Finite Group Databasebeta

← C2×#10593895 #11902562

Subgroups — C2×#10593895 #11902562

Order 1152.

3409 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C212yesmaximal, complemented
2C2×#64078C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×#63908C212yesmaximal, complemented
6C2×#63891C214yesmaximal, complemented
7C2×D3×C4⋊Dic3C212yesmaximal, complemented
8C2×#63857C212yesmaximal, complemented
9#10593895C2116yesmaximal, direct product factor
10C2×#5551—31nomaximal
11C2×#5555—31nomaximal
12C22×#634C2212yes—
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×#625C2214yes—
18C22×D3×Dic3C2214yes—
19C2×#3795—216no—
20C2×#3795C22116yescomplemented
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×C4⋊(C3⋊Dic3)C2212yes—
24#64078C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×C4×D12C2218yescomplemented
30C3×C4×D12C2218yescomplemented
31C2×Dic3⋊Dic3C2214yes—
32C2×(C2×D3)⋊Dic3C2214yes—
33#63908C22116yescomplemented
34#63891C22132yescomplemented
35D3×C4⋊Dic3C22116yescomplemented
36#63857C22116yescomplemented
37C22×#237—32no—
38C22×#235—32no—
39C2×C3×C4×D4—31no—
40C2×C3×C4×D4—31no—
41C2×#938—32no—
42C2×#930—32no—
43C22×C4⋊Dic3—32no—
44C2×#924—32no—
45#5555—316no—
46#5551—316no—
47C2×#897—32no—
48C2×D3×C4⋊C4—32no—
49C2×#886—34no—
50C2×#883—34no—
51C2×C4×D12D311yescharacteristic, complemented
52C2×C4×D12D311yescharacteristic, complemented
53C2×#869—31no—
54C2×#869—31no—
55C2×#869—61no—
56C23×C3×D3C2312yes—
57C23×C3×D3C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2314yes—
62C2×#634—28no—
63C2×#634C2318yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12—24no—
67C2×C3×D12D418yescomplemented
68C2×C3×D12C2314yes—
69C2×C3×D12C2314yes—
70C2×C3×C4×D3—28no—
71C2×C3×C4×D3—28no—
72C2×C3×C4×D3C2318yes—
73C2×C3×C4×D3C2318yes—
74C2×#625—216no—
75C2×#625C23116yes—
76C2×D3×Dic3—216no—
77C2×D3×Dic3C23116yes—
78#3795—264no—
79C32×C42C2314yes—
80C4⋊(C3⋊Dic3)C2318yes—
81C4⋊(C3⋊Dic3)C2318yes—
82C3×(C2×D3)⋊C4C2318yes—
83C3×(C2×D3)⋊C4C2318yes—
84C3×C4⋊Dic3C2314yes—
85C3×C4⋊Dic3C2314yes—
86Dic3⋊Dic3C23116yes—
87(C2×D3)⋊Dic3C23116yes—
88C2×#547—91noSylow
89C22×C3×D4—31no—
90C22×C3×D4—31no—
91C23×C3×C4—32no—
92C23×C3×C4—32no—
93C22×#67—34no—
94C22×#67—34no—
95C23×Dic3—34no—
96C2×#237—316no—
97C2×#237—616no—
98C2×#235—316no—
99C2×#235—616no—
100C22×D12C2×D311yescharacteristic
101C22×D12C2×D311yescharacteristic
102C22×C4×D3—34no—
103C22×C4×D3C2×D312yes—
104C22×C4×D3C2×D312yes—
105C22×Dic6—32no—
106C22×Dic6—32no—
107C22×Dic6—62no—
108C3×C4×D4—38no—
109C3×C4×D4—38no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C42—21no—
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C2×D311yescharacteristic
117C2×#217—34no—
118#938—316no—
119#930—316no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4C2×D312yes—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—34no—
128C2×C4⋊Dic3—316no—
129C2×C4⋊Dic3—62no—
130C2×C4⋊Dic3—62no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D311yescharacteristic
133#924—316no—
134C2×Dic3⋊C4—34no—
135#897—316no—
136D3×C4⋊C4—316no—
137#886—332no—
138#883—332no—
139C4×D12C2×D318yescomplemented
140C4×D12C2×D318yescomplemented
141#869—38no—
142#869—38no—
143#869—68no—
144C23×C32C2411yescharacteristic
145C22×C3×D3—24no—
146C22×C3×D3—24no—
147C22×C3×D3—24no—
148C22×C3×D3—24no—
149C22×C3×D3—24no—
150C22×C3×D3C2×D418yes—
151C22×C3×D3C2414yes—
152C22×C3×D3C2414yes—
153C2×C32×C4—22no—
154C2×C32×C4C2×D414yes—
155C2×C32×C4#4114yescomplemented
156C2×C32×C4C2412yes—
157C2×C32×C4C2412yes—
158C2×C32×C4C2412yes—
159C2×C3⋊Dic3—28no—
160C2×C3⋊Dic3C2418yes—
161#634—216no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3C2414yes—
165C2×C3×Dic3C2414yes—
166C3×D12—28no—
167C3×D12C2×D4116yescomplemented
168C3×C4×D3—216no—
169C3×C4×D3—216no—
170#625—232no—
171D3×Dic3—232no—
172C22×#41—92no—
173#547—916no—
174C2×C4⋊Q8—91no—
175C2×#123—94no—
176C2×C22⋊Q8—92no—
177C2×#121—92no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C22×C4⋊C4—92no—
181C24×C3—32no—
182C24×C3—32no—
183C23×D3C22×D312yes—
184C23×D3C22×D312yes—
185C2×C3×D4—38no—
186C2×C3×D4—34no—
187C2×C3×D4—34no—
188C2×C3×D4—64no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—38no—
195C22×C3×C4—38no—
196C22×C3×C4—68no—
197C22×C3×C4—68no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—316no—
205C2×#67—316no—
206C2×#67—616no—
207C2×#67—616no—
208C22×Dic3—34no—
209C22×Dic3—34no—
210C22×Dic3—316no—
211C22×Dic3—64no—
212C22×Dic3—616no—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215#237—664no—
216#235—664no—
217C2×D12—24no—
218C2×D12D1218yescomplemented
219C2×D12C22×D314yes—
220C2×D12C22×D314yes—
221C2×C4×D3—28no—
222C2×C4×D3—28no—
223C2×C4×D3—316no—
224C2×C4×D3—616no—
225C2×C4×D3C22×D318yes—
226C2×C4×D3C22×D318yes—
227C2×Dic6—38no—
228C2×Dic6—38no—
229C2×Dic6—68no—
230C2×Dic6—68no—
231C2×Dic6—68no—
232C2×Dic6—128no—
233C3×C4⋊C4—34no—
234C3×C4⋊C4—34no—
235C3×C22⋊C4—38no—
236C3×C22⋊C4—38no—
237C3×C42—24no—
238C3×C42C22×D314yes—
239C3×C42C22×D314yes—
240#217—316no—
241(C2×D3)⋊C4—316no—
242(C2×D3)⋊C4C22×D318yes—
243(C2×D3)⋊C4C22×D318yes—
244C4⋊Dic3—38no—
245C4⋊Dic3—38no—
246C4⋊Dic3—38no—
247C4⋊Dic3—38no—
248C4⋊Dic3—316no—
249C4⋊Dic3—68no—
250C4⋊Dic3—68no—
251C4⋊Dic3C22×D314yes—
252C4⋊Dic3C22×D314yes—
253Dic3⋊C4—316no—
254C22×C32C22×D412yes—
255C22×C32C2×#4112yes—
256C22×C322−1+412yes—
257C22×C32C2511yescharacteristic
258C2×C3×D3—216no—
259C2×C3×D3—24no—
260C2×C3×D3—24no—
261C2×C3×D3—24no—
262C2×C3×D3—24no—
263C2×C3×D3—24no—
264C2×C3×D3—48no—
265C2×C3×D3C22×D418yes—
266C32×C4—22no—
267C32×C4C22×D414yes—
268C32×C4C2×#4114yescomplemented
269C3⋊Dic3—28no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C2×#41—916no—
273C2×#41—1816no—
274C22×Q8—92no—
275C22×D4—31no—
276C22×D4—31no—
277C22×D4—94no—
278C23×C4—32no—
279C23×C4—32no—
280C23×C4—94no—
281C4⋊Q8—98no—
282#123—932no—
283C22⋊Q8—916no—
284#121—916no—
285C4×D4—38no—
286C4×D4—38no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—916no—
290C2×C4⋊C4—94no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—92no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—94no—
296C2×C42D3211yescharacteristic
297C23×C3—21no—
298C23×C3—38no—
299C23×C3—34no—
300C23×C3—34no—
301C23×C3—64no—
302C23×C3—64no—
303C23×C3—64no—
304C23×C3—64no—
305C23×C3—64no—
306C23×C3C23×D311yescharacteristic
307C23×C3C23×D311yescharacteristic
308C22×D3—24no—
309C22×D3—24no—
310C22×D3—24no—
311C22×D3—24no—
312C22×D3—24no—
313C22×D3C2×D1218yes—
314C22×D3C23×D314yes—
315C22×D3C23×D314yes—
316C3×D4—316no—
317C3×D4—68no—
318C2×C3×C4—24no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—34no—
327C2×C3×C4—34no—
328C2×C3×C4—64no—
329C2×C3×C4—64no—
330C2×C3×C4—616no—
331C2×C3×C4—616no—
332C2×C3×C4C2×D1214yes—
333C2×C3×C4#23514yescomplemented
334C2×C3×C4D3×D414yes—
335C2×C3×C4#23714yescomplemented
336C2×C3×C4C23×D312yes—
337C2×C3×C4C23×D312yes—
338C2×C3×C4C23×D312yes—
339C2×C3×C4C23×D312yes—
340C2×C3×C4C23×D312yes—
341C2×C3×C4C23×D312yes—
342#67—632no—
343#67—632no—
344C2×Dic3—24no—
345C2×Dic3—24no—
346C2×Dic3—38no—
347C2×Dic3—38no—
348C2×Dic3—68no—
349C2×Dic3—632no—
350C2×Dic3—68no—
351C2×Dic3—68no—
352C2×Dic3—128no—
353C2×Dic3C23×D314yes—
354C2×Dic3C23×D314yes—
355D12—28no—
356D12C2×D12116yescomplemented
357C4×D3—216no—
358C4×D3—216no—
359C4×D3—632no—
360Dic6—616no—
361Dic6—616no—
362Dic6—1216no—
363C2×C32#54714yescomplemented
364C2×C32C23×D411yescharacteristic
365C2×C32C22×#4111yescharacteristic
366C2×C32C2×2−1+411yescharacteristic
367C3×D3—28no—
368C3×D3—44no—
369C24—32no—
370C24—32no—
371#41—1864no—
372C2×Q8—98no—
373C2×Q8—188no—
374C2×D4—34no—
375C2×D4—34no—
376C2×D4—38no—
377C2×D4—64no—
378C2×D4—916no—
379C2×D4—1816no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—38no—
383C22×C4—38no—
384C22×C4—68no—
385C22×C4—68no—
386C22×C4—916no—
387C22×C4—94no—
388C22×C4—1816no—
389C22×C4C2×D3211yescharacteristic
390C22×C4C2×D3211yescharacteristic
391C22×C4C2×D3211yescharacteristic
392C4⋊C4—34no—
393C4⋊C4—34no—
394C4⋊C4—916no—
395C4⋊C4—98no—
396C4⋊C4—98no—
397C22⋊C4—38no—
398C22⋊C4—38no—
399C22⋊C4—916no—
400C42C2×D3214yes—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—38no—
406C22×C3—64no—
407C22×C3—64no—
408C22×C3—616no—
409C22×C3—64no—
410C22×C3—64no—
411C22×C3—64no—
412C22×C3—128no—
413C22×C3C22×D1212yes—
414C22×C3C2×#23512yes—
415C22×C3C2×D3×D412yes—
416C22×C3C2×#23712yes—
417C22×C3#101012yes—
418C22×C3#101012yes—
419C22×C3C24×D311yescharacteristic
420C22×C3C24×D311yescharacteristic
421C2×D3—24no—
422C2×D3—24no—
423C2×D3—216no—
424C2×D3—24no—
425C2×D3—24no—
426C2×D3—24no—
427C2×D3—48no—
428C2×D3C22×D1218yes—
429C3×C4—24no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—24no—
433C3×C4—24no—
434C3×C4—64no—
435C3×C4—64no—
436C3×C4C22×D1214yes—
437C3×C4C2×#23514yescomplemented
438C3×C4C2×D3×D414yes—
439C3×C4C2×#23714yescomplemented
440Dic3—24no—
441Dic3—24no—
442Dic3—68no—
443Dic3—68no—
444Dic3—128no—
445C32C2×#54711yescharacteristic, complemented, Sylow
446C23—38no—
447C23—34no—
448C23—34no—
449C23—64no—
450C23—64no—
451C23—64no—
452C23—64no—
453C23—64no—
454C23C22×D3211yescharacteristic
455Q8—1816no—
456D4—316no—
457D4—68no—
458D4—1832no—
459C2×C4—22no—
460C2×C4—34no—
461C2×C4—34no—
462C2×C4—64no—
463C2×C4—64no—
464C2×C4—616no—
465C2×C4—616no—
466C2×C4—98no—
467C2×C4—1832no—
468C2×C4—188no—
469C2×C4#379514yescomplemented
470C2×C4D3×D1214yes—
471C2×C4C22×D3212yes—
472C2×C4C22×D3212yes—
473C2×C4C22×D3212yes—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—68no—
479C2×C3—124no—
480C2×C3#555114yescomplemented
481C2×C3#555514yescomplemented
482C2×C3C23×D1211yescharacteristic
483C2×C3C22×#23511yescharacteristic
484C2×C3C22×D3×D411yescharacteristic
485C2×C3C22×#23711yescharacteristic
486C2×C3C2×#101011yescharacteristic
487C2×C3C2×#101011yescharacteristic
488D3—28no—
489D3—44no—
490C22—38no—
491C22—64no—
492C22—64no—
493C22—616no—
494C22—64no—
495C22—64no—
496C22—64no—
497C22—128no—
498C22C2×#379512yes—
499C22#6429812yes—
500C22C2×D3×D1212yes—
501C22C23×D3211yescharacteristic
502C4—22no—
503C4—64no—
504C4—64no—
505C4—188no—
506C4C2×#379514yescomplemented
507C4C2×D3×D1214yes—
508C3—21no—
509C3C2×#555511yescharacteristic, complemented
510C3C2×#555111yescharacteristic, complemented
511C2—68no—
512C2—124no—
513C2#1059389514yesdirect product factor
514C2C22×#379511yescharacteristic
515C2C2×#6429811yescharacteristic
516C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#547
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×#64078C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×#63908C2semidirect
6. C2×#63891C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63857C2semidirect
9. #10593895C2direct (N × H)
20. C2×#3795C22semidirect
24. #64078C22semidirect
29. C3×C4×D12C22semidirect
30. C3×C4×D12C22semidirect
33. #63908C22semidirect
34. #63891C22semidirect
35. D3×C4⋊Dic3C22semidirect
36. #63857C22semidirect
51. C2×C4×D12D3semidirect
52. C2×C4×D12D3semidirect
67. C2×C3×D12D4semidirect
139. C4×D12C2×D3semidirect
140. C4×D12C2×D3semidirect
155. C2×C32×C4#41semidirect
167. C3×D12C2×D4semidirect
218. C2×D12D12semidirect
268. C32×C4C2×#41semidirect
333. C2×C3×C4#235semidirect
335. C2×C3×C4#237semidirect
356. D12C2×D12semidirect
363. C2×C32#547semidirect
437. C3×C4C2×#235semidirect
439. C3×C4C2×#237semidirect
445. C32C2×#547semidirect
469. C2×C4#3795semidirect
480. C2×C3#5551semidirect
481. C2×C3#5555semidirect
506. C4C2×#3795semidirect
509. C3C2×#5555semidirect
510. C3C2×#5551semidirect
513. C2#10593895direct (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×#640782
C2×C3×C4×D122
C2×#639082
C2×#638912
C2×D3×C4⋊Dic32
C2×#638572
#105938952
C2×#55513
C2×#55553