Finite Group Databasebeta

← C2×#10593900 #11902724

Subgroups — C2×#10593900 #11902724

Order 1152.

3685 conjugacy classes of subgroups.

The subgroup lattice has 548 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×#874C211yesmaximal, characteristic, complemented
4C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
5C2×#63916C212yesmaximal, complemented
6C2×#63911C212yesmaximal, complemented
7C2×Dic3×D12C212yesmaximal, complemented
8C2×#63886C214yesmaximal, complemented
9#10593900C2116yesmaximal, direct product factor
10C2×#5718—31nomaximal
11C2×#5577—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×D12C2212yes—
15C22×C3×D12C2212yes—
16C22×C3×D12C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C22×#626C2214yes—
19C22×#626C2214yes—
20C22×D3×Dic3C2214yes—
21C2×#3796—216no—
22C2×#3796C22116yescomplemented
23C2×C32×C42C2211yescharacteristic
24C2×#3752C2212yes—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2218yescomplemented
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C3×#874C2218yescomplemented
31C3×C4×Dic6C2218yescomplemented
32C2×(C2×D3)⋊Dic3C2214yes—
33#63916C22116yescomplemented
34#63911C22116yescomplemented
35Dic3×D12C22116yescomplemented
36#63886C22132yescomplemented
37C22×#239—32no—
38C22×#237—32no—
39C2×C3×#127—31no—
40C2×C3×C4×Q8—31no—
41C2×#940—32no—
42C2×#939—34no—
43C2×#938—32no—
44C2×D4×Dic3—32no—
45#5718—316no—
46#5577—316no—
47C2×#895—34no—
48C2×#895—32no—
49C2×#874—32no—
50C2×#874D311yescharacteristic, complemented
51C2×C4×D12—32no—
52C2×C4×D12—31no—
53C2×C4×D12—31no—
54C2×C4×D12—61no—
55C2×C4×Dic6D311yescharacteristic, complemented
56C23×C3⋊D3C2312yes—
57C23×C3×D3C2314yes—
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×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×C3×D12—28no—
69C2×C3×D12—28no—
70C2×C3×D12—44no—
71C2×C3×D12C2318yes—
72C2×C3×D12C2318yes—
73C2×C3×D12C2318yes—
74C2×C3×Dic6D418yescomplemented
75C2×C3×Dic6C2314yes—
76C2×#626—216no—
77C2×#626—48no—
78C2×#626C23116yes—
79C2×#626C23116yes—
80C2×D3×Dic3—216no—
81C2×D3×Dic3C23116yes—
82#3796—264no—
83C32×C42C2314yes—
84#3752C2318yes—
85C4⋊(C3⋊Dic3)C2314yes—
86C3×C4⋊Dic3C2314yes—
87C3×Dic3⋊C4C2318yes—
88C3×C4×Dic3C2318yes—
89(C2×D3)⋊Dic3C23116yes—
90C2×#550—91noSylow
91C22×C3×Q8—31no—
92C22×C3×D4—32no—
93C22×C3×D4—32no—
94C22×C3×D4—32no—
95C22×#67—34no—
96C22×#67—34no—
97C23×Dic3—34no—
98C2×#239—316no—
99C2×#239—616no—
100C2×#237—316no—
101C2×#237—616no—
102C22×D12—34no—
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—34no—
106C22×D12—61no—
107C22×D12C2×D312yes—
108C22×D12C2×D312yes—
109C22×D12C2×D312yes—
110C22×C4×D3—34no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—62no—
114C22×Dic6C2×D311yescharacteristic
115C3×#127—38no—
116C3×C4×Q8—38no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C42—21no—
120C2×C3×C42—32no—
121C2×C3×C42C2×D311yescharacteristic
122C2×C3×C42C2×D311yescharacteristic
123C2×#217—34no—
124#940—316no—
125#939—332no—
126#938—316no—
127D4×Dic3—316no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—62no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4C2×D312yes—
137C2×C4×Dic3C2×D312yes—
138#895—332no—
139#895—316no—
140#874—316no—
141#874C2×D318yescomplemented
142C4×D12—316no—
143C4×D12—38no—
144C4×D12—38no—
145C4×D12—68no—
146C4×Dic6C2×D318yescomplemented
147C23×C32C2411yescharacteristic
148C22×C3⋊D3—24no—
149C22×C3⋊D3—24no—
150C22×C3⋊D3—24no—
151C22×C3⋊D3C2414yes—
152C22×C3×D3—28no—
153C22×C3×D3—28no—
154C22×C3×D3—28no—
155C22×C3×D3C2418yes—
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⋊Dic3C2414yes—
164C4⋊(C3⋊D3)—28no—
165C4×C3⋊D3—216no—
166C2×C3×Dic3—24no—
167C2×C3×Dic3C2×D418yes—
168C2×C3×Dic3C2414yes—
169C2×C3×Dic3C2414yes—
170C3×D12—216no—
171C3×D12—216no—
172C3×D12—48no—
173C3×Dic6C2×D4116yescomplemented
174#626—232no—
175#626—416no—
176D3×Dic3—232no—
177C22×#41—92no—
178#550—916no—
179C2×#127—31no—
180C2×#127—92no—
181C2×#121—92no—
182C2×#121—94no—
183C2×C4×Q8—31no—
184C2×C4×D4—92no—
185C2×C4×D4—91no—
186C24×C3—34no—
187C23×D3—32no—
188C23×D3—32no—
189C23×D3—62no—
190C23×D3C22×D314yes—
191C2×C3×Q8—38no—
192C2×C3×Q8—34no—
193C2×C3×D4—38no—
194C2×C3×D4—38no—
195C2×C3×D4—38no—
196C2×C3×D4—68no—
197C2×C3×D4—68no—
198C2×C3×D4—124no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
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—616no—
213C2×#67—128no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—316no—
217C22×Dic3—62no—
218C22×Dic3—616no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221#239—664no—
222#237—664no—
223C2×D12—28no—
224C2×D12—28no—
225C2×D12—316no—
226C2×D12—34no—
227C2×D12—34no—
228C2×D12—316no—
229C2×D12—44no—
230C2×D12—64no—
231C2×D12—68no—
232C2×D12—616no—
233C2×D12—64no—
234C2×D12—64no—
235C2×D12—128no—
236C2×D12C22×D318yes—
237C2×D12C22×D318yes—
238C2×D12C22×D318yes—
239C2×C4×D3—316no—
240C2×C4×D3—38no—
241C2×C4×D3—38no—
242C2×C4×D3—68no—
243C2×C4×D3—616no—
244C2×C4×D3—68no—
245C2×C4×D3—68no—
246C2×C4×D3—128no—
247C2×Dic6D1218yescomplemented
248C2×Dic6C22×D314yes—
249C3×C4⋊C4—38no—
250C3×C4⋊C4—34no—
251C3×C42—24no—
252C3×C42—38no—
253C3×C42C22×D314yes—
254C3×C42C22×D314yes—
255#217—316no—
256(C2×D3)⋊C4—316no—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—68no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263C4⋊Dic3C22×D314yes—
264Dic3⋊C4C22×D318yes—
265C4×Dic3C22×D318yes—
266C22×C32C22×D412yes—
267C22×C32C2×#4112yes—
268C22×C32H(5,𝔽2)12yes—
269C22×C32C2511yescharacteristic
270C2×C3⋊D3—24no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—24no—
273C2×C3⋊D3—48no—
274C2×C3×D3—28no—
275C2×C3×D3—28no—
276C2×C3×D3—28no—
277C2×C3×D3—416no—
278C32×C4—22no—
279C32×C4C22×D414yes—
280C32×C4C2×#4114yescomplemented
281C3⋊Dic3—24no—
282C3×Dic3—24no—
283C3×Dic3C22×D418yes—
284C2×#41—916no—
285C2×#41—1816no—
286C22×Q8—31no—
287C22×D4—32no—
288C22×D4—32no—
289C22×D4—32no—
290C22×D4—94no—
291C22×D4—94no—
292C22×D4—91no—
293C23×C4—94no—
294C23×C4—92no—
295#127—38no—
296#127—916no—
297#121—916no—
298#121—932no—
299C4×Q8—38no—
300C4×D4—916no—
301C4×D4—98no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—94no—
306C2×C22⋊C4—92no—
307C2×C42—32no—
308C2×C42D3211yescharacteristic
309C23×C3—21no—
310C23×C3—38no—
311C23×C3—68no—
312C23×C3—68no—
313C23×C3—68no—
314C23×C3C23×D311yescharacteristic
315C23×C3C23×D311yescharacteristic
316C22×D3—28no—
317C22×D3—28no—
318C22×D3—28no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—64no—
322C22×D3—68no—
323C22×D3—64no—
324C22×D3—64no—
325C22×D3—64no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—124no—
330C22×D3—124no—
331C22×D3C23×D318yes—
332C3×Q8—316no—
333C3×D4—616no—
334C3×D4—616no—
335C3×D4—128no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—38no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—42no—
347C2×C3×C4—64no—
348C2×C3×C4C2×D1214yes—
349C2×C3×C4D3×D414yes—
350C2×C3×C4#23714yescomplemented
351C2×C3×C4#23914yescomplemented
352C2×C3×C4C23×D312yes—
353C2×C3×C4C23×D312yes—
354C2×C3×C4C23×D312yes—
355C2×C3×C4C23×D312yes—
356C2×C3×C4C23×D312yes—
357C2×C3×C4C23×D312yes—
358#67—632no—
359#67—1216no—
360C2×Dic3—24no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—632no—
367C2×Dic3—124no—
368C2×Dic3C2×D1218yes—
369C2×Dic3C23×D314yes—
370C2×Dic3C23×D314yes—
371D12—216no—
372D12—216no—
373D12—48no—
374D12—616no—
375D12—632no—
376D12—68no—
377D12—68no—
378D12—1216no—
379C4×D3—632no—
380C4×D3—616no—
381C4×D3—616no—
382C4×D3—1216no—
383Dic6C2×D12116yescomplemented
384C2×C32#55014yescomplemented
385C2×C32C23×D411yescharacteristic
386C2×C32C22×#4111yescharacteristic
387C2×C32C2×H(5,𝔽2)11yescharacteristic
388C3⋊D3—44no—
389C3×D3—48no—
390C24—34no—
391C24—92no—
392#41—1864no—
393C2×Q8—34no—
394C2×Q8—38no—
395C2×D4—38no—
396C2×D4—38no—
397C2×D4—38no—
398C2×D4—68no—
399C2×D4—68no—
400C2×D4—916no—
401C2×D4—916no—
402C2×D4—94no—
403C2×D4—124no—
404C2×D4—1816no—
405C2×D4—184no—
406C2×D4—368no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—916no—
410C22×C4—92no—
411C22×C4—98no—
412C22×C4—1816no—
413C22×C4—188no—
414C22×C4C2×D3211yescharacteristic
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—38no—
418C4⋊C4—34no—
419C4⋊C4—94no—
420C22⋊C4—916no—
421C22⋊C4—98no—
422C42—38no—
423C42C2×D3214yes—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—68no—
429C22×C3—68no—
430C22×C3—68no—
431C22×C3—1216no—
432C22×C3C22×D1212yes—
433C22×C3C2×D3×D412yes—
434C22×C3C2×#23712yes—
435C22×C3#100412yes—
436C22×C3C2×#23912yes—
437C22×C3#100912yes—
438C22×C3C24×D311yescharacteristic
439C22×C3C24×D311yescharacteristic
440C2×D3—28no—
441C2×D3—28no—
442C2×D3—28no—
443C2×D3—416no—
444C2×D3—68no—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—64no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—1216no—
454C2×D3—128no—
455C2×D3—128no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—38no—
461C3×C4—42no—
462C3×C4—64no—
463C3×C4C22×D1214yes—
464C3×C4C2×D3×D414yes—
465C3×C4C2×#23714yescomplemented
466C3×C4C2×#23914yescomplemented
467Dic3—24no—
468Dic3—64no—
469Dic3—64no—
470Dic3—124no—
471Dic3C22×D1218yes—
472C32C2×#55011yescharacteristic, complemented, Sylow
473C23—38no—
474C23—68no—
475C23—68no—
476C23—68no—
477C23—94no—
478C23—184no—
479C23—184no—
480C23—184no—
481C23C22×D3211yescharacteristic
482Q8—316no—
483D4—616no—
484D4—616no—
485D4—128no—
486D4—1832no—
487D4—188no—
488D4—3616no—
489C2×C4—22no—
490C2×C4—38no—
491C2×C4—34no—
492C2×C4—34no—
493C2×C4—64no—
494C2×C4—94no—
495C2×C4—1832no—
496C2×C4—184no—
497C2×C4—1816no—
498C2×C4#379614yescomplemented
499C2×C4D3×D1214yes—
500C2×C4C22×D3212yes—
501C2×C4C22×D3212yes—
502C2×C4C22×D3212yes—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—24no—
507C2×C3—128no—
508C2×C3#557714yescomplemented
509C2×C3#571814yescomplemented
510C2×C3C23×D1211yescharacteristic
511C2×C3C22×D3×D411yescharacteristic
512C2×C3C22×#23711yescharacteristic
513C2×C3C2×#100411yescharacteristic
514C2×C3C22×#23911yescharacteristic
515C2×C3C2×#100911yescharacteristic
516D3—48no—
517D3—128no—
518D3—124no—
519D3—124no—
520C22—68no—
521C22—68no—
522C22—68no—
523C22—1216no—
524C22—184no—
525C22—184no—
526C22—184no—
527C22—368no—
528C22C2×#379612yes—
529C22C2×D3×D1212yes—
530C22#6430712yes—
531C22C23×D3211yescharacteristic
532C4—22no—
533C4—38no—
534C4—64no—
535C4—184no—
536C4C2×#379614yescomplemented
537C4C2×D3×D1214yes—
538C3—21no—
539C3C2×#557711yescharacteristic, complemented
540C3C2×#571811yescharacteristic, complemented
541C2—128no—
542C2—364no—
543C2#1059390014yesdirect product factor
544C2C22×#379611yescharacteristic
545C2C22×D3×D1211yescharacteristic
546C2C2×#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×#3796C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×C3×#874C2semidirect
4. C2×C3×C4×Dic6C2semidirect
5. C2×#63916C2semidirect
6. C2×#63911C2semidirect
7. C2×Dic3×D12C2semidirect
8. C2×#63886C2semidirect
9. #10593900C2direct (N × H)
22. C2×#3796C22semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
30. C3×#874C22semidirect
31. C3×C4×Dic6C22semidirect
33. #63916C22semidirect
34. #63911C22semidirect
35. Dic3×D12C22semidirect
36. #63886C22semidirect
50. C2×#874D3semidirect
55. C2×C4×Dic6D3semidirect
74. C2×C3×Dic6D4semidirect
141. #874C2×D3semidirect
146. C4×Dic6C2×D3semidirect
158. C2×C32×C4#41semidirect
173. C3×Dic6C2×D4semidirect
247. C2×Dic6D12semidirect
280. C32×C4C2×#41semidirect
350. C2×C3×C4#237semidirect
351. C2×C3×C4#239semidirect
383. Dic6C2×D12semidirect
384. C2×C32#550semidirect
465. C3×C4C2×#237semidirect
466. C3×C4C2×#239semidirect
472. C32C2×#550semidirect
498. C2×C4#3796semidirect
508. C2×C3#5577semidirect
509. C2×C3#5718semidirect
536. C4C2×#3796semidirect
539. C3C2×#5577semidirect
540. C3C2×#5718semidirect
543. C2#10593900direct (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×#8742
C2×C3×C4×Dic62
C2×#639162
C2×#639112
C2×Dic3×D122
C2×#638862
#105939002
C2×#57183
C2×#55773