Finite Group Databasebeta

← #11780260

Subgroups — #11780260

Order 1152.

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

normal subgroups only

This group has 432 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#10593879C211yesmaximal, characteristic
2C3×#4851C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5#10589352C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic, complemented
8#71126—31nomaximal
9#68209—31nomaximal
10#64078C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63861—22no—
15#63860—21no—
16#63856—21no—
17#63844—21no—
18#63841—21no—
19C2×#3715—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#817—21no—
23C3×#816—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63565—21no—
27#5584—31no—
28#5542—31no—
29C3×#475—31no—
30#5083—31no—
31#5078—31no—
32#5019—31no—
33#4851D311yescharacteristic, complemented
34#4682—31no—
35C3×D4⋊C8—31no—
36#4535—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4483D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)D412yes—
51C2×C3⋊(C3⋊C8)—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60#3724—22no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3715—42no—
65#1650—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68C3×C4×D4—31no—
69#946—61no—
70C2×#215—61no—
71#936—61no—
72C2×#214—61no—
73#926—61no—
74#924—61no—
75#898—62no—
76#892—61no—
77#887—61no—
78#879—62no—
79#875—61no—
80C4×D12C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—61no—
84#869C2×D311yescharacteristic
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×#103—61no—
92C3×C4×C8—31no—
93#835—61no—
94#818—62no—
95#817—21no—
96#816—21no—
97#810—61no—
98#807—62no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108#634—41no—
109#634—41no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125#556—91no—
126#500—91no—
127#475—31no—
128#461—91no—
129#332—91no—
130Q8⋊C8—91no—
131D4⋊C8—31no—
132C2×C3×Q8—31no—
133C2×C3×Q8—61no—
134C2×C3×D4—31no—
135C22×C3×C4—61no—
136C2×D12D1211yescharacteristic
137C2×C4×D3—21no—
138C2×Dic6—21no—
139C2×Dic6—61no—
140C2×Dic6—61no—
141C2×Dic6—121no—
142C2×Dic6#6711yescharacteristic
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—41no—
146C2×C3×C8—61no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42—61no—
155C3×C42C22×D311yescharacteristic
156C3×C42C22×D311yescharacteristic
157#217—62no—
158#217—62no—
159#215—122no—
160#214—122no—
161(C2×D3)⋊C4—21no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3—32no—
167C4⋊Dic3—32no—
168C4⋊Dic3—62no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171C4⋊Dic3—121no—
172C4⋊Dic3D1211yescharacteristic
173C4⋊Dic3#6711yescharacteristic
174Dic3⋊C4—21no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177C4×Dic3—21no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C22×C32#12011yescharacteristic
185C2×C3×D3—41no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C32×C4—21no—
189C32×C4#13511yescharacteristic
190C32×C4#13511yescharacteristic
191C32×C4AGL(1,ℤ/8)11yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—42no—
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—81no—
198C2×SD16—181no—
199C4⋊Q8—31no—
200C4⋊Q8—91no—
201#126—182no—
202#124—181no—
203C22⋊Q8—181no—
204C4×Q8—31no—
205C4×Q8—181no—
206C4×D4—31no—
207#117—181no—
208#107—182no—
209#106—61no—
210C4⋊C8—91no—
211C4⋊C8D3211yescharacteristic
212#103—61no—
213#103—181no—
214C4×C8—31no—
215C23×C3—61no—
216C22×D3—21no—
217C3×Q8—61no—
218C3×Q8—61no—
219C3×Q8—121no—
220C3×Q8—121no—
221C3×D4—61no—
222C3×D4—61no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—61no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—122no—
245D12—21no—
246D12—21no—
247C4×D3—41no—
248C4×D3—41no—
249Dic6—21no—
250Dic6—21no—
251Dic6—41no—
252Dic6—41no—
253Dic6—121no—
254Dic6—121no—
255Dic6—121no—
256Dic6—121no—
257Dic6—241no—
258Dic6—241no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—62no—
262C3×C8—81no—
263C3⋊C8—22no—
264C3⋊C8—121no—
265C3⋊C8—121no—
266C3⋊C8—241no—
267C2×C32#44911yescharacteristic
268C2×C32#45211yescharacteristic
269C2×C32#45611yescharacteristic
270C3×D3—81no—
271C2×Q8—31no—
272C2×Q8—61no—
273C2×Q8—181no—
274C2×D4—31no—
275C22×C4—61no—
276SD16—362no—
277C2×C8—21no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—92no—
286C4⋊C4—182no—
287C4⋊C4—181no—
288C22⋊C4—61no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C42—61no—
292C42—182no—
293C42C2×D3211yescharacteristic
294C22×C3—21no—
295C22×C3—121no—
296C22×C3—121no—
297C22×C3—121no—
298C22×C3#88211yescharacteristic
299C22×C3#93711yescharacteristic
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—121no—
311C3×C4—121no—
312C3×C4—121no—
313C3×C4—241no—
314C3×C4#90411yescharacteristic
315C3×C4#90811yescharacteristic
316C3×C4#91211yescharacteristic
317C3×C4#91411yescharacteristic
318C3×C4#91511yescharacteristic
319C3×C4#91611yescharacteristic
320C3×C4#94211yescharacteristic
321C3×C4#95011yescharacteristic
322Dic3—41no—
323Dic3—41no—
324Dic3—41no—
325Dic3—81no—
326Dic3—122no—
327Dic3—122no—
328Dic3—242no—
329C32#165011yescharacteristic, complemented, Sylow
330C23—61no—
331Q8—61no—
332Q8—61no—
333Q8—121no—
334Q8—121no—
335Q8—361no—
336Q8—361no—
337D4—61no—
338D4—61no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4—182no—
346C2×C4D3×D1211yescharacteristic
347C2×C4#380211yescharacteristic
348C2×C4D3×#6711yescharacteristic
349C8—41no—
350C8—62no—
351C8—361no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—241no—
356C2×C3#473411yescharacteristic
357C2×C3#478311yescharacteristic
358C2×C3#482611yescharacteristic
359C2×C3#504711yescharacteristic
360C2×C3#517211yescharacteristic
361C2×C3#520511yescharacteristic
362D3—81no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22#6392211yescharacteristic
367C4—21no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4—241no—
372C4—362no—
373C4#6379411yescharacteristic
374C4#6380611yescharacteristic
375C4#6393311yescharacteristic
376C4#6394611yescharacteristic
377C3—21no—
378C3#6820911yescharacteristic, complemented
379C3#7112611yescharacteristic, complemented
380C2—241no—
381C2#1059061411yescharacteristic
382C2#1059082311yescharacteristic
383C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1650
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×#4851C2semidirect
4. #10590311C2semidirect
5. #10589352C2semidirect
7. #10589084C2semidirect
33. #4851D3semidirect
329. C32#1650semidirect
378. C3#68209semidirect
379. C3#71126semidirect

Maximal subgroups

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

subgroupindex
#105938792
C3×#48512
#105903632
#105903112
#105893522
C3×#44832
#105890842
#711263
#682093