Finite Group Databasebeta

← C2×#10596010 #11903230

Subgroups — C2×#10596010 #11903230

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×C4×D4C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic
4C2×#64133C212yesmaximal, complemented
5C22×#3750C212yesmaximal, complemented
6#10596010C2116yesmaximal, direct product factor
7C2×#64099C211yesmaximal, characteristic, complemented
8C2×#64097C211yesmaximal, characteristic, complemented
9C2×#64087C212yesmaximal, complemented
10C2×#64087C212yesmaximal, complemented
11C2×#64079C211yesmaximal, characteristic, complemented
12C2×C4×#634C211yesmaximal, characteristic, complemented
13C2×#5539—34nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2212yes—
16C23×C3⋊Dic3C2212yes—
17C23×C3⋊Dic3C2212yes—
18C22×#634C2211yescharacteristic
19C22×#634C2212yes—
20C32×C4×D4C2218yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2212yes—
23C2×C32×C42C2211yescharacteristic
24C2×#3757C2212yes—
25C2×#3757C2212yes—
26D4×C3⋊Dic3C2218yes—
27D4×C3⋊Dic3C2218yes—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2212yes—
32#64133C22116yescomplemented
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2212yes—
36C2×#3750C2212yes—
37C2×#3750C2212yes—
38C2×#3750C2212yes—
39C2×#3750C22116yescomplemented
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#64099C2218yescomplemented
43#64097C2218yescomplemented
44#64087C22116yescomplemented
45#64087C22116yescomplemented
46#64079C2218yescomplemented
47C4×#634C2218yescomplemented
48C2×C3×C4×D4D314yes—
49C2×D4×Dic3—34no—
50C2×D4×Dic3—34no—
51C2×#924—38no—
52C22×Dic3⋊C4—38no—
53#5539—364no—
54C2×#890—34no—
55C2×#888—34no—
56C2×#878—38no—
57C2×#878—38no—
58C2×#870—34no—
59C2×C4×Dic6—34no—
60C24×C32C2312yes—
61C2×C32×D4Q818yescomplemented
62C2×C32×D4C2314yes—
63C22×C32×C4—44no—
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2318yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—28no—
70C22×C3⋊Dic3—44no—
71C22×C3⋊Dic3C2318yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2312yes—
77C22×C3⋊Dic3C2318yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×#634—24no—
80C2×#634—44no—
81C2×#634C2314yes—
82C2×#634C2318yes—
83C32×C4⋊C4C2314yes—
84C32×C22⋊C4C2318yes—
85C32×C42C2314yes—
86#3757C2318yes—
87#3757C2318yes—
88C4⋊(C3⋊Dic3)C2314yes—
89C4⋊(C3⋊Dic3)C2314yes—
90C4⋊(C3⋊Dic3)C2314yes—
91C4⋊(C3⋊Dic3)C2318yes—
92#3750C2314yes—
93#3750C2314yes—
94#3750C2318yes—
95#3750C2318yes—
96#3750C2318yes—
97#3750C2318yes—
98C4×C3⋊Dic3C2314yes—
99C4×C3⋊Dic3C2314yes—
100C2×#554—91noSylow
101C22×C3×D4C2×D314yes—
102C23×C3×C4C2×D318yes—
103C23×Dic3—38no—
104C23×Dic3—38no—
105C22×Dic6—34no—
106C22×Dic6—38no—
107C3×C4×D4C2×D3132yes—
108C2×C3×C4⋊C4C2×D314yes—
109C2×C3×C22⋊C4C2×D318yes—
110C2×C3×C42C2×D314yes—
111C2×#217—38no—
112C2×#217—38no—
113D4×Dic3—332no—
114D4×Dic3—332no—
115C2×C4⋊Dic3—34no—
116C2×C4⋊Dic3—34no—
117C2×C4⋊Dic3—34no—
118C2×C4⋊Dic3—38no—
119#924—364no—
120C2×Dic3⋊C4—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—38no—
123C2×Dic3⋊C4—38no—
124C2×Dic3⋊C4—38no—
125C2×Dic3⋊C4—38no—
126C2×Dic3⋊C4—364no—
127C2×C4×Dic3—34no—
128C2×C4×Dic3—34no—
129#890—332no—
130#888—332no—
131#878—364no—
132#878—364no—
133#870—332no—
134C4×Dic6—332no—
135C23×C32—24no—
136C23×C32—24no—
137C23×C32C2×Q818yes—
138C23×C32C2414yes—
139C23×C32C2411yescharacteristic
140C32×D4C2×Q8116yescomplemented
141C2×C32×C4—22no—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4—48no—
145C2×C32×C4C2×Q814yes—
146C2×C32×C4C2412yes—
147C2×C32×C4C2412yes—
148C2×C32×C4C2414yes—
149C2×C32×C4C2412yes—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—24no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—216no—
156C2×C3⋊Dic3—48no—
157C2×C3⋊Dic3#4114yes—
158C2×C3⋊Dic3C2412yes—
159C2×C3⋊Dic3C2412yes—
160C2×C3⋊Dic3C2412yes—
161C2×C3⋊Dic3C2414yes—
162C2×C3⋊Dic3C2414yes—
163C2×C3⋊Dic3C2412yes—
164#634—28no—
165#634—48no—
166#554—916no—
167C2×C4⋊Q8—91no—
168C2×#125—91no—
169C2×#125—91no—
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×D4C3⋊D311yescharacteristic
177C22×C4⋊C4—92no—
178C24×C3C22×D318yes—
179C2×C3×D4Dic6132yescomplemented
180C2×C3×D4C22×D3116yes—
181C22×C3×C4—416no—
182C22×C3×C4C22×D314yes—
183C22×C3×C4C22×D314yes—
184C22×C3×C4C22×D318yes—
185C22×C3×C4C22×D3132yes—
186C22×C3×C4C22×D314yes—
187C22×Dic3—34no—
188C22×Dic3—332no—
189C22×Dic3—34no—
190C22×Dic3—34no—
191C22×Dic3—34no—
192C22×Dic3—38no—
193C22×Dic3—38no—
194C22×Dic3—332no—
195C22×Dic3—632no—
196C22×Dic3—1216no—
197C2×Dic6—316no—
198C2×Dic6—332no—
199C2×Dic6—616no—
200C2×Dic6—1216no—
201C3×C4⋊C4C22×D3116yes—
202C3×C22⋊C4C22×D3132yes—
203C3×C42C22×D3116yes—
204#217—332no—
205#217—332no—
206C4⋊Dic3—316no—
207C4⋊Dic3—316no—
208C4⋊Dic3—316no—
209C4⋊Dic3—332no—
210Dic3⋊C4—316no—
211Dic3⋊C4—316no—
212Dic3⋊C4—332no—
213Dic3⋊C4—332no—
214Dic3⋊C4—332no—
215Dic3⋊C4—332no—
216C4×Dic3—316no—
217C4×Dic3—316no—
218C22×C32—216no—
219C22×C32—24no—
220C22×C32—24no—
221C22×C32C22×Q818yes—
222C22×C32C22×Q812yes—
223C22×C32C2×#4112yes—
224C22×C32H(5,𝔽2)12yes—
225C22×C32C2511yescharacteristic
226C32×C4—22no—
227C32×C4—24no—
228C32×C4—22no—
229C32×C4C22×Q814yes—
230C3⋊Dic3—22no—
231C3⋊Dic3—24no—
232C3⋊Dic3—22no—
233C3⋊Dic3—24no—
234C3⋊Dic3—22no—
235C3⋊Dic3C2×#4114yes—
236C22×Q8—91no—
237C22×Q8—92no—
238C22×D4C2×C3⋊D311yescharacteristic
239C23×C4—92no—
240C23×C4—92no—
241C23×C4C2×C3⋊D312yes—
242C4⋊Q8—98no—
243#125—98no—
244#125—98no—
245C22⋊Q8—916no—
246C22⋊Q8—916no—
247C22⋊Q8—916no—
248C4×Q8—98no—
249C4×D4—98no—
250C4×D4—98no—
251C4×D4C2×C3⋊D318yes—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—916no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4—92no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4C2×C3⋊D311yescharacteristic
264C2×C22⋊C4—92no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4C2×C3⋊D312yes—
267C2×C42—91no—
268C2×C42—91no—
269C2×C42C2×C3⋊D311yescharacteristic
270C23×C3—216no—
271C23×C3—216no—
272C23×C3C2×Dic6132yes—
273C23×C3C23×D3116yes—
274C23×C3C23×D314yes—
275C3×D4C2×Dic6164yescomplemented
276C2×C3×C4—216no—
277C2×C3×C4—28no—
278C2×C3×C4—28no—
279C2×C3×C4—432no—
280C2×C3×C4C2×Dic6116yes—
281C2×C3×C4C23×D318yes—
282C2×C3×C4C23×D318yes—
283C2×C3×C4C23×D3116yes—
284C2×C3×C4C23×D318yes—
285C2×Dic3—316no—
286C2×Dic3—38no—
287C2×Dic3—38no—
288C2×Dic3—38no—
289C2×Dic3—38no—
290C2×Dic3—316no—
291C2×Dic3—316no—
292C2×Dic3—664no—
293C2×Dic3—68no—
294C2×Dic3—616no—
295C2×Dic3—68no—
296C2×Dic3—68no—
297C2×Dic3—616no—
298C2×Dic3—1232no—
299Dic6—632no—
300Dic6—1232no—
301C2×C32—28no—
302C2×C32#55414yescomplemented
303C2×C32C23×Q811yescharacteristic
304C2×C32C22×#4111yescharacteristic
305C2×C32C2×H(5,𝔽2)11yescharacteristic
306C24C22×C3⋊D312yes—
307C2×Q8—94no—
308C2×Q8—98no—
309C2×Q8—184no—
310C2×Q8—364no—
311C2×D4#63418yescomplemented
312C2×D4C22×C3⋊D314yes—
313C22×C4—44no—
314C22×C4—91no—
315C22×C4—98no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—92no—
320C22×C4—92no—
321C22×C4—98no—
322C22×C4—188no—
323C22×C4—364no—
324C22×C4C22×C3⋊D311yescharacteristic
325C22×C4C22×C3⋊D311yescharacteristic
326C22×C4C22×C3⋊D312yes—
327C22×C4C22×C3⋊D318yes—
328C22×C4C22×C3⋊D311yescharacteristic
329C4⋊C4—94no—
330C4⋊C4—98no—
331C4⋊C4—98no—
332C4⋊C4—98no—
333C4⋊C4—94no—
334C4⋊C4—94no—
335C4⋊C4—94no—
336C4⋊C4—94no—
337C4⋊C4—98no—
338C4⋊C4—98no—
339C4⋊C4C22×C3⋊D314yes—
340C22⋊C4—98no—
341C22⋊C4—98no—
342C22⋊C4C22×C3⋊D318yes—
343C42—94no—
344C42—94no—
345C42C22×C3⋊D314yes—
346C22×C3—216no—
347C22×C3—216no—
348C22×C3—264no—
349C22×C3C22×Dic6132yes—
350C22×C3C22×Dic618yes—
351C22×C3#100418yes—
352C22×C3D3×#4118yes—
353C22×C3C24×D314yes—
354C3×C4—216no—
355C3×C4—28no—
356C3×C4—28no—
357C3×C4C22×Dic6116yes—
358Dic3—316no—
359Dic3—68no—
360Dic3—616no—
361Dic3—68no—
362Dic3—68no—
363Dic3—616no—
364C32C2×#55411yescharacteristic, complemented, Sylow
365C23—24no—
366C23—24no—
367C23C2×#63418yes—
368C23C23×C3⋊D314yes—
369C23C23×C3⋊D311yescharacteristic
370Q8—188no—
371Q8—368no—
372D4C2×#634116yescomplemented
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—48no—
377C2×C4—94no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—1816no—
385C2×C4—182no—
386C2×C4—184no—
387C2×C4—182no—
388C2×C4—184no—
389C2×C4—182no—
390C2×C4—368no—
391C2×C4C2×#63414yes—
392C2×C4C23×C3⋊D312yes—
393C2×C4C23×C3⋊D312yes—
394C2×C4C23×C3⋊D314yes—
395C2×C4C23×C3⋊D312yes—
396C2×C3—232no—
397C2×C3#5539116yescomplemented
398C2×C3C23×Dic614yes—
399C2×C3C2×#100414yes—
400C2×C3C2×D3×#4114yes—
401C22—24no—
402C22—24no—
403C22—216no—
404C22C22×#63418yes—
405C22C22×#63412yes—
406C22#6436112yes—
407C22#41×C3⋊D312yes—
408C22C24×C3⋊D311yescharacteristic
409C4—22no—
410C4—24no—
411C4—22no—
412C4—94no—
413C4—182no—
414C4—184no—
415C4—182no—
416C4—184no—
417C4—182no—
418C4C22×#63414yes—
419C3C2×#553914yescomplemented
420C2—28no—
421C2#1059601014yesdirect product factor
422C2C23×#63411yescharacteristic
423C2C2×#6436111yescharacteristic
424C2C2×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×#64133C2semidirect
5. C22×#3750C2semidirect
6. #10596010C2direct (N × H)
7. C2×#64099C2semidirect
8. C2×#64097C2semidirect
9. C2×#64087C2semidirect
10. C2×#64087C2semidirect
11. C2×#64079C2semidirect
12. C2×C4×#634C2semidirect
32. #64133C22semidirect
39. C2×#3750C22semidirect
42. #64099C22semidirect
43. #64097C22semidirect
44. #64087C22semidirect
45. #64087C22semidirect
46. #64079C22semidirect
47. C4×#634C22semidirect
61. C2×C32×D4Q8semidirect
140. C32×D4C2×Q8semidirect
179. C2×C3×D4Dic6semidirect
275. C3×D4C2×Dic6semidirect
302. C2×C32#554semidirect
311. C2×D4#634semidirect
364. C32C2×#554semidirect
372. D4C2×#634semidirect
397. C2×C3#5539semidirect
419. C3C2×#5539semidirect
421. C2#10596010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×D4×C3⋊Dic32
C2×#641332
C22×#37502
#105960102
C2×#640992
C2×#640972
C2×#640872
C2×#640792
C2×C4×#6342
C2×#55393