Finite Group Databasebeta

← #11790002

Subgroups — #11790002

Order 1152.

523 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
1#10592932C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4#10591119C211yesmaximal, characteristic, complemented
5C2×#63554C211yesmaximal, characteristic, complemented
6#10589165C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70372—31nomaximal
9#69998—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64135C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63662C412yescomplemented
18#63659C412yescomplemented
19C3×#837—22no—
20C3×#830—22no—
21#63572—22no—
22#63554—22no—
23C2×C3×#104—31no—
24C3×#408—31no—
25C2×#837D311yescharacteristic
26#5234D311yescharacteristic
27#5233—31no—
28#5233—31no—
29#5233—61no—
30#5119—31no—
31#5102—31no—
32C2×#815—31no—
33C2×#803—31no—
34#4558—31no—
35#4558—31no—
36#4555—31no—
37#4523—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—
48#3757—21no—
49C4⋊(C3⋊Dic3)C2×C412yes—
50C4×C3⋊Dic3—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)C2×C412yes—
54C3×C4×Dic3—21no—
55C3×C4×Dic3D412yes—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#1938—91noSylow
66C2×C3×#41—21no—
67C2×C3×#41C2×D311yescharacteristic
68C2×C3×#41C2×D311yescharacteristic
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C22×C3×C8—31no—
72C2×C3×C42—31no—
73#926—31no—
74#926—31no—
75#926—61no—
76C2×C4×Dic3C2×D311yescharacteristic
77C2×#208C2×D311yescharacteristic
78C2×#208C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C22×C3⋊C8C2×D311yescharacteristic
83C3×#104—62no—
84C3×C22⋊C8—62no—
85#837—22no—
86#835—32no—
87#835—32no—
88#835—62no—
89#832—32no—
90#832—32no—
91#832—62no—
92#830—22no—
93#815—62no—
94Dic3⋊C8—62no—
95Dic3⋊C8—62no—
96#803—62no—
97C23×C32—21no—
98C23×C32#4111yescharacteristic
99C32×Q8—21no—
100C32×Q8—21no—
101C32×D4—21no—
102C32×D4—21no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—21no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3⋊Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—42no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—22no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8—41no—
121#424—91no—
122C2×#104—31no—
123#416—91no—
124#408—31no—
125C2×#97—91no—
126#341—91no—
127#339—91no—
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—21no—
131C3×#41—21no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41—21no—
135C3×#41—21no—
136C3×#41—21no—
137C3×#41—21no—
138C3×#41—41no—
139C3×#41—41no—
140C2×C3×Q8—21no—
141C2×C3×Q8C4×D311yescharacteristic
142C2×C3×Q8C4×D311yescharacteristic
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—41no—
147C2×C3×D4C4×D311yescharacteristic
148C2×C3×D4C4×D311yescharacteristic
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—41no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—21no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C2×C3×C8—32no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C42—32no—
167C3×C42—61no—
168#217—61no—
169#217—61no—
170#217—121no—
171C4⋊Dic3—32no—
172C4⋊Dic3—32no—
173C4⋊Dic3—62no—
174C4×Dic3—21no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—121no—
178C4×Dic3#6712yes—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8#6712yes—
197C22×C32—22no—
198C22×C32—41no—
199C22×C32—42no—
200C22×C32C4×D411yescharacteristic
201C22×C32#12311yescharacteristic
202C22×C32#12611yescharacteristic
203C32×C4—41no—
204C32×C4#11711yescharacteristic
205C32×C4C4×D411yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12411yescharacteristic
208C3⋊Dic3—42no—
209C3×Dic3—42no—
210C2×#41D3211yescharacteristic
211C2×M16—31no—
212C2×M16—31no—
213C22×C8—31no—
214C22×C8—91no—
215#117—91no—
216C2×C42—31no—
217C4⋊C8—182no—
218#104—62no—
219#103—92no—
220#102—92no—
221C22⋊C8—62no—
222#97—182no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C23×C3#23511yescharacteristic
228C23×C3#23711yescharacteristic
229C3×Q8—22no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—41no—
235C3×D4—22no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—21no—
240C3×D4—41no—
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
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—21no—
255C2×C3×C4—41no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—62no—
263C2×C3×C4—122no—
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4#23711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×Dic3—22no—
277C2×Dic3—42no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—122no—
281C3×C8—62no—
282C3×C8—121no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—41no—
287C3⋊C8—62no—
288C3⋊C8—62no—
289C3⋊C8—122no—
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×Q8#62411yescharacteristic
300C2×D4—21no—
301C2×D4#62411yescharacteristic
302C22×C4—21no—
303C22×C4—61no—
304C22×C4C2×D3211yescharacteristic
305M16—61no—
306M16—61no—
307M16—61no—
308M16—61no—
309C2×C8—32no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—92no—
315C2×C8—181no—
316C2×C8—181no—
317C4⋊C4—92no—
318C22⋊C4—181no—
319C42—32no—
320C42—61no—
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—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—82no—
334C22×C3#87911yescharacteristic
335C22×C3#87911yescharacteristic
336C22×C3#67⋊C411yescharacteristic
337C22×C3#88311yescharacteristic
338C22×C3C4×#6711yescharacteristic
339C22×C3#93511yescharacteristic
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#87711yescharacteristic
350C3×C4#67⋊C411yescharacteristic
351C3×C4#88511yescharacteristic
352C3×C4C4×#6711yescharacteristic
353C3×C4#93611yescharacteristic
354C3×C4#93811yescharacteristic
355C3×C4#93911yescharacteristic
356Dic3—42no—
357Dic3—122no—
358Dic3—122no—
359Dic3—242no—
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—122no—
374C2×C4—182no—
375C2×C4#380411yescharacteristic
376C2×C4#380511yescharacteristic
377C2×C4#380511yescharacteristic
378C2×C4C2×#62411yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—62no—
382C8—121no—
383C8—121no—
384C8—182no—
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#482312yes—
397C2×C3#494411yescharacteristic
398C2×C3#494511yescharacteristic
399C2×C3#514512yes—
400C22—22no—
401C22—42no—
402C22—41no—
403C22#6395211yescharacteristic
404C22#6395611yescharacteristic
405C22#6396911yescharacteristic
406C4—41no—
407C4—122no—
408C4—362no—
409C4#6395211yescharacteristic
410C4#6395711yescharacteristic
411C4#6395911yescharacteristic
412C4#6397011yescharacteristic
413C3—21no—
414C3#6999811yescharacteristic, complemented
415C3#7037211yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—81no—
419C2#1059166312yes—
420C2#1059170311yescharacteristic
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. #10591119C2semidirect
5. C2×#63554C2semidirect
6. #10589165C2semidirect
7. #10589162C2semidirect
17. #63662C4semidirect
18. #63659C4semidirect
360. C32#1938semidirect
414. C3#69998semidirect
415. C3#70372semidirect

Maximal subgroups

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

subgroupindex
#105929322
C2×C3×#8372
C3×#52342
#105911192
C2×#635542
#105891652
#105891622
#703723
#699983