Finite Group Databasebeta

← C2×#10593883 #11901583

Subgroups — C2×#10593883 #11901583

Order 1152.

2173 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C3×C4×Dic6C212yesmaximal, complemented
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63872C211yesmaximal, characteristic, complemented
5C2×#63871C212yesmaximal
6C2×#63868C214yesmaximal
7C2×#63867C214yesmaximal, complemented
8#10593883C2116yesmaximal, direct product factor
9C2×#5583—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2212yes—
12C2×C32×C42C2211yescharacteristic
13C2×#3752C2212yes—
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64081C2218yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×Dic3⋊C4C2214yes—
19C2×C3×C4×Dic3C2214yes—
20C3×C4×Dic6C22116yescomplemented
21C2×#3724C2214yes—
22C2×Dic3⋊Dic3C2214yes—
23C2×Dic3⋊Dic3C2214yes—
24C2×#3722C2214yes—
25#63873C2218yescomplemented
26#63872C2218yescomplemented
27#63871C22116yes—
28#63868C22132yes—
29#63867C22132yescomplemented
30C2×C3×C4×Q8—32no—
31C2×#946—32no—
32C2×#944—32no—
33#5583—332no—
34C2×#898—34no—
35C2×#897—32no—
36C2×#890—32no—
37C2×#889—34no—
38C2×#876—34no—
39C2×#872—32no—
40C2×#872—61no—
41C2×#870—34no—
42C2×C4×Dic6D312yescomplemented
43C23×C3⋊D3C2311yescharacteristic
44C22×C32×C4C2312yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3C2314yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2314yes—
52C2×C3×Dic6—28no—
53C2×C3×Dic6C2318yes—
54C32×C42C2314yes—
55#3752C2318yes—
56#3750C2318yes—
57C4×C3⋊Dic3C2314yes—
58C3×C4⋊Dic3C2318yes—
59C3×Dic3⋊C4C23116yes—
60C3×C4×Dic3C23116yes—
61#3724C23116yes—
62Dic3⋊Dic3C23116yes—
63Dic3⋊Dic3C23116yes—
64#3722C23116yes—
65C2×#541—91noSylow
66C22×C3×Q8—32no—
67C22×C4×D3—32no—
68C22×C4×D3—61no—
69C22×Dic6C2×D312yes—
70C3×C4×Q8—316no—
71C2×C3×C4⋊C4—34no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C42—21no—
74C2×C3×C42—34no—
75C2×C3×C42C2×D312yes—
76#946—316no—
77#944—316no—
78C2×(C2×D3)⋊C4—32no—
79C2×(C2×D3)⋊C4—32no—
80C2×(C2×D3)⋊C4—34no—
81C2×(C2×D3)⋊C4—34no—
82C2×(C2×D3)⋊C4—62no—
83C2×C4⋊Dic3—34no—
84C2×C4⋊Dic3—34no—
85C2×C4⋊Dic3C2×D312yes—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×Dic3⋊C4—34no—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—62no—
93C2×Dic3⋊C4C2×D314yes—
94C2×C4×Dic3—32no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3C2×D314yes—
97#898—332no—
98#897—316no—
99#890—316no—
100#889—332no—
101#876—332no—
102#872—316no—
103#872—68no—
104#870—332no—
105C4×Dic6C2×D3116yescomplemented
106C23×C32C2411yescharacteristic
107C22×C3⋊D3—22no—
108C22×C3⋊D3—24no—
109C22×C3⋊D3C2412yes—
110C2×C32×C4—24no—
111C2×C32×C4#4114yes—
112C2×C32×C4C2414yes—
113C2×C32×C4C2412yes—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—24no—
116C2×C3⋊Dic3C2412yes—
117C2×C3⋊Dic3C2414yes—
118C4×C3⋊D3—28no—
119C2×C3×Dic3—28no—
120C2×C3×Dic3—28no—
121C2×C3×Dic3C2418yes—
122C2×C3×Dic3C2418yes—
123C3×Dic6—216no—
124#541—916no—
125C2×C4⋊Q8—91no—
126C2×#126—94no—
127C2×#125—94no—
128C2×#125—91no—
129C2×C22⋊Q8—92no—
130C2×C4×Q8—32no—
131C2×#117—91no—
132C23×D3—32no—
133C23×D3—61no—
134C2×C3×Q8—38no—
135C2×C3×Q8—68no—
136C22×C3×C4—21no—
137C22×C3×C4—22no—
138C22×C3×C4—34no—
139C22×C3×C4—34no—
140C22×C3×C4C22×D312yes—
141C22×C3×C4C22×D312yes—
142C22×C3×C4C22×D312yes—
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—32no—
146C22×Dic3—61no—
147C22×Dic3—62no—
148C22×Dic3C22×D314yes—
149C22×Dic3C22×D314yes—
150C2×C4×D3—38no—
151C2×C4×D3—64no—
152C2×C4×D3—68no—
153C2×C4×D3—68no—
154C2×Dic6—28no—
155C2×Dic6C22×D318yes—
156C3×C4⋊C4—316no—
157C3×C4⋊C4—38no—
158C3×C42—24no—
159C3×C42—316no—
160C3×C42C22×D318yes—
161(C2×D3)⋊C4—38no—
162(C2×D3)⋊C4—38no—
163(C2×D3)⋊C4—316no—
164(C2×D3)⋊C4—316no—
165(C2×D3)⋊C4—68no—
166C4⋊Dic3—316no—
167C4⋊Dic3—316no—
168C4⋊Dic3C22×D318yes—
169Dic3⋊C4—38no—
170Dic3⋊C4—38no—
171Dic3⋊C4—316no—
172Dic3⋊C4—316no—
173Dic3⋊C4—316no—
174Dic3⋊C4—316no—
175Dic3⋊C4—68no—
176Dic3⋊C4C22×D3116yes—
177C4×Dic3—38no—
178C4×Dic3—64no—
179C4×Dic3C22×D3116yes—
180C22×C32C2×#4112yes—
181C22×C322−1+414yes—
182C22×C32C2511yescharacteristic
183C2×C3⋊D3—22no—
184C2×C3⋊D3—24no—
185C2×C3⋊D3—44no—
186C32×C4—24no—
187C32×C4C2×#4114yes—
188C3⋊Dic3—22no—
189C3⋊Dic3—24no—
190C3×Dic3—28no—
191C3×Dic3—28no—
192C22×Q8—32no—
193C23×C4—91no—
194C4⋊Q8—98no—
195#126—932no—
196#125—932no—
197#125—98no—
198C22⋊Q8—916no—
199C4×Q8—316no—
200#117—98no—
201C2×C4⋊C4—32no—
202C2×C4⋊C4—34no—
203C2×C4⋊C4—94no—
204C2×C4⋊C4—94no—
205C2×C4⋊C4—94no—
206C2×C4⋊C4—92no—
207C2×C22⋊C4—94no—
208C2×C22⋊C4—92no—
209C2×C42—34no—
210C2×C42—91no—
211C2×C42D3211yescharacteristic
212C23×C3—21no—
213C23×C3C23×D312yes—
214C22×D3—34no—
215C22×D3—62no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—64no—
219C22×D3—64no—
220C22×D3—124no—
221C3×Q8—616no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—22no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—38no—
228C2×C3×C4—38no—
229C2×C3×C4—44no—
230C2×C3×C4—68no—
231C2×C3×C4—68no—
232C2×C3×C4#23518yes—
233C2×C3×C4C23×D314yes—
234C2×C3×C4C23×D314yes—
235C2×C3×C4C23×D314yes—
236C2×Dic3—28no—
237C2×Dic3—28no—
238C2×Dic3—34no—
239C2×Dic3—34no—
240C2×Dic3—34no—
241C2×Dic3—62no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—124no—
248C2×Dic3C23×D318yes—
249C2×Dic3C23×D318yes—
250C4×D3—616no—
251C4×D3—616no—
252Dic6—216no—
253C2×C32#54114yescomplemented
254C2×C32C22×#4111yescharacteristic
255C2×C32C2×2−1+412yes—
256C3⋊D3—42no—
257C24—91no—
258C2×Q8—38no—
259C2×Q8—68no—
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—92no—
263C22×C4—91no—
264C22×C4—94no—
265C22×C4—184no—
266C22×C4C2×D3212yes—
267C22×C4C2×D3211yescharacteristic
268C4⋊C4—38no—
269C4⋊C4—316no—
270C4⋊C4—916no—
271C4⋊C4—916no—
272C4⋊C4—916no—
273C4⋊C4—98no—
274C22⋊C4—916no—
275C22⋊C4—98no—
276C42—316no—
277C42—94no—
278C42C2×D3214yes—
279C22×C3—24no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3C2×#23514yes—
283C22×C3#100714yes—
284C22×C3#101014yes—
285C22×C3C24×D312yes—
286C2×D3—64no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—64no—
290C2×D3—124no—
291C2×D3—128no—
292C2×D3—128no—
293C3×C4—24no—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—44no—
297C3×C4—68no—
298C3×C4—68no—
299C3×C4C2×#23518yes—
300Dic3—28no—
301Dic3—28no—
302Dic3—64no—
303Dic3—64no—
304Dic3—64no—
305Dic3—64no—
306Dic3—124no—
307C32C2×#54111yescharacteristic, complemented, Sylow
308C23—92no—
309C23—184no—
310C23—182no—
311C23C22×D3211yescharacteristic
312Q8—616no—
313C2×C4—24no—
314C2×C4—38no—
315C2×C4—38no—
316C2×C4—68no—
317C2×C4—68no—
318C2×C4—94no—
319C2×C4—92no—
320C2×C4—184no—
321C2×C4—182no—
322C2×C4—188no—
323C2×C4#379814yes—
324C2×C4C22×D3214yes—
325C2×C4C22×D3212yes—
326C2×C3—22no—
327C2×C3—21no—
328C2×C3—24no—
329C2×C3#558318yescomplemented
330C2×C3C22×#23512yes—
331C2×C3C2×#100712yes—
332C2×C3C2×#101012yes—
333D3—124no—
334D3—124no—
335C22—184no—
336C22—182no—
337C22—364no—
338C22#6429714yes—
339C22C2×#379812yes—
340C22C23×D3211yescharacteristic
341C4—24no—
342C4—68no—
343C4—68no—
344C4—184no—
345C4—182no—
346C4C2×#379814yes—
347C3—21no—
348C3C2×#558312yescomplemented
349C2—362no—
350C2#1059388314yesdirect product factor
351C2C2×#6429712yes—
352C2C22×#379811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C2×#63873C2semidirect
4. C2×#63872C2semidirect
7. C2×#63867C2semidirect
8. #10593883C2direct (N × H)
20. C3×C4×Dic6C22semidirect
25. #63873C22semidirect
26. #63872C22semidirect
29. #63867C22semidirect
42. C2×C4×Dic6D3semidirect
105. C4×Dic6C2×D3semidirect
253. C2×C32#541semidirect
307. C32C2×#541semidirect
329. C2×C3#5583semidirect
348. C3C2×#5583semidirect
350. C2#10593883direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×C4×Dic62
C2×#638732
C2×#638722
C2×#638712
C2×#638682
C2×#638672
#105938832
C2×#55833