Finite Group Databasebeta

← #11789722

Subgroups — #11789722

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63664C211yesmaximal, characteristic
2C3×#5237C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4#10591141C211yesmaximal, characteristic, complemented
5#10591060C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70401—31nomaximal
9#70130—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63664—21no—
18#63664—21no—
19C3×#837—22no—
20C3×#836C412yescomplemented
21C3×#833C412yescomplemented
22#63577—22no—
23#63555—21no—
24#63553—21no—
25C3×#421—31no—
26C3×#413—31no—
27#5237D311yescharacteristic
28#5236D311yescharacteristic
29C2×#837—31no—
30C2×#837—31no—
31C2×#837—61no—
32#5125—31no—
33#5124—31no—
34Dic3×M16—31no—
35Dic3×M16—31no—
36#4559—31no—
37#4555—31no—
38#4533—31no—
39#4532—31no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4C2×C411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C3×#208C2×C412yes—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—21no—
70C2×C3×#41C2×D311yescharacteristic
71C2×C3×#41C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C3×#117—31no—
76#926C2×D311yescharacteristic
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—62no—
87C3×#101—32no—
88C3×#100—32no—
89#837—22no—
90#837—61no—
91#837—61no—
92#837—61no—
93#837—61no—
94#837—62no—
95#837—62no—
96#836Dic312yescomplemented
97#833Dic312yescomplemented
98#822—62no—
99#819—62no—
100#815—61no—
101#815—61no—
102C8×Dic3—61no—
103C8×Dic3—61no—
104C23×C32—21no—
105C23×C32#4111yescharacteristic
106C32×Q8—21no—
107C32×Q8—21no—
108C32×D4—21no—
109C32×D4—21no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—42no—
124C2×C3×Dic3—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—22no—
129#430—91no—
130#421—31no—
131C2×#104—91no—
132#413—31no—
133C4×M16—91no—
134#344—91no—
135#339—91no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—21no—
146C3×#41—41no—
147C3×#41—41no—
148C2×C3×Q8—21no—
149C2×C3×Q8C4×D311yescharacteristic
150C2×C3×Q8C2×Dic311yescharacteristic
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—41no—
155C2×C3×D4C4×D311yescharacteristic
156C2×C3×D4C2×Dic311yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—41no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C3×M16—32no—
167C3×M16—32no—
168C3×M16—32no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—61no—
178#217—21no—
179C4⋊Dic3—21no—
180C4×Dic3—21no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—121no—
190#208—21no—
191#208—21no—
192#208—21no—
193#208—62no—
194#208—61no—
195#208—61no—
196#208—61no—
197#208—61no—
198#208—121no—
199#208C2×Dic312yes—
200#208C2×Dic312yes—
201#208#6712yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32—81no—
211C22×C32#11711yescharacteristic
212C22×C32#12311yescharacteristic
213C22×C32#12411yescharacteristic
214C32×C4—41no—
215C32×C4C4×D411yescharacteristic
216C32×C4C4×D411yescharacteristic
217C32×C4#12111yescharacteristic
218C32×C4#12611yescharacteristic
219C3⋊Dic3—22no—
220C3⋊Dic3—41no—
221C3×Dic3—81no—
222C2×#41D3211yescharacteristic
223C2×M16—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—91no—
227#117—31no—
228C2×C42—91no—
229#108—182no—
230#104—62no—
231#104—181no—
232#104—181no—
233#101—32no—
234#100—32no—
235#97—181no—
236C4×C8—181no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—41no—
241C23×C3#23511yescharacteristic
242C23×C3#23711yescharacteristic
243C3×Q8—22no—
244C3×Q8—21no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×Q8—21no—
248C3×Q8—41no—
249C3×D4—22no—
250C3×D4—21no—
251C3×D4—21no—
252C3×D4—21no—
253C3×D4—21no—
254C3×D4—41no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—41no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—121no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4#23711yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4#23711yescharacteristic
287C2×C3×C4C22×Dic311yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×Dic3—41no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—124no—
299C3×C8—62no—
300C3×C8—62no—
301C3×C8—62no—
302C3⋊C8—22no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C3⋊C8—122no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—81no—
312C2×C32#38811yescharacteristic
313#41—21no—
314#41—21no—
315#41—21no—
316#41—21no—
317C2×Q8D3×Dic311yescharacteristic
318C2×D4—21no—
319C2×D4D3×Dic311yescharacteristic
320C22×C4—21no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323M16—32no—
324M16—32no—
325M16—32no—
326M16—61no—
327M16—61no—
328M16—61no—
329M16—181no—
330M16—181no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—181no—
335C4⋊C4—61no—
336C22⋊C4—61no—
337C42—61no—
338C42—91no—
339C42—91no—
340C42—181no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—81no—
351C22×C3—81no—
352C22×C3—82no—
353C22×C3#87711yescharacteristic
354C22×C3#88311yescharacteristic
355C22×C3#88311yescharacteristic
356C22×C3#88511yescharacteristic
357C22×C3#92611yescharacteristic
358C22×C3#93611yescharacteristic
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—241no—
367C3×C4#87911yescharacteristic
368C3×C4#87911yescharacteristic
369C3×C4#67⋊C411yescharacteristic
370C3×C4#88411yescharacteristic
371C3×C4C4×#6711yescharacteristic
372C3×C4D4×Dic311yescharacteristic
373C3×C4D4×Dic311yescharacteristic
374C3×C4#93911yescharacteristic
375Dic3—62no—
376Dic3—62no—
377Dic3—81no—
378Dic3—122no—
379Dic3—121no—
380Dic3—121no—
381Dic3—122no—
382C32#193211yescharacteristic, complemented, Sylow
383C23—21no—
384C23#380411yescharacteristic
385Q8—21no—
386Q8—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—121no—
395C2×C4—181no—
396C2×C4—181no—
397C2×C4—362no—
398C2×C4C2×D3×Dic311yescharacteristic
399C2×C4#380411yescharacteristic
400C2×C4#380411yescharacteristic
401C2×C4#380511yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C2×C4#381111yescharacteristic
404C8—62no—
405C8—62no—
406C8—62no—
407C8—361no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—82no—
419C2×C3—81no—
420C2×C3—81no—
421C2×C3#494511yescharacteristic
422C2×C3#495111yescharacteristic
423C22—41no—
424C22—41no—
425C22—81no—
426C22#6395511yescharacteristic
427C22#6395911yescharacteristic
428C22#6397511yescharacteristic
429C4—41no—
430C4—182no—
431C4—241no—
432C4—361no—
433C4#6395611yescharacteristic
434C4#6397111yescharacteristic
435C4Dic3×#6711yescharacteristic
436C4#67⋊Dic311yescharacteristic
437C3—21no—
438C3#7013011yescharacteristic, complemented
439C3#7040111yescharacteristic, complemented
440C2—21no—
441C2—21no—
442C2—21no—
443C2—81no—
444C2#1059170211yescharacteristic
subgroupG/H
centerC4#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#388
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591141C2semidirect
5. #10591060C2semidirect
6. #10589170C2semidirect
7. #10589160C2semidirect
20. C3×#836C4semidirect
21. C3×#833C4semidirect
96. #836Dic3semidirect
97. #833Dic3semidirect
382. C32#1932semidirect
438. C3#70130semidirect
439. C3#70401semidirect

Maximal subgroups

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

subgroupindex
C2×#636642
C3×#52372
C3×#52362
#105911412
#105910602
#105891702
#105891602
#704013
#701303