Finite Group Databasebeta

← #11779472

Subgroups — #11779472

Order 1152.

447 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 447 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593856C211yesmaximal, characteristic
2C3×#4699C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic
6C3×#4456C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71307—31nomaximal
9#68267—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×Dic12—22no—
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63576—21no—
24#63575—21no—
25#63567—21no—
26#63565—21no—
27#5722—31no—
28Q8×Dic6—31no—
29C3×#494—31no—
30#5091—31no—
31#5091—31no—
32#5021—31no—
33#4850—31no—
34#4699D311yescharacteristic
35C3×Q8⋊C8—31no—
36#4546—31no—
37#4481—31no—
38#4456—31no—
39#4456—31no—
40#4456—61no—
41#4456D311yescharacteristic
42C2×#634D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D412yes—
46C2×#627—22no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—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—
61C3×Dic12—44no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#1633—91noSylow
66C2×C3×Q16—62no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×C4×Q8—31no—
70Q8×Dic3—61no—
71#944—62no—
72C2×Dic12—22no—
73#888—61no—
74#888—61no—
75#888—62no—
76#888—61no—
77#887—61no—
78#887—61no—
79#869—61no—
80#869C2×D311yescharacteristic
81#869C2×D311yescharacteristic
82C4×Dic6—31no—
83C4×Dic6—31no—
84C4×Dic6—61no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×C4⋊C8—31no—
88C3×C4×C8—21no—
89C3×C4×C8C2×D311yescharacteristic
90C3×C4×C8C2×D311yescharacteristic
91#835—61no—
92#818—61no—
93#816—61no—
94#810—61no—
95#810—61no—
96#807—61no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108#634—21no—
109#634Q1612yescomplemented
110C2×C3×Dic3—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×Dic6—21no—
115C3×Dic6—42no—
116C3×Dic6—42no—
117C3×Dic6Q1612yescomplemented
118#627—82no—
119C32×C8—22no—
120C3⋊(C3⋊C8)—41no—
121C3×C3⋊C8—41no—
122Q82—91no—
123#494—31no—
124#477—91no—
125#477—91no—
126#333—91no—
127Q8⋊C8—31no—
128Q8⋊C8—91no—
129C2×C3×Q8—31no—
130C2×C3×Q8—32no—
131C2×C3×Q8—61no—
132C2×Dic6—21no—
133C2×Dic6—31no—
134C2×Dic6—31no—
135C2×Dic6—61no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6D1211yescharacteristic
139C2×Dic6#6712yes—
140C3×Q16—124no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—41no—
144C2×C3×C8—61no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C42—21no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—61no—
162C4⋊Dic3—62no—
163C4⋊Dic3D1211yescharacteristic
164Dic3⋊C4—21no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—62no—
168Dic3⋊C4—61no—
169Dic3⋊C4—61no—
170Dic3⋊C4—121no—
171C4×Dic3—21no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—121no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—121no—
181Dic12—44no—
182C22×C32#12011yescharacteristic
183C32×C4—21no—
184C32×C4C2×Q1611yescharacteristic
185C32×C4C2×Q1611yescharacteristic
186C32×C4#13711yescharacteristic
187C32×C4#13711yescharacteristic
188C3⋊Dic3—22no—
189C3⋊Dic3—41no—
190C3×Dic3—22no—
191C3×Dic3—41no—
192C3×Dic3—42no—
193C3×Dic3—81no—
194C2×Q16—62no—
195C4⋊Q8—31no—
196C4⋊Q8—31no—
197C4⋊Q8—181no—
198C4⋊Q8—181no—
199C4⋊Q8—182no—
200C4×Q8—31no—
201C4×Q8—91no—
202C4×Q8—181no—
203C4×Q8—181no—
204#107—181no—
205#107—181no—
206C4⋊C8—31no—
207C4⋊C8—91no—
208#103—181no—
209#103—181no—
210C4×C8D3211yescharacteristic
211C3×Q8—32no—
212C3×Q8—61no—
213C3×Q8—122no—
214C3×Q8—122no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—61no—
219C2×C3×C4—62no—
220C2×C3×C4—61no—
221C2×C3×C4—121no—
222C2×C3×C4C2×D1211yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—22no—
231C2×Dic3—41no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—121no—
237C2×Dic3—121no—
238Dic6—21no—
239Dic6—32no—
240Dic6—32no—
241Dic6—42no—
242Dic6—42no—
243Dic6—62no—
244Dic6—61no—
245Dic6—61no—
246Dic6—121no—
247Dic6—242no—
248Dic6—242no—
249Dic6Dic1212yescomplemented
250C3×C8—22no—
251C3×C8—22no—
252C3×C8—42no—
253C3×C8—121no—
254C3⋊C8—41no—
255C3⋊C8—121no—
256C3⋊C8—121no—
257C3⋊C8—241no—
258C2×C32#45111yescharacteristic
259C2×C32#45111yescharacteristic
260C2×C32#45311yescharacteristic
261C2×Q8—31no—
262C2×Q8—32no—
263C2×Q8—61no—
264C2×Q8—91no—
265C2×Q8—182no—
266Q16—124no—
267C2×C8—21no—
268C2×C8—61no—
269C2×C8—181no—
270C4⋊C4—31no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—91no—
277C4⋊C4—182no—
278C4⋊C4—182no—
279C4⋊C4—181no—
280C42—61no—
281C42—182no—
282C42—181no—
283C42C2×D3211yescharacteristic
284C22×C3—21no—
285C22×C3#88211yescharacteristic
286C22×C3#93711yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—62no—
295C3×C4—121no—
296C3×C4—122no—
297C3×C4—241no—
298C3×C4C2×Dic1211yescharacteristic
299C3×C4#90911yescharacteristic
300C3×C4#91511yescharacteristic
301C3×C4D3×Q1611yescharacteristic
302C3×C4D3×Q1611yescharacteristic
303C3×C4D3×Q1611yescharacteristic
304C3×C4#91811yescharacteristic
305C3×C4#91811yescharacteristic
306Dic3—22no—
307Dic3—42no—
308Dic3—41no—
309Dic3—62no—
310Dic3—62no—
311Dic3—81no—
312Dic3—122no—
313Dic3—121no—
314Dic3—121no—
315Dic3—241no—
316C32#163311yescharacteristic, complemented, Sylow
317Q8—32no—
318Q8—61no—
319Q8—92no—
320Q8—122no—
321Q8—122no—
322Q8—181no—
323Q8—722no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—62no—
327C2×C4—121no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4D3×D1211yescharacteristic
331C2×C4#380211yescharacteristic
332C2×C4D3×#6711yescharacteristic
333C8—22no—
334C8—121no—
335C8—361no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3#473911yescharacteristic
340C2×C3#480911yescharacteristic
341C2×C3#482211yescharacteristic
342C2×C3#507711yescharacteristic
343C2×C3#518611yescharacteristic
344C2×C3#518611yescharacteristic
345C22#6392211yescharacteristic
346C4—21no—
347C4—62no—
348C4—122no—
349C4—121no—
350C4—182no—
351C4—241no—
352C4—361no—
353C4D3×Dic1211yescharacteristic
354C4#6380111yescharacteristic
355C4#6380211yescharacteristic
356C4#6381111yescharacteristic
357C3—21no—
358C3#6826711yescharacteristic, complemented
359C3#7130711yescharacteristic, complemented
360C2#1059039511yescharacteristic
361C2#1059094911yescharacteristic
362C2#1059095011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1633
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
109. #634Q16semidirect
117. C3×Dic6Q16semidirect
249. Dic6Dic12semidirect
316. C32#1633semidirect
358. C3#68267semidirect
359. C3#71307semidirect

Maximal subgroups

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

subgroupindex
#105938562
C3×#46992
#105903102
#105902842
#105893222
C3×#44562
#105890952
#713073
#682673