic
315Dic3—42no—
316C32C2×#35911yescharacteristic, complemented, Sylow
317C23—121no—
318C23#371511yescharacteristic
319Q8—62no—
320Q8—121no—
321D4—62no—
322D4—122no—
323D4—122no—
324D4—121no—
325C2×C4—121no—
326C2×C4—122no—
327C2×C4—122no—
328C2×C4#371311yescharacteristic
329C2×C4#371311yescharacteristic
330C2×C4#371511yescharacteristic
331C2×C4(C2×D3)⋊Dic311yescharacteristic
332C2×C4(C2×D3)⋊Dic311yescharacteristic
333C2×C4C2×#62511yescharacteristic
334C8—122no—
335C8(C2×D3)⋊Dic311yescharacteristic
336C8(C2×D3)⋊Dic311yescharacteristic
337C8C2×D3×Dic311yescharacteristic
338C8C2×#62611yescharacteristic
339C2×C3—22no—
340C2×C3—22no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—22no—
347C2×C3—242no—
348C2×C3#449712yescomplemented
349C2×C3#456712yescomplemented
350C2×C3C2×#80911yescharacteristic
351C2×C3C2×#83211yescharacteristic
352D3—82no—
353C22—22no—
354C22—122no—
355C22—242no—
356C22#6356211yescharacteristic
357C22#6356211yescharacteristic
358C22C2×#371511yescharacteristic
359C4—122no—
360C4#6356211yescharacteristic
361C4#6356211yescharacteristic
362C4C2×#371311yescharacteristic
363C4C2×(C2×D3)⋊Dic311yescharacteristic
364C3—21no—
365C3C2×#449711yescharacteristic, complemented
366C3C2×#456711yescharacteristic, complemented
367C2—21no—
368C2—21no—
369C2—242no—
370C2#1058912012yesdirect product factor
371C2C2×#6356211yescharacteristic
subgroupG/H
centerC2×C4#3713
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. C22×C3⋊(C3⋊C16)C2semidirect
3. C2×C3×#819C2semidirect
4. #10589120C2direct (N × H)
19. C2×C3⋊(C3⋊C16)C22semidirect
21. C3×#819C22semidirect
25. C2×#819D3semidirect
81. #819C2×D3semidirect
258. C2×C32#359semidirect
316. C32C2×#359semidirect
348. C2×C3#4497semidirect
349. C2×C3#4567semidirect
365. C3C2×#4497semidirect
366. C3C2×#4567semidirect
370. C2#10589120direct (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
C22×C3⋊(C3⋊C16)2
C2×C3×#8192
#105891202
C2×#45673
C2×#44973