Finite Group Databasebeta

← C2×#10594022 #11910195

Subgroups — C2×#10594022 #11910195

Order 1152.

2811 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64085C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×#874C211yesmaximal, characteristic, complemented
4C2×#63922C213yesmaximal, complemented
5C2×#63886C213yesmaximal, complemented
6C2×#63885C213yesmaximal, complemented
7C2×#63884C213yesmaximal, complemented
8#10594022C2116yesmaximal, direct product factor
9C2×#5720—31nomaximal
10C2×#5711—31nomaximal
11C23×D32C2211yescharacteristic
12C22×C3×D12C2213yes—
13C22×C3×D12C2213yescomplemented
14C22×#626C2213yes—
15C22×#625C2213yes—
16C22×D3×Dic3C2213yescomplemented
17C2×C32×C42C2211yescharacteristic, complemented
18C2×#3752C2213yes—
19C2×#3750C2213yescomplemented
20#64085C2218yescomplemented
21C2×C3×(C2×D3)⋊C4C2213yes—
22C2×C3×Dic3⋊C4C2213yescomplemented
23C3×#876C2218yescomplemented
24C3×#874C2218yescomplemented
25C2×(C2×D3)⋊Dic3C2213yes—
26C2×(C2×D3)⋊Dic3C2213yescomplemented
27#63922C22124yescomplemented
28#63886C22124yescomplemented
29#63885C22124yescomplemented
30#63884C22124yescomplemented
31C2×C3×#127—31no—
32C2×C3×#126—31no—
33C2×#939—33no—
34C2×#939—33no—
35C2×#937—33no—
36C2×#935—33no—
37#5720—316no—
38#5711—316no—
39C2×#895—33no—
40C2×#894—33no—
41C2×#884—33no—
42C2×#882—33no—
43C2×#876—31no—
44C2×#876—31no—
45C2×#876—61no—
46C2×#876D311yescharacteristic, complemented
47C2×#874D311yescharacteristic, complemented
48C23×C3⋊D3C2311yescharacteristic
49C23×C3×D3C2311yescharacteristic
50C23×C3×D3C2313yes—
51C23×C3×D3C2311yescharacteristic
52C22×D32—46no—
53C22×D32C2314yes—
54C22×C32×C4C2313yes—
55C22×C3⋊Dic3C2313yes—
56C22×C3×Dic3C2313yes—
57C2×C3×D12—46no—
58C2×C3×D12—46no—
59C2×C3×D12C23112yes—
60C2×C3×D12C23112yescomplemented
61C2×#626—46no—
62C2×#626C23112yes—
63C2×#625—46no—
64C2×#625C23112yes—
65C2×D3×Dic3—46no—
66C2×D3×Dic3C23112yescomplemented
67C32×C42C2314yescomplemented
68#3752C23112yes—
69#3750C23112yescomplemented
70C3×(C2×D3)⋊C4C23112yes—
71C3×Dic3⋊C4C23112yescomplemented
72(C2×D3)⋊Dic3C23112yes—
73(C2×D3)⋊Dic3C23112yescomplemented
74C2×#560—91noSylow
75C24×D3—31no—
76C24×D3—31no—
77C22×C3×D4—33no—
78C22×C3×D4—33no—
79C22×#67—33no—
80C22×#67—33no—
81C22×#67—33no—
82C23×Dic3—33no—
83C22×D12—33no—
84C22×D12C2×D313yes—
85C22×D12C2×D313yescomplemented
86C22×C4×D3—33no—
87C3×#127—38no—
88C3×#126—38no—
89C2×C3×C4⋊C4—33no—
90C2×C3×C22⋊C4—33no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic, complemented
93C2×C3×C42C2×D311yescharacteristic, complemented
94C2×#217—33no—
95C2×#217—33no—
96#939—324no—
97#939—324no—
98#937—324no—
99#935—324no—
100C2×(C2×D3)⋊C4—33no—
101C2×(C2×D3)⋊C4—33no—
102C2×(C2×D3)⋊C4—33no—
103C2×(C2×D3)⋊C4—33no—
104C2×(C2×D3)⋊C4—63no—
105C2×(C2×D3)⋊C4C2×D313yes—
106C2×Dic3⋊C4—33no—
107C2×Dic3⋊C4—33no—
108C2×Dic3⋊C4—63no—
109C2×Dic3⋊C4C2×D313yescomplemented
110#895—324no—
111#894—324no—
112#884—324no—
113#882—324no—
114#876—38no—
115#876—38no—
116#876—68no—
117#876C2×D318yescomplemented
118#874C2×D318yescomplemented
119C23×C32C2411yescharacteristic
120C22×C3⋊D3—26no—
121C22×C3⋊D3C2412yes—
122C22×C3×D3—26no—
123C22×C3×D3—26no—
124C22×C3×D3—26no—
125C22×C3×D3—26no—
126C22×C3×D3—26no—
127C22×C3×D3C2412yes—
128C22×C3×D3C2412yes—
129C22×C3×D3C2416yes—
130C2×D32—412no—
131C2×D32—416no—
132C2×C32×C4—26no—
133C2×C32×C4C2416yes—
134C2×C3⋊Dic3—26no—
135C2×C3⋊Dic3C2416yes—
136C2×C3×Dic3—26no—
137C2×C3×Dic3C2416yes—
138C3×D12—412no—
139C3×D12—412no—
140#626—412no—
141#625—412no—
142D3×Dic3—412no—
143#560—916no—
144C2×#127—31no—
145C2×#126—31no—
146C2×#126—91no—
147C2×#123—93no—
148C2×#121—93no—
149C2×#121—93no—
150C2×#120—93no—
151C24×C3—31no—
152C24×C3—33no—
153C24×C3—31no—
154C23×D3—31no—
155C23×D3—31no—
156C23×D3—34no—
157C23×D3—34no—
158C23×D3—61no—
159C23×D3—126no—
160C23×D3—126no—
161C23×D3C22×D311yescharacteristic
162C23×D3C22×D313yes—
163C23×D3C22×D311yescharacteristic
164C2×C3×D4—312no—
165C2×C3×D4—312no—
166C2×C3×D4—126no—
167C2×C3×D4—126no—
168C22×C3×C4—23no—
169C22×C3×C4—33no—
170C22×C3×C4C22×D313yes—
171C22×C3×C4C22×D313yes—
172C2×#67—312no—
173C2×#67—312no—
174C2×#67—312no—
175C2×#67—126no—
176C2×#67—126no—
177C2×#67—126no—
178C22×Dic3—33no—
179C22×Dic3—33no—
180C22×Dic3—312no—
181C22×Dic3—63no—
182C22×Dic3—126no—
183C22×Dic3C22×D313yes—
184C2×D12—312no—
185C2×D12—46no—
186C2×D12—46no—
187C2×D12—126no—
188C2×D12C22×D3112yes—
189C2×D12C22×D3112yescomplemented
190C2×C4×D3—312no—
191C2×C4×D3—126no—
192C3×C4⋊C4—312no—
193C3×C22⋊C4—312no—
194C3×C42—24no—
195C3×C42C22×D314yescomplemented
196C3×C42C22×D314yescomplemented
197#217—312no—
198#217—312no—
199(C2×D3)⋊C4—312no—
200(C2×D3)⋊C4—312no—
201(C2×D3)⋊C4—312no—
202(C2×D3)⋊C4—312no—
203(C2×D3)⋊C4—612no—
204(C2×D3)⋊C4C22×D3112yes—
205Dic3⋊C4—312no—
206Dic3⋊C4—312no—
207Dic3⋊C4—612no—
208Dic3⋊C4C22×D3112yescomplemented
209C22×C32H(5,𝔽2)16yes—
210C22×C32C2511yescharacteristic
211C2×C3⋊D3—26no—
212C2×C3⋊D3—44no—
213C2×C3×D3—26no—
214C2×C3×D3—26no—
215C2×C3×D3—26no—
216C2×C3×D3—26no—
217C2×C3×D3—26no—
218C2×C3×D3—44no—
219C2×C3×D3—44no—
220C2×C3×D3—412no—
221D32—416no—
222C32×C4—26no—
223C3⋊Dic3—26no—
224C3×Dic3—26no—
225C25—91no—
226C22×D4—33no—
227C22×D4—33no—
228C22×D4—93no—
229C22×D4—93no—
230C23×C4—93no—
231#127—38no—
232#126—38no—
233#126—98no—
234#123—924no—
235#121—924no—
236#121—924no—
237#120—924no—
238C2×C4⋊C4—33no—
239C2×C4⋊C4—93no—
240C2×C22⋊C4—33no—
241C2×C22⋊C4—93no—
242C2×C22⋊C4—93no—
243C2×C22⋊C4—93no—
244C2×C42D3211yescharacteristic, complemented
245C23×C3—21no—
246C23×C3—32no—
247C23×C3—36no—
248C23×C3—32no—
249C23×C3—66no—
250C23×C3—66no—
251C23×C3—66no—
252C23×C3—66no—
253C23×C3—66no—
254C23×C3C23×D311yescharacteristic
255C23×C3C23×D311yescharacteristic
256C22×D3—26no—
257C22×D3—26no—
258C22×D3—26no—
259C22×D3—26no—
260C22×D3—26no—
261C22×D3—32no—
262C22×D3—32no—
263C22×D3—62no—
264C22×D3—66no—
265C22×D3—66no—
266C22×D3—126no—
267C22×D3—1212no—
268C22×D3—1212no—
269C22×D3—1216no—
270C22×D3—1216no—
271C22×D3C23×D312yes—
272C22×D3C23×D316yes—
273C22×D3C23×D312yes—
274C3×D4—1212no—
275C3×D4—1212no—
276C2×C3×C4—26no—
277C2×C3×C4—26no—
278C2×C3×C4—26no—
279C2×C3×C4—36no—
280C2×C3×C4—46no—
281C2×C3×C4—66no—
282C2×C3×C4C23×D316yes—
283C2×C3×C4C23×D316yes—
284#67—1212no—
285#67—1212no—
286#67—1212no—
287C2×Dic3—26no—
288C2×Dic3—36no—
289C2×Dic3—36no—
290C2×Dic3—66no—
291C2×Dic3—66no—
292C2×Dic3—66no—
293C2×Dic3—126no—
294C2×Dic3—1212no—
295C2×Dic3C23×D316yes—
296D12—412no—
297D12—412no—
298D12—1212no—
299C4×D3—1212no—
300C2×C32#56014yescomplemented
301C2×C32C2×H(5,𝔽2)13yes—
302C3⋊D3—42no—
303C3×D3—42no—
304C3×D3—42no—
305C3×D3—46no—
306C24—31no—
307C24—31no—
308C24—33no—
309C24—94no—
310C24—91no—
311C24—366no—
312C2×D4—312no—
313C2×D4—312no—
314C2×D4—912no—
315C2×D4—912no—
316C2×D4—126no—
317C2×D4—126no—
318C2×D4—366no—
319C2×D4—366no—
320C22×C4—33no—
321C22×C4—912no—
322C22×C4—93no—
323C22×C4—366no—
324C22×C4C2×D3213yes—
325C4⋊C4—312no—
326C4⋊C4—912no—
327C22⋊C4—312no—
328C22⋊C4—912no—
329C22⋊C4—912no—
330C22⋊C4—912no—
331C42C2×D3214yescomplemented
332C22×C3—26no—
333C22×C3—21no—
334C22×C3—66no—
335C22×C3—66no—
336C22×C3—66no—
337C22×C3—66no—
338C22×C3—66no—
339C22×C3—124no—
340C22×C3—1212no—
341C22×C3—124no—
342C22×C3#100416yes—
343C22×C3#100916yes—
344C22×C3C24×D311yescharacteristic
345C22×C3C24×D311yescharacteristic
346C2×D3—26no—
347C2×D3—26no—
348C2×D3—26no—
349C2×D3—26no—
350C2×D3—26no—
351C2×D3—44no—
352C2×D3—44no—
353C2×D3—412no—
354C2×D3—66no—
355C2×D3—66no—
356C2×D3—126no—
357C2×D3—1216no—
358C2×D3—1216no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—244no—
362C3×C4—26no—
363C3×C4—26no—
364C3×C4—46no—
365C3×C4—66no—
366Dic3—26no—
367Dic3—66no—
368Dic3—66no—
369Dic3—126no—
370C32C2×#56011yescharacteristic, complemented, Sylow
371C23—32no—
372C23—32no—
373C23—36no—
374C23—66no—
375C23—66no—
376C23—66no—
377C23—66no—
378C23—66no—
379C23—92no—
380C23—186no—
381C23—3612no—
382C23—3616no—
383C23C22×D3211yescharacteristic
384D4—1212no—
385D4—1212no—
386D4—3612no—
387D4—3612no—
388C2×C4—26no—
389C2×C4—36no—
390C2×C4—66no—
391C2×C4—96no—
392C2×C4—186no—
393C2×C4—3612no—
394C2×C4C22×D3216yes—
395C2×C3—23no—
396C2×C3—24no—
397C2×C3—122no—
398C2×C3—126no—
399C2×C3—122no—
400C2×C3#571114yescomplemented
401C2×C3#572014yescomplemented
402C2×C3C2×#100413yes—
403C2×C3C2×#100913yes—
404D3—42no—
405D3—42no—
406D3—46no—
407D3—122no—
408D3—122no—
409D3—242no—
410C22—66no—
411C22—66no—
412C22—66no—
413C22—66no—
414C22—66no—
415C22—124no—
416C22—124no—
417C22—1212no—
418C22—186no—
419C22—3616no—
420C22—364no—
421C22#6430716yes—
422C22C23×D3211yescharacteristic
423C4—26no—
424C4—66no—
425C4—186no—
426C3—21no—
427C3C2×#571111yescharacteristic, complemented
428C3C2×#572011yescharacteristic, complemented
429C2—122no—
430C2—122no—
431C2—126no—
432C2—362no—
433C2#1059402214yesdirect product factor
434C2C2×#6430713yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64085C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×#874C2semidirect
4. C2×#63922C2semidirect
5. C2×#63886C2semidirect
6. C2×#63885C2semidirect
7. C2×#63884C2semidirect
8. #10594022C2direct (N × H)
13. C22×C3×D12C22semidirect
16. C22×D3×Dic3C22semidirect
17. C2×C32×C42C22semidirect
19. C2×#3750C22semidirect
20. #64085C22semidirect
22. C2×C3×Dic3⋊C4C22semidirect
23. C3×#876C22semidirect
24. C3×#874C22semidirect
26. C2×(C2×D3)⋊Dic3C22semidirect
27. #63922C22semidirect
28. #63886C22semidirect
29. #63885C22semidirect
30. #63884C22semidirect
46. C2×#876D3semidirect
47. C2×#874D3semidirect
60. C2×C3×D12C23semidirect
66. C2×D3×Dic3C23semidirect
67. C32×C42C23semidirect
69. #3750C23semidirect
71. C3×Dic3⋊C4C23semidirect
73. (C2×D3)⋊Dic3C23semidirect
85. C22×D12C2×D3semidirect
92. C2×C3×C42C2×D3semidirect
93. C2×C3×C42C2×D3semidirect
109. C2×Dic3⋊C4C2×D3semidirect
117. #876C2×D3semidirect
118. #874C2×D3semidirect
189. C2×D12C22×D3semidirect
195. C3×C42C22×D3semidirect
196. C3×C42C22×D3semidirect
208. Dic3⋊C4C22×D3semidirect
244. C2×C42D32semidirect
300. C2×C32#560semidirect
331. C42C2×D32semidirect
370. C32C2×#560semidirect
400. C2×C3#5711semidirect
401. C2×C3#5720semidirect
427. C3C2×#5711semidirect
428. C3C2×#5720semidirect
433. C2#10594022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640852
C2×C3×#8762
C2×C3×#8742
C2×#639222
C2×#638862
C2×#638852
C2×#638842
#105940222
C2×#57203
C2×#57113