Finite Group Databasebeta

← C2×#10594374 #11900724

Subgroups — C2×#10594374 #11900724

Order 1152.

3457 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C212yesmaximal
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×C3×#888C212yesmaximal, complemented
4C2×#63918C212yesmaximal, complemented
5C2×#63900C211yesmaximal, characteristic
6C2×#63883C212yesmaximal
7C2×C4×#624C211yesmaximal, characteristic
8C2×#63839C214yesmaximal, complemented
9#10594374C2116yesmaximal, direct product factor
10C2×D3×C4⋊Q8—32nomaximal
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×Dic6C2214yes—
14C22×#627C2214yes—
15C22×#624C2212yes—
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C2×#3797—216no—
19C2×#3797C22116yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C4⋊C4×C3⋊D3C2218yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×Dic3⋊C4C2214yes—
26C2×C3×C4×Dic3C2212yes—
27C3×#888C22116yescomplemented
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×Dic32C2212yes—
31#63918C22116yescomplemented
32#63900C2218yes—
33#63883C22116yes—
34C4×#624C2218yes—
35#63839C22132yescomplemented
36C22×D3×Q8—34no—
37C2×C3×C4⋊Q8—32no—
38C2×#944—34no—
39D3×C4⋊Q8—332no—
40C2×D3×C4⋊C4—32no—
41C2×D3×C4⋊C4—32no—
42C2×D3×C4⋊C4—34no—
43C2×D3×C4⋊C4—61no—
44C2×#888—34no—
45C2×#888—32no—
46C2×#888D312yescomplemented
47C2×C42×D3—32no—
48C2×#869—32no—
49C23×C3⋊D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—28no—
55C2×C4×C3⋊D3Q818yescomplemented
56C2×C4×C3⋊D3C2318yes—
57C2×C4×C3⋊D3C2314yes—
58C22×C3×Dic3C2314yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C2×C3×Dic6—216no—
62C2×C3×Dic6C23116yes—
63C2×#627—216no—
64C2×#627C23116yes—
65C2×#624—28no—
66C2×#624D418yes—
67C2×#624Q818yescomplemented
68C2×#624C2318yes—
69C2×#624C2314yes—
70C2×#624C2314yes—
71#3797—264no—
72C32×C4⋊C4C2314yes—
73C4⋊(C3⋊Dic3)C2314yes—
74#3750C2318yes—
75C3×C4⋊Dic3C2318yes—
76C3×Dic3⋊C4C23116yes—
77C3×C4×Dic3C2318yes—
78#3724C2318yes—
79Dic3⋊Dic3C23116yes—
80Dic32C2318yes—
81C22×C4⋊Q8—91noSylow
82C22×C3×Q8—34no—
83C2×D3×Q8—332no—
84C2×D3×Q8—632no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—32no—
88C22×C4×D3—34no—
89C22×C4×D3—34no—
90C22×C4×D3—61no—
91C22×C4×D3—62no—
92C22×Dic6—34no—
93C22×Dic6—34no—
94C22×Dic6C2×D314yes—
95C3×C4⋊Q8—316no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4C2×D312yes—
100C2×C3×C42—32no—
101#944—332no—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3—34no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3C2×D312yes—
106C2×Dic3⋊C4—34no—
107C2×Dic3⋊C4—34no—
108C2×Dic3⋊C4—34no—
109C2×Dic3⋊C4—62no—
110C2×Dic3⋊C4C2×D314yes—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3C2×D312yes—
114D3×C4⋊C4—316no—
115D3×C4⋊C4—316no—
116D3×C4⋊C4—332no—
117D3×C4⋊C4—68no—
118#888—332no—
119#888—316no—
120#888C2×D3116yescomplemented
121C42×D3—316no—
122#869—316no—
123C23×C32C2411yescharacteristic
124C22×C3⋊D3C2×D414yes—
125C22×C3⋊D3C2×Q814yes—
126C22×C3⋊D3C2×Q814yes—
127C22×C3⋊D3C2412yes—
128C2×C32×C4—24no—
129C2×C32×C4C2×Q814yescomplemented
130C2×C32×C4C2414yes—
131C2×C32×C4C2412yes—
132C2×C3⋊Dic3—24no—
133C2×C3⋊Dic3C2×Q814yescomplemented
134C2×C3⋊Dic3C2414yes—
135C2×C3⋊Dic3C2412yes—
136C4×C3⋊D3—216no—
137C4×C3⋊D3C2×Q8116yescomplemented
138C2×C3×Dic3—28no—
139C2×C3×Dic3C2×D418yes—
140C2×C3×Dic3C2×Q818yescomplemented
141C2×C3×Dic3C2418yes—
142C2×C3×Dic3C2414yes—
143C2×C3×Dic3C2414yes—
144C3×Dic6—232no—
145#627—232no—
146#624—216no—
147#624C2×D4116yes—
148#624C2×Q8116yescomplemented
149C23×Q8—92no—
150C2×C4⋊Q8—32no—
151C2×C4⋊Q8—92no—
152C2×C4⋊Q8—94no—
153C2×C4⋊Q8—916no—
154C22×C4⋊C4—92no—
155C22×C4⋊C4—91no—
156C22×C4⋊C4—91no—
157C22×C42—91no—
158C23×D3—32no—
159C23×D3—61no—
160C2×C3×Q8—316no—
161C2×C3×Q8—616no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—34no—
167C22×C3×C4C22×D314yes—
168C22×C3×C4C22×D312yes—
169C22×Dic3—32no—
170C22×Dic3—34no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3C22×D314yes—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D312yes—
176D3×Q8—6128no—
177C2×C4×D3—316no—
178C2×C4×D3—38no—
179C2×C4×D3—316no—
180C2×C4×D3—316no—
181C2×C4×D3—38no—
182C2×C4×D3—38no—
183C2×C4×D3—316no—
184C2×C4×D3—316no—
185C2×C4×D3—64no—
186C2×C4×D3—68no—
187C2×C4×D3—68no—
188C2×C4×D3—616no—
189C2×C4×D3—616no—
190C2×C4×D3—128no—
191C2×Dic6—216no—
192C2×Dic6—316no—
193C2×Dic6—316no—
194C2×Dic6—616no—
195C2×Dic6—616no—
196C2×Dic6C22×D3116yes—
197C3×C4⋊C4—24no—
198C3×C4⋊C4—316no—
199C3×C4⋊C4—38no—
200C3×C4⋊C4C22×D318yes—
201C3×C42—38no—
202C4⋊Dic3—38no—
203C4⋊Dic3—316no—
204C4⋊Dic3—64no—
205C4⋊Dic3C22×D318yes—
206Dic3⋊C4—316no—
207Dic3⋊C4—316no—
208Dic3⋊C4—316no—
209Dic3⋊C4—68no—
210Dic3⋊C4C22×D3116yes—
211C4×Dic3—38no—
212C4×Dic3—38no—
213C4×Dic3C22×D318yes—
214C22×C32C22×D412yes—
215C22×C32C22×Q812yes—
216C22×C32C22×Q812yes—
217C22×C32C2511yescharacteristic
218C2×C3⋊D3C4⋊Q8116yescomplemented
219C2×C3⋊D3C22×D414yes—
220C2×C3⋊D3C22×Q814yes—
221C2×C3⋊D3C22×Q814yes—
222C32×C4—24no—
223C32×C4C22×Q814yescomplemented
224C3⋊Dic3—24no—
225C3⋊Dic3C22×Q814yescomplemented
226C3×Dic3—28no—
227C3×Dic3C22×D418yes—
228C3×Dic3C22×Q818yescomplemented
229C22×Q8—34no—
230C22×Q8—94no—
231C22×Q8—916no—
232C22×Q8—1816no—
233C23×C4—91no—
234C23×C4—91no—
235C23×C4—92no—
236C23×C4—91no—
237C23×C4—92no—
238C4⋊Q8—316no—
239C4⋊Q8—916no—
240C4⋊Q8—932no—
241C2×C4⋊C4—34no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—916no—
244C2×C4⋊C4—98no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—94no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—98no—
250C2×C4⋊C4D3211yescharacteristic
251C2×C42—32no—
252C2×C42—98no—
253C2×C42—92no—
254C23×C3—21no—
255C23×C3C23×D312yes—
256C22×D3—38no—
257C22×D3—38no—
258C22×D3—38no—
259C22×D3—34no—
260C22×D3—64no—
261C22×D3—64no—
262C22×D3—64no—
263C22×D3—62no—
264C3×Q8—632no—
265C2×C3×C4—28no—
266C2×C3×C4—22no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—38no—
270C2×C3×C4—38no—
271C2×C3×C4—34no—
272C2×C3×C4—34no—
273C2×C3×C4—38no—
274C2×C3×C4—44no—
275C2×C3×C4—68no—
276C2×C3×C4D3×Q818yescomplemented
277C2×C3×C4C23×D318yes—
278C2×C3×C4C23×D314yes—
279C2×Dic3—28no—
280C2×Dic3—38no—
281C2×Dic3—34no—
282C2×Dic3—38no—
283C2×Dic3—64no—
284C2×Dic3—62no—
285C2×Dic3—64no—
286C2×Dic3—68no—
287C2×Dic3—124no—
288C2×Dic3D3×D418yes—
289C2×Dic3D3×Q818yescomplemented
290C2×Dic3C23×D318yes—
291C2×Dic3C23×D314yes—
292C2×Dic3C23×D314yes—
293C4×D3—332no—
294C4×D3—332no—
295C4×D3—332no—
296C4×D3—616no—
297C4×D3—632no—
298C4×D3—632no—
299C4×D3—1216no—
300Dic6—232no—
301Dic6—632no—
302Dic6—632no—
303C2×C32C2×C4⋊Q814yescomplemented
304C2×C32C23×D411yescharacteristic
305C2×C32C23×Q811yescharacteristic
306C2×C32C23×Q811yescharacteristic
307C3⋊D3C2×C4⋊Q818yescomplemented
308C24—91no—
309C2×Q8—316no—
310C2×Q8—616no—
311C2×Q8—916no—
312C2×Q8—1816no—
313C2×Q8—1864no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—34no—
317C22×C4—94no—
318C22×C4—94no—
319C22×C4—98no—
320C22×C4—98no—
321C22×C4—98no—
322C22×C4—91no—
323C22×C4—94no—
324C22×C4—98no—
325C22×C4—92no—
326C22×C4—98no—
327C22×C4—188no—
328C22×C4—188no—
329C22×C4C2×D3212yes—
330C22×C4C2×D3211yescharacteristic
331C4⋊C4—316no—
332C4⋊C4—38no—
333C4⋊C4—98no—
334C4⋊C4—916no—
335C4⋊C4—98no—
336C4⋊C4—94no—
337C4⋊C4C2×D3214yes—
338C42—38no—
339C42—98no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—21no—
344C22×C3C2×D3×D414yes—
345C22×C3C2×D3×Q814yes—
346C22×C3C2×D3×Q814yes—
347C22×C3C24×D312yes—
348C2×D3—38no—
349C2×D3—38no—
350C2×D3—38no—
351C2×D3—332no—
352C2×D3—64no—
353C2×D3—64no—
354C2×D3—616no—
355C2×D3—64no—
356C3×C4—28no—
357C3×C4—24no—
358C3×C4—38no—
359C3×C4—38no—
360C3×C4—44no—
361C3×C4—68no—
362C3×C4C2×D3×Q818yescomplemented
363Dic3—28no—
364Dic3—38no—
365Dic3—64no—
366Dic3—68no—
367Dic3—124no—
368Dic3C2×D3×D418yes—
369Dic3C2×D3×Q818yescomplemented
370C32C22×C4⋊Q811yescharacteristic, complemented, Sylow
371C23—94no—
372C23—94no—
373C23—94no—
374C23—92no—
375C23C22×D3211yescharacteristic
376Q8—632no—
377Q8—1832no—
378C2×C4—24no—
379C2×C4—38no—
380C2×C4—38no—
381C2×C4—34no—
382C2×C4—34no—
383C2×C4—38no—
384C2×C4—68no—
385C2×C4—916no—
386C2×C4—916no—
387C2×C4—94no—
388C2×C4—92no—
389C2×C4—916no—
390C2×C4—94no—
391C2×C4—1816no—
392C2×C4—1816no—
393C2×C4—184no—
394C2×C4#379714yescomplemented
395C2×C4C22×D3214yes—
396C2×C4C22×D3212yes—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—24no—
400C2×C3—21no—
401C2×C3D3×C4⋊Q818yescomplemented
402C2×C3C22×D3×D412yes—
403C2×C3C22×D3×Q812yes—
404C2×C3C22×D3×Q812yes—
405D3—316no—
406D3—68no—
407C22—94no—
408C22—94no—
409C22—916no—
410C22—94no—
411C22C2×#379712yes—
412C22D32×D412yes—
413C22D32×Q812yes—
414C22C23×D3211yescharacteristic
415C4—24no—
416C4—38no—
417C4—38no—
418C4—68no—
419C4—94no—
420C4—184no—
421C4C2×#379714yescomplemented
422C3—21no—
423C3C2×D3×C4⋊Q812yescomplemented
424C2—98no—
425C2#1059437414yesdirect product factor
426C2C22×#379711yescharacteristic
427C2C2×D32×D411yescharacteristic
428C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C4⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#888C2semidirect
4. C2×#63918C2semidirect
8. C2×#63839C2semidirect
9. #10594374C2direct (N × H)
27. C3×#888C22semidirect
31. #63918C22semidirect
35. #63839C22semidirect
46. C2×#888D3semidirect
55. C2×C4×C3⋊D3Q8semidirect
67. C2×#624Q8semidirect
120. #888C2×D3semidirect
129. C2×C32×C4C2×Q8semidirect
133. C2×C3⋊Dic3C2×Q8semidirect
137. C4×C3⋊D3C2×Q8semidirect
140. C2×C3×Dic3C2×Q8semidirect
148. #624C2×Q8semidirect
218. C2×C3⋊D3C4⋊Q8semidirect
223. C32×C4C22×Q8semidirect
225. C3⋊Dic3C22×Q8semidirect
228. C3×Dic3C22×Q8semidirect
276. C2×C3×C4D3×Q8semidirect
289. C2×Dic3D3×Q8semidirect
303. C2×C32C2×C4⋊Q8semidirect
307. C3⋊D3C2×C4⋊Q8semidirect
362. C3×C4C2×D3×Q8semidirect
369. Dic3C2×D3×Q8semidirect
370. C32C22×C4⋊Q8semidirect
394. C2×C4#3797semidirect
401. C2×C3D3×C4⋊Q8semidirect
421. C4C2×#3797semidirect
423. C3C2×D3×C4⋊Q8semidirect
425. C2#10594374direct (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×#8882
C2×#639182
C2×#639002
C2×#638832
C2×C4×#6242
C2×#638392
#105943742
C2×D3×C4⋊Q83