Finite Group Databasebeta

← #11779349

Subgroups — #11779349

Order 1152.

471 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593951C211yesmaximal, characteristic
2C3×#4850C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic, complemented
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic, complemented
8#71159—31nomaximal
9#68404—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63898—21no—
15Dic3×D12—21no—
16#63884—22no—
17#63863—21no—
18#63860—21no—
19C2×#3715—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#818—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63575—21no—
26#63567—21no—
27#5713—31no—
28#5585—31no—
29C3×#477—31no—
30#5091—31no—
31#5085—31no—
32#5076—31no—
33#4850—31no—
34#4850D311yescharacteristic, complemented
35C3×#331—31no—
36#4535—31no—
37#4485D311yescharacteristic
38#4484—31no—
39#4484—31no—
40#4484—31no—
41#4484—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×D3×Dic3—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3715—44no—
65#1630—91noSylow
66C3×C4⋊Q8—31no—
67C3×#127—31no—
68C3×C4×Q8—31no—
69#947—61no—
70C2×#215—62no—
71#936—61no—
72#936—61no—
73#935—62no—
74D4×Dic3—61no—
75D4×Dic3—61no—
76C2×#214—62no—
77#894—62no—
78#893—61no—
79#875—61no—
80#874C2×D311yescharacteristic
81C4×D12—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#103—61no—
93#818—21no—
94#818—61no—
95#816—21no—
96#816—61no—
97#810—61no—
98#807—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3×D3—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109#634—21no—
110#634—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C3×Dic6—42no—
122D3×Dic3—82no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—41no—
126#559—91no—
127#492—91no—
128#477—31no—
129#477—91no—
130#331—31no—
131Q8⋊C8—91no—
132Q8⋊C8—91no—
133C2×C3×Q8—31no—
134C2×C3×Q8—61no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×Dic3—62no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12D1212yes—
142C2×C4×D3—62no—
143C2×Dic6—21no—
144C2×Dic6—31no—
145C2×Dic6—31no—
146C2×Dic6—61no—
147C2×Dic6#6711yescharacteristic
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C42—21no—
157C3×C42—61no—
158C3×C42C22×D311yescharacteristic
159C3×C42C22×D311yescharacteristic
160#217—62no—
161#217—62no—
162#217—62no—
163#215—124no—
164#214—124no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173C4⋊Dic3#6711yescharacteristic
174Dic3⋊C4—21no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—121no—
178C4×Dic3—21no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—121no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—121no—
186C22×C32#12011yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—21no—
191C32×C4#13511yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4#13711yescharacteristic
194C32×C4#13711yescharacteristic
195C3⋊Dic3—41no—
196C3⋊Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×SD16—182no—
201C4⋊Q8—31no—
202#127—31no—
203#124—181no—
204#124—181no—
205#123—182no—
206C4×Q8—31no—
207C4×Q8—91no—
208C4×D4—181no—
209C4×D4—181no—
210#107—61no—
211#107—181no—
212C4⋊C8—31no—
213C4⋊C8D3211yescharacteristic
214#103—61no—
215#103—181no—
216C4×C8—91no—
217C23×C3—62no—
218C22×D3—22no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—122no—
222C3×D4—122no—
223C3×D4—121no—
224C3×D4—121no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—121no—
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C2×Dic3—242no—
249D12—42no—
250D12—41no—
251D12—41no—
252D12—41no—
253D12—41no—
254C4×D3—242no—
255Dic6—21no—
256Dic6—21no—
257Dic6—42no—
258Dic6—62no—
259Dic6—61no—
260Dic6—61no—
261Dic6—61no—
262Dic6—61no—
263Dic6—121no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—81no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—62no—
270C3⋊C8—62no—
271C3⋊C8—122no—
272C2×C32#45211yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45311yescharacteristic
275C3×D3—82no—
276C2×Q8—31no—
277C2×Q8—61no—
278C2×Q8—91no—
279C2×D4—32no—
280C2×D4—61no—
281C2×D4—61no—
282C22×C4—182no—
283SD16—364no—
284C2×C8—21no—
285C2×C8—61no—
286C2×C8—181no—
287C4⋊C4—31no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—91no—
292C4⋊C4—181no—
293C22⋊C4—182no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C42—61no—
297C42—181no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3#88211yescharacteristic
304C22×C3#93711yescharacteristic
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—121no—
316C3×C4—121no—
317C3×C4—241no—
318C3×C4#91211yescharacteristic
319C3×C4#91211yescharacteristic
320C3×C4#91511yescharacteristic
321C3×C4#91511yescharacteristic
322C3×C4#91811yescharacteristic
323C3×C4#91911yescharacteristic
324C3×C4#94211yescharacteristic
325C3×C4#95011yescharacteristic
326Dic3—41no—
327Dic3—41no—
328Dic3—81no—
329Dic3—122no—
330Dic3—121no—
331Dic3—121no—
332Dic3—121no—
333Dic3—121no—
334Dic3—241no—
335C32#163011yescharacteristic, complemented, Sylow
336C23—62no—
337Q8—61no—
338Q8—61no—
339Q8—122no—
340Q8—181no—
341Q8—181no—
342D4—122no—
343D4—121no—
344D4—121no—
345D4—121no—
346D4—121no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—121no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—722no—
353C2×C4D3×D1211yescharacteristic
354C2×C4#380211yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C8—41no—
357C8—121no—
358C8—182no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—242no—
363C2×C3#474711yescharacteristic
364C2×C3#478311yescharacteristic
365C2×C3#478311yescharacteristic
366C2×C3#504711yescharacteristic
367C2×C3#518711yescharacteristic
368C2×C3#519811yescharacteristic
369D3—82no—
370C22—122no—
371C22—122no—
372C22—122no—
373C22#6392211yescharacteristic
374C4—21no—
375C4—121no—
376C4—121no—
377C4—241no—
378C4—361no—
379C4—361no—
380C4#6381011yescharacteristic
381C4#6381111yescharacteristic
382C4#6393311yescharacteristic
383C4#6394611yescharacteristic
384C3—21no—
385C3#6840411yescharacteristic, complemented
386C3#7115911yescharacteristic, complemented
387C2—242no—
388C2#1059061411yescharacteristic
389C2#1059096511yescharacteristic
390C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4850C2semidirect
4. #10590284C2semidirect
5. #10589350C2semidirect
7. #10589083C2semidirect
34. #4850D3semidirect
335. C32#1630semidirect
385. C3#68404semidirect
386. C3#71159semidirect

Maximal subgroups

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

subgroupindex
#105939512
C3×#48502
#105903752
#105902842
#105893502
C3×#44852
#105890832
#711593
#684043