Finite Group Databasebeta

← C2×#10593989 #11901516

Subgroups — C2×#10593989 #11901516

Order 1152.

2769 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64083C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63910C214yesmaximal, complemented
5C2×#63909C212yesmaximal, complemented
6C2×#63897C214yesmaximal, complemented
7C2×#63894C212yesmaximal, complemented
8#10593989C2116yesmaximal, direct product factor
9C2×#5697—31nomaximal
10C2×#5535—31nomaximal
11C22×C4⋊(C3⋊D3)C2212yes—
12C22×C4⋊(C3⋊D3)C2214yes—
13C22×C3×C4×D3C2211yescharacteristic
14C22×#626C2214yes—
15C22×#624C2214yes—
16C2×C32×C42C2211yescharacteristic
17#64083C2218yescomplemented
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#872C2218yescomplemented
24C3×#870C2218yescomplemented
25C2×#3722C2214yes—
26C2×#3722C2214yes—
27#63910C22132yescomplemented
28#63909C22116yescomplemented
29#63897C22132yescomplemented
30#63894C22116yescomplemented
31C2×C3×#125—31no—
32C2×C3×#117—31no—
33C2×#930—32no—
34#5697—316no—
35#5535—316no—
36C2×#895—32no—
37C2×#895—34no—
38C2×#894—34no—
39C2×#894—34no—
40C2×#893—32no—
41C2×#884—34no—
42C2×#874—31no—
43C2×#874—31no—
44C2×#874—61no—
45C2×C4×D12—32no—
46C2×#872D311yescharacteristic, complemented
47C2×#870D311yescharacteristic, complemented
48C23×C3⋊D3C2314yes—
49C23×C3×D3C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—28no—
53C2×C4⋊(C3⋊D3)—48no—
54C2×C4⋊(C3⋊D3)C2318yes—
55C2×C4⋊(C3⋊D3)C23116yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C22×C3×Dic3C2311yescharacteristic
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3C2314yes—
61C2×#626—48no—
62C2×#626C23116yes—
63C2×#624—48no—
64C2×#624C23116yes—
65C32×C42C2314yes—
66C3×(C2×D3)⋊C4C2318yes—
67C3×C4⋊Dic3C2318yes—
68C3×Dic3⋊C4C2318yes—
69C3×Dic3⋊C4C23116yes—
70C3×C4×Dic3C2314yes—
71#3722C23116yes—
72#3722C23116yes—
73C2×#540—91noSylow
74C23×C3×C4—31no—
75C22×#67—34no—
76C22×D12—32no—
77C22×D12—32no—
78C22×D12—34no—
79C22×D12—34no—
80C22×D12—34no—
81C22×D12—62no—
82C22×D12—64no—
83C22×C4×D3—34no—
84C22×C4×D3—34no—
85C22×C4×D3C2×D311yescharacteristic
86C3×#125—38no—
87C3×#117—38no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C4⋊C4—34no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C22⋊C4—32no—
92C2×C3×C42—21no—
93C2×C3×C42—31no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C2×D311yescharacteristic
96#930—316no—
97C2×(C2×D3)⋊C4—34no—
98C2×(C2×D3)⋊C4—34no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—34no—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×C4⋊Dic3C2×D312yes—
103C2×Dic3⋊C4C2×D314yes—
104C2×Dic3⋊C4C2×D312yes—
105C2×C4×Dic3C2×D311yescharacteristic
106#895—316no—
107#895—332no—
108#894—332no—
109#894—332no—
110#893—316no—
111#884—332no—
112#874—38no—
113#874—38no—
114#874—68no—
115C4×D12—316no—
116#872C2×D318yescomplemented
117#870C2×D318yescomplemented
118C23×C32C2411yescharacteristic
119C22×C3⋊D3—28no—
120C22×C3⋊D3—28no—
121C22×C3⋊D3—28no—
122C22×C3⋊D3C2418yes—
123C22×C3×D3—22no—
124C22×C3×D3—24no—
125C22×C3×D3C2412yes—
126C2×C32×C4—24no—
127C2×C32×C4#4114yes—
128C2×C32×C4C2414yes—
129C2×C32×C4C2412yes—
130C4⋊(C3⋊D3)—216no—
131C4⋊(C3⋊D3)—416no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—28no—
135C2×C3×Dic3C2412yes—
136C2×C3×Dic3C2414yes—
137C2×C3×Dic3C2418yes—
138C3×C4×D3—28no—
139#626—416no—
140#624—416no—
141#540—916no—
142C2×#127—91no—
143C2×#125—31no—
144C2×#123—94no—
145C2×#121—94no—
146C2×#121—92no—
147C2×C4×D4—92no—
148C2×#117—31no—
149C24×C3—31no—
150C23×D3—34no—
151C23×D3—34no—
152C23×D3—64no—
153C23×D3C22×D311yescharacteristic
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—32no—
158C22×C3×C4—34no—
159C22×C3×C4—34no—
160C22×C3×C4—64no—
161C22×C3×C4C22×D312yes—
162C22×C3×C4C22×D312yes—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—316no—
166C2×#67—128no—
167C22×Dic3C22×D312yes—
168C22×Dic3C22×D314yes—
169C22×Dic3C22×D311yescharacteristic
170C2×D12—38no—
171C2×D12—38no—
172C2×D12—316no—
173C2×D12—316no—
174C2×D12—316no—
175C2×D12—68no—
176C2×D12—616no—
177C2×D12—68no—
178C2×D12—68no—
179C2×D12—128no—
180C2×D12—128no—
181C2×D12—128no—
182C2×D12—1216no—
183C2×D12—128no—
184C2×C4×D3—24no—
185C2×C4×D3—316no—
186C2×C4×D3—316no—
187C2×C4×D3—128no—
188C2×C4×D3—128no—
189C2×C4×D3C22×D314yes—
190C3×C4⋊C4—38no—
191C3×C4⋊C4—38no—
192C3×C4⋊C4—316no—
193C3×C22⋊C4—38no—
194C3×C42—24no—
195C3×C42—34no—
196C3×C42C22×D314yes—
197C3×C42C22×D314yes—
198(C2×D3)⋊C4—316no—
199(C2×D3)⋊C4—316no—
200(C2×D3)⋊C4—316no—
201(C2×D3)⋊C4—316no—
202(C2×D3)⋊C4C22×D318yes—
203C4⋊Dic3C22×D318yes—
204Dic3⋊C4C22×D3116yes—
205Dic3⋊C4C22×D318yes—
206C4×Dic3C22×D314yes—
207C22×C32C2×#4112yes—
208C22×C32H(5,𝔽2)14yes—
209C22×C32C2511yescharacteristic
210C2×C3⋊D3—28no—
211C2×C3⋊D3—28no—
212C2×C3⋊D3—28no—
213C2×C3⋊D3—416no—
214C2×C3×D3—22no—
215C2×C3×D3—24no—
216C2×C3×D3—44no—
217C32×C4—24no—
218C32×C4C2×#4114yes—
219C3×Dic3—22no—
220C3×Dic3—24no—
221C3×Dic3—28no—
222C22×D4—94no—
223C22×D4—92no—
224C22×D4—94no—
225C23×C4—31no—
226C23×C4—94no—
227#127—98no—
228#125—38no—
229#123—932no—
230#121—932no—
231#121—916no—
232C4×D4—916no—
233#117—38no—
234C2×C4⋊C4—32no—
235C2×C4⋊C4—32no—
236C2×C4⋊C4—34no—
237C2×C22⋊C4—32no—
238C2×C22⋊C4—94no—
239C2×C22⋊C4—94no—
240C2×C42—31no—
241C2×C42D3211yescharacteristic
242C23×C3—21no—
243C23×C3—32no—
244C23×C3—62no—
245C23×C3—64no—
246C23×C3C23×D311yescharacteristic
247C23×C3C23×D311yescharacteristic
248C22×D3—22no—
249C22×D3—24no—
250C22×D3—38no—
251C22×D3—38no—
252C22×D3—68no—
253C22×D3—68no—
254C22×D3—68no—
255C22×D3—68no—
256C22×D3—68no—
257C22×D3—68no—
258C22×D3—68no—
259C22×D3—128no—
260C22×D3—128no—
261C22×D3—128no—
262C22×D3C23×D312yes—
263C2×C3×C4—28no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—32no—
270C2×C3×C4—34no—
271C2×C3×C4—38no—
272C2×C3×C4—62no—
273C2×C3×C4—64no—
274C2×C3×C4—68no—
275C2×C3×C4—68no—
276C2×C3×C4#23514yes—
277C2×C3×C4#23914yes—
278C2×C3×C4C23×D314yes—
279C2×C3×C4C23×D314yes—
280C2×C3×C4C23×D312yes—
281C2×C3×C4C23×D312yes—
282#67—1216no—
283C2×Dic3—22no—
284C2×Dic3—24no—
285C2×Dic3—28no—
286C2×Dic3C23×D314yes—
287C2×Dic3C23×D318yes—
288C2×Dic3C23×D312yes—
289D12—616no—
290D12—616no—
291D12—1216no—
292D12—1216no—
293D12—1216no—
294D12—1232no—
295D12—1216no—
296C4×D3—28no—
297C4×D3—1216no—
298C4×D3—1216no—
299C2×C32#54014yescomplemented
300C2×C32C22×#4111yescharacteristic
301C2×C32C2×H(5,𝔽2)12yes—
302C3⋊D3—48no—
303C3×D3—42no—
304C24—31no—
305C24—94no—
306C2×D4—916no—
307C2×D4—98no—
308C2×D4—916no—
309C2×D4—188no—
310C2×D4—368no—
311C2×D4—368no—
312C22×C4—32no—
313C22×C4—31no—
314C22×C4—34no—
315C22×C4—34no—
316C22×C4—64no—
317C22×C4—916no—
318C22×C4—368no—
319C22×C4C2×D3212yes—
320C22×C4C2×D3211yescharacteristic
321C4⋊C4—38no—
322C4⋊C4—38no—
323C4⋊C4—316no—
324C22⋊C4—38no—
325C22⋊C4—916no—
326C22⋊C4—916no—
327C42—34no—
328C42C2×D3214yes—
329C22×C3—22no—
330C22×C3—24no—
331C22×C3—21no—
332C22×C3—62no—
333C22×C3—64no—
334C22×C3—124no—
335C22×C3C2×#23512yes—
336C22×C3C2×#23912yes—
337C22×C3#100914yes—
338C22×C3#100914yes—
339C22×C3C24×D311yescharacteristic
340C22×C3C24×D311yescharacteristic
341C2×D3—22no—
342C2×D3—24no—
343C2×D3—44no—
344C2×D3—68no—
345C2×D3—68no—
346C2×D3—68no—
347C2×D3—68no—
348C2×D3—68no—
349C2×D3—68no—
350C2×D3—128no—
351C2×D3—128no—
352C2×D3—128no—
353C2×D3—1216no—
354C2×D3—1216no—
355C2×D3—2416no—
356C3×C4—28no—
357C3×C4—24no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—62no—
361C3×C4—64no—
362C3×C4—68no—
363C3×C4C2×#23514yes—
364C3×C4C2×#23914yes—
365Dic3—22no—
366Dic3—24no—
367Dic3—28no—
368C32C2×#54011yescharacteristic, complemented, Sylow
369C23—32no—
370C23—62no—
371C23—64no—
372C23—98no—
373C23—188no—
374C23—188no—
375C23—188no—
376C23C22×D3211yescharacteristic
377D4—1816no—
378D4—3616no—
379D4—3616no—
380C2×C4—24no—
381C2×C4—34no—
382C2×C4—32no—
383C2×C4—38no—
384C2×C4—62no—
385C2×C4—64no—
386C2×C4—68no—
387C2×C4—68no—
388C2×C4—3616no—
389C2×C4#379914yes—
390C2×C4C22×D3214yes—
391C2×C4C22×D3212yes—
392C2×C3—21no—
393C2×C3—22no—
394C2×C3—24no—
395C2×C3—122no—
396C2×C3#553514yescomplemented
397C2×C3#569714yescomplemented
398C2×C3C22×#23511yescharacteristic
399C2×C3C22×#23911yescharacteristic
400C2×C3C2×#100912yes—
401C2×C3C2×#100912yes—
402D3—42no—
403D3—128no—
404D3—128no—
405D3—248no—
406C22—62no—
407C22—64no—
408C22—124no—
409C22—188no—
410C22—188no—
411C22—188no—
412C22—3616no—
413C22C2×#379912yes—
414C22#6430814yes—
415C22C23×D3211yescharacteristic
416C4—24no—
417C4—62no—
418C4—64no—
419C4—68no—
420C4C2×#379914yes—
421C3—21no—
422C3C2×#553511yescharacteristic, complemented
423C3C2×#569711yescharacteristic, complemented
424C2—122no—
425C2—368no—
426C2#1059398914yesdirect product factor
427C2C22×#379911yescharacteristic
428C2C2×#6430812yes—
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×#64083C2semidirect
2. C2×C3×#872C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63910C2semidirect
5. C2×#63909C2semidirect
6. C2×#63897C2semidirect
7. C2×#63894C2semidirect
8. #10593989C2direct (N × H)
17. #64083C22semidirect
23. C3×#872C22semidirect
24. C3×#870C22semidirect
27. #63910C22semidirect
28. #63909C22semidirect
29. #63897C22semidirect
30. #63894C22semidirect
46. C2×#872D3semidirect
47. C2×#870D3semidirect
116. #872C2×D3semidirect
117. #870C2×D3semidirect
299. C2×C32#540semidirect
368. C32C2×#540semidirect
396. C2×C3#5535semidirect
397. C2×C3#5697semidirect
422. C3C2×#5535semidirect
423. C3C2×#5697semidirect
426. C2#10593989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640832
C2×C3×#8722
C2×C3×#8702
C2×#639102
C2×#639092
C2×#638972
C2×#638942
#105939892
C2×#56973
C2×#55353