Finite Group Databasebeta

← #11793107

Subgroups — #11793107

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C3×#5006C211yesmaximal, characteristic
3#10591110C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5C3×#4533C211yesmaximal, characteristic, complemented
6#10589160C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70038—31nomaximal
9#69042—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64099—21no—
15#64097—21no—
16#64087—22no—
17C4×#634—22no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#806—22no—
22#63568—21no—
23#63568—21no—
24#63568—22no—
25#5517—31no—
26#5517—31no—
27#5517—61no—
28C3×#410—31no—
29#5236—31no—
30C2×#837—31no—
31#5139—31no—
32C2×#825—31no—
33#5006D311yescharacteristic
34C3×#344—31no—
35#4557—31no—
36#4555—31no—
37#4533D311yescharacteristic, complemented
38#4532—31no—
39#4531—31no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C2×#634—22no—
43C2×C3×#67—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C2×C3×D12Q811yescharacteristic, complemented
49C2×C3×C4×D3—21no—
50C2×C3×Dic6Q811yescharacteristic, complemented
51C32×C4⋊C4—21no—
52C32×C22⋊C4D412yes—
53C32×C42—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)—22no—
56C4⋊(C3⋊Dic3)—21no—
57#3750—22no—
58#3750—22no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3D412yes—
61C4×C3⋊Dic3D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4×Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#2031—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C2×C3×M16—31no—
77C3×#117—21no—
78C3×#117—31no—
79C3×#117C2×D311yescharacteristic
80C3×#117C2×D311yescharacteristic
81#926—31no—
82#926—31no—
83#926—61no—
84#926C2×D311yescharacteristic
85C2×C4×Dic3—31no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—61no—
88C2×#208C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90#890—61no—
91#890—61no—
92#890—62no—
93#888—61no—
94#888—61no—
95#888—62no—
96#878—64no—
97#878—62no—
98#878—62no—
99C4×Dic6—62no—
100C4×Dic6—62no—
101C4×Dic6—64no—
102C3×#99—62no—
103#837—61no—
104#837—61no—
105#837—62no—
106#825—61no—
107#825—61no—
108#825—62no—
109#806—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4—22no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—42no—
123#634—44no—
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—41no—
128C3×D12—21no—
129C3×D12—21no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×Dic6—21no—
133C3×Dic6—21no—
134C3×C3⋊C8—41no—
135C3×C3⋊C8—41no—
136#533—91no—
137#421—91no—
138C2×#104—91no—
139#410—31no—
140#344—31no—
141#339—91no—
142H(3,ℤ/4)—91no—
143C3×#41—61no—
144C3×#41—61no—
145C3×#41—61no—
146C3×#41—61no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—21no—
155C22×Dic3—62no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158#235—21no—
159#235—21no—
160#235—21no—
161#235—21no—
162C2×D12Dic611yescharacteristic, complemented
163C2×C4×D3—21no—
164C2×Dic6—64no—
165C2×Dic6—62no—
166C2×Dic6—62no—
167C2×Dic6Dic611yescharacteristic, complemented
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—22no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4D1212yes—
181C3×C22⋊C4#6712yes—
182C3×C42—22no—
183C3×C42—21no—
184C3×C42—21no—
185C3×C42—61no—
186#217—21no—
187#217—62no—
188#217—61no—
189#217—61no—
190C4⋊Dic3—21no—
191C4⋊Dic3—64no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194C4⋊Dic3—62no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197Dic3⋊C4—64no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—64no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C4×Dic3—21no—
204C4×Dic3—32no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—32no—
208C4×Dic3—31no—
209C4×Dic3—31no—
210C4×Dic3—62no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216#208—21no—
217#208—21no—
218#208—21no—
219#208—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C22×C32—41no—
223C22×C32#12011yescharacteristic
224C22×C32C22⋊Q811yescharacteristic
225C22×C32#12411yescharacteristic
226C2×C3×D3—41no—
227C2×C3×D3—81no—
228C32×C4—42no—
229C32×C4C22⋊Q811yescharacteristic
230C32×C4C22⋊Q811yescharacteristic
231C32×C4#12411yescharacteristic
232C32×C4#12411yescharacteristic
233C3⋊Dic3—22no—
234C3⋊Dic3—42no—
235C3⋊Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—81no—
238C2×#41—31no—
239C2×M16—31no—
240C2×M16—31no—
241C4⋊Q8—181no—
242#125—181no—
243C22⋊Q8—182no—
244C4×Q8—182no—
245#117—31no—
246#117—91no—
247#117D3211yescharacteristic
248C2×C42—91no—
249#104—181no—
250#104—181no—
251#104—182no—
252#99—62no—
253C23×C3—21no—
254C23×C3—61no—
255C23×C3C2×D1211yescharacteristic
256C23×C3C2×#6711yescharacteristic
257C22×D3—21no—
258C3×Q8—61no—
259C3×Q8—61no—
260C3×D4—61no—
261C3×D4—61no—
262C3×D4—121no—
263C3×D4—121no—
264C2×C3×C4—24no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—61no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×Dic611yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4#23511yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4D3×Q811yescharacteristic
289#67—41no—
290#67—41no—
291C2×Dic3—21no—
292C2×Dic3—41no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—62no—
297C2×Dic3—64no—
298C2×Dic3—61no—
299C2×Dic3—62no—
300C2×Dic3—61no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—124no—
305D12—21no—
306D12—21no—
307C4×D3—41no—
308C4×D3—41no—
309Dic6—21no—
310Dic6—21no—
311Dic6—128no—
312Dic6—124no—
313Dic6—124no—
314C3×C8—121no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—41no—
318C2×C32—21no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32#39311yescharacteristic
322C3×D3—81no—
323#41—61no—
324#41—61no—
325#41—61no—
326#41—61no—
327C2×Q8—31no—
328C2×Q8—182no—
329C2×D4—31no—
330C2×D4—61no—
331C22×C4—61no—
332C22×C4—181no—
333C22×C4C2×D3211yescharacteristic
334M16—61no—
335M16—61no—
336M16—61no—
337M16—61no—
338C2×C8—61no—
339C2×C8—61no—
340C4⋊C4—21no—
341C4⋊C4—61no—
342C4⋊C4—182no—
343C4⋊C4—182no—
344C4⋊C4—182no—
345C4⋊C4—181no—
346C22⋊C4—61no—
347C22⋊C4—181no—
348C22⋊C4#62612yes—
349C42—21no—
350C42—61no—
351C42—91no—
352C42—91no—
353C42—92no—
354C42—181no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—42no—
361C22×C3—121no—
362C22×C3—241no—
363C22×C3#87511yescharacteristic
364C22×C3#88211yescharacteristic
365C22×C3#89711yescharacteristic
366C22×C3#92411yescharacteristic
367C22×C3#93611yescharacteristic
368C22×C3#93711yescharacteristic
369C2×D3—41no—
370C2×D3—81no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—44no—
376C3×C4—42no—
377C3×C4—42no—
378C3×C4—121no—
379C3×C4—241no—
380C3×C4#87811yescharacteristic
381C3×C4#87811yescharacteristic
382C3×C4#88511yescharacteristic
383C3×C4#88511yescharacteristic
384C3×C4#88511yescharacteristic
385C3×C4#88511yescharacteristic
386C3×C4#89611yescharacteristic
387C3×C4#89611yescharacteristic
388Dic3—41no—
389Dic3—64no—
390Dic3—62no—
391Dic3—62no—
392Dic3—81no—
393Dic3—124no—
394Dic3—122no—
395Dic3—122no—
396Dic3—122no—
397Dic3—121no—
398Dic3—121no—
399C32#203111yescharacteristic, complemented, Sylow
400C23—61no—
401C23C2×#62611yescharacteristic
402Q8—61no—
403Q8—61no—
404Q8—364no—
405D4—61no—
406D4—61no—
407D4—121no—
408D4—121no—
409C2×C4—22no—
410C2×C4—61no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—182no—
417C2×C4—362no—
418C2×C4D3×Dic611yescharacteristic
419C2×C4#379511yescharacteristic
420C2×C4#379511yescharacteristic
421C2×C4#379511yescharacteristic
422C2×C4#381111yescharacteristic
423C2×C4#381111yescharacteristic
424C8—121no—
425C8—121no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3—241no—
437C2×C3#467311yescharacteristic
438C2×C3#494711yescharacteristic
439D3—81no—
440C22—41no—
441C22—121no—
442C22—241no—
443C22#6385711yescharacteristic
444C22#6386011yescharacteristic
445C22#6398111yescharacteristic
446C4—42no—
447C4—121no—
448C4—182no—
449C4—241no—
450C4—361no—
451C4—362no—
452C4#6389611yescharacteristic
453C4#6389611yescharacteristic
454C4#6391311yescharacteristic
455C4#6391311yescharacteristic
456C3—21no—
457C3#6904211yescharacteristic, complemented
458C3#7003811yescharacteristic, complemented
459C2—21no—
460C2—21no—
461C2—21no—
462C2—241no—
463C2#1059132211yescharacteristic
subgroupG/H
centerC4#63913
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
5. C3×#4533C2semidirect
6. #10589160C2semidirect
7. #10589158C2semidirect
37. #4533D3semidirect
48. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
162. C2×D12Dic6semidirect
167. C2×Dic6Dic6semidirect
399. C32#2031semidirect
457. C3#69042semidirect
458. C3#70038semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×#50062
#105911102
C2×#635682
C3×#45332
#105891602
#105891582
#700383
#690423