Finite Group Databasebeta

← #10691033

Subgroups — #10691033

Order 768.

436 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3113C211yesmaximal, characteristic
2#82437C211yesmaximal, characteristic
3#71835C211yesmaximal, characteristic
4#71822C211yesmaximal, characteristic
5#71631C211yesmaximal, characteristic
6#67751C211yesmaximal, characteristic
7#67750C211yesmaximal, characteristic
8#9166—31nomaximal, Sylow
9C3×#533C2211yescharacteristic
10C2×C3×C4×Q8C2211yescharacteristic
11C3×#483—21no—
12C3×#475C411yescharacteristic, complemented
13C3×#475C411yescharacteristic, complemented
14C3×#462C411yescharacteristic, complemented
15C3×#462C411yescharacteristic, complemented
16C3×#451—21no—
17C3×#441—21no—
18C3×#441—21no—
19C3×#432C2211yescharacteristic
20C2×#835—21no—
21#5024—21no—
22#5024—22no—
23Q8×C3⋊C8—21no—
24C4×C4⋊Dic3C2211yescharacteristic
25#4926—21no—
26#4926C2211yescharacteristic
27#4925—21no—
28#4925C2211yescharacteristic
29C2×#803C2211yescharacteristic
30#4543—22no—
31#4538—21no—
32#4538—21no—
33#4529—21no—
34#3113D311yescharacteristic
35#2984—31no—
36#1763—31no—
37#1531—31no—
38#1503—31no—
39#1302—31no—
40#1285—31no—
41C22×C3×Q8D411yescharacteristic
42C2×C3×Q16—21no—
43C2×C3×Q16—21no—
44C3×C4⋊Q8C2×C411yescharacteristic
45C3×C4⋊Q8C2×C411yescharacteristic
46C3×#125—21no—
47C3×C22⋊Q8—21no—
48C3×C22⋊Q8—21no—
49C3×C4×Q8—21no—
50C3×C4×Q8—21no—
51C3×C4×Q8—21no—
52C3×C4×Q8—21no—
53C3×C4×Q8C2×C411yescharacteristic
54C3×C4×Q8C2×C411yescharacteristic
55C3×C4×Q8D411yescharacteristic
56C3×C4×Q8D411yescharacteristic
57C3×#117—21no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4D411yescharacteristic
60C2×C3×C42—21no—
61C2×C3×C42C2311yescharacteristic
62C2×C4⋊Dic3—21no—
63C2×C4×Dic3—21no—
64C22×C3⋊C8—21no—
65C3×#106—21no—
66C3×#106—21no—
67C3×C4⋊C8C2×C411yescharacteristic
68C3×C4⋊C8C2×C411yescharacteristic
69C3×#103—21no—
70C3×#103—21no—
71C3×#103—21no—
72C3×#103—21no—
73C3×C22⋊C8—21no—
74C3×#97—21no—
75#835—24no—
76C3⋊#95—21no—
77#830—21no—
78#830D411yescharacteristic
79#830D411yescharacteristic
80C4⋊(C3⋊C8)—22no—
81C4⋊(C3⋊C8)—22no—
82C4⋊(C3⋊C8)—21no—
83C4⋊(C3⋊C8)—21no—
84#803—22no—
85#803—21no—
86#803—21no—
87#803D412yes—
88C4×C3⋊C8—22no—
89C4×C3⋊C8—21no—
90#533C2×D311yescharacteristic
91C2×C4×Q8C2×D311yescharacteristic
92#483—21no—
93#475Dic311yescharacteristic, complemented
94#475Dic311yescharacteristic, complemented
95#462Dic311yescharacteristic, complemented
96#462Dic311yescharacteristic, complemented
97#451—21no—
98#446—62no—
99#446—61no—
100C8×Q8—61no—
101#441—21no—
102#441—21no—
103#432—31no—
104#432—61no—
105#432C2×D311yescharacteristic
106#431—31no—
107#431—61no—
108C2×#103—61no—
109C2×#97—31no—
110C4×C4⋊C4—31no—
111#340—61no—
112#330—62no—
113#328—61no—
114#328—61no—
115C2×C3×Q8—21no—
116C2×C3×Q8—22no—
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—41no—
120C2×C3×Q8C22⋊C411yescharacteristic
121C2×C3×Q8C22⋊C411yescharacteristic
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4C2×D411yescharacteristic
125C22×C3×C4C2×D411yescharacteristic
126C22×C3×C4#4111yescharacteristic
127C22×Dic3—41no—
128C3×Q16—42no—
129C3×Q16—42no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—41no—
142C3×C4⋊C4—41no—
143C3×C4⋊C4C22⋊C411yescharacteristic
144C3×C4⋊C4C22⋊C411yescharacteristic
145C3×C22⋊C4—41no—
146C3×C42—21no—
147C3×C42—21no—
148C3×C42—21no—
149C3×C42—21no—
150C3×C42—41no—
151C3×C42C22×C411yescharacteristic
152C3×C42C2×D411yescharacteristic
153C3×C42C2×D411yescharacteristic
154C3×C42#4111yescharacteristic
155C4⋊Dic3—22no—
156C4⋊Dic3—41no—
157C4×Dic3—81no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—41no—
163C2×C3⋊C8—41no—
164C22×Q8#6711yescharacteristic
165C2×Q16—21no—
166C2×Q16—21no—
167C22×C8—61no—
168C4⋊Q8C2×Dic311yescharacteristic
169C4⋊Q8C2×Dic311yescharacteristic
170#125—21no—
171C22⋊Q8—21no—
172C22⋊Q8—21no—
173C4×Q8—21no—
174C4×Q8—21no—
175C4×Q8—21no—
176C4×Q8—21no—
177C4×Q8C2×Dic311yescharacteristic
178C4×Q8C2×Dic311yescharacteristic
179C4×Q8#6711yescharacteristic
180C4×Q8#6711yescharacteristic
181#117—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—61no—
184C2×C4⋊C4#6711yescharacteristic
185C2×C42—21no—
186C2×C42—61no—
187C2×C42C22×D311yescharacteristic
188#106—21no—
189#106—21no—
190C4⋊C8—62no—
191C4⋊C8—62no—
192C4⋊C8—61no—
193C4⋊C8—61no—
194C4⋊C8C2×Dic311yescharacteristic
195C4⋊C8C2×Dic311yescharacteristic
196#103—21no—
197#103—21no—
198#103—21no—
199#103—21no—
200#103—64no—
201C22⋊C8—21no—
202C22⋊C8—31no—
203C22⋊C8—31no—
204C22⋊C8—61no—
205#97—21no—
206#97—32no—
207#97—62no—
208#97—61no—
209#97—61no—
210C4×C8—62no—
211C4×C8—61no—
212#95—61no—
213C23×C3#12111yescharacteristic
214C3×Q8—21no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8—42no—
218C3×Q8—41no—
219C3×Q8—41no—
220C3×Q8—81no—
221C3×Q8#10412yes—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—41no—
231C2×C3×C4—42no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4C2×C22⋊C411yescharacteristic
237C2×C3×C4C4×D411yescharacteristic
238C2×C3×C4C4×D411yescharacteristic
239C2×C3×C4#12011yescharacteristic
240C2×C3×C4#12111yescharacteristic
241C2×C3×C4#12311yescharacteristic
242C2×Dic3—42no—
243C2×Dic3—81no—
244C2×Dic3—81no—
245C3×C8—41no—
246C3×C8—41no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C3⋊C8—42no—
250C3⋊C8—42no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8#21711yescharacteristic
257C2×Q8#21711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—121no—
261C22×C4D3×D411yescharacteristic
262C22×C4#23711yescharacteristic
263C22×C4C2×#6711yescharacteristic
264Q16—42no—
265Q16—42no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—62no—
269C2×C8—61no—
270C2×C8—62no—
271C2×C8—61no—
272C2×C8—121no—
273C2×C8—121no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—62no—
286C4⋊C4—121no—
287C4⋊C4#21711yescharacteristic
288C4⋊C4#21711yescharacteristic
289C22⋊C4—41no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—241no—
296C42D3×D411yescharacteristic
297C42#23711yescharacteristic
298C42C22×Dic311yescharacteristic
299C42C2×#6711yescharacteristic
300C22×C3—21no—
301C22×C3—21no—
302C22×C3#38611yescharacteristic
303C22×C3#47111yescharacteristic
304C22×C3#47311yescharacteristic
305C3×C4—21no—
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—81no—
315C3×C4—81no—
316C3×C4C2×#10411yescharacteristic
317C3×C4#42111yescharacteristic
318Dic3—82no—
319C23#93911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—42no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327Q8#83712yes—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—122no—
343C2×C4—241no—
344C2×C4—241no—
345C2×C4D4×Dic311yescharacteristic
346C2×C4D4×Dic311yescharacteristic
347C2×C4#93511yescharacteristic
348C2×C4#93711yescharacteristic
349C2×C4#93911yescharacteristic
350C2×C4C2×#21711yescharacteristic
351C8—41no—
352C8—41no—
353C8—122no—
354C8—121no—
355C8—122no—
356C8—121no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3#187111yescharacteristic
360C2×C3#190511yescharacteristic
361C2×C3#190811yescharacteristic
362C22—21no—
363C22—21no—
364C22#520311yescharacteristic
365C22#520411yescharacteristic
366C22#522011yescharacteristic
367C4—21no—
368C4—22no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—81no—
378C4—242no—
379C4C2×#83711yescharacteristic
380C4#523611yescharacteristic
381C3#916611yescharacteristic, complemented, Sylow
382C2—21no—
383C2—21no—
384C2#7171311yescharacteristic
385C2#7210111yescharacteristic
386C2#7210311yescharacteristic
subgroupG/H
centerC22#5220
commutatorC3×C42C22×C4
FrattiniC2×C42C22×D3
FittingC3×#3113C2
socleC22×C3#386
prime radicalC23×C3#121
cosocleC2×C3×C42C23
hypercenter#3113D3
hypocenterC3#9166
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
12. C3×#475C4semidirect
13. C3×#475C4semidirect
14. C3×#462C4semidirect
15. C3×#462C4semidirect
93. #475Dic3semidirect
94. #475Dic3semidirect
95. #462Dic3semidirect
96. #462Dic3semidirect
381. C3#9166semidirect

Maximal subgroups

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

subgroupindex
C3×#31132
#824372
#718352
#718222
#716312
#677512
#677502
#91663