Finite Group Databasebeta

← C2×#10594730 #11918609

Subgroups — C2×#10594730 #11918609

Order 1152.

3177 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C212yesmaximal, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#912C212yesmaximal, complemented
4C2×#63935C214yesmaximal, complemented
5C2×#63930C212yesmaximal, complemented
6#10594730C2116yesmaximal, direct product factor
7C2×#63808C212yesmaximal, complemented
8C2×#63802C211yesmaximal, characteristic, complemented
9C2×D32×C8C211yesmaximal, characteristic, complemented
10C2×D3×#135—32nomaximal
11C2×D4×C3⋊D3C2212yes—
12C2×C3×#237C2214yescomplemented
13C2×#3811—22no—
14C22×#624—22no—
15C2×#3804—24no—
16#64312—28no—
17#64312C22116yescomplemented
18C2×C4×D32C2211yescharacteristic
19C2×#3799C2214yescomplemented
20C2×#3797C2212yes—
21C2×C32×D8C2211yescharacteristic, complemented
22C2×#3753C2212yescomplemented
23D8×C3⋊D3C2218yescomplemented
24C2×#3745C2211yescharacteristic, complemented
25C2×C8×C3⋊D3C2211yescharacteristic
26C2×C3×#214C2214yescomplemented
27C3×#912C22116yescomplemented
28C2×C3×Dic12C2212yescomplemented
29C2×C3×D3×C8C2212yescomplemented
30#63935C22132yescomplemented
31#63930C22116yescomplemented
32C2×#3718C2212yescomplemented
33C2×#3717C2214yescomplemented
34C2×#3710C2211yescharacteristic
35C2×D3×C3⋊C8C2212yescomplemented
36#63808C22116yescomplemented
37#63802C2218yescomplemented
38D32×C8C2218yescomplemented
39C2×D3×#41—34no—
40C2×C3×#135—32no—
41C2×#950—34no—
42D3×#135—332no—
43C2×#919—32no—
44C2×D3×Q16—32no—
45C2×#916—34no—
46C2×D3×SD16—34no—
47C2×#912D312yescomplemented
48C2×D3×D8—32no—
49C2×D3×D8—61no—
50C2×#904—32no—
51C22×D3×C8—32no—
52C23×C3⋊D3—22no—
53C22×D32D411yescharacteristic
54C2×C32×D4C2312yes—
55C2×#638—22no—
56D4×C3⋊D3—24no—
57D4×C3⋊D3C2318yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×#67—24no—
61C22×C3×Dic3—24no—
62C3×#237—28no—
63C3×#237C23116yescomplemented
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6C2314yes—
66#3811—216no—
67C2×#627—22no—
68C2×#626—24no—
69C2×#624—22no—
70C2×#624—24no—
71C2×#624—216no—
72C2×#624D411yescharacteristic
73#3804—232no—
74C2×D3×Dic3D412yes—
75C4×D32D414yes—
76C4×D32C2314yes—
77#3799—28no—
78#3799C23116yescomplemented
79#3797—24no—
80#3797C2318yes—
81C32×D8C2314yescomplemented
82C2×C32×C8C2311yescharacteristic
83#3753C2318yescomplemented
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3745C2314yescomplemented
86C8×C3⋊D3C2314yes—
87C3×#214C23116yescomplemented
88C2×C3×C3⋊C8C2312yes—
89C3×Dic12C2318yescomplemented
90C3×D3×C8C2318yescomplemented
91#3718C2318yescomplemented
92#3717C23116yescomplemented
93#3710C2314yes—
94D3×C3⋊C8C2318yescomplemented
95C22×#135—91noSylow
96C2×C3×#41—34no—
97D3×#41—332no—
98D3×#41—616no—
99C2×#239—34no—
100C2×D3×Q8—34no—
101C2×#237—64no—
102C2×#237C2×D314yescomplemented
103C2×D3×D4—34no—
104C2×D3×D4—62no—
105C2×D3×D4—64no—
106C2×#235—34no—
107C2×#235—64no—
108C22×C4×D3—32no—
109C22×C4×D3—64no—
110C3×#135—316no—
111C2×C3×Q16—32no—
112C2×C3×SD16—34no—
113C2×C3×D8—21no—
114C2×C3×D8C2×D312yescomplemented
115C22×C3×C8—32no—
116#950—332no—
117C2×#216—34no—
118C2×#215—34no—
119C2×#214C2×D314yescomplemented
120C2×#213—34no—
121C2×#213—62no—
122C22×C3⋊C8—32no—
123#919—316no—
124D3×Q16—316no—
125#916—332no—
126D3×SD16—332no—
127#912C2×D3116yescomplemented
128D3×D8—316no—
129D3×D8—68no—
130C2×Dic12C2×D312yescomplemented
131#904—316no—
132C2×D24—32no—
133C2×D24—61no—
134C2×#204—34no—
135C2×D3×C8—32no—
136C2×D3×C8—32no—
137C2×D3×C8—32no—
138C2×D3×C8—316no—
139C2×D3×C8—61no—
140C2×D3×C8C2×D312yescomplemented
141C23×C32—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—28no—
144C22×C3⋊D3—48no—
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3C2×D412yes—
147C2×D32—24no—
148C2×D32C2×D414yes—
149C32×D4—22no—
150C32×D4C2414yes—
151C2×C32×C4C2411yescharacteristic
152#638—28no—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)C2414yes—
156C4×C3⋊D3C2×D412yes—
157C4×C3⋊D3C2412yes—
158C3×#67—216no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—216no—
161C2×C3×Dic3C2×D412yes—
162C3×C4×D3C2×D414yes—
163C3×C4×D3C2414yes—
164C3×Dic6—24no—
165C3×Dic6C2418yes—
166#627—28no—
167#626—216no—
168#624—28no—
169#624—216no—
170#624C2×D414yes—
171D3×Dic3C2×D418yes—
172C32×C8C2412yes—
173C3⋊(C3⋊C8)C2412yes—
174C3×C3⋊C8C2414yes—
175C22×#41—92no—
176C2×#135—32no—
177C2×#135—92no—
178C2×#135—94no—
179C2×#135—916no—
180C22×Q16—91no—
181C22×SD16—92no—
182C22×D8—91no—
183C23×C8—91no—
184C23×D3—32no—
185C23×D3—64no—
186C23×D3—122no—
187C3×#41—316no—
188C3×#41—68no—
189C2×C3×Q8—34no—
190C2×C3×D4—22no—
191C2×C3×D4—64no—
192C2×C3×D4C22×D314yes—
193C22×C3×C4—32no—
194C22×C3×C4—64no—
195C2×#67—24no—
196C2×#67—64no—
197C2×#67—64no—
198C2×#67—122no—
199C22×Dic3—24no—
200C22×Dic3—32no—
201#239—316no—
202#239—68no—
203D3×Q8—316no—
204D3×Q8—68no—
205#237—28no—
206#237—632no—
207#237C22×D3116yescomplemented
208D3×D4—316no—
209D3×D4—68no—
210D3×D4—68no—
211D3×D4—632no—
212D3×D4—124no—
213#235—316no—
214#235—68no—
215#235—632no—
216C2×D12—34no—
217C2×D12—62no—
218C2×D12—64no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—38no—
223C2×C4×D3—38no—
224C2×C4×D3—61no—
225C2×C4×D3—632no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3C22×D312yes—
230C2×Dic6—64no—
231C2×Dic6C22×D314yes—
232C3×Q16—38no—
233C3×SD16—316no—
234C3×D8—24no—
235C3×D8C22×D318yescomplemented
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8—38no—
239C2×C3×C8C22×D312yes—
240#216—316no—
241#215—316no—
242#214C22×D3116yescomplemented
243#213—316no—
244#213—68no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—38no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8C22×D312yes—
249Dic12C22×D318yescomplemented
250D24—38no—
251D24—64no—
252#204—316no—
253D3×C8—38no—
254D3×C8—38no—
255D3×C8—38no—
256D3×C8—64no—
257D3×C8C22×D318yescomplemented
258C22×C32—24no—
259C22×C32—44no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—24no—
262C2×C3⋊D3—44no—
263C2×C3⋊D3—416no—
264C2×C3⋊D3#13514yescomplemented
265C2×C3⋊D3C22×D412yes—
266C2×C3×D3—24no—
267C2×C3×D3C22×D414yes—
268D32—28no—
269C32×C4C22×D411yescharacteristic
270C32×C4C2511yescharacteristic
271C3⋊Dic3C22×D412yes—
272C3×Dic3—28no—
273C3×Dic3C22×D414yes—
274C2×#41—34no—
275C2×#41—94no—
276C2×#41—916no—
277C2×#41—184no—
278C2×#41—188no—
279C22×Q8—92no—
280C22×D4—92no—
281C22×D4—182no—
282C23×C4—91no—
283C23×C4—182no—
284#135—316no—
285#135—916no—
286#135—932no—
287C2×Q16—32no—
288C2×Q16—98no—
289C2×Q16—92no—
290C2×SD16—34no—
291C2×SD16—94no—
292C2×SD16—916no—
293C2×D8—92no—
294C2×D8—98no—
295C2×D8—91no—
296C2×D8D3211yescharacteristic, complemented
297C22×C8—32no—
298C22×C8—91no—
299C22×C8—98no—
300C22×C8—92no—
301C22×C8—91no—
302C23×C3—24no—
303C23×C3—32no—
304C23×C3—42no—
305C22×D3—32no—
306C22×D3—38no—
307C22×D3—61no—
308C22×D3—68no—
309C22×D3—616no—
310C22×D3—64no—
311C22×D3—128no—
312C22×D3—122no—
313C22×D3—1216no—
314C22×D3—248no—
315C22×D3D3×D412yes—
316C3×Q8—38no—
317C3×Q8—64no—
318C3×D4—24no—
319C3×D4—24no—
320C3×D4—42no—
321C3×D4—616no—
322C3×D4C23×D318yes—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—34no—
326C2×C3×C4—34no—
327C2×C3×C4—616no—
328C2×C3×C4—64no—
329C2×C3×C4C23×D312yes—
330#67—216no—
331#67—616no—
332#67—616no—
333#67—128no—
334C2×Dic3—24no—
335C2×Dic3—216no—
336C2×Dic3—32no—
337C2×Dic3—38no—
338C2×Dic3—61no—
339C2×Dic3D3×D412yes—
340D12—38no—
341D12—64no—
342D12—616no—
343D12—64no—
344D12—122no—
345C4×D3—38no—
346C4×D3—34no—
347C4×D3—34no—
348C4×D3—38no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—616no—
352C4×D3—616no—
353C4×D3—616no—
354C4×D3D3×D414yes—
355C4×D3C23×D314yes—
356Dic6—24no—
357Dic6—616no—
358Dic6C23×D318yes—
359C3×C8—22no—
360C3×C8—34no—
361C3×C8C23×D314yes—
362C3⋊C8—34no—
363C3⋊C8—62no—
364C3⋊C8C23×D314yes—
365C2×C32—44no—
366C2×C32C2×#13512yescomplemented
367C2×C32C23×D411yescharacteristic
368C3⋊D3—44no—
369C3⋊D3C2×#13514yescomplemented
370C3×D3—24no—
371C24—91no—
372C24—182no—
373#41—316no—
374#41—68no—
375#41—916no—
376#41—188no—
377#41—1832no—
378C2×Q8—34no—
379C2×Q8—98no—
380C2×Q8—182no—
381C2×Q8—184no—
382C2×D4—64no—
383C2×D4—98no—
384C2×D4—92no—
385C2×D4—184no—
386C2×D4—184no—
387C2×D4—182no—
388C2×D4—1816no—
389C2×D4C2×D3212yes—
390C22×C4—32no—
391C22×C4—64no—
392C22×C4—94no—
393C22×C4—91no—
394C22×C4—94no—
395C22×C4—92no—
396C22×C4—91no—
397C22×C4—184no—
398C22×C4—1816no—
399C22×C4—182no—
400Q16—38no—
401Q16—98no—
402SD16—316no—
403SD16—916no—
404D8—98no—
405D8—94no—
406D8C2×D3214yescomplemented
407C2×C8—32no—
408C2×C8—38no—
409C2×C8—94no—
410C2×C8—98no—
411C2×C8—91no—
412C2×C8—94no—
413C2×C8C2×D3211yescharacteristic
414C22×C3—28no—
415C22×C3—21no—
416C22×C3—34no—
417C22×C3—44no—
418C22×C3—48no—
419C22×C3—64no—
420C22×C3—84no—
421C22×C3C2×D3×D412yes—
422C2×D3—24no—
423C2×D3—34no—
424C2×D3—38no—
425C2×D3—62no—
426C2×D3—64no—
427C2×D3—616no—
428C2×D3—68no—
429C2×D3—124no—
430C2×D3—1232no—
431C2×D3—128no—
432C2×D3—2416no—
433C2×D3—244no—
434C2×D3C2×D3×D414yes—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—34no—
438C3×C4—68no—
439C3×C4C2×D3×D412yes—
440C3×C4C24×D312yes—
441Dic3—28no—
442Dic3—34no—
443Dic3—62no—
444Dic3C2×D3×D414yes—
445C32C22×#13511yescharacteristic, complemented, Sylow
446C23—22no—
447C23—32no—
448C23—94no—
449C23—91no—
450C23—188no—
451C23—184no—
452C23—182no—
453C23—368no—
454Q8—38no—
455Q8—64no—
456Q8—188no—
457D4—22no—
458D4—616no—
459D4—94no—
460D4—1816no—
461D4—188no—
462D4—182no—
463D4C22×D3214yes—
464C2×C4—32no—
465C2×C4—34no—
466C2×C4—34no—
467C2×C4—616no—
468C2×C4—64no—
469C2×C4—94no—
470C2×C4—98no—
471C2×C4—91no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—1816no—
475C2×C4—188no—
476C2×C4C22×D3211yescharacteristic
477C8—34no—
478C8—92no—
479C8C22×D3212yes—
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—48no—
483C2×C3—64no—
484C2×C3—84no—
485C2×C3D3×#13514yescomplemented
486C2×C3C22×D3×D412yes—
487D3—24no—
488D3—38no—
489D3—64no—
490D3—128no—
491D3—244no—
492C22—24no—
493C22—34no—
494C22—44no—
495C22—64no—
496C22—92no—
497C22—94no—
498C22—188no—
499C22—184no—
500C22—3616no—
501C22—364no—
502C22D32×D411yescharacteristic
503C4—34no—
504C4—68no—
505C4—92no—
506C4D32×D411yescharacteristic
507C4C23×D3211yescharacteristic
508C3—21no—
509C3C2×D3×#13512yescomplemented
510C2—44no—
511C2—64no—
512C2—94no—
513C2—364no—
514C2#1059473012yesdirect product factor
515C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C22×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64312C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. C2×C3×#912C2semidirect
4. C2×#63935C2semidirect
5. C2×#63930C2semidirect
6. #10594730C2direct (N × H)
7. C2×#63808C2semidirect
8. C2×#63802C2semidirect
9. C2×D32×C8C2semidirect
12. C2×C3×#237C22semidirect
17. #64312C22semidirect
19. C2×#3799C22semidirect
21. C2×C32×D8C22semidirect
22. C2×#3753C22semidirect
23. D8×C3⋊D3C22semidirect
24. C2×#3745C22semidirect
26. C2×C3×#214C22semidirect
27. C3×#912C22semidirect
28. C2×C3×Dic12C22semidirect
29. C2×C3×D3×C8C22semidirect
30. #63935C22semidirect
31. #63930C22semidirect
32. C2×#3718C22semidirect
33. C2×#3717C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63808C22semidirect
37. #63802C22semidirect
38. D32×C8C22semidirect
47. C2×#912D3semidirect
63. C3×#237C23semidirect
78. #3799C23semidirect
81. C32×D8C23semidirect
83. #3753C23semidirect
85. #3745C23semidirect
87. C3×#214C23semidirect
89. C3×Dic12C23semidirect
90. C3×D3×C8C23semidirect
91. #3718C23semidirect
92. #3717C23semidirect
94. D3×C3⋊C8C23semidirect
102. C2×#237C2×D3semidirect
114. C2×C3×D8C2×D3semidirect
119. C2×#214C2×D3semidirect
127. #912C2×D3semidirect
130. C2×Dic12C2×D3semidirect
140. C2×D3×C8C2×D3semidirect
207. #237C22×D3semidirect
235. C3×D8C22×D3semidirect
242. #214C22×D3semidirect
249. Dic12C22×D3semidirect
257. D3×C8C22×D3semidirect
264. C2×C3⋊D3#135semidirect
296. C2×D8D32semidirect
366. C2×C32C2×#135semidirect
369. C3⋊D3C2×#135semidirect
406. D8C2×D32semidirect
445. C32C22×#135semidirect
485. C2×C3D3×#135semidirect
509. C3C2×D3×#135semidirect
514. C2#10594730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643122
C2×D8×C3⋊D32
C2×C3×#9122
C2×#639352
C2×#639302
#105947302
C2×#638082
C2×#638022
C2×D32×C82
C2×D3×#1353