Finite Group Databasebeta

← #11793101

Subgroups — #11793101

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C2×C3×#805C211yesmaximal, characteristic
3#10591231C211yesmaximal, characteristic
4#10591110C211yesmaximal, characteristic
5C3×#4523C211yesmaximal, characteristic, complemented
6#10589171C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70368—31nomaximal
9#68779—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13#64135C2211yescharacteristic
14#64133—22no—
15#64079—21no—
16#64078—21no—
17C4×#634—22no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#805—21no—
22C3×#805—21no—
23#63580—22no—
24#63568—22no—
25#5470—31no—
26#5470—31no—
27#5470—61no—
28C2×C3×#104—31no—
29#5240—31no—
30#5236—31no—
31#5139—31no—
32#5006—31no—
33C2×#805D311yescharacteristic
34C3×#339—31no—
35#4559—31no—
36#4557—31no—
37#4556—31no—
38#4531—31no—
39#4523D311yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
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×C42—21no—
52C32×C42D411yescharacteristic
53C32×C42D411yescharacteristic
54#3757—21no—
55#3757D412yes—
56C4⋊(C3⋊Dic3)—22no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59#3750—24no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3D412yes—
62C3×#217—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#2031—91noSylow
72C2×C3×#41—31no—
73C2×#235C2×D311yescharacteristic
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C3×#117—31no—
77C2×C3×C42—21no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80#926—31no—
81#926—31no—
82#926—31no—
83#926—31no—
84#926—61no—
85#926—61no—
86#926C2×D311yescharacteristic
87#924—62no—
88#924—62no—
89#924—64no—
90C2×#208C2×D311yescharacteristic
91C2×#208C2×D311yescharacteristic
92#870—62no—
93#870—61no—
94#870—61no—
95#869—62no—
96#869—61no—
97#869—61no—
98C4×Dic6—62no—
99C4×Dic6—62no—
100C4×Dic6—64no—
101C3×#104—61no—
102C3×#104—61no—
103#837—62no—
104#834—62no—
105#825—62no—
106#806—62no—
107#805—21no—
108#805—21no—
109C23×C32C2×D411yescharacteristic
110C22×C3×D3—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—42no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122#634—44no—
123C3×#67—41no—
124C3×#67—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C3×D12—21no—
128C3×D12—21no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C3×Dic6—21no—
132C3×Dic6—21no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#533—91no—
136#421—91no—
137C2×#104—31no—
138#410—91no—
139#344—91no—
140#339—31no—
141H(3,ℤ/4)—91no—
142C3×#41—61no—
143C3×#41—61no—
144C3×#41—61no—
145C3×#41—61no—
146C2×C3×Q8—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—21no—
157#235—21no—
158#235—21no—
159#235—21no—
160#235—21no—
161C2×D12Dic611yescharacteristic, complemented
162C2×C4×D3—21no—
163C2×Dic6—64no—
164C2×Dic6—62no—
165C2×Dic6—62no—
166C2×Dic6Dic611yescharacteristic, complemented
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C42—22no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—61no—
181C3×C42D1211yescharacteristic
182C3×C42D1211yescharacteristic
183C3×C42#6711yescharacteristic
184C3×C42#6711yescharacteristic
185#217—21no—
186#217—32no—
187#217—32no—
188#217—62no—
189#217—62no—
190#217—61no—
191#217—61no—
192C4⋊Dic3—21no—
193C4⋊Dic3—64no—
194C4⋊Dic3—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202Dic3⋊C4—68no—
203Dic3⋊C4—64no—
204Dic3⋊C4—64no—
205C4×Dic3—21no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212#208—21no—
213#208—21no—
214#208—21no—
215#208—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C22×C32—41no—
219C22×C32#12011yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C22×C32#12411yescharacteristic
222C2×C3×D3—41no—
223C2×C3×D3—81no—
224C32×C4—22no—
225C32×C4—41no—
226C32×C4C22⋊Q811yescharacteristic
227C32×C4C22⋊Q811yescharacteristic
228C32×C4#12411yescharacteristic
229C32×C4#12411yescharacteristic
230C3⋊Dic3—42no—
231C3⋊Dic3—42no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C2×#41—31no—
235C2×M16—31no—
236C2×M16—31no—
237C4⋊Q8—181no—
238#125—181no—
239C22⋊Q8—182no—
240C4×Q8—182no—
241#117—31no—
242#117—91no—
243#117—91no—
244C2×C42D3211yescharacteristic
245#104—61no—
246#104—61no—
247#104—182no—
248#99—182no—
249C23×C3—21no—
250C23×C3—61no—
251C23×C3D3×D411yescharacteristic
252C23×C3D3×D411yescharacteristic
253C22×D3—21no—
254C3×Q8—61no—
255C3×Q8—61no—
256C3×D4—61no—
257C3×D4—61no—
258C3×D4—121no—
259C3×D4—121no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—44no—
275C2×C3×C4—61no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4C2×Dic611yescharacteristic
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4#23511yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4D3×Q811yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291#67—41no—
292#67—41no—
293C2×Dic3—21no—
294C2×Dic3—41no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301D12—21no—
302D12—21no—
303C4×D3—41no—
304C4×D3—41no—
305Dic6—21no—
306Dic6—21no—
307Dic6—128no—
308Dic6—124no—
309Dic6—124no—
310C3×C8—121no—
311C3×C8—121no—
312C3⋊C8—41no—
313C3⋊C8—41no—
314C2×C32—21no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32#39311yescharacteristic
318C3×D3—81no—
319#41—61no—
320#41—61no—
321#41—61no—
322#41—61no—
323C2×Q8—31no—
324C2×Q8—182no—
325C2×D4—31no—
326C2×D4—61no—
327C22×C4—21no—
328C22×C4—61no—
329C22×C4C2×D3211yescharacteristic
330M16—61no—
331M16—61no—
332M16—61no—
333M16—61no—
334C2×C8—61no—
335C2×C8—61no—
336C4⋊C4—61no—
337C4⋊C4—184no—
338C4⋊C4—182no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C22⋊C4—61no—
342C22⋊C4—92no—
343C22⋊C4—181no—
344C42—21no—
345C42—61no—
346C42—92no—
347C42—181no—
348C42#62611yescharacteristic
349C42#62611yescharacteristic
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—42no—
356C22×C3—121no—
357C22×C3—241no—
358C22×C3#87811yescharacteristic
359C22×C3#88211yescharacteristic
360C22×C3#88511yescharacteristic
361C22×C3#88511yescharacteristic
362C22×C3#89611yescharacteristic
363C22×C3#93711yescharacteristic
364C2×D3—41no—
365C2×D3—81no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—121no—
377C3×C4—241no—
378C3×C4#87511yescharacteristic
379C3×C4#87811yescharacteristic
380C3×C4#88511yescharacteristic
381C3×C4#88511yescharacteristic
382C3×C4#89611yescharacteristic
383C3×C4#89711yescharacteristic
384C3×C4#92411yescharacteristic
385C3×C4#93611yescharacteristic
386Dic3—41no—
387Dic3—81no—
388Dic3—124no—
389Dic3—124no—
390Dic3—122no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394C32#203111yescharacteristic, complemented, Sylow
395C23—61no—
396C23#381111yescharacteristic
397Q8—61no—
398Q8—61no—
399Q8—364no—
400D4—61no—
401D4—61no—
402D4—121no—
403D4—121no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—61no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4D3×Dic611yescharacteristic
414C2×C4#379511yescharacteristic
415C2×C4#379511yescharacteristic
416C2×C4#379511yescharacteristic
417C2×C4C2×#62611yescharacteristic
418C2×C4#381111yescharacteristic
419C8—121no—
420C8—121no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—241no—
432C2×C3#467311yescharacteristic
433C2×C3#494711yescharacteristic
434D3—81no—
435C22—41no—
436C22—121no—
437C22—241no—
438C22#6389611yescharacteristic
439C22#6391311yescharacteristic
440C22#6398111yescharacteristic
441C4—22no—
442C4—41no—
443C4—121no—
444C4—241no—
445C4—362no—
446C4—362no—
447C4#6385711yescharacteristic
448C4#6386011yescharacteristic
449C4#6389611yescharacteristic
450C4#6391311yescharacteristic
451C3—21no—
452C3#6877911yescharacteristic, complemented
453C3#7036811yescharacteristic, complemented
454C2—21no—
455C2—21no—
456C2—21no—
457C2—241no—
458C2#1059132211yescharacteristic
subgroupG/H
centerC4#63913
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenterC2×C42D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
5. C3×#4523C2semidirect
6. #10589171C2semidirect
7. #10589158C2semidirect
39. #4523D3semidirect
48. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
161. C2×D12Dic6semidirect
166. C2×Dic6Dic6semidirect
394. C32#2031semidirect
452. C3#68779semidirect
453. C3#70368semidirect

Maximal subgroups

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

subgroupindex
#105959412
C2×C3×#8052
#105912312
#105911102
C3×#45232
#105891712
#105891582
#703683
#687793