Finite Group Databasebeta

← C2×#3377 #61315

Subgroups — C2×#3377 #61315

Order 256.

905 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557C211yesmaximal, characteristic, complemented
2C2×#556C211yesmaximal, characteristic
3#3377C2116yesmaximal, direct product factor
4C2×#491C211yesmaximal, characteristic, complemented
5C2×#489C211yesmaximal, characteristic
6C2×#488C211yesmaximal, characteristic
7C2×#479C211yesmaximal, characteristic, complemented
8C2×#477C211yesmaximal, characteristic, complemented
9C2×#478C211yesmaximal, characteristic
10C2×#464C211yesmaximal, characteristic
11C2×#464C211yesmaximal, characteristic
12C2×#462C211yesmaximal, characteristic, complemented
13C2×#446C211yesmaximal, characteristic, complemented
14C2×#441C211yesmaximal, characteristic, complemented
15C2×#440C211yesmaximal, characteristic
16C2×C4×Q16C211yesmaximal, characteristic, complemented
17C22×Q16C2211yescharacteristic
18C22×Q16C2211yescharacteristic
19C22×SD16C2211yescharacteristic
20#557—24no—
21#557C2218yescomplemented
22#556—24no—
23#556C2218yes—
24C2×C4⋊Q8—21no—
25C2×C4⋊Q8C2211yescharacteristic
26C2×C4⋊Q8C2211yescharacteristic
27C2×#126—21no—
28C2×#126—21no—
29C2×#125—21no—
30C2×#125—21no—
31C2×#125C2211yescharacteristic
32C2×#125C2211yescharacteristic
33C2×#124C2211yescharacteristic
34C2×#124C2211yescharacteristic
35C2×C22⋊Q8—21no—
36C2×C4×Q8—21no—
37C2×C4×Q8C2211yescharacteristic
38C2×C4×Q8C2211yescharacteristic
39C2×C4×Q8C2211yescharacteristic
40C2×C4×Q8C2211yescharacteristic
41C2×C4×Q8C2211yescharacteristic
42C2×C4×Q8C2211yescharacteristic
43C2×C4×D4C2211yescharacteristic
44C2×#117—21no—
45#491C2218yescomplemented
46#489C2218yes—
47#488C2218yes—
48#479C2218yescomplemented
49#478C2218yes—
50#477C2218yescomplemented
51#464C2218yes—
52#464C2218yes—
53#462C2218yescomplemented
54#446C2218yescomplemented
55#441C2218yescomplemented
56#440C2218yes—
57C4×Q16C2218yescomplemented
58C2×#107C2211yescharacteristic
59C2×#107C2211yescharacteristic
60C2×#106C2211yescharacteristic
61C2×C4⋊C8C2211yescharacteristic
62C2×C4⋊C8C2211yescharacteristic
63C2×C4⋊C8C2211yescharacteristic
64C2×#103C2211yescharacteristic
65C2×#103C2211yescharacteristic
66C2×#103C2211yescharacteristic
67C2×#103C2211yescharacteristic
68C2×#103C2211yescharacteristic
69C2×#103C2211yescharacteristic
70C2×#103C2211yescharacteristic
71C2×#102C2211yescharacteristic
72C2×#102C2211yescharacteristic
73C2×#102C2211yescharacteristic
74C2×#97C2211yescharacteristic
75C2×#97C2211yescharacteristic
76C2×C4×C8C2211yescharacteristic
77C22×Q8—21no—
78C22×Q8D411yescharacteristic
79C22×Q8C2311yescharacteristic
80C22×Q8C2311yescharacteristic
81C22×Q8C2311yescharacteristic
82C22×D4C2311yescharacteristic
83C23×C4—21no—
84C2×Q16—24no—
85C2×Q16—24no—
86C2×Q16C2314yes—
87C2×Q16C2314yes—
88C2×SD16—24no—
89C2×SD16C2314yes—
90C22×C8C2311yescharacteristic
91C22×C8C2311yescharacteristic
92C22×C8C2311yescharacteristic
93C22×C8C2311yescharacteristic
94C4⋊Q8—28no—
95C4⋊Q8—22no—
96C4⋊Q8—22no—
97C4⋊Q8C2314yes—
98C4⋊Q8C2314yes—
99#126—28no—
100#126—28no—
101#125—28no—
102#125—28no—
103#125—22no—
104#125—22no—
105#125C2314yes—
106#125C2314yes—
107#124—22no—
108#124—22no—
109#124C2314yes—
110#124C2314yes—
111C22⋊Q8—28no—
112C4×Q8—28no—
113C4×Q8—22no—
114C4×Q8—22no—
115C4×Q8—22no—
116C4×Q8—22no—
117C4×Q8—22no—
118C4×Q8D414yes—
119C4×Q8C2314yes—
120C4×Q8C2314yes—
121C4×Q8C2314yes—
122C4×Q8C2314yes—
123C4×Q8C2314yes—
124C4×Q8C2314yes—
125C4×D4—22no—
126C4×D4C2314yes—
127#117—28no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4D411yescharacteristic
141C2×C4⋊C4D411yescharacteristic
142C2×C4⋊C4D411yescharacteristic
143C2×C4⋊C4C2311yescharacteristic
144C2×C4⋊C4C2311yescharacteristic
145C2×C4⋊C4C2311yescharacteristic
146C2×C4⋊C4C2311yescharacteristic
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42C2311yescharacteristic
158C2×C42C2311yescharacteristic
159C2×C42C2311yescharacteristic
160#107C2314yes—
161#107C2314yes—
162#106C2314yes—
163C4⋊C8C2314yes—
164C4⋊C8C2314yes—
165C4⋊C8C2314yes—
166#103C2314yes—
167#103C2314yes—
168#103C2314yes—
169#103C2314yes—
170#103C2314yes—
171#103C2314yes—
172#103C2314yes—
173#102C2314yes—
174#102C2314yes—
175#102C2314yes—
176#97C2314yes—
177#97C2314yes—
178C4×C8C2314yes—
179C24—21no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—21no—
183C2×Q8—24no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—42no—
190C2×Q8—44no—
191C2×Q8C2×D414yes—
192C2×Q8#4114yes—
193C2×Q8C2412yes—
194C2×Q8C2412yes—
195C2×Q8C2412yes—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4C2412yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—44no—
209C22×C4C2×D411yescharacteristic
210C22×C4C2×D411yescharacteristic
211C22×C4C2×D411yescharacteristic
212C22×C4C2×D411yescharacteristic
213C22×C4C2×D411yescharacteristic
214C22×C4C2×D411yescharacteristic
215C22×C4C2411yescharacteristic
216Q16—28no—
217Q16—28no—
218SD16—28no—
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8C2412yes—
224C2×C8C2412yes—
225C2×C8C2412yes—
226C2×C8C2412yes—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—24no—
231C4⋊C4—24no—
232C4⋊C4—24no—
233C4⋊C4—24no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—24no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4C2×D414yes—
244C4⋊C4C2×D414yes—
245C4⋊C4C2×D414yes—
246C4⋊C4C2412yes—
247C4⋊C4C2412yes—
248C4⋊C4C2412yes—
249C4⋊C4C2412yes—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—24no—
255C42—24no—
256C42—24no—
257C42—24no—
258C42—24no—
259C42—24no—
260C42C2×D412yes—
261C42C2×D412yes—
262C42C2×D412yes—
263C42C2412yes—
264C42C2412yes—
265C42C2412yes—
266C23—22no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23C22×D411yescharacteristic
271Q8—24no—
272Q8—22no—
273Q8—22no—
274Q8—22no—
275Q8—22no—
276Q8—22no—
277Q8—44no—
278Q8—48no—
279Q8—42no—
280Q8—42no—
281Q8C2×#4114yes—
282D4—22no—
283D4—22no—
284D4—42no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—48no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4C22×D412yes—
307C2×C4C22×D412yes—
308C2×C4C22×D412yes—
309C2×C4C22×D412yes—
310C2×C4C22×D412yes—
311C2×C4C22×D412yes—
312C2×C4C22×D411yescharacteristic
313C2×C4C2×#4112yes—
314C2×C42−1+412yes—
315C2×C4C2511yescharacteristic
316C8—22no—
317C8—22no—
318C8—22no—
319C8—22no—
320C22—42no—
321C22—42no—
322C22—42no—
323C22—84no—
324C22#54812yes—
325C22#57512yes—
326C22#57812yes—
327C22C23×D411yescharacteristic
328C4—24no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—22no—
335C4—42no—
336C4—42no—
337C4—42no—
338C4—42no—
339C4—42no—
340C4—42no—
341C4#54812yes—
342C4C22×#4111yescharacteristic
343C4C2×2−1+411yescharacteristic
344C2—82no—
345C2#337714yesdirect product factor
346C2C2×#54811yescharacteristic
347C2C2×#57511yescharacteristic
348C2C2×#57811yescharacteristic
subgroupG/H
center, socleC23C22×D4
commutator, Frattini, cosocleC2×C4C25
prime radicalC22×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#557C2semidirect
3. #3377C2direct (N × H)
4. C2×#491C2semidirect
7. C2×#479C2semidirect
8. C2×#477C2semidirect
12. C2×#462C2semidirect
13. C2×#446C2semidirect
14. C2×#441C2semidirect
16. C2×C4×Q16C2semidirect
21. #557C22semidirect
45. #491C22semidirect
48. #479C22semidirect
50. #477C22semidirect
53. #462C22semidirect
54. #446C22semidirect
55. #441C22semidirect
57. C4×Q16C22semidirect
345. C2#3377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#5572
C2×#5562
#33772
C2×#4912
C2×#4892
C2×#4882
C2×#4792
C2×#4772
C2×#4782
C2×#4642
C2×#4622
C2×#4462
C2×#4412
C2×#4402
C2×C4×Q162