Finite Group Databasebeta

← #11780168

Subgroups — #11780168

Order 1152.

436 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593864C211yesmaximal, characteristic
2#10592550C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#68460—31nomaximal
9#68272—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63873—21no—
15#63869—21no—
16#63847—22no—
17#63844—21no—
18#63843—21no—
19C2×#3719—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#5721—31no—
28#5567—31no—
29#5078—31no—
30#5031—31no—
31#4851—31no—
32#4851—31no—
33#4851—61no—
34#4849—31no—
35#4682—31no—
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38#4486D311yescharacteristic
39#4484—31no—
40#4484D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D412yes—
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3—21no—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60#3724—22no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3719—42no—
65#1648—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68Q8×Dic3—61no—
69#944—61no—
70#944—61no—
71C2×#216—61no—
72C2×Dic12—61no—
73#890—61no—
74#889—62no—
75#889—62no—
76#887—61no—
77#887—61no—
78#870—61no—
79#869—31no—
80#869—31no—
81#869—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6—61no—
87C4×Dic6C2×D311yescharacteristic
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
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—41no—
111#634—21no—
112#634—41no—
113#634—41no—
114#634Q1612yescomplemented
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—41no—
125#557—91no—
126#500—91no—
127#475—91no—
128#462—91no—
129#332—31no—
130Q8⋊C8—31no—
131Q8⋊C8—91no—
132C2×C3×Q8—31no—
133C2×C3×Q8—61no—
134C2×Dic6—21no—
135C2×Dic6—31no—
136C2×Dic6—31no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C2×Dic6D1211yescharacteristic
142C2×C3×C8—22no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—32no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C42—21no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#216—122no—
156C4⋊Dic3—21no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—61no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—121no—
167C4⋊Dic3D1211yescharacteristic
168C4⋊Dic3D1212yes—
169Dic3⋊C4—21no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—121no—
178C4×Dic3—21no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—121no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186Dic12—122no—
187C22×C32#12011yescharacteristic
188C32×C4—21no—
189C32×C4C2×Q1611yescharacteristic
190C32×C4#13511yescharacteristic
191C32×C4AGL(1,ℤ/8)11yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—22no—
194C3⋊Dic3—41no—
195C3⋊Dic3—81no—
196C3×Dic3—41no—
197C3×Dic3—42no—
198C3×Dic3—41no—
199C2×Q16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—91no—
202C4⋊Q8—181no—
203#125—181no—
204#125—182no—
205C4×Q8—31no—
206C4×Q8—91no—
207C4×Q8—181no—
208C4×Q8—181no—
209#107—182no—
210#106—181no—
211C4⋊C8—31no—
212C4⋊C8D3211yescharacteristic
213#103—181no—
214#103—181no—
215C4×C8—31no—
216C3×Q8—61no—
217C3×Q8—61no—
218C3×Q8—121no—
219C3×Q8—121no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—61no—
224C2×C3×C4—62no—
225C2×C3×C4—61no—
226C2×C3×C4C2×D1211yescharacteristic
227C2×C3×C4C2×D1211yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—22no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241C2×Dic3—122no—
242C2×Dic3—121no—
243C2×Dic3—121no—
244Dic6—21no—
245Dic6—21no—
246Dic6—32no—
247Dic6—32no—
248Dic6—41no—
249Dic6—41no—
250Dic6—62no—
251Dic6—61no—
252Dic6—61no—
253Dic6—121no—
254Dic6—121no—
255Dic6—121no—
256Dic6—121no—
257Dic6—121no—
258Dic6—241no—
259Dic6—241no—
260C3×C8—42no—
261C3×C8—41no—
262C3×C8—41no—
263C3×C8—62no—
264C3×C8—121no—
265C3⋊C8—22no—
266C3⋊C8—41no—
267C2×C32#44911yescharacteristic
268C2×C32#45111yescharacteristic
269C2×C32#45611yescharacteristic
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8—91no—
273C2×Q8—181no—
274Q16—362no—
275C2×C8—21no—
276C2×C8—61no—
277C2×C8—61no—
278C4⋊C4—31no—
279C4⋊C4—32no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—91no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4—182no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C42—61no—
290C42—182no—
291C42—181no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3#88211yescharacteristic
295C22×C3#88211yescharacteristic
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—122no—
304C3×C4—121no—
305C3×C4—121no—
306C3×C4#90411yescharacteristic
307C3×C4#90811yescharacteristic
308C3×C4#91111yescharacteristic
309C3×C4#91511yescharacteristic
310C3×C4#91511yescharacteristic
311C3×C4#91611yescharacteristic
312C3×C4D3×Q1611yescharacteristic
313C3×C4D3×Q1611yescharacteristic
314Dic3—41no—
315Dic3—42no—
316Dic3—41no—
317Dic3—62no—
318Dic3—62no—
319Dic3—122no—
320Dic3—121no—
321Dic3—121no—
322Dic3—241no—
323Dic3—242no—
324Dic3—241no—
325Dic3—241no—
326C32#164811yescharacteristic, complemented, Sylow
327Q8—61no—
328Q8—61no—
329Q8—92no—
330Q8—121no—
331Q8—121no—
332Q8—181no—
333Q8—361no—
334Q8—361no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—62no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—361no—
341C2×C4D3×D1211yescharacteristic
342C2×C4D3×D1211yescharacteristic
343C2×C4#381111yescharacteristic
344C8—41no—
345C8—62no—
346C8—121no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3#473411yescharacteristic
351C2×C3#475211yescharacteristic
352C2×C3#478111yescharacteristic
353C2×C3#480911yescharacteristic
354C2×C3#480911yescharacteristic
355C2×C3#482611yescharacteristic
356C22#6392311yescharacteristic
357C4—21no—
358C4—121no—
359C4—121no—
360C4—122no—
361C4—182no—
362C4—361no—
363C4—721no—
364C4#6379511yescharacteristic
365C4#6380611yescharacteristic
366C4#6393111yescharacteristic
367C4#6394411yescharacteristic
368C3—21no—
369C3#6827211yescharacteristic, complemented
370C3#6846011yescharacteristic, complemented
371C2#1059060511yescharacteristic
372C2#1059096811yescharacteristic
373C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1648
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
114. #634Q16semidirect
326. C32#1648semidirect
369. C3#68272semidirect
370. C3#68460semidirect

Maximal subgroups

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

subgroupindex
#105938642
#105925502
#105903852
#105903112
C3×#44862
C3×#44842
#105890852
#684603
#682723