Finite Group Databasebeta

← C2×#10593896 #11902560

Subgroups — C2×#10593896 #11902560

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C212yesmaximal, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×#63909C212yesmaximal, complemented
6C2×#63890C214yesmaximal, complemented
7C2×D3×C4⋊Dic3C212yesmaximal, complemented
8C2×#63871C212yesmaximal, complemented
9#10593896C2116yesmaximal, direct product factor
10C2×#5726—31nomaximal
11C2×#5555—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#626C2214yes—
18C22×D3×Dic3C2214yes—
19C2×#3796—216no—
20C2×#3796C22116yescomplemented
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2212yes—
29C3×C4×D12C2218yescomplemented
30C3×#869C2218yescomplemented
31C2×Dic3⋊Dic3C2214yes—
32C2×#3722C2214yes—
33#63909C22116yescomplemented
34#63890C22132yescomplemented
35D3×C4⋊Dic3C22116yescomplemented
36#63871C22116yescomplemented
37C22×#239—32no—
38C22×#237—32no—
39C2×C3×C4⋊Q8—31no—
40C2×C3×C4×D4—31no—
41C2×#946—32no—
42C2×#930—32no—
43C22×C4⋊Dic3—32no—
44#5726—316no—
45#5555—316no—
46C2×#897—32no—
47C2×#895—32no—
48C2×#894—34no—
49C2×D3×C4⋊C4—32no—
50C2×#886—34no—
51C2×C4×D12—31no—
52C2×C4×D12—31no—
53C2×C4×D12—61no—
54C2×C4×D12D311yescharacteristic, complemented
55C2×#869D311yescharacteristic, complemented
56C23×C3⋊D3C2312yes—
57C23×C3×D3C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2312yes—
62C2×C4⋊(C3⋊D3)—24no—
63C2×C4⋊(C3⋊D3)C2314yes—
64C2×C4×C3⋊D3—28no—
65C2×C4×C3⋊D3C2318yes—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2312yes—
68C2×C3×D12D418yescomplemented
69C2×C3×D12C2314yes—
70C2×C3×C4×D3—28no—
71C2×C3×C4×D3C2318yes—
72C2×C3×Dic6—28no—
73C2×C3×Dic6C2318yes—
74C2×#626—216no—
75C2×#626C23116yes—
76C2×D3×Dic3—216no—
77C2×D3×Dic3C23116yes—
78#3796—264no—
79C32×C42C2314yes—
80#3752C2318yes—
81C4⋊(C3⋊Dic3)C2314yes—
82C3×(C2×D3)⋊C4C2318yes—
83C3×C4⋊Dic3C2314yes—
84C3×C4⋊Dic3C2318yes—
85C3×C4⋊Dic3C2318yes—
86Dic3⋊Dic3C23116yes—
87#3722C23116yes—
88C2×#547—91noSylow
89C22×C3×Q8—32no—
90C22×C3×D4—31no—
91C23×C3×C4—32no—
92C22×#67—34no—
93C23×Dic3—34no—
94C2×#239—316no—
95C2×#239—616no—
96C2×#237—316no—
97C2×#237—616no—
98C22×D12—34no—
99C22×D12—31no—
100C22×D12—31no—
101C22×D12—61no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—34no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—62no—
107C22×C4×D3C2×D312yes—
108C22×Dic6C2×D312yes—
109C3×C4⋊Q8—38no—
110C3×C4×D4—38no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—21no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118#946—316no—
119#930—316no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—62no—
125C2×(C2×D3)⋊C4C2×D312yes—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—34no—
129C2×C4⋊Dic3—316no—
130C2×C4⋊Dic3—61no—
131C2×C4⋊Dic3C2×D312yes—
132C2×C4⋊Dic3C2×D312yes—
133C2×C4⋊Dic3C2×D311yescharacteristic
134C2×Dic3⋊C4—34no—
135#897—316no—
136#895—316no—
137#894—332no—
138D3×C4⋊C4—316no—
139#886—332no—
140C4×D12—38no—
141C4×D12—38no—
142C4×D12—68no—
143C4×D12C2×D318yescomplemented
144#869C2×D318yescomplemented
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—24no—
147C22×C3⋊D3—24no—
148C22×C3⋊D3—24no—
149C22×C3⋊D3C2414yes—
150C22×C3×D3—24no—
151C22×C3×D3—24no—
152C22×C3×D3C2×D418yes—
153C22×C3×D3C2414yes—
154C2×C32×C4—22no—
155C2×C32×C4C2×D414yes—
156C2×C32×C4#4114yescomplemented
157C2×C32×C4C2412yes—
158C2×C32×C4C2412yes—
159C2×C32×C4C2412yes—
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3C2414yes—
162C4⋊(C3⋊D3)—28no—
163C4×C3⋊D3—216no—
164C2×C3×Dic3—28no—
165C2×C3×Dic3—24no—
166C2×C3×Dic3C2414yes—
167C2×C3×Dic3C2418yes—
168C3×D12C2×D4116yescomplemented
169C3×C4×D3—216no—
170C3×Dic6—216no—
171#626—232no—
172D3×Dic3—232no—
173C22×#41—92no—
174#547—916no—
175C2×C4⋊Q8—31no—
176C2×#123—94no—
177C2×C22⋊Q8—92no—
178C2×#121—92no—
179C2×C4×D4—31no—
180C2×C4×D4—91no—
181C22×C4⋊C4—92no—
182C24×C3—32no—
183C23×D3—32no—
184C23×D3—32no—
185C23×D3—62no—
186C23×D3C22×D312yes—
187C2×C3×Q8—38no—
188C2×C3×Q8—68no—
189C2×C3×D4—38no—
190C2×C3×D4—34no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—34no—
195C22×C3×C4—32no—
196C22×C3×C4—38no—
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—616no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—316no—
209C22×Dic3—62no—
210C22×Dic3—616no—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D314yes—
213#239—664no—
214#237—664no—
215C2×D12—316no—
216C2×D12—34no—
217C2×D12—34no—
218C2×D12—64no—
219C2×D12—68no—
220C2×D12—616no—
221C2×D12—64no—
222C2×D12—64no—
223C2×D12D1218yescomplemented
224C2×D12C22×D314yes—
225C2×C4×D3—28no—
226C2×C4×D3—316no—
227C2×C4×D3—38no—
228C2×C4×D3—38no—
229C2×C4×D3—68no—
230C2×C4×D3—616no—
231C2×C4×D3—68no—
232C2×C4×D3—68no—
233C2×C4×D3—128no—
234C2×C4×D3C22×D318yes—
235C2×Dic6—28no—
236C2×Dic6C22×D318yes—
237C3×C4⋊C4—38no—
238C3×C4⋊C4—38no—
239C3×C4⋊C4—34no—
240C3×C22⋊C4—38no—
241C3×C42—24no—
242C3×C42C22×D314yes—
243C3×C42C22×D314yes—
244(C2×D3)⋊C4—38no—
245(C2×D3)⋊C4—38no—
246(C2×D3)⋊C4—316no—
247(C2×D3)⋊C4—316no—
248(C2×D3)⋊C4—68no—
249(C2×D3)⋊C4C22×D318yes—
250C4⋊Dic3—34no—
251C4⋊Dic3—34no—
252C4⋊Dic3—316no—
253C4⋊Dic3—64no—
254C4⋊Dic3C22×D318yes—
255C4⋊Dic3C22×D318yes—
256C4⋊Dic3C22×D314yes—
257Dic3⋊C4—316no—
258C22×C32C22×D412yes—
259C22×C32C2×#4112yes—
260C22×C322−1+412yes—
261C22×C32C2511yescharacteristic
262C2×C3⋊D3—24no—
263C2×C3⋊D3—24no—
264C2×C3⋊D3—24no—
265C2×C3⋊D3—48no—
266C2×C3×D3—216no—
267C2×C3×D3—24no—
268C2×C3×D3—24no—
269C2×C3×D3C22×D418yes—
270C32×C4—22no—
271C32×C4C22×D414yes—
272C32×C4C2×#4114yescomplemented
273C3⋊Dic3—24no—
274C3×Dic3—28no—
275C3×Dic3—24no—
276C2×#41—916no—
277C2×#41—1816no—
278C22×Q8—32no—
279C22×D4—31no—
280C22×D4—94no—
281C22×D4—91no—
282C23×C4—32no—
283C23×C4—94no—
284C23×C4—92no—
285C4⋊Q8—38no—
286#123—932no—
287C22⋊Q8—916no—
288#121—916no—
289C4×D4—38no—
290C4×D4—98no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4—916no—
295C2×C4⋊C4—94no—
296C2×C4⋊C4—91no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4—94no—
299C2×C22⋊C4—92no—
300C2×C42D3211yescharacteristic
301C23×C3—21no—
302C23×C3—38no—
303C23×C3—34no—
304C23×C3—64no—
305C23×C3—64no—
306C23×C3C23×D311yescharacteristic
307C23×C3C23×D311yescharacteristic
308C22×D3—24no—
309C22×D3—24no—
310C22×D3—34no—
311C22×D3—34no—
312C22×D3—64no—
313C22×D3—68no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—64no—
320C22×D3—124no—
321C22×D3—124no—
322C22×D3C2×D1218yes—
323C22×D3C23×D314yes—
324C3×Q8—616no—
325C3×D4—316no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—38no—
334C2×C3×C4—34no—
335C2×C3×C4—42no—
336C2×C3×C4—68no—
337C2×C3×C4—64no—
338C2×C3×C4—616no—
339C2×C3×C4C2×D1214yes—
340C2×C3×C4D3×D414yes—
341C2×C3×C4#23714yescomplemented
342C2×C3×C4#23914yescomplemented
343C2×C3×C4C23×D312yes—
344C2×C3×C4C23×D312yes—
345C2×C3×C4C23×D312yes—
346C2×C3×C4C23×D312yes—
347C2×C3×C4C23×D312yes—
348C2×C3×C4C23×D312yes—
349#67—632no—
350C2×Dic3—28no—
351C2×Dic3—24no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—64no—
355C2×Dic3—632no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—124no—
359C2×Dic3C23×D314yes—
360C2×Dic3C23×D318yes—
361D12—616no—
362D12—632no—
363D12—68no—
364D12—68no—
365D12C2×D12116yescomplemented
366C4×D3—216no—
367C4×D3—632no—
368C4×D3—616no—
369C4×D3—616no—
370C4×D3—1216no—
371Dic6—216no—
372C2×C32#54714yescomplemented
373C2×C32C23×D411yescharacteristic
374C2×C32C22×#4111yescharacteristic
375C2×C32C2×2−1+411yescharacteristic
376C3⋊D3—44no—
377C3×D3—28no—
378C24—32no—
379C24—92no—
380#41—1864no—
381C2×Q8—38no—
382C2×Q8—68no—
383C2×D4—34no—
384C2×D4—38no—
385C2×D4—916no—
386C2×D4—94no—
387C2×D4—1816no—
388C2×D4—184no—
389C22×C4—32no—
390C22×C4—34no—
391C22×C4—38no—
392C22×C4—68no—
393C22×C4—916no—
394C22×C4—92no—
395C22×C4—98no—
396C22×C4—1816no—
397C22×C4—188no—
398C22×C4C2×D3211yescharacteristic
399C22×C4C2×D3211yescharacteristic
400C22×C4C2×D3211yescharacteristic
401C4⋊C4—38no—
402C4⋊C4—34no—
403C4⋊C4—38no—
404C4⋊C4—916no—
405C4⋊C4—94no—
406C22⋊C4—38no—
407C22⋊C4—916no—
408C22⋊C4—98no—
409C42C2×D3214yes—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—38no—
415C22×C3—64no—
416C22×C3—64no—
417C22×C3—616no—
418C22×C3C22×D1212yes—
419C22×C3C2×D3×D412yes—
420C22×C3C2×#23712yes—
421C22×C3C2×#23912yes—
422C22×C3#100712yes—
423C22×C3#101012yes—
424C22×C3C24×D311yescharacteristic
425C22×C3C24×D311yescharacteristic
426C2×D3—24no—
427C2×D3—24no—
428C2×D3—216no—
429C2×D3—68no—
430C2×D3—64no—
431C2×D3—64no—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—64no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—1216no—
439C2×D3—128no—
440C2×D3—128no—
441C2×D3C22×D1218yes—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—24no—
445C3×C4—24no—
446C3×C4—42no—
447C3×C4—68no—
448C3×C4—64no—
449C3×C4C22×D1214yes—
450C3×C4C2×D3×D414yes—
451C3×C4C2×#23714yescomplemented
452C3×C4C2×#23914yescomplemented
453Dic3—28no—
454Dic3—24no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458C32C2×#54711yescharacteristic, complemented, Sylow
459C23—38no—
460C23—34no—
461C23—64no—
462C23—64no—
463C23—94no—
464C23—184no—
465C23—184no—
466C23—184no—
467C23C22×D3211yescharacteristic
468Q8—616no—
469D4—316no—
470D4—1832no—
471D4—188no—
472C2×C4—22no—
473C2×C4—34no—
474C2×C4—38no—
475C2×C4—64no—
476C2×C4—68no—
477C2×C4—616no—
478C2×C4—94no—
479C2×C4—1832no—
480C2×C4—184no—
481C2×C4—1816no—
482C2×C4#379614yescomplemented
483C2×C4D3×D1214yes—
484C2×C4C22×D3212yes—
485C2×C4C22×D3212yes—
486C2×C4C22×D3212yes—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—24no—
491C2×C3—68no—
492C2×C3#555514yescomplemented
493C2×C3#572614yescomplemented
494C2×C3C23×D1211yescharacteristic
495C2×C3C22×D3×D411yescharacteristic
496C2×C3C22×#23711yescharacteristic
497C2×C3C22×#23911yescharacteristic
498C2×C3C2×#100711yescharacteristic
499C2×C3C2×#101011yescharacteristic
500D3—28no—
501D3—128no—
502D3—124no—
503D3—124no—
504C22—38no—
505C22—64no—
506C22—64no—
507C22—616no—
508C22—184no—
509C22—184no—
510C22—184no—
511C22—368no—
512C22C2×#379612yes—
513C22#6429712yes—
514C22C2×D3×D1212yes—
515C22C23×D3211yescharacteristic
516C4—22no—
517C4—64no—
518C4—68no—
519C4—184no—
520C4C2×#379614yescomplemented
521C4C2×D3×D1214yes—
522C3—21no—
523C3C2×#555511yescharacteristic, complemented
524C3C2×#572611yescharacteristic, complemented
525C2—68no—
526C2—364no—
527C2#1059389614yesdirect product factor
528C2C22×#379611yescharacteristic
529C2C2×#6429711yescharacteristic
530C2C22×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×#3796C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C2×C3×#869C2semidirect
5. C2×#63909C2semidirect
6. C2×#63890C2semidirect
7. C2×D3×C4⋊Dic3C2semidirect
8. C2×#63871C2semidirect
9. #10593896C2direct (N × H)
20. C2×#3796C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
29. C3×C4×D12C22semidirect
30. C3×#869C22semidirect
33. #63909C22semidirect
34. #63890C22semidirect
35. D3×C4⋊Dic3C22semidirect
36. #63871C22semidirect
54. C2×C4×D12D3semidirect
55. C2×#869D3semidirect
68. C2×C3×D12D4semidirect
143. C4×D12C2×D3semidirect
144. #869C2×D3semidirect
156. C2×C32×C4#41semidirect
168. C3×D12C2×D4semidirect
223. C2×D12D12semidirect
272. C32×C4C2×#41semidirect
341. C2×C3×C4#237semidirect
342. C2×C3×C4#239semidirect
365. D12C2×D12semidirect
372. C2×C32#547semidirect
451. C3×C4C2×#237semidirect
452. C3×C4C2×#239semidirect
458. C32C2×#547semidirect
482. C2×C4#3796semidirect
492. C2×C3#5555semidirect
493. C2×C3#5726semidirect
520. C4C2×#3796semidirect
523. C3C2×#5555semidirect
524. C3C2×#5726semidirect
527. C2#10593896direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×D122
C2×C3×#8692
C2×#639092
C2×#638902
C2×D3×C4⋊Dic32
C2×#638712
#105938962
C2×#57263
C2×#55553