Finite Group Databasebeta

← C2×#10594363 #11899930

Subgroups — C2×#10594363 #11899930

Order 1152.

3537 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×C3×#887C212yesmaximal, complemented
4C2×#63883C212yesmaximal
5C2×C4×#624C211yesmaximal, characteristic
6C2×C4×#624C212yesmaximal
7C2×Dic3×Dic6C212yesmaximal, complemented
8C2×#63837C214yesmaximal, complemented
9#10594363C2116yesmaximal, direct product factor
10C2×C4×D3×Q8—32nomaximal
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×Dic6C2212yes—
14C22×#627C2212yes—
15C22×#624C2211yescharacteristic
16C22×#624C2212yes—
17C22×#624C2211yescharacteristic
18C2×#3797C4116yescomplemented
19C2×#3797C2218yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C4⋊C4×C3⋊D3C2218yes—
24C2×C3×Dic3⋊C4C2214yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2214yes—
27C3×#887C22116yescomplemented
28C2×Dic3⋊Dic3C2214yes—
29C2×Dic32C2214yes—
30C2×Dic32C2212yes—
31#63883C22116yes—
32C4×#624C2218yes—
33C4×#624C22116yes—
34Dic3×Dic6C22116yescomplemented
35#63837C22132yescomplemented
36C22×D3×Q8—32no—
37C2×C3×C4×Q8—32no—
38C2×Q8×Dic3—32no—
39C4×D3×Q8—332no—
40C2×D3×C4⋊C4—32no—
41C2×D3×C4⋊C4—34no—
42C2×D3×C4⋊C4—61no—
43C2×#887—34no—
44C2×#887D312yescomplemented
45C2×C42×D3—32no—
46C2×C42×D3—34no—
47C2×C4×Dic6—32no—
48C2×C4×Dic6—34no—
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—28no—
55C2×C4×C3⋊D3C2×C418yes—
56C2×C4×C3⋊D3C2318yes—
57C2×C4×C3⋊D3C2314yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2314yes—
60C22×C3×Dic3C2312yes—
61C2×C3×Dic6C2×C4116yescomplemented
62C2×C3×Dic6C2318yes—
63C2×#627C2×C4116yescomplemented
64C2×#627C2318yes—
65C2×#624—24no—
66C2×#624C2×C4116yes—
67C2×#624Q818yescomplemented
68C2×#624C2314yes—
69C2×#624C2318yes—
70C2×#624C2314yes—
71#3797C2×C4164yescomplemented
72C32×C4⋊C4C2314yes—
73C4⋊(C3⋊Dic3)C2314yes—
74#3750C2318yes—
75C3×Dic3⋊C4C23116yes—
76C3×C4×Dic3C23116yes—
77C3×C4×Dic3C2318yes—
78Dic3⋊Dic3C23116yes—
79Dic32C2318yes—
80Dic32C23116yes—
81C22×C4×Q8—91noSylow
82C22×C3×Q8—32no—
83C2×D3×Q8—332no—
84C2×D3×Q8—316no—
85C22×C4×D3—32no—
86C22×C4×D3—34no—
87C22×C4×D3—32no—
88C22×C4×D3—34no—
89C22×C4×D3—32no—
90C22×C4×D3—61no—
91C22×C4×D3—62no—
92C22×Dic6—34no—
93C22×Dic6C2×D312yes—
94C3×C4×Q8—316no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—34no—
97C2×C3×C4⋊C4C2×D312yes—
98C2×C3×C42—34no—
99C2×C3×C42—32no—
100Q8×Dic3—316no—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—34no—
103C2×C4⋊Dic3—61no—
104C2×Dic3⋊C4—34no—
105C2×Dic3⋊C4—34no—
106C2×Dic3⋊C4—62no—
107C2×Dic3⋊C4C2×D314yes—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—34no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—34no—
112C2×C4×Dic3C2×D314yes—
113C2×C4×Dic3C2×D312yes—
114D3×C4⋊C4—316no—
115D3×C4⋊C4—332no—
116D3×C4⋊C4—68no—
117#887—332no—
118#887C2×D3116yescomplemented
119C42×D3—316no—
120C42×D3—332no—
121C4×Dic6—316no—
122C4×Dic6—332no—
123C23×C32C2411yescharacteristic
124C22×C3⋊D3C22×C414yes—
125C22×C3⋊D3C2×Q814yes—
126C22×C3⋊D3#4114yes—
127C22×C3⋊D3C2412yes—
128C2×C32×C4—24no—
129C2×C32×C4C22×C414yes—
130C2×C32×C4C2414yes—
131C2×C32×C4C2412yes—
132C2×C3⋊Dic3—24no—
133C2×C3⋊Dic3C22×C414yes—
134C2×C3⋊Dic3C2414yes—
135C2×C3⋊Dic3C2412yes—
136C4×C3⋊D3—216no—
137C4×C3⋊D3C22×C4116yes—
138C2×C3×Dic3—24no—
139C2×C3×Dic3C22×C4116yes—
140C2×C3×Dic3C2×Q818yescomplemented
141C2×C3×Dic3C2414yes—
142C2×C3×Dic3C2418yes—
143C2×C3×Dic3C2414yes—
144C3×Dic6C22×C4132yescomplemented
145#627C22×C4132yescomplemented
146#624—28no—
147#624C22×C4132yes—
148#624C2×Q8116yescomplemented
149C23×Q8—91no—
150C2×C4×Q8—32no—
151C2×C4×Q8—94no—
152C2×C4×Q8—92no—
153C2×C4×Q8—916no—
154C22×C4⋊C4—92no—
155C22×C4⋊C4—91no—
156C22×C42—92no—
157C22×C42—91no—
158C23×D3—32no—
159C23×D3—61no—
160C2×C3×Q8—316no—
161C2×C3×Q8—38no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—32no—
165C22×C3×C4—34no—
166C22×C3×C4—32no—
167C22×C3×C4C22×D314yes—
168C22×C3×C4C22×D312yes—
169C22×Dic3—32no—
170C22×Dic3—34no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3C22×D312yes—
174C22×Dic3C22×D314yes—
175C22×Dic3C22×D312yes—
176D3×Q8—3128no—
177C2×C4×D3—316no—
178C2×C4×D3—38no—
179C2×C4×D3—332no—
180C2×C4×D3—316no—
181C2×C4×D3—38no—
182C2×C4×D3—316no—
183C2×C4×D3—316no—
184C2×C4×D3—38no—
185C2×C4×D3—64no—
186C2×C4×D3—68no—
187C2×C4×D3—68no—
188C2×C4×D3—68no—
189C2×C4×D3—616no—
190C2×C4×D3—128no—
191C2×Dic6—332no—
192C2×Dic6—316no—
193C2×Dic6C4×D3116yescomplemented
194C2×Dic6C22×D318yes—
195C3×C4⋊C4—24no—
196C3×C4⋊C4—316no—
197C3×C4⋊C4C22×D318yes—
198C3×C42—316no—
199C3×C42—38no—
200C4⋊Dic3—38no—
201C4⋊Dic3—316no—
202C4⋊Dic3—64no—
203Dic3⋊C4—316no—
204Dic3⋊C4—316no—
205Dic3⋊C4—68no—
206Dic3⋊C4C22×D3116yes—
207C4×Dic3—38no—
208C4×Dic3—316no—
209C4×Dic3—38no—
210C4×Dic3—316no—
211C4×Dic3C22×D3116yes—
212C4×Dic3C22×D318yes—
213C22×C32C23×C412yes—
214C22×C32C22×Q812yes—
215C22×C32C2×#4112yes—
216C22×C32C2511yescharacteristic
217C2×C3⋊D3C4×Q8116yescomplemented
218C2×C3⋊D3C23×C414yes—
219C2×C3⋊D3C22×Q814yes—
220C2×C3⋊D3C2×#4114yes—
221C32×C4—24no—
222C32×C4C23×C414yes—
223C3⋊Dic3—24no—
224C3⋊Dic3C23×C414yes—
225C3×Dic3—24no—
226C3×Dic3C23×C4116yes—
227C3×Dic3C22×Q818yescomplemented
228C22×Q8—32no—
229C22×Q8—92no—
230C22×Q8—98no—
231C22×Q8—916no—
232C23×C4—92no—
233C23×C4—91no—
234C23×C4—91no—
235C23×C4—91no—
236C23×C4—92no—
237C4×Q8—316no—
238C4×Q8—932no—
239C4×Q8—916no—
240C2×C4⋊C4—34no—
241C2×C4⋊C4—916no—
242C2×C4⋊C4—94no—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—98no—
246C2×C4⋊C4D3211yescharacteristic
247C2×C42—34no—
248C2×C42—32no—
249C2×C42—916no—
250C2×C42—98no—
251C2×C42—94no—
252C2×C42—92no—
253C23×C3—21no—
254C23×C3C23×D312yes—
255C22×D3—38no—
256C22×D3—38no—
257C22×D3—38no—
258C22×D3—34no—
259C22×D3—64no—
260C22×D3—64no—
261C22×D3—64no—
262C22×D3—62no—
263C3×Q8—332no—
264C2×C3×C4—28no—
265C2×C3×C4—22no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—316no—
269C2×C3×C4—38no—
270C2×C3×C4—34no—
271C2×C3×C4—38no—
272C2×C3×C4—34no—
273C2×C3×C4—44no—
274C2×C3×C4—64no—
275C2×C3×C4C2×C4×D318yes—
276C2×C3×C4C23×D318yes—
277C2×C3×C4C23×D314yes—
278C2×Dic3—24no—
279C2×Dic3—38no—
280C2×Dic3—34no—
281C2×Dic3—38no—
282C2×Dic3—64no—
283C2×Dic3—62no—
284C2×Dic3—64no—
285C2×Dic3—68no—
286C2×Dic3—124no—
287C2×Dic3C2×C4×D3116yes—
288C2×Dic3D3×Q818yescomplemented
289C2×Dic3C23×D314yes—
290C2×Dic3C23×D318yes—
291C2×Dic3C23×D314yes—
292C4×D3—332no—
293C4×D3—364no—
294C4×D3—332no—
295C4×D3—616no—
296C4×D3—616no—
297C4×D3—632no—
298C4×D3—1216no—
299Dic6—364no—
300Dic6C2×C4×D3132yescomplemented
301C2×C32C2×C4×Q814yescomplemented
302C2×C32C24×C411yescharacteristic
303C2×C32C23×Q811yescharacteristic
304C2×C32C22×#4111yescharacteristic
305C3⋊D3C2×C4×Q818yescomplemented
306C24—91no—
307C2×Q8—38no—
308C2×Q8—316no—
309C2×Q8—98no—
310C2×Q8—916no—
311C2×Q8—964no—
312C22×C4—32no—
313C22×C4—34no—
314C22×C4—32no—
315C22×C4—94no—
316C22×C4—98no—
317C22×C4—916no—
318C22×C4—98no—
319C22×C4—94no—
320C22×C4—91no—
321C22×C4—94no—
322C22×C4—98no—
323C22×C4—92no—
324C22×C4—98no—
325C22×C4—188no—
326C22×C4—184no—
327C22×C4C2×D3212yes—
328C22×C4C2×D3211yescharacteristic
329C4⋊C4—316no—
330C4⋊C4—916no—
331C4⋊C4—98no—
332C4⋊C4—94no—
333C4⋊C4C2×D3214yes—
334C42—316no—
335C42—38no—
336C42—916no—
337C42—98no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3C22×C4×D314yes—
343C22×C3C2×D3×Q814yes—
344C22×C3D3×#4114yes—
345C22×C3C24×D312yes—
346C2×D3—38no—
347C2×D3—38no—
348C2×D3—38no—
349C2×D3—332no—
350C2×D3—64no—
351C2×D3—64no—
352C2×D3—616no—
353C2×D3—64no—
354C3×C4—28no—
355C3×C4—24no—
356C3×C4—316no—
357C3×C4—38no—
358C3×C4—44no—
359C3×C4—64no—
360C3×C4C22×C4×D318yes—
361Dic3—24no—
362Dic3—38no—
363Dic3—64no—
364Dic3—68no—
365Dic3—124no—
366Dic3C22×C4×D3116yes—
367Dic3C2×D3×Q818yescomplemented
368C32C22×C4×Q811yescharacteristic, complemented, Sylow
369C23—94no—
370C23—94no—
371C23—94no—
372C23—92no—
373C23C22×D3211yescharacteristic
374Q8—332no—
375Q8—932no—
376C2×C4—24no—
377C2×C4—316no—
378C2×C4—38no—
379C2×C4—34no—
380C2×C4—38no—
381C2×C4—34no—
382C2×C4—64no—
383C2×C4—932no—
384C2×C4—916no—
385C2×C4—94no—
386C2×C4—92no—
387C2×C4—916no—
388C2×C4—94no—
389C2×C4—1816no—
390C2×C4—188no—
391C2×C4—184no—
392C2×C4C4×D3214yes—
393C2×C4C22×D3214yes—
394C2×C4C22×D3212yes—
395C2×C3—21no—
396C2×C3—24no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3C4×D3×Q818yescomplemented
400C2×C3C23×C4×D312yes—
401C2×C3C22×D3×Q812yes—
402C2×C3C2×D3×#4112yes—
403D3—316no—
404D3—68no—
405C22—94no—
406C22—916no—
407C22—94no—
408C22—94no—
409C22C2×C4×D3212yes—
410C22#6431212yes—
411C22D32×Q812yes—
412C22C23×D3211yescharacteristic
413C4—24no—
414C4—316no—
415C4—38no—
416C4—64no—
417C4—94no—
418C4—184no—
419C4C2×C4×D3214yes—
420C3—21no—
421C3C2×C4×D3×Q812yescomplemented
422C2—98no—
423C2#1059436314yesdirect product factor
424C2C22×C4×D3211yescharacteristic
425C2C2×#6431211yescharacteristic
426C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
cosocleC22×C32C25
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C4×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#887C2semidirect
7. C2×Dic3×Dic6C2semidirect
8. C2×#63837C2semidirect
9. #10594363C2direct (N × H)
18. C2×#3797C4semidirect
27. C3×#887C22semidirect
34. Dic3×Dic6C22semidirect
35. #63837C22semidirect
44. C2×#887D3semidirect
61. C2×C3×Dic6C2×C4semidirect
63. C2×#627C2×C4semidirect
67. C2×#624Q8semidirect
71. #3797C2×C4semidirect
118. #887C2×D3semidirect
140. C2×C3×Dic3C2×Q8semidirect
144. C3×Dic6C22×C4semidirect
145. #627C22×C4semidirect
148. #624C2×Q8semidirect
193. C2×Dic6C4×D3semidirect
217. C2×C3⋊D3C4×Q8semidirect
227. C3×Dic3C22×Q8semidirect
288. C2×Dic3D3×Q8semidirect
300. Dic6C2×C4×D3semidirect
301. C2×C32C2×C4×Q8semidirect
305. C3⋊D3C2×C4×Q8semidirect
367. Dic3C2×D3×Q8semidirect
368. C32C22×C4×Q8semidirect
399. C2×C3C4×D3×Q8semidirect
421. C3C2×C4×D3×Q8semidirect
423. C2#10594363direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C2×C4⋊C4×C3⋊D32
C2×C3×#8872
C2×#638832
C2×C4×#6242
C2×Dic3×Dic62
C2×#638372
#105943632
C2×C4×D3×Q83