Finite Group Databasebeta

← C2×#10593906 #11902725

Subgroups — C2×#10593906 #11902725

Order 1152.

3621 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C212yesmaximal, complemented
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C2×C3×#874C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×#63914C212yesmaximal, complemented
6C2×#63908C212yesmaximal, complemented
7C2×#63898C212yesmaximal, complemented
8C2×#63885C214yesmaximal, complemented
9#10593906C2116yesmaximal, direct product factor
10C2×#5718—31nomaximal
11C2×#5553—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2212yes—
14C22×C3×D12C2212yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×D12C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×#625C2214yes—
19C22×#625C2214yes—
20C22×D3×Dic3C2214yes—
21C2×#3795—216no—
22C2×#3795C22116yescomplemented
23C2×C32×C42C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C4×#634C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#874C2218yescomplemented
31C3×C4×D12C2218yescomplemented
32C2×(C2×D3)⋊Dic3C2214yes—
33#63914C22116yescomplemented
34#63908C22116yescomplemented
35#63898C22116yescomplemented
36#63885C22132yescomplemented
37C22×#237—32no—
38C22×#235—32no—
39C2×C3×#127—31no—
40C2×C3×C4×D4—31no—
41C2×#940—32no—
42C2×#940—32no—
43C2×#939—34no—
44C2×#938—32no—
45C2×D4×Dic3—32no—
46C2×#930—32no—
47#5718—316no—
48#5553—316no—
49C2×#893—32no—
50C2×#884—34no—
51C2×#874D311yescharacteristic, complemented
52C2×C4×D12D311yescharacteristic, complemented
53C2×C4×Dic6—31no—
54C2×C4×Dic6—31no—
55C2×C4×Dic6—61no—
56C23×C3×D3C2312yes—
57C23×C3×D3C2314yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2312yes—
63C2×#634D418yescomplemented
64C2×#634C2314yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12—28no—
67C2×C3×D12—24no—
68C2×C3×D12—28no—
69C2×C3×D12—44no—
70C2×C3×D12C2318yes—
71C2×C3×D12C2318yes—
72C2×C3×D12C2314yes—
73C2×C3×D12C2318yes—
74C2×C3×C4×D3—28no—
75C2×C3×C4×D3C2318yes—
76C2×#625—216no—
77C2×#625—48no—
78C2×#625C23116yes—
79C2×#625C23116yes—
80C2×D3×Dic3—216no—
81C2×D3×Dic3C23116yes—
82#3795—264no—
83C32×C42C2314yes—
84C4⋊(C3⋊Dic3)C2314yes—
85#3750C2318yes—
86C4×C3⋊Dic3C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×C4⋊Dic3C2314yes—
89(C2×D3)⋊Dic3C23116yes—
90C2×#550—91noSylow
91C22×C3×D4—32no—
92C22×C3×D4—32no—
93C22×C3×D4—31no—
94C22×C3×D4—32no—
95C23×C3×C4—32no—
96C22×#67—34no—
97C22×#67—34no—
98C22×#67—34no—
99C22×#67—34no—
100C23×Dic3—34no—
101C2×#237—316no—
102C2×#237—616no—
103C2×#235—316no—
104C2×#235—616no—
105C22×D12C2×D312yes—
106C22×D12C2×D311yescharacteristic
107C22×D12C2×D312yes—
108C22×D12C2×D312yes—
109C22×C4×D3—34no—
110C22×C4×D3C2×D312yes—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C3×#127—38no—
115C3×C4×D4—38no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—21no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C2×D311yescharacteristic
121C2×#217—34no—
122#940—316no—
123#940—316no—
124#939—332no—
125#938—316no—
126D4×Dic3—316no—
127#930—316no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—62no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—62no—
140#893—316no—
141#884—332no—
142#874C2×D318yescomplemented
143C4×D12C2×D318yescomplemented
144C4×Dic6—38no—
145C4×Dic6—38no—
146C4×Dic6—68no—
147C23×C32C2411yescharacteristic
148C22×C3×D3—28no—
149C22×C3×D3—24no—
150C22×C3×D3—24no—
151C22×C3×D3—28no—
152C22×C3×D3—24no—
153C22×C3×D3—28no—
154C22×C3×D3C2418yes—
155C22×C3×D3C2414yes—
156C2×C32×C4—22no—
157C2×C32×C4C2×D414yes—
158C2×C32×C4#4114yescomplemented
159C2×C32×C4C2412yes—
160C2×C32×C4C2412yes—
161C2×C32×C4C2412yes—
162C2×C3⋊Dic3—24no—
163C2×C3⋊Dic3C2×D418yes—
164C2×C3⋊Dic3C2414yes—
165C2×C3⋊Dic3C2414yes—
166#634C2×D4116yescomplemented
167C2×C3×Dic3—24no—
168C2×C3×Dic3C2414yes—
169C3×D12—216no—
170C3×D12—28no—
171C3×D12—216no—
172C3×D12—48no—
173C3×C4×D3—216no—
174#625—232no—
175#625—416no—
176D3×Dic3—232no—
177C22×#41—92no—
178#550—916no—
179C2×#127—31no—
180C2×#127—92no—
181C2×#121—94no—
182C2×#121—92no—
183C2×C4×Q8—91no—
184C2×C4×D4—31no—
185C2×C4×D4—92no—
186C24×C3—34no—
187C24×C3—32no—
188C23×D3C22×D314yes—
189C23×D3C22×D312yes—
190C2×C3×D4—38no—
191C2×C3×D4—38no—
192C2×C3×D4—34no—
193C2×C3×D4—38no—
194C2×C3×D4—68no—
195C2×C3×D4—68no—
196C2×C3×D4—64no—
197C2×C3×D4—124no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—32no—
202C22×C3×C4—38no—
203C22×C3×C4—68no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—316no—
211C2×#67—316no—
212C2×#67—316no—
213C2×#67—316no—
214C2×#67—616no—
215C2×#67—616no—
216C2×#67—128no—
217C2×#67—128no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—316no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—616no—
226C22×Dic3C22×D312yes—
227#237—664no—
228#235—664no—
229C2×D12—24no—
230C2×D12—28no—
231C2×D12—28no—
232C2×D12—44no—
233C2×D12C22×D314yes—
234C2×D12C22×D318yes—
235C2×D12C22×D318yes—
236C2×D12C22×D318yes—
237C2×C4×D3—28no—
238C2×C4×D3—316no—
239C2×C4×D3—616no—
240C2×C4×D3C22×D318yes—
241C2×Dic6—38no—
242C2×Dic6—38no—
243C2×Dic6—34no—
244C2×Dic6—34no—
245C2×Dic6—64no—
246C2×Dic6—68no—
247C3×C4⋊C4—34no—
248C3×C22⋊C4—38no—
249C3×C42—24no—
250C3×C42C22×D314yes—
251C3×C42C22×D314yes—
252#217—316no—
253(C2×D3)⋊C4—316no—
254(C2×D3)⋊C4C22×D318yes—
255C4⋊Dic3—34no—
256C4⋊Dic3—34no—
257C4⋊Dic3—64no—
258C4⋊Dic3C22×D314yes—
259Dic3⋊C4—38no—
260Dic3⋊C4—38no—
261Dic3⋊C4—68no—
262C4×Dic3—38no—
263C4×Dic3—38no—
264C4×Dic3—68no—
265C22×C32C22×D412yes—
266C22×C32C2×#4112yes—
267C22×C32H(5,𝔽2)12yes—
268C22×C32C2511yescharacteristic
269C2×C3×D3—28no—
270C2×C3×D3—24no—
271C2×C3×D3—24no—
272C2×C3×D3—28no—
273C2×C3×D3—24no—
274C2×C3×D3—28no—
275C2×C3×D3—416no—
276C2×C3×D3—48no—
277C32×C4—22no—
278C32×C4C22×D414yes—
279C32×C4C2×#4114yescomplemented
280C3⋊Dic3—24no—
281C3⋊Dic3C22×D418yes—
282C3×Dic3—24no—
283C2×#41—916no—
284C2×#41—1816no—
285C22×Q8—91no—
286C22×D4—31no—
287C22×D4—32no—
288C22×D4—32no—
289C22×D4—32no—
290C22×D4—94no—
291C22×D4—94no—
292C23×C4—32no—
293C23×C4—94no—
294#127—38no—
295#127—916no—
296#121—932no—
297#121—916no—
298C4×Q8—98no—
299C4×D4—38no—
300C4×D4—916no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—91no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—94no—
306C2×C42—92no—
307C2×C42D3211yescharacteristic
308C23×C3—21no—
309C23×C3—38no—
310C23×C3—34no—
311C23×C3—68no—
312C23×C3—68no—
313C23×C3—64no—
314C23×C3—64no—
315C23×C3—64no—
316C23×C3—68no—
317C23×C3C23×D311yescharacteristic
318C23×C3C23×D311yescharacteristic
319C22×D3—24no—
320C22×D3—24no—
321C22×D3—28no—
322C22×D3—28no—
323C22×D3—28no—
324C22×D3—24no—
325C22×D3C23×D318yes—
326C22×D3C23×D314yes—
327C3×D4—616no—
328C3×D4—616no—
329C3×D4—68no—
330C3×D4—128no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—34no—
339C2×C3×C4—42no—
340C2×C3×C4—64no—
341C2×C3×C4—616no—
342C2×C3×C4#23514yescomplemented
343C2×C3×C4D3×D414yes—
344C2×C3×C4D3×D414yes—
345C2×C3×C4#23714yescomplemented
346C2×C3×C4C23×D312yes—
347C2×C3×C4C23×D312yes—
348C2×C3×C4C23×D312yes—
349C2×C3×C4C23×D312yes—
350C2×C3×C4C23×D312yes—
351C2×C3×C4C23×D312yes—
352#67—632no—
353#67—632no—
354#67—1216no—
355#67—1216no—
356C2×Dic3—24no—
357C2×Dic3—38no—
358C2×Dic3—38no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—68no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—632no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—124no—
370C2×Dic3C23×D314yes—
371D12—28no—
372D12—216no—
373D12—216no—
374D12—48no—
375C4×D3—216no—
376C4×D3—632no—
377Dic6—316no—
378Dic6—316no—
379Dic6—616no—
380C2×C32#55014yescomplemented
381C2×C32C23×D411yescharacteristic
382C2×C32C22×#4111yescharacteristic
383C2×C32C2×H(5,𝔽2)11yescharacteristic
384C3×D3—48no—
385C3×D3—44no—
386C24—32no—
387C24—34no—
388#41—1864no—
389C2×Q8—94no—
390C2×Q8—98no—
391C2×D4—34no—
392C2×D4—38no—
393C2×D4—38no—
394C2×D4—38no—
395C2×D4—64no—
396C2×D4—68no—
397C2×D4—68no—
398C2×D4—916no—
399C2×D4—916no—
400C2×D4—124no—
401C2×D4—1816no—
402C2×D4—368no—
403C22×C4—32no—
404C22×C4—38no—
405C22×C4—68no—
406C22×C4—916no—
407C22×C4—92no—
408C22×C4—92no—
409C22×C4—1816no—
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C22×C4C2×D3211yescharacteristic
413C4⋊C4—34no—
414C4⋊C4—98no—
415C4⋊C4—94no—
416C22⋊C4—38no—
417C22⋊C4—916no—
418C42—98no—
419C42C2×D3214yes—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—68no—
425C22×C3—68no—
426C22×C3—64no—
427C22×C3—64no—
428C22×C3—64no—
429C22×C3—68no—
430C22×C3—128no—
431C22×C3—1216no—
432C22×C3C2×#23512yes—
433C22×C3C2×D3×D412yes—
434C22×C3C2×D3×D412yes—
435C22×C3C2×#23712yes—
436C22×C3#100412yes—
437C22×C3#100912yes—
438C22×C3C24×D311yescharacteristic
439C22×C3C24×D311yescharacteristic
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—28no—
443C2×D3—28no—
444C2×D3—28no—
445C2×D3—24no—
446C2×D3—416no—
447C2×D3—48no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—42no—
453C3×C4—64no—
454C3×C4C2×#23514yescomplemented
455C3×C4C2×D3×D414yes—
456C3×C4C2×D3×D414yes—
457C3×C4C2×#23714yescomplemented
458Dic3—24no—
459Dic3—38no—
460Dic3—38no—
461Dic3—68no—
462Dic3—64no—
463Dic3—64no—
464Dic3—124no—
465C32C2×#55011yescharacteristic, complemented, Sylow
466C23—34no—
467C23—38no—
468C23—64no—
469C23—68no—
470C23—64no—
471C23—68no—
472C23—68no—
473C23—64no—
474C23C22×D3211yescharacteristic
475Q8—916no—
476D4—68no—
477D4—616no—
478D4—616no—
479D4—128no—
480D4—1832no—
481D4—3616no—
482C2×C4—22no—
483C2×C4—34no—
484C2×C4—64no—
485C2×C4—616no—
486C2×C4—98no—
487C2×C4—94no—
488C2×C4—94no—
489C2×C4—1832no—
490C2×C4—184no—
491C2×C4#379514yescomplemented
492C2×C4#380214yes—
493C2×C4C22×D3212yes—
494C2×C4C22×D3212yes—
495C2×C4C22×D3212yes—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—24no—
500C2×C3—124no—
501C2×C3—128no—
502C2×C3#555314yescomplemented
503C2×C3#571814yescomplemented
504C2×C3C22×#23511yescharacteristic
505C2×C3C22×D3×D411yescharacteristic
506C2×C3C22×D3×D411yescharacteristic
507C2×C3C22×#23711yescharacteristic
508C2×C3C2×#100411yescharacteristic
509C2×C3C2×#100911yescharacteristic
510D3—48no—
511D3—44no—
512C22—64no—
513C22—68no—
514C22—64no—
515C22—68no—
516C22—68no—
517C22—64no—
518C22—128no—
519C22—1216no—
520C22C2×#379512yes—
521C22C2×#380212yes—
522C22#6430712yes—
523C22C23×D3211yescharacteristic
524C4—22no—
525C4—64no—
526C4—98no—
527C4—184no—
528C4C2×#379514yescomplemented
529C4C2×#380214yes—
530C3—21no—
531C3C2×#555311yescharacteristic, complemented
532C3C2×#571811yescharacteristic, complemented
533C2—124no—
534C2—128no—
535C2#1059390614yesdirect product factor
536C2C22×#379511yescharacteristic
537C2C22×#380211yescharacteristic
538C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3795C2semidirect
2. C2×C4×#634C2semidirect
3. C2×C3×#874C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×#63914C2semidirect
6. C2×#63908C2semidirect
7. C2×#63898C2semidirect
8. C2×#63885C2semidirect
9. #10593906C2direct (N × H)
22. C2×#3795C22semidirect
27. C4×#634C22semidirect
30. C3×#874C22semidirect
31. C3×C4×D12C22semidirect
33. #63914C22semidirect
34. #63908C22semidirect
35. #63898C22semidirect
36. #63885C22semidirect
51. C2×#874D3semidirect
52. C2×C4×D12D3semidirect
63. C2×#634D4semidirect
142. #874C2×D3semidirect
143. C4×D12C2×D3semidirect
158. C2×C32×C4#41semidirect
166. #634C2×D4semidirect
279. C32×C4C2×#41semidirect
342. C2×C3×C4#235semidirect
345. C2×C3×C4#237semidirect
380. C2×C32#550semidirect
454. C3×C4C2×#235semidirect
457. C3×C4C2×#237semidirect
465. C32C2×#550semidirect
491. C2×C4#3795semidirect
502. C2×C3#5553semidirect
503. C2×C3#5718semidirect
528. C4C2×#3795semidirect
531. C3C2×#5553semidirect
532. C3C2×#5718semidirect
535. C2#10593906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C4×#6342
C2×C3×#8742
C2×C3×C4×D122
C2×#639142
C2×#639082
C2×#638982
C2×#638852
#105939062
C2×#57183
C2×#55533