Finite Group Databasebeta

← #11790001

Subgroups — #11790001

Order 1152.

529 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63664C211yesmaximal, characteristic
2C3×#5234C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4#10591116C211yesmaximal, characteristic, complemented
5C2×#63555C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70288—31nomaximal
9#69998—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63664—22no—
18C3×#835C412yescomplemented
19C3×#832C412yescomplemented
20C3×#830—22no—
21Dic3⋊(C3⋊C8)—22no—
22#63555—22no—
23C3×#416—31no—
24C3×#408—31no—
25C2×#837—31no—
26C2×#837—31no—
27C2×#837—61no—
28#5234D311yescharacteristic
29#5233D311yescharacteristic
30#5102—31no—
31C2×#815—31no—
32C2×#815—31no—
33#4999—31no—
34#4558—31no—
35#4555—31no—
36#4552—31no—
37#4532—31no—
38C32×#41—21no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C2×C32×Q8C2×C411yescharacteristic
43C2×C32×D4—21no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3D412yes—
50#3748—21no—
51#3748—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#217—21no—
54C3×C4⋊Dic3C2×C412yes—
55C3×C4×Dic3—21no—
56C3×#208—21no—
57C3×#208—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8C2×C412yes—
64C2×C3×C3⋊C8D412yes—
65#1938—91noSylow
66C2×C3×#41—21no—
67C2×C3×#41C2×D311yescharacteristic
68C2×C3×#41C2×D311yescharacteristic
69C2×C3×M16—31no—
70C22×C3×C8—31no—
71C22×C3×C8—31no—
72C3×#117—31no—
73#926C2×D311yescharacteristic
74C2×C4×Dic3—31no—
75C2×C4×Dic3—31no—
76C2×C4×Dic3—61no—
77C2×#208—31no—
78C2×#208—31no—
79C2×#208—61no—
80C2×#208C2×D311yescharacteristic
81C22×C3⋊C8C2×D311yescharacteristic
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#103—32no—
84C3×#102—32no—
85C3×C22⋊C8—62no—
86#837—62no—
87#837—62no—
88#837—64no—
89#835Dic312yescomplemented
90#832Dic312yescomplemented
91#830—22no—
92#815—62no—
93#815—62no—
94Dic3⋊C8—62no—
95C4⋊(C3⋊C8)—62no—
96C23×C32—21no—
97C23×C32#4111yescharacteristic
98C32×Q8—21no—
99C32×Q8—21no—
100C32×D4—21no—
101C32×D4—21no—
102C32×D4—41no—
103C32×D4—41no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3×Dic3—22no—
116C3⋊(C3⋊C8)—41no—
117C3×C3⋊C8—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120#424—91no—
121C2×#104—91no—
122#416—31no—
123#408—31no—
124C2×#97—91no—
125#341—91no—
126#339—91no—
127C3×#41—22no—
128C3×#41—22no—
129C3×#41—21no—
130C3×#41—21no—
131C3×#41—21no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41—21no—
135C3×#41—21no—
136C3×#41—21no—
137C3×#41—41no—
138C3×#41—41no—
139C2×C3×Q8—21no—
140C2×C3×Q8C4×D311yescharacteristic
141C2×C3×Q8C2×Dic311yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—41no—
146C2×C3×D4C4×D311yescharacteristic
147C2×C3×D4C2×Dic311yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—41no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—121no—
157C3×M16—61no—
158C3×M16—61no—
159C2×C3×C8—32no—
160C2×C3×C8—32no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—32no—
167C3×C22⋊C4—61no—
168C3×C42—61no—
169#217—21no—
170C4⋊Dic3C2×Dic312yes—
171C4×Dic3—21no—
172C4×Dic3—32no—
173C4×Dic3—32no—
174C4×Dic3—62no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—121no—
178#208—21no—
179#208—21no—
180#208—62no—
181#208—61no—
182#208—61no—
183#208—61no—
184#208—61no—
185#208—121no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C2×C3⋊C8C2×Dic312yes—
195C2×C3⋊C8#6712yes—
196C22×C32—22no—
197C22×C32—41no—
198C22×C32—42no—
199C22×C32C4×D411yescharacteristic
200C22×C32#12311yescharacteristic
201C22×C32#12611yescharacteristic
202C32×C4—41no—
203C32×C4#11711yescharacteristic
204C32×C4C4×D411yescharacteristic
205C32×C4#12111yescharacteristic
206C32×C4#12411yescharacteristic
207C3⋊Dic3—42no—
208C3×Dic3—42no—
209C2×#41D3211yescharacteristic
210C2×M16—31no—
211C2×M16—91no—
212C22×C8—31no—
213C22×C8—31no—
214#117—31no—
215C2×C42—91no—
216C4⋊C8—182no—
217#104—182no—
218#103—32no—
219#102—32no—
220C22⋊C8—62no—
221#97—182no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—41no—
226C23×C3#23511yescharacteristic
227C23×C3#23711yescharacteristic
228C3×Q8—22no—
229C3×Q8—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—41no—
234C3×D4—22no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—41no—
240C3×D4—42no—
241C3×D4—42no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—62no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4C22×Dic311yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×Dic3—22no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—124no—
281C3×C8—62no—
282C3×C8—62no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—22no—
286C3⋊C8—41no—
287C3⋊C8—122no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—81no—
293C2×C32#38811yescharacteristic
294C2×C32#44412yes—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299C2×Q8D3×Dic311yescharacteristic
300C2×D4—21no—
301C2×D4D3×Dic311yescharacteristic
302C22×C4—21no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—61no—
306M16—61no—
307M16—181no—
308M16—181no—
309C2×C8—32no—
310C2×C8—32no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—181no—
317C4⋊C4—32no—
318C22⋊C4—61no—
319C42—61no—
320C42—92no—
321C42—181no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—42no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—82no—
334C22×C3#87911yescharacteristic
335C22×C3#87911yescharacteristic
336C22×C3#88311yescharacteristic
337C22×C3#88311yescharacteristic
338C22×C3C4×#6711yescharacteristic
339C22×C3D4×Dic311yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—42no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—122no—
348C3×C4#87711yescharacteristic
349C3×C4#67⋊C411yescharacteristic
350C3×C4#88411yescharacteristic
351C3×C4#88511yescharacteristic
352C3×C4#92611yescharacteristic
353C3×C4D4×Dic311yescharacteristic
354C3×C4#93611yescharacteristic
355C3×C4#93911yescharacteristic
356Dic3—42no—
357Dic3—122no—
358Dic3—122no—
359Dic3—124no—
360C32#193811yescharacteristic, complemented, Sylow
361C23—21no—
362C23#380411yescharacteristic
363Q8—21no—
364Q8—21no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—62no—
373C2×C4—182no—
374C2×C4—362no—
375C2×C4C2×D3×Dic311yescharacteristic
376C2×C4#380411yescharacteristic
377C2×C4#380411yescharacteristic
378C2×C4#380511yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C2×C4#381111yescharacteristic
381C8—62no—
382C8—62no—
383C8—121no—
384C8—361no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—82no—
394C2×C3—81no—
395C2×C3—81no—
396C2×C3#494511yescharacteristic
397C2×C3#495111yescharacteristic
398C2×C3#514512yes—
399C2×C3#519712yes—
400C22—22no—
401C22—42no—
402C22—41no—
403C22#6395611yescharacteristic
404C22Dic3×#6711yescharacteristic
405C22#6397511yescharacteristic
406C4—41no—
407C4—122no—
408C4—362no—
409C4#6395511yescharacteristic
410C4#6395911yescharacteristic
411C4#6397111yescharacteristic
412C4#67⋊Dic311yescharacteristic
413C3—21no—
414C3#6999811yescharacteristic, complemented
415C3#7028811yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—81no—
419C2#1059167412yes—
420C2#1059170211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C4×D4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591116C2semidirect
5. C2×#63555C2semidirect
6. #10589166C2semidirect
7. #10589160C2semidirect
18. C3×#835C4semidirect
19. C3×#832C4semidirect
89. #835Dic3semidirect
90. #832Dic3semidirect
360. C32#1938semidirect
414. C3#69998semidirect
415. C3#70288semidirect

Maximal subgroups

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

subgroupindex
C2×#636642
C3×#52342
C3×#52332
#105911162
C2×#635552
#105891662
#105891602
#702883
#699983