Finite Group Databasebeta

← #11780262

Subgroups — #11780262

Order 1152.

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

normal subgroups only

This group has 448 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#10593863C211yesmaximal, characteristic
2#10592550C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic, complemented
8#68437—31nomaximal
9#68209—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63863—21no—
15#63858—22no—
16#63857—21no—
17#63843—21no—
18#63841—21no—
19C2×#3716—21no—
20C32×C4⋊C8C2211yescharacteristic
21#63644—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63567—21no—
27#5732—31no—
28#5542—31no—
29#5078—31no—
30#5019—31no—
31#4851—31no—
32#4851—31no—
33#4851—61no—
34#4841—31no—
35#4682—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4484—31no—
40#4483D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D412yes—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3716—42no—
65#1650—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—31no—
68#947—61no—
69Q8×Dic3—61no—
70#936—61no—
71C2×#214—61no—
72#926—61no—
73#924—61no—
74C2×#204—61no—
75#898—62no—
76#897—61no—
77#892—61no—
78#887—61no—
79#879—62no—
80C4×D12C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—61no—
84#869C2×D311yescharacteristic
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4×C8—31no—
93#818—62no—
94#817—61no—
95#817—61no—
96#817—62no—
97#816—61no—
98#816—61no—
99#816—62no—
100#816—61no—
101#810—61no—
102#807—62no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112#634—21no—
113#634—21no—
114#634—41no—
115#634—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C32×C8—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—91no—
128#500—91no—
129#475—91no—
130#461—91no—
131#332—31no—
132Q8⋊C8—91no—
133D4⋊C8—31no—
134C2×C3×Q8—61no—
135C2×C3×D4—31no—
136C22×C3×C4—61no—
137C2×D12D1211yescharacteristic
138C2×C4×D3—21no—
139C2×Dic6—21no—
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—121no—
146C2×C3×C8—22no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151C3×C4⋊C4—32no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—61no—
154C3×C22⋊C4—61no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C22×D311yescharacteristic
158#217—62no—
159#217—62no—
160#214—122no—
161(C2×D3)⋊C4—21no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164C4⋊Dic3—21no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—61no—
168C4⋊Dic3—62no—
169C4⋊Dic3—62no—
170C4⋊Dic3—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—121no—
175C4⋊Dic3D1211yescharacteristic
176C4⋊Dic3D1212yes—
177Dic3⋊C4—62no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4—121no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—121no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188#204—122no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4#13511yescharacteristic
195C32×C4#13511yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4#13711yescharacteristic
198C3⋊Dic3—41no—
199C3⋊Dic3—41no—
200C3⋊Dic3—81no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×SD16—181no—
204C4⋊Q8—31no—
205C4⋊Q8—91no—
206#126—182no—
207#124—181no—
208C22⋊Q8—181no—
209C4×Q8—91no—
210C4×Q8—181no—
211C4×D4—31no—
212#117—181no—
213#107—182no—
214#106—181no—
215C4⋊C8—31no—
216C4⋊C8D3211yescharacteristic
217#103—181no—
218#103—181no—
219C4×C8—31no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—61no—
225C3×D4—61no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—61no—
230C2×C3×C4—62no—
231C2×C3×C4—121no—
232C2×C3×C4—121no—
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—22no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—122no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250D12—21no—
251D12—21no—
252C4×D3—41no—
253C4×D3—41no—
254Dic6—41no—
255Dic6—41no—
256Dic6—62no—
257Dic6—61no—
258Dic6—61no—
259Dic6—61no—
260Dic6—61no—
261Dic6—121no—
262Dic6—121no—
263Dic6—121no—
264Dic6—121no—
265Dic6—121no—
266Dic6—241no—
267Dic6—241no—
268C3×C8—42no—
269C3×C8—41no—
270C3×C8—41no—
271C3×C8—62no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45611yescharacteristic
278C3×D3—81no—
279C2×Q8—61no—
280C2×Q8—91no—
281C2×Q8—181no—
282C2×D4—31no—
283C22×C4—61no—
284SD16—362no—
285C2×C8—21no—
286C2×C8—61no—
287C2×C8—61no—
288C4⋊C4—31no—
289C4⋊C4—32no—
290C4⋊C4—61no—
291C4⋊C4—91no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C22⋊C4—61no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C42—182no—
300C42—181no—
301C42C2×D3211yescharacteristic
302C22×C3—21no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3#88211yescharacteristic
307C22×C3#88211yescharacteristic
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—122no—
319C3×C4—121no—
320C3×C4#90411yescharacteristic
321C3×C4#90811yescharacteristic
322C3×C4#91111yescharacteristic
323C3×C4#91211yescharacteristic
324C3×C4#91511yescharacteristic
325C3×C4#91611yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4#91811yescharacteristic
328Dic3—42no—
329Dic3—41no—
330Dic3—122no—
331Dic3—121no—
332Dic3—121no—
333Dic3—121no—
334Dic3—121no—
335Dic3—241no—
336Dic3—242no—
337Dic3—241no—
338Dic3—241no—
339C32#165011yescharacteristic, complemented, Sylow
340C23—61no—
341Q8—121no—
342Q8—121no—
343Q8—181no—
344Q8—181no—
345Q8—361no—
346Q8—361no—
347D4—61no—
348D4—61no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—361no—
356C2×C4D3×D1211yescharacteristic
357C2×C4D3×D1211yescharacteristic
358C2×C4#381111yescharacteristic
359C8—41no—
360C8—62no—
361C8—121no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#473411yescharacteristic
367C2×C3#475211yescharacteristic
368C2×C3#478111yescharacteristic
369C2×C3#478311yescharacteristic
370C2×C3#480811yescharacteristic
371C2×C3#482611yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6392311yescharacteristic
377C4—21no—
378C4—121no—
379C4—122no—
380C4—361no—
381C4—361no—
382C4—721no—
383C4#6379511yescharacteristic
384C4#6380611yescharacteristic
385C4#6393611yescharacteristic
386C4#6395111yescharacteristic
387C3—21no—
388C3#6820911yescharacteristic, complemented
389C3#6843711yescharacteristic, complemented
390C2—241no—
391C2#1059061811yescharacteristic
392C2#1059096811yescharacteristic
393C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
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. #10592550C2semidirect
4. #10590311C2semidirect
5. C3×#4486C2semidirect
7. #10589085C2semidirect
38. #4486D3semidirect
339. C32#1650semidirect
388. C3#68209semidirect
389. C3#68437semidirect

Maximal subgroups

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

subgroupindex
#105938632
#105925502
#105903652
#105903112
C3×#44862
C3×#44832
#105890852
#684373
#682093