Finite Group Databasebeta

← C2×#10594670 #11918500

Subgroups — C2×#10594670 #11918500

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C22×#3743C211yesmaximal, characteristic, complemented
3C2×C3×#901C212yesmaximal, complemented
4C2×#63818C211yesmaximal, characteristic, complemented
5C2×#63815C212yesmaximal, complemented
6C2×#63804C214yesmaximal, complemented
7#10594670C2116yesmaximal, direct product factor
8C2×D3×ΓL(1,𝔽25)C214yesmaximal, complemented
9C2×#5750—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2212yes—
12C2×#3811C412yes—
13C2×#3805C412yes—
14#64306C418yes—
15#64306C2218yes—
16C2×#3802C411yescharacteristic
17C2×C4×D32C2212yes—
18C2×#3798C2212yes—
19C2×#3797C411yescharacteristic
20C2×#3796C412yes—
21C22×C32×C8C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×#3743C2212yes—
24C2×#3743C2218yescomplemented
25C2×#3743C2212yescomplemented
26C2×C3×#208C2212yescomplemented
27C3×#901C22116yescomplemented
28C2×C3×ΓL(1,𝔽25)C2214yescomplemented
29C2×C3×D3×C8C2214yescomplemented
30C2×#3712C2212yes—
31C2×#3711C2214yescomplemented
32#63818C2218yescomplemented
33C2×#3710C2212yescomplemented
34#63815C22116yescomplemented
35C2×D3×C3⋊C8C2214yescomplemented
36#63804C22132yescomplemented
37D3×ΓL(1,𝔽25)C22132yescomplemented
38C2×D3×#41—32no—
39C2×C3×#131—32no—
40C2×#948—32no—
41#5750—332no—
42C2×#907—32no—
43C2×#907—34no—
44C2×D3×M16—32no—
45C2×D3×M16—34no—
46C2×#901—34no—
47C2×#901D312yescomplemented
48C22×ΓL(1,𝔽25)—32no—
49C22×ΓL(1,𝔽25)—34no—
50C22×ΓL(1,𝔽25)—61no—
51C23×C3⋊D3C2×C411yescharacteristic
52C22×D32C2×C412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2×C411yescharacteristic
55C2×C4×C3⋊D3C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C414yes—
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C4×C3⋊D3C2314yes—
61C2×C3×#67C2×C414yes—
62C3×#235C2×C418yes—
63C3×#235C2318yes—
64C2×C3×D12C2×C412yes—
65C2×C3×C4×D3C2314yes—
66C2×C3×Dic6C2×C412yes—
67#3811C2×C4116yes—
68C2×#627C2×C412yes—
69C2×#626C2×C414yes—
70C2×#625C2×C412yes—
71C2×#624C2×C412yes—
72#3805C2×C4116yes—
73C2×D3×Dic3C2×C414yes—
74#3802C2×C418yes—
75C4×D32C2×C418yes—
76C4×D32C2318yes—
77#3798C2×C418yes—
78#3798C2318yes—
79#3797C2×C418yes—
80#3796C2×C4116yes—
81C2×C32×C8C2312yes—
82C2×C32×C8C2314yescomplemented
83C2×C3⋊(C3⋊C8)C2312yes—
84C2×C3⋊(C3⋊C8)C2314yescomplemented
85#3743C2318yes—
86#3743C2318yescomplemented
87C3×#208C2318yescomplemented
88C2×C3×C3⋊C8C2314yes—
89C3×ΓL(1,𝔽25)C23116yescomplemented
90C3×D3×C8C23116yescomplemented
91#3712C2318yes—
92#3711C23116yescomplemented
93#3710C2318yescomplemented
94D3×C3⋊C8C23116yescomplemented
95C2×#568—91noSylow
96C2×C3×#41—32no—
97D3×#41—316no—
98D3×#41—316no—
99C2×#239—32no—
100C2×D3×Q8—32no—
101C2×#237—34no—
102C2×#237—32no—
103C2×D3×D4—34no—
104C2×D3×D4—32no—
105C2×#235—34no—
106C2×#235C2×D312yes—
107C22×C4×D3—32no—
108C22×C4×D3—34no—
109C22×C4×D3—61no—
110C3×#131—316no—
111C2×C3×M16—32no—
112C2×C3×M16—34no—
113C22×C3×C8—21no—
114C22×C3×C8—34no—
115C22×C3×C8C2×D312yescomplemented
116#948—316no—
117C2×#208—34no—
118C2×#208C2×D312yescomplemented
119C22×C3⋊C8—32no—
120C22×C3⋊C8—34no—
121C22×C3⋊C8—61no—
122#907—316no—
123#907—332no—
124D3×M16—316no—
125D3×M16—332no—
126#901—332no—
127#901C2×D3116yescomplemented
128C2×ΓL(1,𝔽25)—34no—
129C2×ΓL(1,𝔽25)—32no—
130C2×ΓL(1,𝔽25)—32no—
131C2×ΓL(1,𝔽25)—32no—
132C2×ΓL(1,𝔽25)—32no—
133C2×ΓL(1,𝔽25)—316no—
134C2×ΓL(1,𝔽25)—34no—
135C2×ΓL(1,𝔽25)—332no—
136C2×ΓL(1,𝔽25)—62no—
137C2×ΓL(1,𝔽25)—62no—
138C2×ΓL(1,𝔽25)—68no—
139C2×ΓL(1,𝔽25)C2×D314yescomplemented
140C2×D3×C8—34no—
141C2×D3×C8—34no—
142C2×D3×C8C2×D314yescomplemented
143C23×C32C22×C411yescharacteristic
144C22×C3⋊D3—42no—
145C22×C3⋊D3C22×C411yescharacteristic
146C22×C3⋊D3C22×C411yescharacteristic
147C22×C3⋊D3C22×C414yes—
148C22×C3×D3C22×C414yes—
149C2×D32—44no—
150C2×D32C22×C418yes—
151C2×C32×C4C22×C411yescharacteristic
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C32×C4C2412yes—
155C2×C3⋊Dic3C22×C411yescharacteristic
156C2×C3⋊Dic3C22×C414yes—
157C2×C3⋊Dic3C22×C411yescharacteristic
158C4×C3⋊D3C22×C414yes—
159C4×C3⋊D3C22×C414yes—
160C4×C3⋊D3C22×C412yes—
161C4×C3⋊D3C22×C412yes—
162C4×C3⋊D3C2412yes—
163C4×C3⋊D3C2412yes—
164C3×#67C22×C4116yes—
165C2×C3×Dic3C22×C414yes—
166C3×D12C22×C418yes—
167C3×C4×D3C22×C418yes—
168C3×C4×D3C2418yes—
169C3×Dic6C22×C418yes—
170#627C22×C418yes—
171#626C22×C4116yes—
172#625C22×C418yes—
173#624C22×C418yes—
174D3×Dic3C22×C4116yes—
175C32×C8C2414yes—
176C3⋊(C3⋊C8)C2414yes—
177C3×C3⋊C8C2418yes—
178C22×#41—91no—
179#568—916no—
180C2×#131—32no—
181C2×#131—94no—
182C2×#131—92no—
183C22×M16—94no—
184C22×M16—91no—
185C22×M16—91no—
186C23×D3—32no—
187C23×D3—34no—
188C23×D3—61no—
189C3×#41—38no—
190C3×#41—38no—
191C2×C3×Q8—32no—
192C2×C3×D4—34no—
193C2×C3×D4—32no—
194C22×C3×C4—21no—
195C22×C3×C4—34no—
196C22×C3×C4C22×D312yes—
197C2×#67—34no—
198C2×#67—34no—
199C2×#67C4×D314yes—
200C22×Dic3—32no—
201C22×Dic3—34no—
202C22×Dic3—61no—
203#239—316no—
204D3×Q8—316no—
205#237—332no—
206#237—316no—
207D3×D4—332no—
208D3×D4—316no—
209#235—316no—
210#235—316no—
211#235C4×D318yes—
212#235C22×D318yes—
213C2×D12—34no—
214C2×D12C4×D312yes—
215C2×C4×D3—34no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—38no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—38no—
222C2×C4×D3—34no—
223C2×C4×D3—316no—
224C2×C4×D3—316no—
225C2×C4×D3—64no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—64no—
231C2×C4×D3C22×D314yes—
232C2×Dic6—34no—
233C2×Dic6C4×D312yes—
234C3×M16—38no—
235C3×M16—316no—
236C2×C3×C8—22no—
237C2×C3×C8—24no—
238C2×C3×C8—34no—
239C2×C3×C8—316no—
240C2×C3×C8C22×D312yes—
241C2×C3×C8C22×D312yes—
242C2×C3×C8C22×D318yescomplemented
243#208—316no—
244#208C22×D318yescomplemented
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—38no—
248C2×C3⋊C8—316no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8C22×D314yes—
252ΓL(1,𝔽25)—316no—
253ΓL(1,𝔽25)—38no—
254ΓL(1,𝔽25)—38no—
255ΓL(1,𝔽25)—38no—
256ΓL(1,𝔽25)—38no—
257ΓL(1,𝔽25)—316no—
258ΓL(1,𝔽25)—68no—
259ΓL(1,𝔽25)—68no—
260ΓL(1,𝔽25)C22×D3116yescomplemented
261D3×C8—316no—
262D3×C8—316no—
263D3×C8C22×D3116yescomplemented
264C22×C32—22no—
265C22×C32C23×C412yes—
266C22×C32C23×C411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3C23×C412yes—
271C2×C3⋊D3C23×C412yes—
272C2×C3×D3—28no—
273C2×C3×D3C23×C418yes—
274D32—48no—
275C32×C4C23×C412yes—
276C32×C4C23×C411yescharacteristic
277C32×C4C2511yescharacteristic
278C3⋊Dic3C23×C412yes—
279C3⋊Dic3C23×C412yes—
280C3×Dic3C23×C418yes—
281C2×#41—32no—
282C2×#41—92no—
283C2×#41—92no—
284C2×#41—92no—
285C2×#41—98no—
286C2×#41—98no—
287C22×Q8—91no—
288C22×D4—92no—
289C22×D4—91no—
290C23×C4—92no—
291C23×C4—91no—
292#131—316no—
293#131—932no—
294#131—916no—
295C2×M16—32no—
296C2×M16—34no—
297C2×M16—92no—
298C2×M16—932no—
299C2×M16—94no—
300C2×M16—98no—
301C2×M16—92no—
302C2×M16—92no—
303C2×M16—98no—
304C22×C8—34no—
305C22×C8—92no—
306C22×C8—94no—
307C22×C8—91no—
308C22×C8D3211yescharacteristic, complemented
309C23×C3—21no—
310C23×C3—34no—
311C23×C3C2×C4×D312yes—
312C22×D3—32no—
313C22×D3—32no—
314C22×D3—38no—
315C22×D3—316no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—64no—
319C22×D3—128no—
320C22×D3—124no—
321C22×D3—124no—
322C22×D3C2×C4×D314yes—
323C3×Q8—38no—
324C3×D4—316no—
325C3×D4—38no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—34no—
331C2×C3×C4—38no—
332C2×C3×C4—38no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D314yes—
335C2×C3×C4C23×D314yes—
336C2×C3×C4C23×D312yes—
337#67—316no—
338#67—316no—
339#67C2×C4×D3116yes—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—38no—
343C2×Dic3—316no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—64no—
347C2×Dic3C2×C4×D314yes—
348D12—316no—
349D12C2×C4×D318yes—
350C4×D3—316no—
351C4×D3—34no—
352C4×D3—34no—
353C4×D3—38no—
354C4×D3—38no—
355C4×D3—34no—
356C4×D3—34no—
357C4×D3—316no—
358C4×D3—62no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3C2×C4×D318yes—
365C4×D3C23×D318yes—
366Dic6—316no—
367Dic6C2×C4×D318yes—
368C3×C8—24no—
369C3×C8—38no—
370C3×C8C23×D314yes—
371C3×C8C23×D314yes—
372C3⋊C8—34no—
373C3⋊C8—34no—
374C3⋊C8—64no—
375C3⋊C8C23×D318yes—
376C2×C32—22no—
377C2×C32#56812yescomplemented
378C2×C32C24×C411yescharacteristic
379C3⋊D3—22no—
380C3⋊D3—22no—
381C3×D3—28no—
382C24—92no—
383C24—91no—
384#41—38no—
385#41—38no—
386#41—98no—
387#41—98no—
388#41—916no—
389#41—916no—
390C2×Q8—32no—
391C2×Q8—92no—
392C2×Q8—98no—
393C2×D4—34no—
394C2×D4—32no—
395C2×D4—94no—
396C2×D4—916no—
397C2×D4—98no—
398C2×D4—92no—
399C22×C4—34no—
400C22×C4—98no—
401C22×C4—92no—
402C22×C4—98no—
403C22×C4—94no—
404C22×C4—91no—
405C22×C4—94no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—94no—
411C22×C4C2×D3211yescharacteristic
412M16—38no—
413M16—316no—
414M16—98no—
415M16—916no—
416M16—98no—
417M16—98no—
418C2×C8—34no—
419C2×C8—316no—
420C2×C8—98no—
421C2×C8—916no—
422C2×C8—94no—
423C2×C8—92no—
424C2×C8C2×D3212yes—
425C2×C8C2×D3214yescomplemented
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—38no—
431C22×C3—68no—
432C22×C3C22×C4×D314yes—
433C22×C3C22×C4×D312yes—
434C2×D3—28no—
435C2×D3—34no—
436C2×D3—34no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—1216no—
444C2×D3—128no—
445C2×D3—128no—
446C2×D3C22×C4×D318yes—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—38no—
451C3×C4C22×C4×D314yes—
452C3×C4C22×C4×D312yes—
453C3×C4C24×D312yes—
454Dic3—34no—
455Dic3—34no—
456Dic3—62no—
457Dic3—62no—
458Dic3C22×C4×D318yes—
459C32C2×#56811yescharacteristic, complemented, Sylow
460C23—34no—
461C23—98no—
462C23—91no—
463C23—91no—
464C23—94no—
465C23—362no—
466C23—364no—
467C23C4×D3211yescharacteristic
468Q8—38no—
469Q8—98no—
470D4—316no—
471D4—38no—
472D4—916no—
473D4—98no—
474C2×C4—34no—
475C2×C4—38no—
476C2×C4—38no—
477C2×C4—98no—
478C2×C4—916no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—94no—
482C2×C4—92no—
483C2×C4—94no—
484C2×C4—94no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4C4×D3211yescharacteristic
489C2×C4C4×D3212yes—
490C2×C4C22×D3212yes—
491C2×C4C22×D3211yescharacteristic
492C8—38no—
493C8—94no—
494C8C22×D3214yes—
495C2×C3—24no—
496C2×C3—24no—
497C2×C3—21no—
498C2×C3—22no—
499C2×C3—68no—
500C2×C3#575014yescomplemented
501C2×C3C23×C4×D312yes—
502D3—28no—
503D3—64no—
504D3—64no—
505D3—122no—
506D3—122no—
507C22—22no—
508C22—38no—
509C22—68no—
510C22—92no—
511C22—92no—
512C22—182no—
513C22—182no—
514C22—364no—
515C22—368no—
516C22C2×C4×D3212yes—
517C22C2×C4×D3211yescharacteristic
518C4—38no—
519C4—92no—
520C4—92no—
521C4C2×C4×D3211yescharacteristic
522C4C2×C4×D3212yes—
523C4C23×D3211yescharacteristic
524C3—21no—
525C3C2×#575012yescomplemented
526C2—22no—
527C2—68no—
528C2—182no—
529C2—182no—
530C2#1059467012yesdirect product factor
531C2C22×C4×D3211yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C23×C4
prime radicalC2×#64306C2
cosocleC32×C4C25
hypercenterC22×C8D32
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#3743C2semidirect
3. C2×C3×#901C2semidirect
4. C2×#63818C2semidirect
5. C2×#63815C2semidirect
6. C2×#63804C2semidirect
7. #10594670C2direct (N × H)
8. C2×D3×ΓL(1,𝔽25)C2semidirect
21. C22×C32×C8C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
24. C2×#3743C22semidirect
25. C2×#3743C22semidirect
26. C2×C3×#208C22semidirect
27. C3×#901C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
31. C2×#3711C22semidirect
32. #63818C22semidirect
33. C2×#3710C22semidirect
34. #63815C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63804C22semidirect
37. D3×ΓL(1,𝔽25)C22semidirect
47. C2×#901D3semidirect
82. C2×C32×C8C23semidirect
84. C2×C3⋊(C3⋊C8)C23semidirect
86. #3743C23semidirect
87. C3×#208C23semidirect
89. C3×ΓL(1,𝔽25)C23semidirect
90. C3×D3×C8C23semidirect
92. #3711C23semidirect
93. #3710C23semidirect
94. D3×C3⋊C8C23semidirect
115. C22×C3×C8C2×D3semidirect
118. C2×#208C2×D3semidirect
127. #901C2×D3semidirect
139. C2×ΓL(1,𝔽25)C2×D3semidirect
142. C2×D3×C8C2×D3semidirect
242. C2×C3×C8C22×D3semidirect
244. #208C22×D3semidirect
260. ΓL(1,𝔽25)C22×D3semidirect
263. D3×C8C22×D3semidirect
308. C22×C8D32semidirect
377. C2×C32#568semidirect
425. C2×C8C2×D32semidirect
459. C32C2×#568semidirect
500. C2×C3#5750semidirect
525. C3C2×#5750semidirect
530. C2#10594670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37432
C2×C3×#9012
C2×#638182
C2×#638152
C2×#638042
#105946702
C2×D3×ΓL(1,𝔽25)2
C2×#57503