Finite Group Databasebeta

← C2×#10596161 #11903221

Subgroups — C2×#10596161 #11903221

Order 1152.

3600 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic, complemented
2#10596161C2116yesmaximal, direct product factor
3C2×#64106C212yesmaximal, complemented
4C2×#64105C212yesmaximal, complemented
5C2×#64105C212yesmaximal, complemented
6C2×#64102C211yesmaximal, characteristic
7C2×#64102C211yesmaximal, characteristic
8C2×C4⋊C4×C3⋊D3C212yesmaximal, complemented
9C2×#64099C211yesmaximal, characteristic, complemented
10C2×#64097C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
12C2×C4×#634C211yesmaximal, characteristic, complemented
13C2×#5690—34nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2212yes—
17C22×C4×C3⋊D3C2212yes—
18C22×#634C2211yescharacteristic
19C22×#634C2212yes—
20C32×#125C2218yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2212yes—
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C42C2211yescharacteristic
26C2×#3752C2212yes—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2212yes—
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2212yes—
35C2×#3750C2212yes—
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64106C22116yescomplemented
39#64105C22116yescomplemented
40#64105C22116yescomplemented
41#64102C2218yes—
42#64102C2218yes—
43C4⋊C4×C3⋊D3C22116yescomplemented
44#64099C2218yescomplemented
45#64097C2218yescomplemented
46C4×C4⋊(C3⋊D3)C2218yes—
47C4×#634C2218yescomplemented
48C2×C3×#125D314yescomplemented
49#5690—364no—
50C2×#897—38no—
51C2×#896—38no—
52C2×#896—38no—
53C2×#893—34no—
54C2×#893—34no—
55C2×D3×C4⋊C4—38no—
56C2×#890—34no—
57C2×#888—34no—
58C2×C4×D12—34no—
59C2×C4×Dic6—34no—
60C23×C3⋊D3C2312yes—
61C22×C32×C4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4⋊(C3⋊D3)Q818yescomplemented
72C2×C4⋊(C3⋊D3)C2314yes—
73C2×C4×C3⋊D3—28no—
74C2×C4×C3⋊D3—44no—
75C2×C4×C3⋊D3—44no—
76C2×C4×C3⋊D3C2318yes—
77C2×C4×C3⋊D3C2318yes—
78C2×C4×C3⋊D3C2318yes—
79C2×#634—24no—
80C2×#634—44no—
81C2×#634C2314yes—
82C2×#634C2318yes—
83C32×C4⋊C4C2314yes—
84C32×C4⋊C4C2314yes—
85C32×C4⋊C4C2318yes—
86C32×C4⋊C4C2318yes—
87C32×C42C2314yes—
88#3752C2318yes—
89#3752C2318yes—
90#3752C2318yes—
91C4⋊(C3⋊Dic3)C2314yes—
92C4⋊(C3⋊Dic3)C2314yes—
93C4⋊(C3⋊Dic3)C2318yes—
94#3750C2314yes—
95#3750C2314yes—
96#3750C2318yes—
97#3750C2318yes—
98C4×C3⋊Dic3C2314yes—
99C4×C3⋊Dic3C2314yes—
100C2×#554—91noSylow
101C22×D12—34no—
102C22×C4×D3—38no—
103C22×C4×D3—38no—
104C22×C4×D3—38no—
105C22×Dic6—34no—
106C22×Dic6—38no—
107C3×#125C2×D3132yescomplemented
108C2×C3×C4⋊C4C2×D314yes—
109C2×C3×C4⋊C4C2×D314yes—
110C2×C3×C4⋊C4C2×D318yes—
111C2×C3×C4⋊C4C2×D318yes—
112C2×C3×C42C2×D314yes—
113C2×(C2×D3)⋊C4—38no—
114C2×(C2×D3)⋊C4—38no—
115C2×(C2×D3)⋊C4—38no—
116C2×C4⋊Dic3—34no—
117C2×C4⋊Dic3—34no—
118C2×C4⋊Dic3—38no—
119C2×Dic3⋊C4—34no—
120C2×Dic3⋊C4—34no—
121C2×Dic3⋊C4—38no—
122C2×Dic3⋊C4—38no—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—34no—
125#897—364no—
126#896—364no—
127#896—364no—
128#893—332no—
129#893—332no—
130D3×C4⋊C4—364no—
131#890—332no—
132#888—332no—
133C4×D12—332no—
134C4×Dic6—332no—
135C23×C32C2411yescharacteristic
136C22×C3⋊D3—24no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3C2×Q818yes—
139C22×C3⋊D3C2414yes—
140C2×C32×C4—22no—
141C2×C32×C4—24no—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4C2×Q814yes—
145C2×C32×C4C2412yes—
146C2×C32×C4C2414yes—
147C2×C32×C4C2414yes—
148C2×C32×C4C2412yes—
149C2×C32×C4C2412yes—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—24no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3#4114yes—
155C2×C3⋊Dic3C2412yes—
156C2×C3⋊Dic3C2412yes—
157C2×C3⋊Dic3C2412yes—
158C2×C3⋊Dic3C2414yes—
159C2×C3⋊Dic3C2412yes—
160C4⋊(C3⋊D3)C2×Q8116yescomplemented
161C4×C3⋊D3—216no—
162C4×C3⋊D3—48no—
163C4×C3⋊D3—48no—
164#634—28no—
165#634—48no—
166#554—916no—
167C2×C4⋊Q8—91no—
168C2×#125—91no—
169C2×#125C3⋊D311yescharacteristic, complemented
170C2×C22⋊Q8—92no—
171C2×C22⋊Q8—92no—
172C2×C22⋊Q8—92no—
173C2×C4×Q8—91no—
174C2×C4×D4—91no—
175C2×C4×D4—91no—
176C2×C4×D4—91no—
177C22×C4⋊C4—92no—
178C23×D3—38no—
179C22×C3×C4C22×D314yes—
180C22×C3×C4C22×D318yes—
181C22×C3×C4C22×D318yes—
182C22×C3×C4C22×D314yes—
183C22×C3×C4C22×D314yes—
184C22×Dic3—34no—
185C22×Dic3—34no—
186C22×Dic3—34no—
187C22×Dic3—34no—
188C22×Dic3—38no—
189C2×D12—332no—
190C2×D12—316no—
191C2×C4×D3—332no—
192C2×C4×D3—332no—
193C2×C4×D3—332no—
194C2×C4×D3—632no—
195C2×C4×D3—1216no—
196C2×C4×D3—1216no—
197C2×Dic6—316no—
198C2×Dic6—332no—
199C2×Dic6—616no—
200C2×Dic6—1216no—
201C3×C4⋊C4C22×D3116yes—
202C3×C4⋊C4C22×D3116yes—
203C3×C4⋊C4C22×D3132yes—
204C3×C4⋊C4C22×D3132yes—
205C3×C42C22×D3116yes—
206(C2×D3)⋊C4—332no—
207(C2×D3)⋊C4—332no—
208(C2×D3)⋊C4—332no—
209C4⋊Dic3—316no—
210C4⋊Dic3—316no—
211C4⋊Dic3—332no—
212Dic3⋊C4—316no—
213Dic3⋊C4—316no—
214Dic3⋊C4—332no—
215Dic3⋊C4—332no—
216C4×Dic3—316no—
217C4×Dic3—316no—
218C22×C32C22×Q812yes—
219C22×C32C2×#4112yes—
220C22×C32H(5,𝔽2)12yes—
221C22×C32C2511yescharacteristic
222C2×C3⋊D3—216no—
223C2×C3⋊D3—24no—
224C2×C3⋊D3—24no—
225C2×C3⋊D3C22×Q818yes—
226C32×C4—22no—
227C32×C4—24no—
228C32×C4—24no—
229C32×C4—22no—
230C32×C4C22×Q814yes—
231C3⋊Dic3—22no—
232C3⋊Dic3—22no—
233C3⋊Dic3—24no—
234C3⋊Dic3—22no—
235C3⋊Dic3C2×#4114yes—
236C22×Q8—91no—
237C22×Q8—92no—
238C22×D4—91no—
239C23×C4—92no—
240C23×C4—92no—
241C23×C4—92no—
242C4⋊Q8—98no—
243#125—98no—
244#125C2×C3⋊D318yescomplemented
245C22⋊Q8—916no—
246C22⋊Q8—916no—
247C22⋊Q8—916no—
248C4×Q8—98no—
249C4×D4—98no—
250C4×D4—98no—
251C4×D4—98no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—916no—
260C2×C4⋊C4C2×C3⋊D312yes—
261C2×C4⋊C4C2×C3⋊D311yescharacteristic
262C2×C4⋊C4C2×C3⋊D311yescharacteristic
263C2×C4⋊C4C2×C3⋊D312yes—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C42—91no—
268C2×C42—91no—
269C2×C42C2×C3⋊D311yescharacteristic
270C23×C3C23×D314yes—
271C22×D3—332no—
272C22×D3—316no—
273C22×D3—616no—
274C22×D3—616no—
275C2×C3×C4—28no—
276C2×C3×C4—216no—
277C2×C3×C4—216no—
278C2×C3×C4—28no—
279C2×C3×C4D3×Q8116yes—
280C2×C3×C4C23×D318yes—
281C2×C3×C4C23×D3116yes—
282C2×C3×C4C23×D3116yes—
283C2×C3×C4C23×D318yes—
284C2×C3×C4C23×D318yes—
285C2×Dic3—316no—
286C2×Dic3—38no—
287C2×Dic3—38no—
288C2×Dic3—38no—
289C2×Dic3—38no—
290C2×Dic3—316no—
291C2×Dic3—68no—
292C2×Dic3—68no—
293C2×Dic3—616no—
294C2×Dic3—68no—
295D12—364no—
296C4×D3—664no—
297C4×D3—1232no—
298C4×D3—1232no—
299Dic6—632no—
300Dic6—1232no—
301C2×C32#55414yescomplemented
302C2×C32C23×Q811yescharacteristic
303C2×C32C22×#4111yescharacteristic
304C2×C32C2×H(5,𝔽2)11yescharacteristic
305C3⋊D3—28no—
306C24—92no—
307C2×Q8—94no—
308C2×Q8—98no—
309C2×Q8—184no—
310C2×Q8—364no—
311C2×D4—94no—
312C2×D4—98no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—92no—
318C22×C4—98no—
319C22×C4—98no—
320C22×C4—98no—
321C22×C4—188no—
322C22×C4—364no—
323C22×C4—364no—
324C22×C4C22×C3⋊D311yescharacteristic
325C22×C4C22×C3⋊D311yescharacteristic
326C22×C4C22×C3⋊D312yes—
327C22×C4C22×C3⋊D312yes—
328C22×C4C22×C3⋊D311yescharacteristic
329C4⋊C4—94no—
330C4⋊C4—98no—
331C4⋊C4—98no—
332C4⋊C4—94no—
333C4⋊C4—94no—
334C4⋊C4—94no—
335C4⋊C4—98no—
336C4⋊C4C22×C3⋊D318yes—
337C4⋊C4C22×C3⋊D314yes—
338C4⋊C4C22×C3⋊D314yes—
339C4⋊C4C22×C3⋊D318yes—
340C22⋊C4—98no—
341C22⋊C4—98no—
342C22⋊C4—98no—
343C42—94no—
344C42—94no—
345C42C22×C3⋊D314yes—
346C22×C3C2×D3×Q818yes—
347C22×C3D3×#4118yes—
348C22×C3#100918yes—
349C22×C3C24×D314yes—
350C2×D3—332no—
351C2×D3—664no—
352C2×D3—616no—
353C2×D3—616no—
354C3×C4—28no—
355C3×C4—216no—
356C3×C4—216no—
357C3×C4—28no—
358C3×C4C2×D3×Q8116yes—
359Dic3—316no—
360Dic3—68no—
361Dic3—68no—
362Dic3—616no—
363Dic3—68no—
364C32C2×#55411yescharacteristic, complemented, Sylow
365C23—98no—
366C23—94no—
367C23—184no—
368C23—184no—
369C23C23×C3⋊D311yescharacteristic
370Q8—188no—
371Q8—368no—
372D4—916no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—94no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—94no—
383C2×C4—1816no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—184no—
387C2×C4—182no—
388C2×C4—368no—
389C2×C4—368no—
390C2×C4Q8×C3⋊D314yes—
391C2×C4C23×C3⋊D312yes—
392C2×C4C23×C3⋊D312yes—
393C2×C4C23×C3⋊D314yes—
394C2×C4C23×C3⋊D314yes—
395C2×C4C23×C3⋊D312yes—
396C2×C3#5690116yescomplemented
397C2×C3C22×D3×Q814yes—
398C2×C3C2×D3×#4114yes—
399C2×C3C2×#100914yes—
400D3—632no—
401C22—98no—
402C22—1816no—
403C22—184no—
404C22—184no—
405C22C2×Q8×C3⋊D312yes—
406C22#41×C3⋊D312yes—
407C22#6436612yes—
408C22C24×C3⋊D311yescharacteristic
409C4—24no—
410C4—22no—
411C4—22no—
412C4—24no—
413C4—94no—
414C4—182no—
415C4—182no—
416C4—184no—
417C4—182no—
418C4C2×Q8×C3⋊D314yes—
419C3C2×#569014yescomplemented
420C2—188no—
421C2#1059616114yesdirect product factor
422C2C22×Q8×C3⋊D311yescharacteristic
423C2C2×#41×C3⋊D311yescharacteristic
424C2C2×#6436611yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#125C2
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×#125C3⋊D3
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
2. #10596161C2direct (N × H)
3. C2×#64106C2semidirect
4. C2×#64105C2semidirect
5. C2×#64105C2semidirect
8. C2×C4⋊C4×C3⋊D3C2semidirect
9. C2×#64099C2semidirect
10. C2×#64097C2semidirect
12. C2×C4×#634C2semidirect
20. C32×#125C22semidirect
38. #64106C22semidirect
39. #64105C22semidirect
40. #64105C22semidirect
43. C4⋊C4×C3⋊D3C22semidirect
44. #64099C22semidirect
45. #64097C22semidirect
47. C4×#634C22semidirect
48. C2×C3×#125D3semidirect
71. C2×C4⋊(C3⋊D3)Q8semidirect
107. C3×#125C2×D3semidirect
160. C4⋊(C3⋊D3)C2×Q8semidirect
169. C2×#125C3⋊D3semidirect
244. #125C2×C3⋊D3semidirect
301. C2×C32#554semidirect
364. C32C2×#554semidirect
396. C2×C3#5690semidirect
419. C3C2×#5690semidirect
421. C2#10596161direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
#105961612
C2×#641062
C2×#641052
C2×#641022
C2×C4⋊C4×C3⋊D32
C2×#640992
C2×#640972
C2×C4×C4⋊(C3⋊D3)2
C2×C4×#6342
C2×#56903