Finite Group Databasebeta

← C2×#10595413 #11903417

Subgroups — C2×#10595413 #11903417

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#946C212yesmaximal, complemented
3#10595413C2116yesmaximal, direct product factor
4C2×#63919C211yesmaximal, characteristic, complemented
5C2×#63915C212yesmaximal
6C2×C4×#625C211yesmaximal, characteristic
7C2×#63861C214yesmaximal, complemented
8C2×#63841C212yesmaximal, complemented
9C2×#63838C212yesmaximal, complemented
10C2×#5641—32nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×C4×D3C2212yes—
13C22×#627C2212yes—
14C22×#625C2211yescharacteristic
15Q8×C3⋊Dic3C2218yescomplemented
16C2×C4⋊(C3⋊Dic3)C2212yes—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20C3×#946C22116yescomplemented
21C2×C3×(C2×D3)⋊C4C2214yes—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2214yes—
24C2×#3724C2212yes—
25C2×#3724C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2214yes—
28C2×Dic32C2214yes—
29#63919C2218yescomplemented
30#63915C22116yes—
31C4×#625C2218yes—
32#63861C22132yescomplemented
33#63841C22116yescomplemented
34#63838C22116yescomplemented
35C2×C3×C22⋊Q8—32no—
36C2×#946D312yescomplemented
37C2×Q8×Dic3—32no—
38C2×Q8×Dic3—61no—
39C2×C4×#67—32no—
40C2×#926—32no—
41#5641—332no—
42C2×#898—34no—
43C2×#892—32no—
44C2×#888—32no—
45C2×#887—34no—
46C2×#885—34no—
47C2×#879—34no—
48C23×C3×D3C2312yes—
49C2×C32×Q8—24no—
50C2×C32×Q8C2314yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C2×C3×C4×D3—28no—
59C2×C3×C4×D3C2318yes—
60C2×#627—28no—
61C2×#627C2318yes—
62C2×#625—24no—
63C2×#625C2314yes—
64C4⋊(C3⋊Dic3)C2314yes—
65C4⋊(C3⋊Dic3)C2318yes—
66C4×C3⋊Dic3C2318yes—
67C4×C3⋊Dic3C2314yes—
68C3×(C2×D3)⋊C4C23116yes—
69C3×C4⋊Dic3C2318yes—
70C3×Dic3⋊C4C23116yes—
71#3724C2314yes—
72#3724C2318yes—
73(C2×D3)⋊Dic3C23116yes—
74(C2×D3)⋊Dic3C2318yes—
75Dic32C23116yes—
76C2×#556—91noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D312yes—
79C23×C3×C4—32no—
80C22×#67—32no—
81C22×C4×D3C2×D312yes—
82C22×Dic6—34no—
83C3×C22⋊Q8—316no—
84C2×C3×C4⋊C4—34no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C22⋊C4—34no—
87C2×#217—32no—
88C2×#217—34no—
89#946C2×D3116yescomplemented
90Q8×Dic3—316no—
91Q8×Dic3—68no—
92C4×#67—316no—
93C2×(C2×D3)⋊C4—34no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4C2×D314yes—
96#926—316no—
97C2×C4⋊Dic3—34no—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—62no—
101C2×C4⋊Dic3C2×D312yes—
102C2×Dic3⋊C4—34no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4C2×D314yes—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—34no—
108C2×C4×Dic3—34no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—62no—
111#898—332no—
112#892—316no—
113#888—316no—
114#887—332no—
115#885—332no—
116#879—332no—
117C23×C32C2411yescharacteristic
118C22×C3×D3—24no—
119C22×C3×D3—24no—
120C22×C3×D3—24no—
121C22×C3×D3C2414yes—
122C32×Q8—28no—
123C2×C32×C4—24no—
124C2×C32×C4#4114yes—
125C2×C32×C4C2414yes—
126C2×C32×C4C2412yes—
127C2×C3⋊Dic3—24no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3#4114yes—
130C2×C3⋊Dic3C2414yes—
131C2×C3⋊Dic3C2412yes—
132C2×C3⋊Dic3C2412yes—
133C2×C3×Dic3—28no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3C2414yes—
136C2×C3×Dic3C2418yes—
137C3×C4×D3—216no—
138#627—216no—
139#625—28no—
140#556—916no—
141C2×C4⋊Q8—91no—
142C2×#126—94no—
143C2×#124—92no—
144C2×C22⋊Q8—32no—
145C2×C4×Q8—92no—
146C2×C4×Q8—91no—
147C2×C4×D4—91no—
148C2×#117—92no—
149C24×C3—32no—
150C23×D3C22×D312yes—
151C2×C3×Q8—28no—
152C2×C3×Q8—28no—
153C2×C3×Q8—24no—
154C2×C3×Q8C22×D318yes—
155C22×C3×C4—22no—
156C22×C3×C4—21no—
157C22×C3×C4—32no—
158C22×C3×C4—34no—
159C22×C3×C4—38no—
160C22×C3×C4—68no—
161C22×C3×C4C22×D314yes—
162C22×C3×C4C22×D312yes—
163C2×#67—38no—
164C2×#67—68no—
165C22×Dic3—32no—
166C22×Dic3—34no—
167C22×Dic3—32no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3—61no—
171C22×Dic3C22×D312yes—
172C22×Dic3C22×D314yes—
173C2×C4×D3—28no—
174C2×C4×D3C22×D318yes—
175C2×Dic6—316no—
176C2×Dic6—616no—
177C3×C4⋊C4—316no—
178C3×C4⋊C4—38no—
179C3×C22⋊C4—316no—
180#217—38no—
181#217—316no—
182(C2×D3)⋊C4—316no—
183(C2×D3)⋊C4—38no—
184(C2×D3)⋊C4C22×D3116yes—
185C4⋊Dic3—316no—
186C4⋊Dic3—38no—
187C4⋊Dic3—64no—
188C4⋊Dic3—68no—
189C4⋊Dic3C22×D318yes—
190Dic3⋊C4—316no—
191Dic3⋊C4—38no—
192Dic3⋊C4C22×D3116yes—
193C4×Dic3—316no—
194C4×Dic3—38no—
195C4×Dic3—316no—
196C4×Dic3—316no—
197C4×Dic3—64no—
198C4×Dic3—68no—
199C22×C32C2×#4112yes—
200C22×C32C2×#4112yes—
201C22×C322−1+412yes—
202C22×C32C2511yescharacteristic
203C2×C3×D3—24no—
204C2×C3×D3—24no—
205C2×C3×D3—24no—
206C2×C3×D3—48no—
207C32×C4—24no—
208C32×C4C2×#4114yes—
209C3⋊Dic3—24no—
210C3⋊Dic3—22no—
211C3⋊Dic3C2×#4114yes—
212C3×Dic3—28no—
213C3×Dic3—24no—
214C22×Q8—92no—
215C22×Q8D3211yescharacteristic
216C22×D4—91no—
217C23×C4—32no—
218C4⋊Q8—98no—
219#126—932no—
220#124—916no—
221C22⋊Q8—316no—
222C4×Q8—916no—
223C4×Q8—98no—
224C4×D4—98no—
225#117—916no—
226C2×C4⋊C4—32no—
227C2×C4⋊C4—34no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—92no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—92no—
232C2×C22⋊C4—34no—
233C2×C22⋊C4—94no—
234C2×C22⋊C4—92no—
235C2×C42—94no—
236C2×C42—91no—
237C2×C42—92no—
238C23×C3—21no—
239C23×C3—34no—
240C23×C3—64no—
241C23×C3—64no—
242C23×C3—64no—
243C23×C3C23×D312yes—
244C22×D3—24no—
245C22×D3—24no—
246C22×D3—24no—
247C22×D3C23×D314yes—
248C3×Q8—216no—
249C3×Q8—216no—
250C2×C3×C4—28no—
251C2×C3×C4—28no—
252C2×C3×C4—24no—
253C2×C3×C4—22no—
254C2×C3×C4—24no—
255C2×C3×C4—34no—
256C2×C3×C4—38no—
257C2×C3×C4—64no—
258C2×C3×C4—68no—
259C2×C3×C4—616no—
260C2×C3×C4#23718yes—
261C2×C3×C4C23×D318yes—
262C2×C3×C4C23×D314yes—
263#67—616no—
264C2×Dic3—24no—
265C2×Dic3—28no—
266C2×Dic3—38no—
267C2×Dic3—34no—
268C2×Dic3—38no—
269C2×Dic3—34no—
270C2×Dic3—64no—
271C2×Dic3—62no—
272C2×Dic3—64no—
273C2×Dic3—62no—
274C2×Dic3—68no—
275C2×Dic3—64no—
276C2×Dic3—124no—
277C2×Dic3—122no—
278C2×Dic3C23×D314yes—
279C2×Dic3C23×D318yes—
280C4×D3—216no—
281Dic6—632no—
282C2×C32#55614yescomplemented
283C2×C32C22×#4111yescharacteristic
284C2×C32C22×#4111yescharacteristic
285C2×C32C2×2−1+411yescharacteristic
286C3×D3—44no—
287C24—32no—
288C2×Q8—24no—
289C2×Q8—98no—
290C2×Q8—188no—
291C2×Q8C2×D3214yes—
292C2×D4—94no—
293C2×D4—184no—
294C22×C4—32no—
295C22×C4—34no—
296C22×C4—38no—
297C22×C4—68no—
298C22×C4—91no—
299C22×C4—92no—
300C22×C4—91no—
301C22×C4C2×D3212yes—
302C22×C4C2×D3211yescharacteristic
303C4⋊C4—38no—
304C4⋊C4—316no—
305C4⋊C4—94no—
306C4⋊C4—98no—
307C4⋊C4—94no—
308C4⋊C4—98no—
309C22⋊C4—316no—
310C22⋊C4—916no—
311C22⋊C4—98no—
312C42—916no—
313C42—94no—
314C42—98no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—64no—
320C22×C3—64no—
321C22×C3—64no—
322C22×C3—128no—
323C22×C3C2×#23714yes—
324C22×C3#100714yes—
325C22×C3D3×#4114yes—
326C22×C3C24×D312yes—
327C2×D3—24no—
328C2×D3—24no—
329C2×D3—24no—
330C2×D3—48no—
331C3×C4—28no—
332C3×C4—28no—
333C3×C4—24no—
334C3×C4—64no—
335C3×C4—68no—
336C3×C4C2×#23718yes—
337Dic3—24no—
338Dic3—28no—
339Dic3—38no—
340Dic3—64no—
341Dic3—68no—
342Dic3—64no—
343Dic3—124no—
344Dic3—122no—
345C32C2×#55611yescharacteristic, complemented, Sylow
346C23—34no—
347C23—64no—
348C23—64no—
349C23—64no—
350C23C22×D3211yescharacteristic
351Q8—28no—
352Q8—1816no—
353D4—188no—
354C2×C4—24no—
355C2×C4—34no—
356C2×C4—38no—
357C2×C4—68no—
358C2×C4—64no—
359C2×C4—616no—
360C2×C4—94no—
361C2×C4—92no—
362C2×C4—94no—
363C2×C4—92no—
364C2×C4—184no—
365C2×C4—182no—
366C2×C4#380514yes—
367C2×C4C22×D3214yes—
368C2×C4C22×D3212yes—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—24no—
372C2×C3—21no—
373C2×C3—124no—
374C2×C3#564118yescomplemented
375C2×C3C22×#23712yes—
376C2×C3C2×#100712yes—
377C2×C3C2×D3×#4112yes—
378D3—44no—
379C22—64no—
380C22—64no—
381C22—64no—
382C22—128no—
383C22#6431612yes—
384C22#6431912yes—
385C22C2×#380512yes—
386C22C23×D3211yescharacteristic
387C4—24no—
388C4—68no—
389C4—64no—
390C4—94no—
391C4—184no—
392C4—182no—
393C4C2×#380514yes—
394C3—21no—
395C3C2×#564112yescomplemented
396C2—124no—
397C2#1059541314yesdirect product factor
398C2C2×#6431611yescharacteristic
399C2C2×#6431911yescharacteristic
400C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC22×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
2. C2×C3×#946C2semidirect
3. #10595413C2direct (N × H)
4. C2×#63919C2semidirect
7. C2×#63861C2semidirect
8. C2×#63841C2semidirect
9. C2×#63838C2semidirect
15. Q8×C3⋊Dic3C22semidirect
20. C3×#946C22semidirect
29. #63919C22semidirect
32. #63861C22semidirect
33. #63841C22semidirect
34. #63838C22semidirect
36. C2×#946D3semidirect
89. #946C2×D3semidirect
282. C2×C32#556semidirect
345. C32C2×#556semidirect
374. C2×C3#5641semidirect
395. C3C2×#5641semidirect
397. C2#10595413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#9462
#105954132
C2×#639192
C2×#639152
C2×C4×#6252
C2×#638612
C2×#638412
C2×#638382
C2×#56413