Finite Group Databasebeta

← C2×#10593949 #11901518

Subgroups — C2×#10593949 #11901518

Order 1152.

2633 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#874C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63908C212yesmaximal, complemented
5C2×Dic3×D12C212yesmaximal, complemented
6C2×#63885C214yesmaximal, complemented
7C2×#63884C214yesmaximal, complemented
8#10593949C2116yesmaximal, direct product factor
9C2×#5719—31nomaximal
10C2×#5535—31nomaximal
11C22×C3×D12C2212yes—
12C22×C3×D12C2214yes—
13C22×C3×C4×D3C2211yescharacteristic
14C22×#625C2214yes—
15C22×D3×Dic3C2214yes—
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2212yes—
18C2×#3750C2214yes—
19#64079C2218yescomplemented
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#874C2218yescomplemented
24C3×#872C2218yescomplemented
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27#63908C22116yescomplemented
28Dic3×D12C22116yescomplemented
29#63885C22132yescomplemented
30#63884C22132yescomplemented
31C2×C3×#127—31no—
32C2×C3×#117—31no—
33C2×#939—34no—
34C2×#938—32no—
35C2×#935—34no—
36C2×D4×Dic3—32no—
37C2×#930—32no—
38#5719—316no—
39#5535—316no—
40C2×#894—34no—
41C2×#884—34no—
42C2×#874D311yescharacteristic, complemented
43C2×C4×D12—32no—
44C2×#872D311yescharacteristic, complemented
45C2×#870—31no—
46C2×#870—31no—
47C2×#870—61no—
48C23×C3×D3C2311yescharacteristic
49C23×C3×D3C2314yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2311yescharacteristic
55C2×C3×D12—28no—
56C2×C3×D12—48no—
57C2×C3×D12C2318yes—
58C2×C3×D12C23116yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3C2314yes—
61C2×#625—48no—
62C2×#625C23116yes—
63C2×D3×Dic3—48no—
64C2×D3×Dic3C23116yes—
65C32×C42C2314yes—
66C4⋊(C3⋊Dic3)C2318yes—
67#3750C23116yes—
68C3×(C2×D3)⋊C4C2318yes—
69C3×Dic3⋊C4C2318yes—
70C3×C4×Dic3C2314yes—
71(C2×D3)⋊Dic3C23116yes—
72(C2×D3)⋊Dic3C23116yes—
73C2×#540—91noSylow
74C22×C3×D4—32no—
75C22×C3×D4—34no—
76C23×C3×C4—31no—
77C22×#67—34no—
78C22×#67—34no—
79C23×Dic3—34no—
80C22×D12C2×D312yes—
81C22×D12C2×D314yes—
82C22×C4×D3—34no—
83C22×C4×D3C2×D311yescharacteristic
84C3×#127—38no—
85C3×#117—38no—
86C2×C3×C4⋊C4—32no—
87C2×C3×C22⋊C4—32no—
88C2×C3×C42—21no—
89C2×C3×C42—31no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C2×#217—34no—
93C2×#217—34no—
94#939—332no—
95#938—316no—
96#935—332no—
97D4×Dic3—316no—
98#930—316no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—34no—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3—62no—
105C2×Dic3⋊C4—34no—
106C2×Dic3⋊C4—34no—
107C2×Dic3⋊C4—64no—
108C2×Dic3⋊C4C2×D312yes—
109C2×C4×Dic3C2×D311yescharacteristic
110#894—332no—
111#884—332no—
112#874C2×D318yescomplemented
113C4×D12—316no—
114#872C2×D318yescomplemented
115#870—38no—
116#870—38no—
117#870—68no—
118C23×C32C2411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—28no—
121C22×C3×D3—28no—
122C22×C3×D3—24no—
123C22×C3×D3—28no—
124C22×C3×D3C2418yes—
125C22×C3×D3C2412yes—
126C2×C32×C4—24no—
127C2×C32×C4#4114yes—
128C2×C32×C4C2414yes—
129C2×C32×C4C2412yes—
130C2×C3⋊Dic3—28no—
131C2×C3⋊Dic3C2418yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3C2412yes—
135C2×C3×Dic3C2414yes—
136C3×D12—216no—
137C3×D12—416no—
138C3×C4×D3—28no—
139#625—416no—
140D3×Dic3—416no—
141#540—916no—
142C2×#127—31no—
143C2×#125—91no—
144C2×#123—94no—
145C2×#121—94no—
146C2×#121—92no—
147C2×C4×D4—92no—
148C2×#117—31no—
149C24×C3—34no—
150C24×C3—31no—
151C23×D3C22×D314yes—
152C23×D3C22×D311yescharacteristic
153C2×C3×D4—38no—
154C2×C3×D4—316no—
155C2×C3×D4—68no—
156C2×C3×D4—128no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—31no—
160C22×C3×C4—32no—
161C22×C3×C4—34no—
162C22×C3×C4—64no—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—316no—
168C2×#67—316no—
169C2×#67—128no—
170C2×#67—128no—
171C22×Dic3—34no—
172C22×Dic3—34no—
173C22×Dic3—316no—
174C22×Dic3—64no—
175C22×Dic3—128no—
176C22×Dic3C22×D312yes—
177C22×Dic3C22×D311yescharacteristic
178C2×D12—28no—
179C2×D12—48no—
180C2×D12C22×D318yes—
181C2×D12C22×D3116yes—
182C2×C4×D3—24no—
183C2×C4×D3—316no—
184C2×C4×D3—128no—
185C2×C4×D3C22×D314yes—
186C3×C4⋊C4—38no—
187C3×C22⋊C4—38no—
188C3×C42—24no—
189C3×C42—34no—
190C3×C42C22×D314yes—
191C3×C42C22×D314yes—
192#217—316no—
193#217—316no—
194(C2×D3)⋊C4—316no—
195(C2×D3)⋊C4—316no—
196(C2×D3)⋊C4C22×D318yes—
197C4⋊Dic3—38no—
198C4⋊Dic3—38no—
199C4⋊Dic3—68no—
200Dic3⋊C4—316no—
201Dic3⋊C4—316no—
202Dic3⋊C4—616no—
203Dic3⋊C4C22×D318yes—
204C4×Dic3C22×D314yes—
205C22×C32C2×#4112yes—
206C22×C32H(5,𝔽2)14yes—
207C22×C32C2511yescharacteristic
208C2×C3×D3—22no—
209C2×C3×D3—28no—
210C2×C3×D3—28no—
211C2×C3×D3—24no—
212C2×C3×D3—28no—
213C2×C3×D3—416no—
214C2×C3×D3—44no—
215C32×C4—24no—
216C32×C4C2×#4114yes—
217C3⋊Dic3—28no—
218C3×Dic3—22no—
219C3×Dic3—24no—
220C22×D4—32no—
221C22×D4—34no—
222C22×D4—94no—
223C23×C4—31no—
224C23×C4—94no—
225#127—38no—
226#125—98no—
227#123—932no—
228#121—932no—
229#121—916no—
230C4×D4—916no—
231#117—38no—
232C2×C4⋊C4—32no—
233C2×C4⋊C4—92no—
234C2×C4⋊C4—94no—
235C2×C22⋊C4—32no—
236C2×C22⋊C4—94no—
237C2×C22⋊C4—94no—
238C2×C42—31no—
239C2×C42D3211yescharacteristic
240C23×C3—21no—
241C23×C3—38no—
242C23×C3—32no—
243C23×C3—68no—
244C23×C3—62no—
245C23×C3—64no—
246C23×C3—68no—
247C23×C3—68no—
248C23×C3C23×D311yescharacteristic
249C23×C3C23×D311yescharacteristic
250C22×D3—22no—
251C22×D3—28no—
252C22×D3—28no—
253C22×D3—28no—
254C22×D3—24no—
255C22×D3C23×D318yes—
256C22×D3C23×D312yes—
257C3×D4—616no—
258C3×D4—1216no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—32no—
265C2×C3×C4—34no—
266C2×C3×C4—44no—
267C2×C3×C4—62no—
268C2×C3×C4—64no—
269C2×C3×C4—68no—
270C2×C3×C4#23514yes—
271C2×C3×C4#23714yes—
272C2×C3×C4C23×D314yes—
273C2×C3×C4C23×D314yes—
274C2×C3×C4C23×D312yes—
275C2×C3×C4C23×D312yes—
276#67—1216no—
277#67—1216no—
278C2×Dic3—22no—
279C2×Dic3—24no—
280C2×Dic3—38no—
281C2×Dic3—38no—
282C2×Dic3—68no—
283C2×Dic3—68no—
284C2×Dic3—68no—
285C2×Dic3—128no—
286C2×Dic3—1216no—
287C2×Dic3C23×D314yes—
288C2×Dic3C23×D312yes—
289D12—216no—
290D12—416no—
291C4×D3—28no—
292C4×D3—1216no—
293C2×C32#54014yescomplemented
294C2×C32C22×#4111yescharacteristic
295C2×C32C2×H(5,𝔽2)12yes—
296C3×D3—48no—
297C3×D3—42no—
298C24—31no—
299C24—34no—
300C2×D4—38no—
301C2×D4—316no—
302C2×D4—68no—
303C2×D4—916no—
304C2×D4—128no—
305C2×D4—368no—
306C22×C4—32no—
307C22×C4—31no—
308C22×C4—34no—
309C22×C4—64no—
310C22×C4—916no—
311C22×C4—94no—
312C22×C4—368no—
313C22×C4C2×D3212yes—
314C22×C4C2×D3211yescharacteristic
315C4⋊C4—38no—
316C4⋊C4—98no—
317C4⋊C4—916no—
318C22⋊C4—38no—
319C22⋊C4—916no—
320C22⋊C4—916no—
321C42—34no—
322C42C2×D3214yes—
323C22×C3—22no—
324C22×C3—24no—
325C22×C3—21no—
326C22×C3—68no—
327C22×C3—62no—
328C22×C3—64no—
329C22×C3—68no—
330C22×C3—68no—
331C22×C3—124no—
332C22×C3—1216no—
333C22×C3C2×#23512yes—
334C22×C3C2×#23712yes—
335C22×C3#100414yes—
336C22×C3#100914yes—
337C22×C3C24×D311yescharacteristic
338C22×C3C24×D311yescharacteristic
339C2×D3—22no—
340C2×D3—28no—
341C2×D3—28no—
342C2×D3—28no—
343C2×D3—24no—
344C2×D3—416no—
345C2×D3—44no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—44no—
350C3×C4—62no—
351C3×C4—64no—
352C3×C4C2×#23514yes—
353C3×C4C2×#23714yes—
354Dic3—22no—
355Dic3—24no—
356Dic3—68no—
357Dic3—68no—
358Dic3—128no—
359C32C2×#54011yescharacteristic, complemented, Sylow
360C23—32no—
361C23—38no—
362C23—62no—
363C23—68no—
364C23—68no—
365C23—68no—
366C23—64no—
367C23C22×D3211yescharacteristic
368D4—616no—
369D4—1216no—
370D4—3616no—
371C2×C4—24no—
372C2×C4—34no—
373C2×C4—32no—
374C2×C4—62no—
375C2×C4—64no—
376C2×C4—68no—
377C2×C4—98no—
378C2×C4—188no—
379C2×C4—3616no—
380C2×C4#379514yes—
381C2×C4C22×D3214yes—
382C2×C4C22×D3212yes—
383C2×C3—21no—
384C2×C3—22no—
385C2×C3—24no—
386C2×C3—122no—
387C2×C3—128no—
388C2×C3#553514yescomplemented
389C2×C3#571914yescomplemented
390C2×C3C22×#23511yescharacteristic
391C2×C3C22×#23711yescharacteristic
392C2×C3C2×#100412yes—
393C2×C3C2×#100912yes—
394D3—48no—
395D3—42no—
396C22—62no—
397C22—68no—
398C22—68no—
399C22—68no—
400C22—64no—
401C22—124no—
402C22—1216no—
403C22C2×#379512yes—
404C22#6430714yes—
405C22C23×D3211yescharacteristic
406C4—24no—
407C4—62no—
408C4—64no—
409C4—188no—
410C4C2×#379514yes—
411C3—21no—
412C3C2×#553511yescharacteristic, complemented
413C3C2×#571911yescharacteristic, complemented
414C2—122no—
415C2—128no—
416C2#1059394914yesdirect product factor
417C2C22×#379511yescharacteristic
418C2C2×#6430712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
2. C2×C3×#874C2semidirect
3. C2×C3×#872C2semidirect
4. C2×#63908C2semidirect
5. C2×Dic3×D12C2semidirect
6. C2×#63885C2semidirect
7. C2×#63884C2semidirect
8. #10593949C2direct (N × H)
19. #64079C22semidirect
23. C3×#874C22semidirect
24. C3×#872C22semidirect
27. #63908C22semidirect
28. Dic3×D12C22semidirect
29. #63885C22semidirect
30. #63884C22semidirect
42. C2×#874D3semidirect
44. C2×#872D3semidirect
112. #874C2×D3semidirect
114. #872C2×D3semidirect
293. C2×C32#540semidirect
359. C32C2×#540semidirect
388. C2×C3#5535semidirect
389. C2×C3#5719semidirect
412. C3C2×#5535semidirect
413. C3C2×#5719semidirect
416. C2#10593949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8742
C2×C3×#8722
C2×#639082
C2×Dic3×D122
C2×#638852
C2×#638842
#105939492
C2×#57193
C2×#55353