Finite Group Databasebeta

← C2×#10594990 #11900095

Subgroups — C2×#10594990 #11900095

Order 1152.

3725 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63952C214yesmaximal, complemented
5#10594990C2116yesmaximal, direct product factor
6C2×#63900C212yesmaximal, complemented
7C2×#63894C212yesmaximal, complemented
8C2×#63849C212yesmaximal, complemented
9C2×#63844C212yesmaximal, complemented
10C2×#5523—31nomaximal
11C2×#5504—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#638C2212yes—
14C2×#3828C4116yescomplemented
15C2×#3828C2218yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2212yes—
18C22×#634C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C22×#624C2214yes—
21C2×C3×#217C2212yes—
22C3×#926C2218yescomplemented
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2218yescomplemented
28C2×C3×C4×Dic3C2212yes—
29C2×#3724C2214yes—
30C2×#3722C2214yes—
31C2×Dic32C2214yes—
32#63952C22132yescomplemented
33#63900C22116yescomplemented
34#63894C22116yescomplemented
35#63849C22116yescomplemented
36#63844C22116yescomplemented
37C22×#235—31no—
38C22×#235—31no—
39C22×#235—61no—
40C2×C3×#117—31no—
41C22×C3×C4⋊C4—31no—
42C2×C4×#67—34no—
43C2×#926D311yescharacteristic, complemented
44C22×C4⋊Dic3D311yescharacteristic, complemented
45#5523—316no—
46#5504—316no—
47C2×#893—32no—
48C2×#892—32no—
49C2×#892—32no—
50C2×D3×C4⋊C4—32no—
51C2×D3×C4⋊C4—32no—
52C2×#887—32no—
53C2×#67⋊C4—34no—
54C2×C4×D12—32no—
55C2×C4×Dic6—32no—
56C24×C32C2311yescharacteristic
57C23×C3⋊D3C2312yes—
58C22×C32×C4C2×C418yescomplemented
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2314yes—
62C2×#638C2×C4116yescomplemented
63C2×#638C2318yes—
64C22×C3⋊Dic3C2312yes—
65#3828C2×C4164yescomplemented
66C2×C4⋊(C3⋊D3)C2×C418yescomplemented
67C2×C4⋊(C3⋊D3)C2314yes—
68C2×C4×C3⋊D3C2×C4116yescomplemented
69C2×C4×C3⋊D3C2318yes—
70C2×#634C2×C418yescomplemented
71C2×#634C2314yes—
72C22×C3×Dic3—44no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2314yes—
76C22×C3×Dic3C2318yes—
77C2×#624—48no—
78C2×#624C23116yes—
79C3×#217C2318yes—
80C3×C4⋊Dic3C2318yes—
81C3×C4⋊Dic3C2318yes—
82C3×C4⋊Dic3C2314yes—
83C3×C4⋊Dic3C2314yes—
84C3×C4×Dic3C2318yes—
85#3724C23116yes—
86#3722C23116yes—
87Dic32C23116yes—
88C2×#520—91noSylow
89C23×C3×C4—21no—
90C23×C3×C4—32no—
91C23×C3×C4C2×D311yescharacteristic
92C23×C3×C4C2×D311yescharacteristic
93C22×#67—32no—
94C22×#67—32no—
95C22×#67—62no—
96C23×Dic3C2×D312yes—
97C2×#235—316no—
98C2×#235—316no—
99C2×#235—38no—
100C2×#235—38no—
101C2×#235—616no—
102C2×#235—68no—
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—61no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—34no—
109C22×C4×D3—34no—
110C22×C4×D3—62no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C3×#117—38no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—38no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C42—32no—
122C2×#217C2×D312yes—
123C4×#67—332no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126#926C2×D318yescomplemented
127C2×C4⋊Dic3C2×D312yes—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×C4⋊Dic3C2×D312yes—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×C4⋊Dic3C2×D318yescomplemented
132C2×Dic3⋊C4—34no—
133C2×Dic3⋊C4—34no—
134C2×C4×Dic3—34no—
135C2×C4×Dic3—34no—
136C2×C4×Dic3C2×D312yes—
137#893—316no—
138#892—316no—
139#892—316no—
140D3×C4⋊C4—316no—
141D3×C4⋊C4—316no—
142#887—316no—
143#67⋊C4—332no—
144C4×D12—316no—
145C4×Dic6—316no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C22×C414yes—
149C23×C32C2412yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—24no—
152C22×C3⋊D3—24no—
153C22×C3⋊D3C22×C418yes—
154C22×C3⋊D3C2414yes—
155C2×C32×C4C22×C414yes—
156C2×C32×C4C22×C414yes—
157C2×C32×C4C22×C4116yescomplemented
158C2×C32×C4C2412yes—
159C2×C32×C4C2412yes—
160#638C22×C4132yescomplemented
161C2×C3⋊Dic3C22×C418yes—
162C2×C3⋊Dic3C2414yes—
163C4⋊(C3⋊D3)C22×C4116yescomplemented
164C4×C3⋊D3C22×C4132yescomplemented
165#634C22×C4116yescomplemented
166C2×C3×Dic3—24no—
167C2×C3×Dic3—28no—
168C2×C3×Dic3—24no—
169C2×C3×Dic3—48no—
170C2×C3×Dic3C2414yes—
171C2×C3×Dic3C2418yes—
172C2×C3×Dic3C2414yes—
173#624—416no—
174C22×#41—91no—
175#520—916no—
176C2×C4×Q8—92no—
177C2×C4×D4—92no—
178C2×C4×D4—94no—
179C2×#117—31no—
180C2×#117—92no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—92no—
183C24×C3—21no—
184C24×C3C22×D311yescharacteristic
185C24×C3C22×D311yescharacteristic
186C23×D3—32no—
187C23×D3—32no—
188C23×D3—62no—
189C22×C3×C4—28no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—24no—
193C22×C3×C4—32no—
194C22×C3×C4—34no—
195C22×C3×C4—32no—
196C22×C3×C4—38no—
197C22×C3×C4—124no—
198C22×C3×C4C4×D318yescomplemented
199C22×C3×C4C4×D318yescomplemented
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D314yes—
205C22×C3×C4C22×D314yes—
206C2×#67—316no—
207C2×#67—316no—
208C2×#67—38no—
209C2×#67—38no—
210C2×#67—616no—
211C2×#67—68no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—44no—
215C22×Dic3—62no—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D314yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D318yes—
220#235—364no—
221#235—364no—
222#235—664no—
223C2×D12—38no—
224C2×D12—38no—
225C2×D12—34no—
226C2×D12—34no—
227C2×D12—68no—
228C2×D12—64no—
229C2×C4×D3—316no—
230C2×C4×D3—316no—
231C2×C4×D3—38no—
232C2×C4×D3—38no—
233C2×C4×D3—316no—
234C2×C4×D3—316no—
235C2×C4×D3—616no—
236C2×C4×D3—68no—
237C2×C4×D3—128no—
238C2×C4×D3—128no—
239C2×Dic6—38no—
240C2×Dic6—38no—
241C2×Dic6—34no—
242C2×Dic6—34no—
243C2×Dic6—68no—
244C2×Dic6—64no—
245C3×C4⋊C4—38no—
246C3×C4⋊C4—34no—
247C3×C4⋊C4—38no—
248C3×C4⋊C4—34no—
249C3×C22⋊C4—38no—
250C3×C42—38no—
251#217C22×D318yes—
252(C2×D3)⋊C4—316no—
253(C2×D3)⋊C4—316no—
254C4⋊Dic3C22×D318yes—
255C4⋊Dic3C22×D314yes—
256C4⋊Dic3C22×D318yes—
257C4⋊Dic3C22×D314yes—
258Dic3⋊C4—316no—
259Dic3⋊C4—316no—
260C4×Dic3—316no—
261C4×Dic3—316no—
262C4×Dic3C22×D318yes—
263C22×C32—28no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32C23×C414yes—
267C22×C32C23×C412yes—
268C22×C32H(5,𝔽2)12yes—
269C22×C322−1+412yes—
270C22×C32C2511yescharacteristic
271C2×C3⋊D3—216no—
272C2×C3⋊D3—24no—
273C2×C3⋊D3—24no—
274C2×C3⋊D3C23×C418yes—
275C32×C4C23×C414yes—
276C32×C4C23×C414yes—
277C3⋊Dic3C23×C418yes—
278C3×Dic3—24no—
279C3×Dic3—28no—
280C3×Dic3—24no—
281C2×#41—916no—
282C2×#41—98no—
283C22×Q8—91no—
284C22×D4—92no—
285C22×D4—91no—
286C23×C4—32no—
287C23×C4—94no—
288C23×C4—92no—
289C23×C4D3211yescharacteristic
290C4×Q8—916no—
291C4×D4—916no—
292C4×D4—932no—
293#117—38no—
294#117—916no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—38no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—916no—
301C2×C4⋊C4—94no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—94no—
304C2×C42—32no—
305C2×C42—94no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—24no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3C2×C4×D314yes—
316C23×C3C2×C4×D314yes—
317C23×C3C23×D312yes—
318C23×C3C23×D312yes—
319C23×C3C23×D311yescharacteristic
320C23×C3C23×D311yescharacteristic
321C22×D3—38no—
322C22×D3—38no—
323C22×D3—34no—
324C22×D3—34no—
325C22×D3—68no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—64no—
331C22×D3—124no—
332C22×D3—124no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—216no—
338C2×C3×C4—34no—
339C2×C3×C4—38no—
340C2×C3×C4—34no—
341C2×C3×C4—64no—
342C2×C3×C4—64no—
343C2×C3×C4—68no—
344C2×C3×C4—128no—
345C2×C3×C4C2×C4×D314yes—
346C2×C3×C4C2×C4×D314yes—
347C2×C3×C4C2×C4×D314yes—
348C2×C3×C4C2×C4×D314yes—
349C2×C3×C4C2×C4×D3116yescomplemented
350C2×C3×C4C2×C4×D3116yescomplemented
351C2×C3×C4C23×D312yes—
352C2×C3×C4C23×D312yes—
353C2×C3×C4C23×D312yes—
354C2×C3×C4C23×D312yes—
355#67—332no—
356#67—332no—
357#67—632no—
358C2×Dic3—28no—
359C2×Dic3—24no—
360C2×Dic3—24no—
361C2×Dic3—38no—
362C2×Dic3—38no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—48no—
366C2×Dic3—68no—
367C2×Dic3—64no—
368C2×Dic3C23×D314yes—
369C2×Dic3C23×D318yes—
370C2×Dic3C23×D314yes—
371D12—316no—
372D12—316no—
373D12—616no—
374C4×D3—332no—
375C4×D3—332no—
376C4×D3—632no—
377C4×D3—1216no—
378C4×D3—1216no—
379Dic6—316no—
380Dic6—316no—
381Dic6—616no—
382C2×C32—24no—
383C2×C32#52014yescomplemented
384C2×C32C24×C411yescharacteristic
385C2×C32C2×H(5,𝔽2)11yescharacteristic
386C2×C32C2×2−1+411yescharacteristic
387C3⋊D3—28no—
388C24—92no—
389C24C2×D3211yescharacteristic
390#41—964no—
391C2×Q8—94no—
392C2×Q8—98no—
393C2×D4—98no—
394C2×D4—916no—
395C2×D4—94no—
396C2×D4—98no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—34no—
400C22×C4—38no—
401C22×C4—916no—
402C22×C4—92no—
403C22×C4—98no—
404C22×C4—916no—
405C22×C4—124no—
406C22×C4—368no—
407C22×C4#62418yescomplemented
408C22×C4C2×D3211yescharacteristic
409C22×C4C2×D3211yescharacteristic
410C22×C4C2×D3214yes—
411C4⋊C4—38no—
412C4⋊C4—38no—
413C4⋊C4—34no—
414C4⋊C4—34no—
415C4⋊C4—916no—
416C22⋊C4—38no—
417C22⋊C4—916no—
418C42—38no—
419C42—916no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—28no—
425C22×C3—28no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—48no—
434C22×C3C22×C4×D314yes—
435C22×C3C22×C4×D314yes—
436C22×C3C22×C4×D312yes—
437C22×C3C22×C4×D312yes—
438C22×C3#100412yes—
439C22×C3#100712yes—
440C22×C3#100912yes—
441C22×C3#101012yes—
442C22×C3C24×D311yescharacteristic
443C22×C3C24×D311yescharacteristic
444C2×D3—38no—
445C2×D3—38no—
446C2×D3—68no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—64no—
451C2×D3—616no—
452C2×D3—616no—
453C2×D3—124no—
454C2×D3—124no—
455C2×D3—1216no—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—64no—
459C3×C4—64no—
460C3×C4—68no—
461C3×C4C22×C4×D314yes—
462C3×C4C22×C4×D314yes—
463C3×C4C22×C4×D314yes—
464C3×C4C22×C4×D314yes—
465Dic3—28no—
466Dic3—24no—
467Dic3—24no—
468Dic3—38no—
469Dic3—38no—
470Dic3—68no—
471C32C2×#52011yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—98no—
475C23—94no—
476C23—184no—
477C23—184no—
478C23C2×#62414yes—
479C23C22×D3212yes—
480C23C22×D3211yescharacteristic
481Q8—916no—
482D4—932no—
483D4—916no—
484C2×C4—34no—
485C2×C4—34no—
486C2×C4—38no—
487C2×C4—64no—
488C2×C4—68no—
489C2×C4—64no—
490C2×C4—98no—
491C2×C4—94no—
492C2×C4—932no—
493C2×C4—128no—
494C2×C4—3616no—
495C2×C4C2×#62414yes—
496C2×C4C2×#62414yes—
497C2×C4C2×#624116yescomplemented
498C2×C4C22×D3212yes—
499C2×C4C22×D3212yes—
500C2×C3—24no—
501C2×C3—24no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—24no—
506C2×C3—44no—
507C2×C3#550414yescomplemented
508C2×C3#552314yescomplemented
509C2×C3C23×C4×D311yescharacteristic
510C2×C3C23×C4×D311yescharacteristic
511C2×C3C2×#100411yescharacteristic
512C2×C3C2×#100711yescharacteristic
513C2×C3C2×#100911yescharacteristic
514C2×C3C2×#101011yescharacteristic
515D3—68no—
516D3—68no—
517D3—128no—
518C22—22no—
519C22—22no—
520C22—28no—
521C22—98no—
522C22—184no—
523C22—184no—
524C22—1816no—
525C22#6429712yes—
526C22#6430712yes—
527C22C22×#62414yes—
528C22C22×#62412yes—
529C22C23×D3211yescharacteristic
530C4—64no—
531C4—68no—
532C4—64no—
533C4—98no—
534C4C22×#62414yes—
535C4C22×#62414yes—
536C3—21no—
537C3C2×#550411yescharacteristic, complemented
538C3C2×#552311yescharacteristic, complemented
539C2—24no—
540C2—188no—
541C2#1059499014yesdirect product factor
542C2C2×#6429711yescharacteristic
543C2C2×#6430711yescharacteristic
544C2C23×#62411yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×#3828C2
cosocleC22×C32C25
hypercenterC23×C4D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C2×#63952C2semidirect
5. #10594990C2direct (N × H)
6. C2×#63900C2semidirect
7. C2×#63894C2semidirect
8. C2×#63849C2semidirect
9. C2×#63844C2semidirect
14. C2×#3828C4semidirect
22. C3×#926C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
32. #63952C22semidirect
33. #63900C22semidirect
34. #63894C22semidirect
35. #63849C22semidirect
36. #63844C22semidirect
43. C2×#926D3semidirect
44. C22×C4⋊Dic3D3semidirect
58. C22×C32×C4C2×C4semidirect
62. C2×#638C2×C4semidirect
65. #3828C2×C4semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
70. C2×#634C2×C4semidirect
126. #926C2×D3semidirect
131. C2×C4⋊Dic3C2×D3semidirect
157. C2×C32×C4C22×C4semidirect
160. #638C22×C4semidirect
163. C4⋊(C3⋊D3)C22×C4semidirect
164. C4×C3⋊D3C22×C4semidirect
165. #634C22×C4semidirect
198. C22×C3×C4C4×D3semidirect
199. C22×C3×C4C4×D3semidirect
349. C2×C3×C4C2×C4×D3semidirect
350. C2×C3×C4C2×C4×D3semidirect
383. C2×C32#520semidirect
407. C22×C4#624semidirect
471. C32C2×#520semidirect
497. C2×C4C2×#624semidirect
507. C2×C3#5504semidirect
508. C2×C3#5523semidirect
537. C3C2×#5504semidirect
538. C3C2×#5523semidirect
541. C2#10594990direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9262
C22×C3×C4⋊Dic32
C2×#639522
#105949902
C2×#639002
C2×#638942
C2×#638492
C2×#638442
C2×#55233
C2×#55043