Finite Group Databasebeta

← C2×#10595501 #11900446

Subgroups — C2×#10595501 #11900446

Order 1152.

4441 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×C3×#953C212yesmaximal, complemented
4C2×#63982C212yesmaximal, complemented
5C2×#63980C212yesmaximal, complemented
6#10595501C2116yesmaximal, direct product factor
7C2×#67⋊Dic3C214yesmaximal, complemented
8C2×#63962C212yesmaximal, complemented
9C2×#63957C211yesmaximal, characteristic, complemented
10C2×#5586—32nomaximal
11C25×C32C2211yescharacteristic
12C23×C3⋊Dic3—28no—
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2212yes—
15C23×C3⋊Dic3C2212yes—
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3⋊Dic3C2218yescomplemented
18C22×C3×#67C2212yes—
19C22×C3×#67C2214yes—
20C22×#627C2211yescharacteristic, complemented
21C22×#625C2211yescharacteristic, complemented
22C2×#3805—28no—
23C2×#3805C2218yescomplemented
24C22×D3×Dic3C2212yescomplemented
25C3×#953C22116yescomplemented
26C2×C3×#217C2212yes—
27C2×C3×#217C2214yes—
28#63982C22116yescomplemented
29#63980C22116yescomplemented
30#67⋊Dic3C22132yescomplemented
31C2×#3724C2212yescomplemented
32C2×Dic3⋊Dic3C2214yescomplemented
33#63962C22116yescomplemented
34C2×(C2×D3)⋊Dic3C2214yescomplemented
35#63957C2218yescomplemented
36C2×Dic32C2212yescomplemented
37C24×Dic3—32no—
38C24×Dic3—61no—
39C22×#237—32no—
40C2×C3×#120—32no—
41C2×#953D312yescomplemented
42C2×#939—34no—
43C2×#935—32no—
44C2×D4×Dic3—34no—
45#5586—332no—
46C2×#886—32no—
47C2×#67⋊C4—34no—
48C2×#878—34no—
49C2×#877—32no—
50C24×C32—24no—
51C24×C32—28no—
52C24×C32C2314yes—
53C24×C32C2311yescharacteristic
54C24×C32C2312yes—
55C23×C3×D3C2312yes—
56C22×C3⋊Dic3—24no—
57C22×C3⋊Dic3—28no—
58C22×C3⋊Dic3—28no—
59C22×C3⋊Dic3—232no—
60C22×C3⋊Dic3D418yescomplemented
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2314yes—
63C22×C3⋊Dic3C2318yes—
64C22×C3⋊Dic3C2318yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2314yes—
68C2×C3×#67—28no—
69C2×C3×#67—216no—
70C2×C3×#67C2318yes—
71C2×C3×#67C23116yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2314yes—
74C2×#627—24no—
75C2×#627C2314yescomplemented
76C2×#625—24no—
77C2×#625C2314yescomplemented
78#3805—232no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3C2318yescomplemented
81C3×#217C2318yes—
82C3×#217C23116yes—
83#3724C2318yescomplemented
84Dic3⋊Dic3C23116yescomplemented
85(C2×D3)⋊Dic3C23116yescomplemented
86Dic32C2318yescomplemented
87C2×#525—91noSylow
88C25×C3—21no—
89C25×C3C2×D312yes—
90C22×C3×D4—32no—
91C22×C3×D4—34no—
92C22×#67—32no—
93C22×#67C2×D312yes—
94C22×#67C2×D314yes—
95C23×Dic3—32no—
96C23×Dic3—34no—
97C23×Dic3—34no—
98C23×Dic3—32no—
99C23×Dic3—316no—
100C23×Dic3—32no—
101C23×Dic3—61no—
102C23×Dic3—62no—
103C23×Dic3—62no—
104C23×Dic3—61no—
105C23×Dic3—68no—
106C23×Dic3—616no—
107C23×Dic3—616no—
108C2×#237—316no—
109C2×#237—616no—
110C22×C4×D3—32no—
111C22×Dic6—32no—
112C3×#120—316no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—34no—
115#953C2×D3116yescomplemented
116C2×#217—34no—
117C2×#217C2×D312yes—
118C2×#217C2×D314yes—
119#939—332no—
120#935—316no—
121D4×Dic3—332no—
122C2×(C2×D3)⋊C4—34no—
123C2×C4⋊Dic3—34no—
124C2×Dic3⋊C4—34no—
125C2×Dic3⋊C4—34no—
126C2×C4×Dic3—34no—
127#886—316no—
128#67⋊C4—332no—
129#878—332no—
130#877—316no—
131C23×C32—232no—
132C23×C32—28no—
133C23×C32—24no—
134C23×C32—24no—
135C23×C32—24no—
136C23×C32—216no—
137C23×C32C2×D414yes—
138C23×C32#4118yescomplemented
139C23×C32C2412yes—
140C23×C32C2414yes—
141C23×C32C2411yescharacteristic
142C22×C3×D3—24no—
143C22×C3×D3—28no—
144C22×C3×D3C2414yes—
145C2×C3⋊Dic3—28no—
146C2×C3⋊Dic3—24no—
147C2×C3⋊Dic3—216no—
148C2×C3⋊Dic3—216no—
149C2×C3⋊Dic3C2×D414yes—
150C2×C3⋊Dic3C2×D414yes—
151C2×C3⋊Dic3C2×D4116yescomplemented
152C2×C3⋊Dic3C2414yes—
153C2×C3⋊Dic3C2412yes—
154C2×C3⋊Dic3C2412yes—
155C3×#67—216no—
156C3×#67—232no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—28no—
159C2×C3×Dic3C2418yes—
160C2×C3×Dic3C2414yes—
161#627—28no—
162#625—28no—
163D3×Dic3—216no—
164C22×#41—91no—
165C24×C4—91no—
166#525—916no—
167C2×#123—92no—
168C2×C22⋊Q8—92no—
169C2×#121—92no—
170C2×#120—32no—
171C2×C4×D4—94no—
172C2×#117—91no—
173C24×C3—216no—
174C24×C3—28no—
175C24×C3—28no—
176C24×C3—216no—
177C24×C3—24no—
178C24×C3—22no—
179C24×C3—21no—
180C24×C3—32no—
181C24×C3C22×D318yes—
182C24×C3C22×D312yes—
183C24×C3C22×D314yes—
184C23×D3C22×D312yes—
185C2×C3×D4—316no—
186C2×C3×D4—38no—
187C2×C3×D4—68no—
188C2×C3×D4—616no—
189C22×C3×C4—34no—
190C22×C3×C4—32no—
191C2×#67—28no—
192C2×#67—216no—
193C2×#67—38no—
194C2×#67—68no—
195C2×#67C22×D3116yes—
196C2×#67C22×D318yes—
197C22×Dic3—316no—
198C22×Dic3—38no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—316no—
202C22×Dic3—316no—
203C22×Dic3—38no—
204C22×Dic3—34no—
205C22×Dic3—38no—
206C22×Dic3—68no—
207C22×Dic3—64no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—68no—
211C22×Dic3—68no—
212C22×Dic3—64no—
213C22×Dic3—62no—
214C22×Dic3—68no—
215C22×Dic3—616no—
216C22×Dic3—616no—
217C22×Dic3—664no—
218C22×Dic3—616no—
219C22×Dic3—616no—
220C22×Dic3—664no—
221C22×Dic3—68no—
222C22×Dic3—68no—
223C22×Dic3C22×D314yes—
224C22×Dic3C22×D312yes—
225#237—664no—
226C2×C4×D3—38no—
227C2×C4×D3—68no—
228C2×Dic6—38no—
229C2×Dic6—68no—
230C3×C22⋊C4—38no—
231C3×C22⋊C4—316no—
232#217—316no—
233#217C22×D318yes—
234#217C22×D3116yes—
235(C2×D3)⋊C4—316no—
236C4⋊Dic3—316no—
237Dic3⋊C4—316no—
238Dic3⋊C4—316no—
239C4×Dic3—316no—
240C22×C32—232no—
241C22×C32—28no—
242C22×C32—216no—
243C22×C32—24no—
244C22×C32—24no—
245C22×C32—24no—
246C22×C32C22×D414yes—
247C22×C32C22×D412yes—
248C22×C32C2×#4114yes—
249C22×C32C2×#4118yescomplemented
250C22×C32C2511yescharacteristic
251C2×C3×D3—24no—
252C2×C3×D3—28no—
253C2×C3×D3—48no—
254C3⋊Dic3—24no—
255C3⋊Dic3C22×D414yes—
256C3⋊Dic3C22×D414yes—
257C3×Dic3—24no—
258C3×Dic3—28no—
259C25D3211yescharacteristic
260C2×#41—98no—
261C2×#41—188no—
262C22×Q8—91no—
263C22×D4—34no—
264C22×D4—32no—
265C22×D4—91no—
266C23×C4—92no—
267C23×C4—91no—
268C23×C4—92no—
269C23×C4—92no—
270C23×C4—91no—
271C23×C4—98no—
272C23×C4—188no—
273#123—916no—
274C22⋊Q8—916no—
275#121—916no—
276#120—316no—
277C4×D4—932no—
278#117—98no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—94no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—34no—
283C2×C22⋊C4—94no—
284C2×C42—92no—
285C23×C3—216no—
286C23×C3—28no—
287C23×C3—264no—
288C23×C3—264no—
289C23×C3—28no—
290C23×C3—28no—
291C23×C3—232no—
292C23×C3—216no—
293C23×C3—28no—
294C23×C3—28no—
295C23×C3—28no—
296C23×C3—232no—
297C23×C3—24no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—28no—
301C23×C3—24no—
302C23×C3—34no—
303C23×C3—64no—
304C23×C3—68no—
305C23×C3D3×D418yes—
306C23×C3#237116yescomplemented
307C23×C3C23×D314yes—
308C23×C3C23×D318yes—
309C23×C3C23×D312yes—
310C22×D3—24no—
311C22×D3—28no—
312C22×D3C23×D314yes—
313C3×D4—616no—
314C3×D4—632no—
315C2×C3×C4—38no—
316C2×C3×C4—34no—
317C2×C3×C4—64no—
318C2×C3×C4—68no—
319#67—216no—
320#67—232no—
321#67—616no—
322C2×Dic3—24no—
323C2×Dic3—28no—
324C2×Dic3—38no—
325C2×Dic3—38no—
326C2×Dic3—332no—
327C2×Dic3—34no—
328C2×Dic3—34no—
329C2×Dic3—38no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—616no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—64no—
336C2×Dic3—616no—
337C2×Dic3—632no—
338C2×Dic3—632no—
339C2×Dic3—632no—
340C2×Dic3—632no—
341C2×Dic3—616no—
342C2×Dic3—68no—
343C2×Dic3—616no—
344C2×Dic3—68no—
345C2×Dic3C23×D318yes—
346C2×Dic3C23×D314yes—
347C4×D3—616no—
348Dic6—616no—
349C2×C32—24no—
350C2×C32—28no—
351C2×C32#52514yescomplemented
352C2×C32C23×D411yescharacteristic
353C2×C32C22×#4112yes—
354C3×D3—44no—
355C24—28no—
356C24—24no—
357C24—32no—
358C24C2×D3214yes—
359C24C2×D3212yes—
360C24C2×D3211yescharacteristic
361#41—1832no—
362C2×Q8—94no—
363C2×Q8—184no—
364C2×D4—316no—
365C2×D4—38no—
366C2×D4—616no—
367C2×D4—68no—
368C2×D4—94no—
369C2×D4—184no—
370C22×C4—34no—
371C22×C4—32no—
372C22×C4—98no—
373C22×C4—94no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—98no—
377C22×C4—98no—
378C22×C4—98no—
379C22×C4—94no—
380C22×C4—92no—
381C22×C4—188no—
382C22×C4—188no—
383C22×C4—188no—
384C22×C4—1832no—
385C22×C4—184no—
386C4⋊C4—98no—
387C4⋊C4—916no—
388C22⋊C4—38no—
389C22⋊C4—316no—
390C22⋊C4—916no—
391C42—98no—
392C22×C3—28no—
393C22×C3—264no—
394C22×C3—264no—
395C22×C3—28no—
396C22×C3—28no—
397C22×C3—232no—
398C22×C3—216no—
399C22×C3—28no—
400C22×C3—28no—
401C22×C3—28no—
402C22×C3—216no—
403C22×C3—232no—
404C22×C3—24no—
405C22×C3—28no—
406C22×C3—24no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—64no—
410C22×C3—68no—
411C22×C3—128no—
412C22×C3C2×D3×D418yes—
413C22×C3C2×D3×D414yes—
414C22×C3C2×#23718yes—
415C22×C3C2×#237116yescomplemented
416C22×C3C24×D312yes—
417C2×D3—24no—
418C2×D3—28no—
419C2×D3—48no—
420C3×C4—64no—
421C3×C4—68no—
422Dic3—24no—
423Dic3—28no—
424Dic3—38no—
425Dic3—38no—
426Dic3—64no—
427Dic3—64no—
428Dic3—68no—
429Dic3—68no—
430C32C2×#52511yescharacteristic, complemented, Sylow
431C23—232no—
432C23—24no—
433C23—24no—
434C23—216no—
435C23—28no—
436C23—24no—
437C23—34no—
438C23—68no—
439C23—64no—
440C23#380518yescomplemented
441C23#381114yes—
442C23C22×D3214yes—
443C23C22×D3212yes—
444C23C22×D3211yescharacteristic
445Q8—188no—
446D4—632no—
447D4—616no—
448D4—188no—
449C2×C4—38no—
450C2×C4—34no—
451C2×C4—68no—
452C2×C4—64no—
453C2×C4—94no—
454C2×C4—94no—
455C2×C4—916no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—94no—
459C2×C4—1816no—
460C2×C4—1816no—
461C2×C4—1816no—
462C2×C4—188no—
463C2×C4—184no—
464C2×C3—216no—
465C2×C3—28no—
466C2×C3—28no—
467C2×C3—216no—
468C2×C3—22no—
469C2×C3—21no—
470C2×C3—24no—
471C2×C3—124no—
472C2×C3#558618yescomplemented
473C2×C3C22×D3×D412yes—
474C2×C3C22×#23714yes—
475D3—44no—
476C22—232no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—216no—
481C22—28no—
482C22—68no—
483C22—64no—
484C22—128no—
485C22C2×#380514yes—
486C22C2×#380518yescomplemented
487C22C2×#381114yes—
488C22C2×#381112yes—
489C22C23×D3211yescharacteristic
490C4—68no—
491C4—64no—
492C4—94no—
493C4—94no—
494C4—184no—
495C3—21no—
496C3C2×#558612yescomplemented
497C2—28no—
498C2—24no—
499C2—124no—
500C2#1059550114yesdirect product factor
501C2C22×#380512yes—
502C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C24×C3⋊Dic3C2semidirect
2. C22×#3805C2semidirect
3. C2×C3×#953C2semidirect
4. C2×#63982C2semidirect
5. C2×#63980C2semidirect
6. #10595501C2direct (N × H)
7. C2×#67⋊Dic3C2semidirect
8. C2×#63962C2semidirect
9. C2×#63957C2semidirect
17. C23×C3⋊Dic3C22semidirect
20. C22×#627C22semidirect
21. C22×#625C22semidirect
23. C2×#3805C22semidirect
24. C22×D3×Dic3C22semidirect
25. C3×#953C22semidirect
28. #63982C22semidirect
29. #63980C22semidirect
30. #67⋊Dic3C22semidirect
31. C2×#3724C22semidirect
32. C2×Dic3⋊Dic3C22semidirect
33. #63962C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. #63957C22semidirect
36. C2×Dic32C22semidirect
41. C2×#953D3semidirect
60. C22×C3⋊Dic3D4semidirect
75. C2×#627C23semidirect
77. C2×#625C23semidirect
80. C2×D3×Dic3C23semidirect
83. #3724C23semidirect
84. Dic3⋊Dic3C23semidirect
85. (C2×D3)⋊Dic3C23semidirect
86. Dic32C23semidirect
115. #953C2×D3semidirect
138. C23×C32#41semidirect
151. C2×C3⋊Dic3C2×D4semidirect
249. C22×C32C2×#41semidirect
306. C23×C3#237semidirect
351. C2×C32#525semidirect
415. C22×C3C2×#237semidirect
430. C32C2×#525semidirect
440. C23#3805semidirect
472. C2×C3#5586semidirect
486. C22C2×#3805semidirect
496. C3C2×#5586semidirect
500. C2#10595501direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3⋊Dic32
C22×#38052
C2×C3×#9532
C2×#639822
C2×#639802
#105955012
C2×#67⋊Dic32
C2×#639622
C2×#639572
C2×#55863