Finite Group Databasebeta

← #11779177

Subgroups — #11779177

Order 1152.

479 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 479 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593860C211yesmaximal, characteristic, complemented
2#10592393C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic
4#10590367C211yesmaximal, characteristic
5C3×#4456C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68265—31nomaximal
9#68252—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63869—21no—
15#63866—21no—
16#63845—22no—
17#63844—21no—
18Dic3×Dic6—21no—
19C2×#3717—21no—
20C2×#3717—21no—
21C32×C4×C8C2211yescharacteristic
22#63648—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63564—21no—
26#63564—21no—
27#5570—31no—
28#5567—31no—
29#5027—31no—
30#5027—31no—
31#4848—31no—
32#4848—31no—
33#4694—31no—
34#4694—31no—
35#4694—61no—
36C3×Q8⋊C8—31no—
37C3×Q8⋊C8—31no—
38#4486—31no—
39#4482—31no—
40#4456D311yescharacteristic, complemented
41#4456D311yescharacteristic, complemented
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D411yescharacteristic
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D412yes—
52C3×C4⋊Dic3D411yescharacteristic
53C3×C4⋊Dic3D411yescharacteristic
54C3×Dic3⋊C4—21no—
55C3×Dic3⋊C4—21no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60#3724—22no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3717—42no—
65#3717—42no—
66#1626—91noSylow
67C3×C4×Q8—31no—
68C3×C4×Q8—31no—
69Q8×Dic3—61no—
70#944—61no—
71C2×#215—61no—
72C2×#215—61no—
73C2×#204—61no—
74C2×#204—61no—
75#890—61no—
76#890—62no—
77#889—62no—
78#887—61no—
79#874—31no—
80#874—31no—
81#874—61no—
82#870—61no—
83#869—31no—
84#869—31no—
85#869—61no—
86#869—61no—
87C4×Dic6—61no—
88C4×Dic6—61no—
89C4×Dic6C2×D311yescharacteristic
90C4×Dic6C2×D311yescharacteristic
91C3×C4⋊C8—31no—
92C3×C4⋊C8—31no—
93C3×C4×C8—21no—
94C3×C4×C8C2×D311yescharacteristic
95C3×C4×C8C2×D311yescharacteristic
96#821—62no—
97#821—62no—
98#821—64no—
99#821—61no—
100#821—61no—
101#809—61no—
102#809—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3⋊D3—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110C4⋊(C3⋊D3)—42no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115#634—41no—
116#634—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3×Dic6—21no—
124C3×Dic6SD1612yescomplemented
125C32×C8—41no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128#557—91no—
129#486—91no—
130#460—91no—
131#460—91no—
132#332—91no—
133Q8⋊C8—31no—
134Q8⋊C8—31no—
135C2×C3×Q8—31no—
136C2×C3×Q8—31no—
137C2×D12—62no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—121no—
145C2×D12—121no—
146C2×Dic6—61no—
147C2×Dic6—61no—
148C2×Dic6—121no—
149C2×Dic6D1211yescharacteristic
150C2×Dic6D1211yescharacteristic
151C2×C3×C8—22no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C42—21no—
161C3×C42—61no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#215—122no—
166#215—122no—
167C4⋊Dic3—32no—
168C4⋊Dic3—32no—
169C4⋊Dic3—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—121no—
175C4⋊Dic3D1211yescharacteristic
176C4⋊Dic3D1211yescharacteristic
177Dic3⋊C4—21no—
178Dic3⋊C4—21no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183C4×Dic3—21no—
184C4×Dic3—21no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189#204—122no—
190#204—122no—
191C22×C32#12011yescharacteristic
192C2×C3⋊D3—81no—
193C2×C3⋊D3—81no—
194C2×C3⋊D3—81no—
195C32×C4—21no—
196C32×C4C2×SD1611yescharacteristic
197C32×C4#13511yescharacteristic
198C32×C4AGL(1,ℤ/8)11yescharacteristic
199C32×C4#13711yescharacteristic
200C3⋊Dic3—42no—
201C3×Dic3—22no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C2×SD16—181no—
206C2×SD16—181no—
207C4⋊Q8—91no—
208C4⋊Q8—181no—
209#127—91no—
210#125—181no—
211#125—182no—
212C4×Q8—31no—
213C4×Q8—31no—
214C4×Q8—181no—
215C4×Q8—181no—
216C4⋊C8—31no—
217C4⋊C8—31no—
218#102—181no—
219#102—181no—
220#102—182no—
221C4×C8D3211yescharacteristic
222C22×D3—122no—
223C22×D3—121no—
224C22×D3—121no—
225C3×Q8—32no—
226C3×Q8—61no—
227C3×Q8—61no—
228C3×Q8—61no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4C2×D1211yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—122no—
249D12—124no—
250D12—122no—
251D12—122no—
252D12—121no—
253D12—121no—
254D12—121no—
255D12—121no—
256D12—121no—
257D12—121no—
258D12—121no—
259D12—121no—
260D12—241no—
261D12—241no—
262D12—241no—
263D12—241no—
264Dic6—21no—
265Dic6—21no—
266Dic6—21no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271Dic6—241no—
272Dic6—241no—
273Dic6#20412yescomplemented
274C3×C8—42no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—121no—
278C3×C8—121no—
279C3⋊C8—41no—
280C3⋊C8—41no—
281C2×C32#44811yescharacteristic
282C2×C32#44911yescharacteristic
283C2×C32#45411yescharacteristic
284C3⋊D3—161no—
285C2×Q8—31no—
286C2×Q8—31no—
287C2×Q8—181no—
288C2×D4—181no—
289C2×D4—181no—
290C2×D4—181no—
291SD16—362no—
292SD16—362no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—61no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—92no—
301C4⋊C4—182no—
302C4⋊C4—182no—
303C4⋊C4—182no—
304C4⋊C4—181no—
305C42—61no—
306C42—61no—
307C42—182no—
308C42C2×D3211yescharacteristic
309C22×C3—21no—
310C22×C3#88211yescharacteristic
311C22×C3#88211yescharacteristic
312C2×D3—242no—
313C2×D3—242no—
314C2×D3—242no—
315C2×D3—241no—
316C2×D3—241no—
317C2×D3—241no—
318C2×D3—241no—
319C2×D3—241no—
320C2×D3—241no—
321C3×C4—22no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—62no—
329C3×C4—121no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4C2×#20411yescharacteristic
333C3×C4#90411yescharacteristic
334C3×C4#90811yescharacteristic
335C3×C4#90911yescharacteristic
336C3×C4D3×SD1611yescharacteristic
337C3×C4#91411yescharacteristic
338C3×C4#91811yescharacteristic
339C3×C4#91911yescharacteristic
340Dic3—22no—
341Dic3—41no—
342Dic3—41no—
343Dic3—41no—
344Dic3—122no—
345Dic3—122no—
346Dic3—242no—
347C32#162611yescharacteristic, complemented, Sylow
348C23—361no—
349Q8—32no—
350Q8—61no—
351Q8—61no—
352Q8—61no—
353Q8—361no—
354Q8—361no—
355D4—362no—
356D4—361no—
357D4—361no—
358D4—361no—
359D4—361no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—182no—
365C2×C4D3×D1211yescharacteristic
366C2×C4D3×D1211yescharacteristic
367C2×C4#381111yescharacteristic
368C8—41no—
369C8—121no—
370C8—121no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3#473411yescharacteristic
375C2×C3#473811yescharacteristic
376C2×C3#480611yescharacteristic
377C2×C3#481011yescharacteristic
378C2×C3#482711yescharacteristic
379C2×C3#482711yescharacteristic
380D3—482no—
381D3—481no—
382D3—481no—
383C22—721no—
384C22—721no—
385C22—721no—
386C22#6392311yescharacteristic
387C4—21no—
388C4—62no—
389C4—121no—
390C4—121no—
391C4—121no—
392C4—362no—
393C4D3×#20411yescharacteristic
394C4#6379411yescharacteristic
395C4#6380111yescharacteristic
396C4#6380811yescharacteristic
397C3—21no—
398C3#6825211yescharacteristic, complemented
399C3#6826511yescharacteristic, complemented
400C2—1441no—
401C2#1059040211yescharacteristic
402C2#1059095111yescharacteristic
403C2#1059096711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1626
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
1. #10593860C2semidirect
5. C3×#4456C2semidirect
6. C3×#4456C2semidirect
7. #10589094C2semidirect
40. #4456D3semidirect
41. #4456D3semidirect
124. C3×Dic6SD16semidirect
273. Dic6#204semidirect
347. C32#1626semidirect
398. C3#68252semidirect
399. C3#68265semidirect

Maximal subgroups

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

subgroupindex
#105938602
#105923932
#105903672
C3×#44562
#105890942
#682653
#682523