Finite Group Databasebeta

← #11860900

Subgroups — #11860900

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2#10594361C212yesmaximal, complemented
3C3⋊D3×#107C211yesmaximal, characteristic, complemented
4C3×#4873C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6Dic3×Dic12C211yesmaximal, characteristic, complemented
7Dic3×D24C211yesmaximal, characteristic, complemented
8#10590700C211yesmaximal, characteristic, complemented
9#10590612C212yesmaximal, complemented
10#10590478C212yesmaximal, complemented
11#10590454C212yesmaximal, complemented
12#79721—31nomaximal
13#79589—31nomaximal
14C2×#3796C2212yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic
19C3×#893C2212yes—
20C3×#887C2212yes—
21C4×#626—22no—
22Dic3×D12C2212yes—
23#63881—22no—
24#63877—22no—
25D3×Dic3⋊C4—22no—
26#63874C2211yescharacteristic
27Dic3×Dic6C2212yes—
28C2×#3715C2212yes—
29C2×#3712C2211yescharacteristic
30#63810C418yescomplemented
31C32×#107C2211yescharacteristic
32#63645C2211yescharacteristic
33#63634C2212yes—
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38#63566C2212yes—
39#63563C2212yes—
40#63554C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×#919—31no—
43C2×#912—31no—
44#5574—32no—
45#5546—32no—
46C3×C4×Q16—31no—
47C3×C4×D8—31no—
48Dic3×Q16—31no—
49Dic3×D8—31no—
50#5026—32no—
51#5018—32no—
52D3×#107—31no—
53D3×#107—31no—
54D3×#107—61no—
55#4873D311yescharacteristic, complemented
56#4872D311yescharacteristic, complemented
57#4817—32no—
58#4803—32no—
59#4771—32no—
60#4757—32no—
61C4×Dic12—31no—
62C4×D24—31no—
63#4689—31no—
64#4689—31no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6C2312yes—
70C2×#626—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77C4⋊(C3⋊Dic3)C2312yes—
78#3750—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C8×C3⋊D3C2×C414yescomplemented
81C3×(C2×D3)⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3C2311yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D24C2×C414yescomplemented
90#3724D411yescharacteristic
91#3724D411yescharacteristic
92Dic3⋊Dic3—22no—
93#3722D411yescharacteristic
94#3722D411yescharacteristic
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3715C2×C418yescomplemented
98#3712—22no—
99#2951—91noSylow
100C2×#239—32no—
101C2×#237—32no—
102C2×C3×Q16—31no—
103C2×C3×D8—31no—
104C3×C4×Q8—32no—
105C3×C4×D4—32no—
106Q8×Dic3—32no—
107C2×#215—32no—
108D4×Dic3—32no—
109C2×#214—32no—
110C4×#67—62no—
111C2×Dic3⋊C4—62no—
112#919—38no—
113#912—38no—
114C2×Dic12C2×D311yescharacteristic
115C2×D24C2×D311yescharacteristic
116C2×ΓL(1,𝔽25)—31no—
117C2×ΓL(1,𝔽25)—31no—
118C2×D3×C8—31no—
119C2×D3×C8—31no—
120C2×D3×C8—61no—
121#893—62no—
122#893C2×D312yes—
123D3×C4⋊C4—32no—
124D3×C4⋊C4—32no—
125D3×C4⋊C4—62no—
126D3×C4⋊C4—62no—
127#887C2×D312yes—
128#67⋊C4—62no—
129#877—62no—
130C4×D12—32no—
131C4×D12—62no—
132#872—31no—
133#872—31no—
134#872—62no—
135C4×Dic6—32no—
136C3×#107—21no—
137C3×#107C2×D311yescharacteristic
138C3×#107C2×D311yescharacteristic
139C3×#103—32no—
140C3×#102—32no—
141C3×C4×C8—31no—
142C3×C4×C8—31no—
143#835—32no—
144#832—32no—
145#821—32no—
146#818—31no—
147#818—31no—
148#818—61no—
149#816—32no—
150#815—31no—
151#815—31no—
152C8×Dic3C2×D311yescharacteristic
153C8×Dic3C2×D311yescharacteristic
154#810C2×D312yes—
155#809C2×D312yes—
156#807—32no—
157#807—32no—
158#807—62no—
159#803—31no—
160#803—31no—
161C22×C3⋊D3C2×D411yescharacteristic
162C22×C3×D3—22no—
163C2×C32×C4—22no—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4×C3⋊D3—82no—
168C4×C3⋊D3C22×C412yes—
169C4×C3⋊D3#4112yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C2×C3×Dic3C2×D411yescharacteristic
175C3×D12—22no—
176C3×D12C22×C414yes—
177C3×C4×D3—82no—
178C3×Dic6—22no—
179C3×Dic6C22×C414yes—
180#626—28no—
181D3×Dic3—28no—
182D3×Dic3—82no—
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)C22×C412yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187C2×#135—91no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—31no—
192C4×Q16—91no—
193C4×D8—31no—
194C4×D8—91no—
195C2×#107—91no—
196#417—92no—
197#405—91no—
198C2×C3×Q8—32no—
199C2×C3×D4—32no—
200C22×C3×C4—62no—
201C2×#67—62no—
202C22×Dic3—62no—
203C22×Dic3—62no—
204#239—38no—
205#239—64no—
206#237—38no—
207#237—64no—
208C2×D12—62no—
209C2×D12C22×D312yes—
210C2×C4×D3—22no—
211C2×C4×D3—31no—
212C2×C4×D3—31no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—122no—
219C2×Dic6C22×D312yes—
220C3×Q16—34no—
221C3×D8—34no—
222C2×C3×C8—21no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—22no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—62no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—62no—
235#217—62no—
236#215—38no—
237#214—38no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—31no—
240(C2×D3)⋊C4—31no—
241(C2×D3)⋊C4—31no—
242(C2×D3)⋊C4—31no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3—32no—
245C4⋊Dic3—32no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248Dic3⋊C4—22no—
249Dic3⋊C4—31no—
250Dic3⋊C4—31no—
251Dic3⋊C4—31no—
252Dic3⋊C4—31no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—122no—
257C4×Dic3—22no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3C22×D311yescharacteristic
261C4×Dic3C22×D311yescharacteristic
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12C4×D314yescomplemented
268D24C4×D314yescomplemented
269ΓL(1,𝔽25)—62no—
270ΓL(1,𝔽25)—62no—
271D3×C8—34no—
272D3×C8—34no—
273D3×C8—64no—
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3C4×D412yes—
278C2×C3×D3—24no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C32×C4—42no—
282C32×C4C23×C411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—42no—
285C3⋊Dic3C4×D412yes—
286C3×Dic3—24no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—21no—
290C3×Dic3—21no—
291C2×#41—92no—
292#135—98no—
293C2×Q16—31no—
294C2×SD16—92no—
295C2×D8—31no—
296C2×M16—91no—
297C22×C8—91no—
298C4×Q8—32no—
299C4×Q8—92no—
300C4×D4—32no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—91no—
305#117—182no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—182no—
308#107—91no—
309#107—92no—
310#107D3211yescharacteristic
311#103—32no—
312#103—92no—
313#102—32no—
314#102—92no—
315#97—91no—
316#97—91no—
317C4×C8—31no—
318C4×C8—31no—
319C23×C3—62no—
320C22×D3—22no—
321C22×D3—31no—
322C22×D3—31no—
323C22×D3—61no—
324C3×Q8—34no—
325C3×Q8—62no—
326C3×D4—34no—
327C3×D4—62no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—31no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—42no—
336C2×C3×C4—62no—
337C2×C3×C4—242no—
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340#67—68no—
341C2×Dic3—22no—
342C2×Dic3—31no—
343C2×Dic3—31no—
344C2×Dic3—61no—
345C2×Dic3—68no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—242no—
350C2×Dic3D3×D411yescharacteristic
351C2×Dic3D3×D411yescharacteristic
352C2×Dic3D3×D411yescharacteristic
353C2×Dic3D3×D411yescharacteristic
354D12—22no—
355D12—68no—
356D12C2×C4×D314yes—
357C4×D3—32no—
358C4×D3—32no—
359C4×D3—32no—
360C4×D3—32no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—68no—
364C4×D3—82no—
365C4×D3—242no—
366C4×D3—242no—
367C4×D3—242no—
368C4×D3—244no—
369Dic6—22no—
370Dic6C2×C4×D314yes—
371C3×C8—22no—
372C3×C8—61no—
373C3×C8—61no—
374C3×C8C2×C4×D312yes—
375C3×C8C2×C4×D312yes—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C3⋊C8—32no—
379C3⋊C8—32no—
380C3⋊C8—62no—
381C2×C32C2×C4×D411yescharacteristic
382C2×C32#57611yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—22no—
385C3×D3—44no—
386#41—98no—
387#41—184no—
388C2×Q8—32no—
389C2×D4—32no—
390C2×D4—182no—
391C22×C4—62no—
392C22×C4—91no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—182no—
396Q16—34no—
397SD16—98no—
398D8—34no—
399M16—182no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—91no—
403C2×C8—94no—
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—62no—
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4C2×D3212yes—
412C22⋊C4—62no—
413C22⋊C4—91no—
414C22⋊C4—91no—
415C22⋊C4—182no—
416C42—31no—
417C42—31no—
418C42—62no—
419C42—182no—
420C22×C3—21no—
421C22×C3—64no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C2×D3×D411yescharacteristic
426C2×D3—24no—
427C2×D3—32no—
428C2×D3—32no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—61no—
435C2×D3—61no—
436C2×D3—61no—
437C2×D3—61no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—61no—
443C3×C4—61no—
444C3×C4—61no—
445C3×C4—61no—
446C3×C4—64no—
447C3×C4—82no—
448C3×C4C22×C4×D311yescharacteristic
449C3×C4C22×C4×D311yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4D3×#4111yescharacteristic
452Dic3—21no—
453Dic3—21no—
454Dic3—21no—
455Dic3—21no—
456Dic3—24no—
457Dic3—32no—
458Dic3—32no—
459Dic3—62no—
460Dic3—122no—
461Dic3—122no—
462Dic3—242no—
463C32#295111yescharacteristic, complemented, Sylow
464C23—62no—
465C23—91no—
466Q8—34no—
467Q8—62no—
468D4—34no—
469D4—62no—
470D4—188no—
471C2×C4—22no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—62no—
477C2×C4—91no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—188no—
481C2×C4—182no—
482C2×C4—242no—
483C2×C4—722no—
484C2×C4—722no—
485C2×C4C22×D3211yescharacteristic
486C8—61no—
487C8—61no—
488C8—92no—
489C8C4×D3212yes—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—124no—
494C2×C3C4×D3×D411yescharacteristic
495C2×C3C4×D3×D411yescharacteristic
496C2×C3#575711yescharacteristic
497C2×C3#576611yescharacteristic
498C2×C3#576911yescharacteristic
499C2×C3#577111yescharacteristic
500D3—44no—
501D3—64no—
502D3—62no—
503D3—62no—
504C22—64no—
505C22—92no—
506C22—122no—
507C22—122no—
508C22—181no—
509C22—181no—
510C22D32×D411yescharacteristic
511C4—42no—
512C4—64no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—92no—
518C4—362no—
519C4C2×C4×D3211yescharacteristic
520C4#6431911yescharacteristic
521C3—21no—
522C3#7958911yescharacteristic, complemented
523C3#7972111yescharacteristic, complemented
524C2—124no—
525C2—182no—
526C2#1059460511yescharacteristic
527C2#1059473411yescharacteristic
528C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594361C2semidirect
3. C3⋊D3×#107C2semidirect
4. C3×#4873C2semidirect
5. C3×#4872C2semidirect
6. Dic3×Dic12C2semidirect
7. Dic3×D24C2semidirect
8. #10590700C2semidirect
9. #10590612C2semidirect
10. #10590478C2semidirect
11. #10590454C2semidirect
30. #63810C4semidirect
55. #4873D3semidirect
56. #4872D3semidirect
74. #3796C2×C4semidirect
80. C8×C3⋊D3C2×C4semidirect
88. C3×Dic12C2×C4semidirect
89. C3×D24C2×C4semidirect
97. #3715C2×C4semidirect
267. Dic12C4×D3semidirect
268. D24C4×D3semidirect
463. C32#2951semidirect
522. C3#79589semidirect
523. C3#79721semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105943612
C3⋊D3×#1072
C3×#48732
C3×#48722
Dic3×Dic122
Dic3×D242
#105907002
#105906122
#105904782
#105904542
#797213
#795893