Finite Group Databasebeta

← C2×#10596519 #11902567

Subgroups — C2×#10596519 #11902567

Order 1152.

2522 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C212yesmaximal, complemented
2C2×D4×#157C211yesmaximal, characteristic, complemented
3C2×#64242C212yesmaximal, complemented
4C22×#3773C212yesmaximal, complemented
5C2×#64233C214yesmaximal, complemented
6#10596519C2116yesmaximal, direct product factor
7C2×C4×GO+(4,𝔽2)C211yesmaximal, characteristic, complemented
8C2×#64222C211yesmaximal, characteristic, complemented
9C2×D32⋊Q8C212yesmaximal, complemented
10C23×#157C2212yes—
11C22×GO+(4,𝔽2)C2211yescharacteristic
12C2×D4×C3⋊D3C2211yescharacteristic
13C2×C3×#237—22no—
14C2×#3811C2214yes—
15C22×#624C2214yes—
16C2×#3804—24no—
17#64312—28no—
18#64312C22116yescomplemented
19C2×C4×D32C2212yes—
20C2×#3799—22no—
21C2×#3797C2212yes—
22C2×C22⋊#157C2212yes—
23D4×#157C2218yescomplemented
24C2×C4⋊#157C2211yescharacteristic
25C2×C4×#157C2211yescharacteristic
26#64242C22116yescomplemented
27C2×#3773C2214yes—
28C2×#3773C2212yes—
29C2×#3773C2212yes—
30C2×#3773C2211yescharacteristic
31C2×#3773C22116yescomplemented
32#64233C22132yescomplemented
33C2×D32⋊C4C2214yes—
34C2×D32⋊C4C2212yes—
35C4×GO+(4,𝔽2)C2218yescomplemented
36#64222C2218yescomplemented
37D32⋊Q8C22116yescomplemented
38C2×D3×#41—62no—
39C23×C3⋊D3C2312yes—
40C22×D32C2312yes—
41C22×#157—28no—
42C22×#157C2311yescharacteristic
43C22×#157C2312yes—
44C22×#157C2318yes—
45C22×#157C2311yescharacteristic
46C2×GO+(4,𝔽2)—24no—
47C2×GO+(4,𝔽2)C2314yes—
48C2×C32×D4D411yescharacteristic, complemented
49C2×#638D412yescomplemented
50D4×C3⋊D3D414yescomplemented
51D4×C3⋊D3C2314yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C3×#67—24no—
55C22×C3×Dic3—24no—
56C3×#237—216no—
57C2×C3×C4×D3—22no—
58C2×C3×Dic6—22no—
59#3811—28no—
60#3811C23116yes—
61C2×#627—22no—
62C2×#626—24no—
63C2×#624—24no—
64C2×#624—28no—
65C2×#624C2314yes—
66C2×#624C2312yes—
67C2×#624C23116yes—
68#3804—232no—
69C2×D3×Dic3—22no—
70C4×D32—24no—
71C4×D32C2318yes—
72#3799—216no—
73#3797—24no—
74#3797C2318yes—
75C22⋊#157C2318yes—
76C4⋊#157C2314yes—
77C4×#157C2314yes—
78#3773C23116yes—
79#3773C2318yes—
80#3773C2318yes—
81#3773C2314yes—
82D32⋊C4C23116yes—
83D32⋊C4C2318yes—
84C2×#547—91nomaximal, Sylow
85C2×C3×#41—62no—
86D3×#41—616no—
87D3×#41—616no—
88C2×#239—62no—
89C2×D3×Q8—62no—
90C2×#237—22no—
91C2×#237—64no—
92C2×D3×D4—64no—
93C2×D3×D4—62no—
94C2×#235—62no—
95C2×#235—64no—
96C22×C4×D3—62no—
97C22×C4×D3—64no—
98C23×C32C2×D412yes—
99C22×C3⋊D3—24no—
100C22×C3⋊D3—24no—
101C22×C3⋊D3C2×D412yes—
102C22×C3⋊D3C2×D414yes—
103C22×C3⋊D3C2414yes—
104C22×C3⋊D3C2411yescharacteristic
105C22×C3×D3—22no—
106C2×D32—22no—
107C2×D32—24no—
108C2×D32—24no—
109C2×D32C2414yes—
110C2×#157—24no—
111C2×#157—22no—
112C2×#157—216no—
113C2×#157#4114yescomplemented
114C2×#157C2414yes—
115C2×#157C2412yes—
116C2×#157C2412yes—
117GO+(4,𝔽2)—28no—
118C32×D4C2×D414yescomplemented
119C2×C32×C4C2×D411yescharacteristic
120#638C2×D418yescomplemented
121C2×C3⋊Dic3C2×D411yescharacteristic
122C4⋊(C3⋊D3)C2×D414yescomplemented
123C4×C3⋊D3C2×D412yes—
124C4×C3⋊D3C2412yes—
125C3×#67—216no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—216no—
128C2×C3×Dic3—24no—
129C3×C4×D3—28no—
130C3×Dic6—28no—
131#627—28no—
132#626—216no—
133#624—24no—
134#624—216no—
135#624—22no—
136#624C2418yes—
137#624C2414yes—
138D3×Dic3—28no—
139C22×#41—92no—
140#547—916no—
141C2×C4⋊Q8—91no—
142C2×#123—94no—
143C2×C22⋊Q8—92no—
144C2×#121—92no—
145C2×C4×D4—91no—
146C2×C4×D4—91no—
147C22×C4⋊C4—92no—
148C23×D3—62no—
149C23×D3—64no—
150C3×#41—616no—
151C2×C3×Q8—62no—
152C2×C3×D4—22no—
153C2×C3×D4—64no—
154C22×C3×C4—62no—
155C22×C3×C4—64no—
156C2×#67—24no—
157C2×#67—64no—
158C2×#67—64no—
159C22×Dic3—24no—
160C22×Dic3—62no—
161#239—616no—
162D3×Q8—68no—
163D3×Q8—68no—
164#237—216no—
165#237—632no—
166D3×D4—616no—
167D3×D4—68no—
168D3×D4—68no—
169D3×D4—616no—
170#235—616no—
171#235—632no—
172C2×D12—62no—
173C2×D12—64no—
174C2×C4×D3—22no—
175C2×C4×D3—68no—
176C2×C4×D3—62no—
177C2×C4×D3—64no—
178C2×C4×D3—616no—
179C2×C4×D3—62no—
180C2×C4×D3—68no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×C4×D3—616no—
184C2×C4×D3—62no—
185C2×Dic6—22no—
186C2×Dic6—64no—
187C22×C32—24no—
188C22×C32C22×D414yes—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—24no—
191C2×C3⋊D3—28no—
192C2×C3⋊D3—24no—
193C2×C3⋊D3—24no—
194C2×C3⋊D3C22×D414yes—
195C2×C3⋊D3C22×D411yescharacteristic
196C2×C3⋊D3C2×#4112yes—
197C2×C3⋊D32−1+412yes—
198C2×C3⋊D3C2511yescharacteristic
199C2×C3×D3—24no—
200C2×C3×D3—44no—
201D32—24no—
202D32—24no—
203D32—44no—
204#157—24no—
205#157—22no—
206#157C2×#4114yescomplemented
207C32×C4C22×D412yes—
208C3⋊Dic3C22×D412yes—
209C3×Dic3—24no—
210C3×Dic3—28no—
211C2×#41—62no—
212C2×#41—916no—
213C2×#41—184no—
214C2×#41—182no—
215C2×#41—188no—
216C22×Q8—92no—
217C22×D4—94no—
218C22×D4—91no—
219C22×D4—91no—
220C23×C4—94no—
221C23×C4—92no—
222C23×C4—92no—
223C4⋊Q8—98no—
224#123—932no—
225C22⋊Q8—916no—
226#121—916no—
227C4×D4—98no—
228C4×D4—98no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—92no—
231C2×C4⋊C4—94no—
232C2×C4⋊C4—916no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—92no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—92no—
237C2×C22⋊C4—94no—
238C2×C42—91no—
239C23×C3—24no—
240C23×C3—62no—
241C22×D3—22no—
242C22×D3—64no—
243C22×D3—62no—
244C22×D3—64no—
245C22×D3—68no—
246C22×D3—68no—
247C22×D3—64no—
248C22×D3—124no—
249C22×D3—124no—
250C22×D3—128no—
251C22×D3—128no—
252C3×Q8—68no—
253C3×D4—28no—
254C3×D4—616no—
255C2×C3×C4—22no—
256C2×C3×C4—68no—
257C2×C3×C4—64no—
258C2×C3×C4—62no—
259C2×C3×C4—616no—
260#67—216no—
261#67—616no—
262#67—616no—
263C2×Dic3—24no—
264C2×Dic3—22no—
265C2×Dic3—216no—
266C2×Dic3—62no—
267C2×Dic3—68no—
268D12—68no—
269D12—616no—
270C4×D3—28no—
271C4×D3—64no—
272C4×D3—68no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—64no—
276C4×D3—616no—
277C4×D3—68no—
278C4×D3—616no—
279C4×D3—68no—
280Dic6—28no—
281Dic6—616no—
282C2×C32—24no—
283C2×C32#54712yescomplemented
284C2×C32C23×D411yescharacteristic
285C3⋊D3—24no—
286C3⋊D3#54712yescomplemented
287C3⋊D3C22×#4111yescharacteristic
288C3⋊D3C2×2−1+411yescharacteristic
289C3×D3—44no—
290C24—92no—
291C24—92no—
292#41—616no—
293#41—1832no—
294#41—1816no—
295C2×Q8—62no—
296C2×Q8—98no—
297C2×Q8—182no—
298C2×Q8—184no—
299C2×D4—64no—
300C2×D4—916no—
301C2×D4—92no—
302C2×D4—94no—
303C2×D4—94no—
304C2×D4—94no—
305C2×D4—91no—
306C2×D4—184no—
307C2×D4—184no—
308C2×D4—188no—
309C2×D4GO+(4,𝔽2)11yescharacteristic, complemented
310C22×C4—64no—
311C22×C4—62no—
312C22×C4—92no—
313C22×C4—94no—
314C22×C4—916no—
315C22×C4—98no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—92no—
320C22×C4—98no—
321C22×C4—184no—
322C22×C4—188no—
323C22×C4—184no—
324C22×C4—182no—
325C22×C4—188no—
326C4⋊C4—94no—
327C4⋊C4—98no—
328C4⋊C4—916no—
329C4⋊C4—94no—
330C4⋊C4—98no—
331C22⋊C4—98no—
332C22⋊C4—98no—
333C22⋊C4—916no—
334C42—94no—
335C22×C3—28no—
336C22×C3—22no—
337C22×C3—48no—
338C22×C3—64no—
339C22×C3—124no—
340C2×D3—24no—
341C2×D3—44no—
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—68no—
347C2×D3—124no—
348C2×D3—124no—
349C2×D3—128no—
350C2×D3—1216no—
351C2×D3—128no—
352C2×D3—128no—
353C2×D3—128no—
354C3×C4—24no—
355C3×C4—68no—
356C3×C4—64no—
357Dic3—28no—
358Dic3—24no—
359Dic3—64no—
360C32C2×#54711yescharacteristic, complemented, Sylow
361C23—62no—
362C23—94no—
363C23—91no—
364C23—94no—
365C23—94no—
366C23—92no—
367C23—184no—
368C23—184no—
369C23—182no—
370C23—184no—
371C23—184no—
372C23C2×GO+(4,𝔽2)12yes—
373Q8—68no—
374Q8—188no—
375D4—616no—
376D4—98no—
377D4—94no—
378D4—1816no—
379D4—188no—
380D4C2×GO+(4,𝔽2)14yescomplemented
381C2×C4—616no—
382C2×C4—62no—
383C2×C4—64no—
384C2×C4—68no—
385C2×C4—94no—
386C2×C4—98no—
387C2×C4—92no—
388C2×C4—94no—
389C2×C4—91no—
390C2×C4—92no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—94no—
394C2×C4—182no—
395C2×C4—184no—
396C2×C4—1816no—
397C2×C4—188no—
398C2×C4—1816no—
399C2×C4—184no—
400C2×C4—182no—
401C2×C4C2×GO+(4,𝔽2)11yescharacteristic
402C2×C3—24no—
403C2×C3—22no—
404C2×C3—48no—
405C2×C3—124no—
406D3—44no—
407D3—64no—
408D3—62no—
409D3—62no—
410D3—128no—
411C22—24no—
412C22—64no—
413C22—92no—
414C22—92no—
415C22—91no—
416C22—91no—
417C22—94no—
418C22—124no—
419C22—184no—
420C22—184no—
421C22—188no—
422C22—184no—
423C22—184no—
424C22—184no—
425C22—364no—
426C22C22×GO+(4,𝔽2)14yes—
427C22C22×GO+(4,𝔽2)11yescharacteristic
428C4—64no—
429C4—68no—
430C4—94no—
431C4—92no—
432C4—184no—
433C4—182no—
434C4C22×GO+(4,𝔽2)12yes—
435C3—22no—
436C2—24no—
437C2—91no—
438C2—91no—
439C2—92no—
440C2—124no—
441C2—184no—
442C2#1059651912yesdirect product factor
443C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC22×C32C22×D4
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32C2×#547
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64312C2semidirect
2. C2×D4×#157C2semidirect
3. C2×#64242C2semidirect
4. C22×#3773C2semidirect
5. C2×#64233C2semidirect
6. #10596519C2direct (N × H)
7. C2×C4×GO+(4,𝔽2)C2semidirect
8. C2×#64222C2semidirect
9. C2×D32⋊Q8C2semidirect
18. #64312C22semidirect
23. D4×#157C22semidirect
26. #64242C22semidirect
31. C2×#3773C22semidirect
32. #64233C22semidirect
35. C4×GO+(4,𝔽2)C22semidirect
36. #64222C22semidirect
37. D32⋊Q8C22semidirect
48. C2×C32×D4D4semidirect
49. C2×#638D4semidirect
50. D4×C3⋊D3D4semidirect
52. C2×C4⋊(C3⋊D3)D4semidirect
113. C2×#157#41semidirect
118. C32×D4C2×D4semidirect
120. #638C2×D4semidirect
122. C4⋊(C3⋊D3)C2×D4semidirect
206. #157C2×#41semidirect
283. C2×C32#547semidirect
286. C3⋊D3#547semidirect
309. C2×D4GO+(4,𝔽2)semidirect
360. C32C2×#547semidirect
380. D4C2×GO+(4,𝔽2)semidirect
442. C2#10596519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643122
C2×D4×#1572
C2×#642422
C22×#37732
C2×#642332
#105965192
C2×C4×GO+(4,𝔽2)2
C2×#642222
C2×D32⋊Q82
C2×#5479