Finite Group Databasebeta

← C2×#10593970 #11900781

Subgroups — C2×#10593970 #11900781

Order 1152.

3705 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
1C22×#3799C212yesmaximal, complemented
2C2×#64083C211yesmaximal, characteristic, complemented
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×#63909C214yesmaximal, complemented
6C2×#63894C214yesmaximal, complemented
7C2×#63864C212yesmaximal, complemented
8#10593970C2116yesmaximal, direct product factor
9C2×#5725—31nomaximal
10C2×#5477—31nomaximal
11C22×C4⋊(C3⋊D3)C2212yes—
12C22×C4⋊(C3⋊D3)C2214yes—
13C22×C3×C4×D3C2212yes—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2212yes—
16C22×#626C2214yes—
17C22×#624C2214yes—
18C2×#3799—216no—
19C2×#3799C22116yescomplemented
20C2×C32×C42C2211yescharacteristic
21#64083C2218yescomplemented
22C2×C3×C4⋊Dic3C2214yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C3×C42×D3C2218yescomplemented
26C3×#869C2218yescomplemented
27C2×#3722C2218yes—
28#63909C22132yescomplemented
29#63894C22132yescomplemented
30#63864C22116yescomplemented
31C22×#239—32no—
32C22×#235—32no—
33C2×C3×C4⋊Q8—31no—
34C22×C3×C42—31no—
35C2×#947—32no—
36C2×#930—34no—
37#5725—316no—
38C2×#895—34no—
39C2×#893—34no—
40#5477—316no—
41C2×#875—32no—
42C2×#874—31no—
43C2×#874—31no—
44C2×#874—61no—
45C2×C4×D12—34no—
46C2×C42×D3D311yescharacteristic, complemented
47C2×#869D311yescharacteristic, complemented
48C23×C3⋊D3C2314yes—
49C23×C3×D3C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C2×C4⋊(C3⋊D3)—28no—
53C2×C4⋊(C3⋊D3)—216no—
54C2×C4⋊(C3⋊D3)C2318yes—
55C2×C4⋊(C3⋊D3)C23116yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C22×C3×Dic3C2311yescharacteristic
59C2×C3×C4×D3—28no—
60C2×C3×C4×D3D418yescomplemented
61C2×C3×C4×D3C2318yes—
62C2×C3×C4×D3C2314yes—
63C2×C3×Dic6—28no—
64C2×C3×Dic6C2318yes—
65C2×#626—216no—
66C2×#626C23116yes—
67C2×#624—216no—
68C2×#624C23116yes—
69#3799—264no—
70C32×C42C2314yes—
71C3×C4⋊Dic3C23116yes—
72C3×C4×Dic3C2314yes—
73C3×C4×Dic3C2318yes—
74#3722C23132yes—
75C2×#532—91noSylow
76C22×C3×Q8—32no—
77C23×C3×C4—31no—
78C23×C3×C4—32no—
79C22×#67—34no—
80C2×#239—316no—
81C2×#239—616no—
82C2×#235—316no—
83C2×#235—616no—
84C22×D12—34no—
85C22×D12—32no—
86C22×D12—32no—
87C22×D12—34no—
88C22×D12—34no—
89C22×D12—64no—
90C22×D12—62no—
91C22×C4×D3—34no—
92C22×C4×D3—34no—
93C22×C4×D3C2×D312yes—
94C22×C4×D3C2×D311yescharacteristic
95C22×Dic6C2×D312yes—
96C3×C4⋊Q8—38no—
97C2×C3×C4⋊C4—34no—
98C2×C3×C42—21no—
99C2×C3×C42—32no—
100C2×C3×C42—31no—
101C2×C3×C42—38no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104#947—316no—
105#930—332no—
106C2×(C2×D3)⋊C4—38no—
107C2×(C2×D3)⋊C4—38no—
108C2×C4⋊Dic3C2×D314yes—
109C2×C4×Dic3C2×D312yes—
110C2×C4×Dic3C2×D311yescharacteristic
111#895—332no—
112#893—332no—
113#875—316no—
114#874—38no—
115#874—38no—
116#874—68no—
117C4×D12—332no—
118C42×D3C2×D318yescomplemented
119#869C2×D318yescomplemented
120C23×C32C2411yescharacteristic
121C22×C3⋊D3—28no—
122C22×C3⋊D3—216no—
123C22×C3⋊D3C2418yes—
124C22×C3×D3—24no—
125C22×C3×D3C2×D414yes—
126C22×C3×D3C2412yes—
127C2×C32×C4C2×D414yes—
128C2×C32×C4#4118yescomplemented
129C2×C32×C4C2412yes—
130C2×C32×C4C2414yes—
131C4⋊(C3⋊D3)—216no—
132C4⋊(C3⋊D3)—232no—
133C2×C3×Dic3—28no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3C2×D414yes—
136C2×C3×Dic3C2414yes—
137C2×C3×Dic3C2418yes—
138C2×C3×Dic3C2412yes—
139C3×C4×D3—216no—
140C3×C4×D3C2×D4116yescomplemented
141C3×Dic6—216no—
142#626—232no—
143#624—232no—
144C22×#41—92no—
145#532—916no—
146C2×C4⋊Q8—31no—
147C2×#127—91no—
148C2×#124—92no—
149C2×#121—94no—
150C2×C4×D4—94no—
151C22×C42—31no—
152C24×C3—31no—
153C23×D3—34no—
154C23×D3—34no—
155C23×D3—64no—
156C23×D3C22×D311yescharacteristic
157C2×C3×Q8—38no—
158C2×C3×Q8—68no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—38no—
163C22×C3×C4—34no—
164C22×C3×C4—32no—
165C22×C3×C4—34no—
166C22×C3×C4—38no—
167C22×C3×C4—68no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D312yes—
172C2×#67—316no—
173C2×#67—616no—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D314yes—
176C22×Dic3C22×D311yescharacteristic
177#239—664no—
178#235—664no—
179C2×D12—316no—
180C2×D12—316no—
181C2×D12—38no—
182C2×D12—316no—
183C2×D12—38no—
184C2×D12—616no—
185C2×D12—68no—
186C2×D12—616no—
187C2×D12—68no—
188C2×D12—616no—
189C2×D12—68no—
190C2×D12—616no—
191C2×D12—1216no—
192C2×D12—128no—
193C2×C4×D3—28no—
194C2×C4×D3—316no—
195C2×C4×D3—316no—
196C2×C4×D3—616no—
197C2×C4×D3—616no—
198C2×C4×D3D1218yescomplemented
199C2×C4×D3C22×D318yes—
200C2×C4×D3C22×D314yes—
201C2×Dic6—28no—
202C2×Dic6C22×D318yes—
203C3×C4⋊C4—316no—
204C3×C42—24no—
205C3×C42—38no—
206C3×C42—34no—
207C3×C42C22×D314yes—
208C3×C42C22×D314yes—
209(C2×D3)⋊C4—332no—
210(C2×D3)⋊C4—332no—
211C4⋊Dic3C22×D3116yes—
212C4×Dic3C22×D318yes—
213C4×Dic3C22×D314yes—
214C22×C32C22×D412yes—
215C22×C32C2×#4114yes—
216C22×C32C2511yescharacteristic
217C2×C3⋊D3—28no—
218C2×C3⋊D3—216no—
219C2×C3⋊D3—416no—
220C2×C3×D3—28no—
221C2×C3×D3—24no—
222C2×C3×D3C22×D414yes—
223C32×C4C22×D414yes—
224C32×C4C2×#4118yescomplemented
225C3×Dic3—28no—
226C3×Dic3—24no—
227C3×Dic3C22×D414yes—
228C2×#41—916no—
229C2×#41—1816no—
230C22×Q8—32no—
231C22×D4—94no—
232C22×D4—94no—
233C22×D4—92no—
234C23×C4—31no—
235C23×C4—32no—
236C23×C4—94no—
237C4⋊Q8—38no—
238#127—98no—
239#124—916no—
240#121—932no—
241C4×D4—932no—
242C2×C4⋊C4—34no—
243C2×C22⋊C4—98no—
244C2×C42—32no—
245C2×C42—31no—
246C2×C42—38no—
247C2×C42D3211yescharacteristic
248C23×C3—21no—
249C23×C3—34no—
250C23×C3—32no—
251C23×C3—64no—
252C23×C3C23×D311yescharacteristic
253C23×C3C23×D311yescharacteristic
254C22×D3—24no—
255C22×D3—38no—
256C22×D3—38no—
257C22×D3—68no—
258C22×D3—68no—
259C22×D3—616no—
260C22×D3—68no—
261C22×D3—616no—
262C22×D3—1216no—
263C22×D3—128no—
264C22×D3C2×D1214yes—
265C22×D3C23×D312yes—
266C3×Q8—616no—
267C2×C3×C4—24no—
268C2×C3×C4—22no—
269C2×C3×C4—28no—
270C2×C3×C4—24no—
271C2×C3×C4—34no—
272C2×C3×C4—32no—
273C2×C3×C4—316no—
274C2×C3×C4—34no—
275C2×C3×C4—38no—
276C2×C3×C4—68no—
277C2×C3×C4—64no—
278C2×C3×C4—616no—
279C2×C3×C4C2×D1214yes—
280C2×C3×C4#23518yescomplemented
281C2×C3×C4D3×D414yes—
282C2×C3×C4#23918yescomplemented
283C2×C3×C4C23×D312yes—
284C2×C3×C4C23×D314yes—
285C2×C3×C4C23×D312yes—
286C2×C3×C4C23×D314yes—
287#67—632no—
288C2×Dic3—24no—
289C2×Dic3—28no—
290C2×Dic3C2×D1214yes—
291C2×Dic3C23×D314yes—
292C2×Dic3C23×D318yes—
293C2×Dic3C23×D312yes—
294D12—632no—
295D12—616no—
296D12—632no—
297D12—616no—
298D12—632no—
299D12—1232no—
300D12—1216no—
301C4×D3—216no—
302C4×D3—632no—
303C4×D3—632no—
304C4×D3C2×D12116yescomplemented
305Dic6—216no—
306C2×C32#53214yescomplemented
307C2×C32C23×D411yescharacteristic
308C2×C32C22×#4112yes—
309C3⋊D3—48no—
310C3×D3—24no—
311C24—31no—
312C24—94no—
313#41—1864no—
314C2×Q8—38no—
315C2×Q8—68no—
316C2×D4—916no—
317C2×D4—916no—
318C2×D4—98no—
319C2×D4—1816no—
320C2×D4—1816no—
321C2×D4—188no—
322C22×C4—31no—
323C22×C4—34no—
324C22×C4—38no—
325C22×C4—32no—
326C22×C4—34no—
327C22×C4—38no—
328C22×C4—68no—
329C22×C4—916no—
330C22×C4—1816no—
331C22×C4C2×D3212yes—
332C22×C4C2×D3211yescharacteristic
333C4⋊C4—316no—
334C22⋊C4—932no—
335C42—38no—
336C42—34no—
337C42C2×D3214yes—
338C22×C3—24no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—34no—
342C22×C3—64no—
343C22×C3—68no—
344C22×C3C22×D1212yes—
345C22×C3C2×#23514yes—
346C22×C3C2×D3×D412yes—
347C22×C3C2×#23914yes—
348C22×C3C24×D311yescharacteristic
349C22×C3C24×D311yescharacteristic
350C2×D3—24no—
351C2×D3—28no—
352C2×D3—68no—
353C2×D3—616no—
354C2×D3—68no—
355C2×D3—616no—
356C2×D3—1216no—
357C2×D3—128no—
358C2×D3—1216no—
359C2×D3—1216no—
360C2×D3—2416no—
361C2×D3C22×D1214yes—
362C3×C4—28no—
363C3×C4—24no—
364C3×C4—34no—
365C3×C4—68no—
366C3×C4—64no—
367C3×C4C22×D1214yes—
368C3×C4C2×#23518yescomplemented
369C3×C4C2×D3×D414yes—
370C3×C4C2×#23918yescomplemented
371Dic3—24no—
372Dic3—28no—
373Dic3C22×D1214yes—
374C32C2×#53211yescharacteristic, complemented, Sylow
375C23—34no—
376C23—32no—
377C23—64no—
378C23—98no—
379C23—1816no—
380C23—188no—
381C23C22×D3211yescharacteristic
382Q8—616no—
383D4—1832no—
384D4—1832no—
385D4—1816no—
386C2×C4—34no—
387C2×C4—32no—
388C2×C4—316no—
389C2×C4—34no—
390C2×C4—38no—
391C2×C4—64no—
392C2×C4—68no—
393C2×C4—616no—
394C2×C4—1832no—
395C2×C4#379918yescomplemented
396C2×C4D3×D1214yes—
397C2×C4C22×D3214yes—
398C2×C4C22×D3212yes—
399C2×C3—22no—
400C2×C3—21no—
401C2×C3—24no—
402C2×C3—64no—
403C2×C3#547714yescomplemented
404C2×C3#572514yescomplemented
405C2×C3C23×D1211yescharacteristic
406C2×C3C22×#23512yes—
407C2×C3C22×D3×D411yescharacteristic
408C2×C3C22×#23912yes—
409D3—24no—
410D3—128no—
411D3—128no—
412D3—248no—
413C22—34no—
414C22—64no—
415C22—68no—
416C22—1816no—
417C22—188no—
418C22—3616no—
419C22C2×#379914yes—
420C22C2×D3×D1212yes—
421C22C23×D3211yescharacteristic
422C4—34no—
423C4—64no—
424C4—68no—
425C4C2×#379918yescomplemented
426C4C2×D3×D1214yes—
427C3—21no—
428C3C2×#547711yescharacteristic, complemented
429C3C2×#572511yescharacteristic, complemented
430C2—64no—
431C2—368no—
432C2#1059397014yesdirect product factor
433C2C22×#379912yes—
434C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C2×#64083C2semidirect
3. C2×C3×C42×D3C2semidirect
4. C2×C3×#869C2semidirect
5. C2×#63909C2semidirect
6. C2×#63894C2semidirect
7. C2×#63864C2semidirect
8. #10593970C2direct (N × H)
19. C2×#3799C22semidirect
21. #64083C22semidirect
25. C3×C42×D3C22semidirect
26. C3×#869C22semidirect
28. #63909C22semidirect
29. #63894C22semidirect
30. #63864C22semidirect
46. C2×C42×D3D3semidirect
47. C2×#869D3semidirect
60. C2×C3×C4×D3D4semidirect
118. C42×D3C2×D3semidirect
119. #869C2×D3semidirect
128. C2×C32×C4#41semidirect
140. C3×C4×D3C2×D4semidirect
198. C2×C4×D3D12semidirect
224. C32×C4C2×#41semidirect
280. C2×C3×C4#235semidirect
282. C2×C3×C4#239semidirect
304. C4×D3C2×D12semidirect
306. C2×C32#532semidirect
368. C3×C4C2×#235semidirect
370. C3×C4C2×#239semidirect
374. C32C2×#532semidirect
395. C2×C4#3799semidirect
403. C2×C3#5477semidirect
404. C2×C3#5725semidirect
425. C4C2×#3799semidirect
428. C3C2×#5477semidirect
429. C3C2×#5725semidirect
432. C2#10593970direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#640832
C2×C3×C42×D32
C2×C3×#8692
C2×#639092
C2×#638942
C2×#638642
#105939702
C2×#57253
C2×#54773