Finite Group Databasebeta

← #10950898

Subgroups — #10950898

Order 768.

516 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#81907C211yesmaximal, characteristic, complemented
2#81809C211yesmaximal, characteristic, complemented
3C3×#2242C211yesmaximal, characteristic, complemented
4#71354C211yesmaximal, characteristic, complemented
5#71320C211yesmaximal, characteristic, complemented
6#69230C211yesmaximal, characteristic, complemented
7#69229C211yesmaximal, characteristic, complemented
8#69209C211yesmaximal, characteristic, complemented
9#69208C211yesmaximal, characteristic, complemented
10#69198C211yesmaximal, characteristic, complemented
11#69197C211yesmaximal, characteristic
12#69177C211yesmaximal, characteristic, complemented
13#69176C211yesmaximal, characteristic, complemented
14#69059C211yesmaximal, characteristic, complemented
15C4×#798C211yesmaximal, characteristic, complemented
16#33750—31nomaximal, Sylow
17#5691—21no—
18#5680—21no—
19C3×#499C2211yescharacteristic
20C3×#495C2211yescharacteristic
21#5188C2211yescharacteristic
22Dic3×Q16C2211yescharacteristic
23C2×#829C2211yescharacteristic
24C2×#828C2211yescharacteristic
25#5171—21no—
26Dic3×SD16—21no—
27#5157C2211yescharacteristic
28Dic3×D8C2211yescharacteristic
29C2×#827C2211yescharacteristic
30C2×#826C2211yescharacteristic
31#5068—21no—
32#5056—21no—
33C2×#798C2211yescharacteristic
34C2×#798C2211yescharacteristic
35#4887C2211yescharacteristic
36#4883C2211yescharacteristic
37#4873C2211yescharacteristic
38#4872C2211yescharacteristic
39#4864—21no—
40#4852—21no—
41#4696C2211yescharacteristic
42C4×D3×C8C2211yescharacteristic
43#4683C2211yescharacteristic
44C3×#358C2211yescharacteristic
45C3×#358C2211yescharacteristic
46C3×#357C2211yescharacteristic
47C3×#357C2211yescharacteristic
48C3×C4×C16C2211yescharacteristic
49#4509C2211yescharacteristic
50#4509C2211yescharacteristic
51#4503C2211yescharacteristic
52#4503C2211yescharacteristic
53#4502C2211yescharacteristic
54#4502C2211yescharacteristic
55#4490C2211yescharacteristic
56#4490C2211yescharacteristic
57#4489C2211yescharacteristic
58#4489C2211yescharacteristic
59C4×C3⋊C16C2211yescharacteristic
60#3168—31no—
61#3168—31no—
62#2253—31no—
63#2249—31no—
64#2242—31no—
65#2242D311yescharacteristic, complemented
66#2220—31no—
67#2220—31no—
68#2219—31no—
69#2218—31no—
70#2177—31no—
71#2176—31no—
72#2175—31no—
73#2175—31no—
74C4×M32—31no—
75C2×C3×Q16C2311yescharacteristic
76C2×C3×SD16—21no—
77C2×C3×D8C2311yescharacteristic
78C3×#125—21no—
79C3×#124—21no—
80#946—21no—
81Q8×Dic3—21no—
82#938—21no—
83D4×Dic3—21no—
84C2×Dic12C2311yescharacteristic
85C2×D24C2311yescharacteristic
86C2×#204—21no—
87C2×D3×C8D411yescharacteristic
88C2×D3×C8C2311yescharacteristic
89#898—41no—
90#897—21no—
91#895—21no—
92#894—41no—
93#893—21no—
94#893—41no—
95#892—41no—
96#887—21no—
97#883—41no—
98#67⋊C4—41no—
99#879—41no—
100#877—41no—
101#875—21no—
102C42×D3D411yescharacteristic
103#870—21no—
104C2×C3×C16C2311yescharacteristic
105C2×C3×C16C2311yescharacteristic
106C3×#107C2311yescharacteristic
107C3×#107C2311yescharacteristic
108C3×#106—21no—
109C3×C4×C8C2311yescharacteristic
110#835—21no—
111#835—21no—
112#832—21no—
113#832—21no—
114#829—22no—
115#828—22no—
116#827—22no—
117#826—22no—
118#818C2311yescharacteristic
119#818C2311yescharacteristic
120#817—21no—
121C8×Dic3D411yescharacteristic
122C8×Dic3C2311yescharacteristic
123C2×C3⋊C16C2311yescharacteristic
124C2×C3⋊C16C2311yescharacteristic
125#810—21no—
126#810—21no—
127#809—21no—
128#809—21no—
129C4×C3⋊C8D411yescharacteristic
130#798—22no—
131#798—22no—
132#529—61no—
133#529—61no—
134C2×Q32—31no—
135C2×SD32—31no—
136C2×SD32—31no—
137C2×D16—31no—
138C2×M32—31no—
139C2×M32—31no—
140#499—31no—
141#499C2×D311yescharacteristic
142#495—31no—
143#495C2×D311yescharacteristic
144#488—61no—
145#488—61no—
146#467—31no—
147#467—31no—
148#466—31no—
149#466—31no—
150#465—61no—
151#465—61no—
152C4×Q16—31no—
153C4×Q16—31no—
154C4×SD16—61no—
155C4×SD16—61no—
156C4×D8—31no—
157C4×D8—31no—
158C2×C4×C8—31no—
159#367—31no—
160#367—31no—
161#366—31no—
162#366—31no—
163#358—31no—
164#358—31no—
165#358C2×D311yescharacteristic
166#358C2×D311yescharacteristic
167#357—31no—
168#357—31no—
169#357C2×D311yescharacteristic
170#357C2×D311yescharacteristic
171#346—31no—
172#346—31no—
173C4×C16—31no—
174C4×C16C2×D311yescharacteristic
175C2×C3×Q8—21no—
176C2×C3×D4—21no—
177C2×#67—41no—
178C22×Dic3—41no—
179C2×D12—21no—
180C2×D12—41no—
181C2×C4×D3—41no—
182C2×C4×D3D811yescharacteristic
183C2×C4×D3D811yescharacteristic
184C2×C4×D3C2×D411yescharacteristic
185C2×Dic6—21no—
186C3×Q16—21no—
187C3×Q16—21no—
188C3×SD16—42no—
189C3×D8—21no—
190C3×D8—21no—
191C2×C3×C8C2×D411yescharacteristic
192C2×C3×C8C2411yescharacteristic
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—41no—
197C3×C22⋊C4—41no—
198C3×C22⋊C4—41no—
199C3×C42C2×D411yescharacteristic
200#217—41no—
201#217—41no—
202(C2×D3)⋊C4—41no—
203(C2×D3)⋊C4—41no—
204(C2×D3)⋊C4—41no—
205(C2×D3)⋊C4—41no—
206(C2×D3)⋊C4—41no—
207(C2×D3)⋊C4—41no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—41no—
211C4⋊Dic3—41no—
212Dic3⋊C4—41no—
213Dic3⋊C4—41no—
214Dic3⋊C4—41no—
215Dic3⋊C4—41no—
216C4×Dic3—41no—
217C4×Dic3—41no—
218C4×Dic3D811yescharacteristic
219C4×Dic3D811yescharacteristic
220C4×Dic3C2×D411yescharacteristic
221C2×C3⋊C8C2×D411yescharacteristic
222C2×C3⋊C8C2×D411yescharacteristic
223Dic12—21no—
224Dic12—21no—
225D24—21no—
226D24—21no—
227#204—42no—
228D3×C8—22no—
229D3×C8—21no—
230D3×C8—21no—
231C3×C16—21no—
232C3×C16—21no—
233C3⋊C16#4112yes—
234C3⋊C16#4112yes—
235C2×Q16—31no—
236C2×Q16C22×D311yescharacteristic
237C2×SD16—21no—
238C2×SD16—61no—
239C2×D8—31no—
240C2×D8C22×D311yescharacteristic
241C22×C8—31no—
242C22×C8—31no—
243#126—121no—
244#126—121no—
245#125—21no—
246#125—61no—
247#124—21no—
248#124—61no—
249#123—121no—
250#123—121no—
251C22⋊Q8—61no—
252C22⋊Q8—61no—
253#121—61no—
254#121—61no—
255C4×Q8—61no—
256C4×Q8—61no—
257C4×D4—61no—
258C4×D4—61no—
259C4×D4—121no—
260C4×D4—121no—
261#117—121no—
262#117—121no—
263C2×C42—31no—
264Q32—62no—
265SD32—62no—
266SD32—62no—
267D16—62no—
268M32—62no—
269M32—62no—
270C2×C16—31no—
271C2×C16—31no—
272C2×C16C22×D311yescharacteristic
273C2×C16C22×D311yescharacteristic
274#107—31no—
275#107—31no—
276#107C22×D311yescharacteristic
277#107C22×D311yescharacteristic
278#106—21no—
279#106—61no—
280#103—61no—
281#103—61no—
282#103—61no—
283#103—61no—
284#102—61no—
285#102—61no—
286#102—61no—
287#102—61no—
288C4×C8—31no—
289C4×C8—31no—
290C4×C8—31no—
291C4×C8C22×D311yescharacteristic
292C23×C3—41no—
293C22×D3—41no—
294C22×D3C2×D811yescharacteristic
295C3×Q8—41no—
296C3×Q8—41no—
297C3×D4—41no—
298C3×D4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4C2×D811yescharacteristic
303C2×C3×C4C2×D811yescharacteristic
304C2×C3×C4C22×D411yescharacteristic
305#67—82no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—82no—
310C2×Dic3C2×D811yescharacteristic
311C2×Dic3C2×D811yescharacteristic
312C2×Dic3C2×D811yescharacteristic
313D12—41no—
314D12—41no—
315D12—82no—
316C4×D3—21no—
317C4×D3—21no—
318C4×D3—41no—
319C4×D3—41no—
320C4×D3—82no—
321Dic6—41no—
322Dic6—41no—
323C3×C8#13512yes—
324C3×C8C2×#4111yescharacteristic
325C3×C8C2×#4111yescharacteristic
326C3⋊C8—21no—
327C3⋊C8—21no—
328C2×Q8—21no—
329C2×Q8—61no—
330C2×D4—21no—
331C2×D4—61no—
332C2×D4—121no—
333C2×D4—121no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—121no—
338C22×C4—121no—
339Q16—21no—
340Q16—21no—
341Q16—61no—
342Q16—61no—
343SD16—42no—
344SD16—122no—
345D8—21no—
346D8—21no—
347D8—61no—
348D8—61no—
349C2×C8—31no—
350C2×C8—31no—
351C2×C8—62no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8D3×D411yescharacteristic
355C2×C8C23×D311yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—121no—
363C4⋊C4—121no—
364C4⋊C4—121no—
365C4⋊C4—121no—
366C4⋊C4—121no—
367C4⋊C4—121no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—121no—
371C22⋊C4—121no—
372C22⋊C4—121no—
373C22⋊C4—121no—
374C22⋊C4—121no—
375C22⋊C4—121no—
376C22⋊C4—121no—
377C22⋊C4—121no—
378C42—31no—
379C42—31no—
380C42—31no—
381C42—121no—
382C42—121no—
383C42D3×D411yescharacteristic
384C16—21no—
385C16—21no—
386C16—32no—
387C16—32no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3—81no—
391C22×C3C22×D811yescharacteristic
392C2×D3—21no—
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—81no—
396C2×D3—81no—
397C2×D3—81no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—81no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4#53211yescharacteristic
404C3×C4C2×#13511yescharacteristic
405Dic3—21no—
406Dic3—21no—
407Dic3—21no—
408Dic3—81no—
409Dic3—81no—
410Dic3—81no—
411C23—31no—
412C23—41no—
413C23—121no—
414Q8—41no—
415Q8—41no—
416Q8—121no—
417Q8—121no—
418D4—41no—
419D4—41no—
420D4—121no—
421D4—121no—
422D4—242no—
423D4—242no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—31no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—242no—
438C2×C4—242no—
439C2×C4D3×D811yescharacteristic
440C2×C4D3×D811yescharacteristic
441C2×C4C2×D3×D411yescharacteristic
442C8—61no—
443C8—61no—
444C8#91612yes—
445C8D3×#4111yescharacteristic
446C8D3×#4111yescharacteristic
447C2×C3—161no—
448C2×C3#316911yescharacteristic
449C2×C3#341411yescharacteristic
450C2×C3#341411yescharacteristic
451D3—41no—
452D3—161no—
453C22—61no—
454C22—61no—
455C22—61no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—241no—
460C22—241no—
461C22—241no—
462C22C2×D3×D811yescharacteristic
463C4—21no—
464C4—21no—
465C4—61no—
466C4—61no—
467C4—61no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—241no—
472C4—241no—
473C4—241no—
474C4#566811yescharacteristic
475C4C2×#91611yescharacteristic
476C3#3375011yescharacteristic, complemented, Sylow
477C2—121no—
478C2—161no—
479C2—481no—
480C2#8155711yescharacteristic
481C2#8203011yescharacteristic
482C2#8203011yescharacteristic
subgroupG/H
centerC22C2×D3×D8
commutator, cosocleC2×C3×C8C24
FrattiniC2×C8C23×D3
FittingC3×#2242C2
socleC22×C3C22×D8
prime radical#69197C2
hypercenter#2242D3
hypocenterC3#33750
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #81907C2semidirect
2. #81809C2semidirect
3. C3×#2242C2semidirect
4. #71354C2semidirect
5. #71320C2semidirect
6. #69230C2semidirect
7. #69229C2semidirect
8. #69209C2semidirect
9. #69208C2semidirect
10. #69198C2semidirect
12. #69177C2semidirect
13. #69176C2semidirect
14. #69059C2semidirect
15. C4×#798C2semidirect
65. #2242D3semidirect
476. C3#33750semidirect

Maximal subgroups

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

subgroupindex
#819072
#818092
C3×#22422
#713542
#713202
#692302
#692292
#692092
#692082
#691982
#691972
#691772
#691762
#690592
C4×#7982
#337503