Finite Group Databasebeta

← #11798773

Subgroups — #11798773

Order 1152.

505 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 505 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#5672C211yesmaximal, characteristic, complemented
2#10592761C211yesmaximal, characteristic
3#10591650C212yesmaximal, complemented
4C3×#4542C211yesmaximal, characteristic, complemented
5#10589184C212yesmaximal, complemented
6#71959—31nomaximal
7#69162—31nomaximal
8#64364C2211yescharacteristic
9C32×#124C2211yescharacteristic
10#64141—21no—
11C3×#944C2212yes—
12C3×#935—21no—
13C3×#879—22no—
14C3×#878—22no—
15C3×#870—21no—
16#63833—22no—
17#63663C2211yescharacteristic
18#63632—21no—
19C3×#836C2212yes—
20#63570—22no—
21C3×#563—31no—
22#5672D311yescharacteristic, complemented
23#5095—32no—
24#5062—31no—
25#5062—31no—
26#5062—61no—
27#4752—32no—
28C3×#355—31no—
29#4548—32no—
30#4542D311yescharacteristic, complemented
31#4478—32no—
32C2×C32×Q8C2311yescharacteristic
33C2×C32×D4D411yescharacteristic
34#3832—41no—
35Q8×C3⋊D3—41no—
36#3828—21no—
37#3828—22no—
38C22×C3×Dic3—21no—
39C2×C3×Dic6D412yes—
40C32×C22⋊C4—22no—
41C32×C42D411yescharacteristic
42#3754—41no—
43#3753—41no—
44#3748—21no—
45C3×#217—22no—
46C3×#217—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3D412yes—
53C3×#208—22no—
54#3719—42no—
55#3717—42no—
56#2203—91noSylow
57#1007—31no—
58#1007—31no—
59#1007—61no—
60C3×C4⋊Q8—32no—
61C3×#126—62no—
62C3×#125—61no—
63C3×#124—21no—
64C3×#124C2×D311yescharacteristic
65C3×#124C2×D311yescharacteristic
66C3×#123—61no—
67C3×C22⋊Q8—62no—
68#944C2×D312yes—
69#942—62no—
70#935—21no—
71#932—62no—
72#932—61no—
73#932—61no—
74#909—62no—
75#879—22no—
76#878—22no—
77#870—21no—
78C3×#101—32no—
79#836—31no—
80#836—31no—
81#836—61no—
82#836C2×D312yes—
83#825—62no—
84#805—62no—
85#805—62no—
86#805—61no—
87#805—61no—
88C23×C32—21no—
89C32×Q8—41no—
90C32×D4—41no—
91C2×C32×C4—21no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D412yes—
94#638—41no—
95C4⋊(C3⋊D3)—21no—
96C4⋊(C3⋊D3)—22no—
97C4×C3⋊D3—41no—
98C4×C3⋊D3—42no—
99#634—21no—
100#634—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—81no—
104C3×Dic6—42no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—42no—
107#563—31no—
108#456—92no—
109#454—91no—
110#356—92no—
111#355—31no—
112C2×C3×Q8—21no—
113C2×C3×Q8—32no—
114C2×C3×Q8C22×D311yescharacteristic
115C2×C3×Q8C22×D311yescharacteristic
116C2×C3×D4—21no—
117C2×C3×D4D1211yescharacteristic
118C2×C3×D4#6711yescharacteristic
119C22×C3×C4—61no—
120C22×Dic3—21no—
121#239—121no—
122#239—121no—
123#239—122no—
124D3×Q8—121no—
125D3×Q8—121no—
126D3×Q8—122no—
127#235—62no—
128#235—61no—
129#235—62no—
130#235—61no—
131#235—62no—
132#235—122no—
133C2×Dic6#6712yes—
134C3×M16—62no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—22no—
142C3×C22⋊C4—42no—
143C3×C22⋊C4—62no—
144C3×C22⋊C4—61no—
145C3×C42—21no—
146C3×C42—32no—
147C3×C42D1211yescharacteristic
148C3×C42#6711yescharacteristic
149#217—22no—
150#217—21no—
151#216—122no—
152#215—122no—
153#214—121no—
154#214—121no—
155#214—122no—
156#213—121no—
157#213—121no—
158#213—122no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161Dic3⋊C4—22no—
162Dic3⋊C4—22no—
163Dic3⋊C4—22no—
164C4×Dic3#6712yes—
165#208—22no—
166#208—62no—
167#208—61no—
168#208—61no—
169Dic12—122no—
170#204—122no—
171C22×C32—42no—
172C22×C32—41no—
173C22×C32#12011yescharacteristic
174C2×C3⋊D3—41no—
175C32×C4—21no—
176C32×C4—22no—
177C32×C4—41no—
178C3⋊Dic3—41no—
179C3×Dic3—42no—
180C3×Dic3—42no—
1812−1+4—91no—
182#137—182no—
183AGL(1,ℤ/8)—181no—
184C4⋊Q8—32no—
185#126—62no—
186#125—61no—
187#124D3211yescharacteristic
188#123—61no—
189C22⋊Q8—62no—
190#104—182no—
191#104—181no—
192#101—32no—
193#101—91no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—41no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—42no—
200C3×Q8—122no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—42no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—22no—
208C2×C3×C4—41no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—241no—
212C2×C3×C4C2×D1211yescharacteristic
213C2×C3×C4D3×D412yes—
214C2×C3×C4C2×#6711yescharacteristic
215C2×C3×C4C2×#6712yes—
216#67—122no—
217#67—121no—
218#67—121no—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—81no—
222D12—62no—
223D12—62no—
224D12—61no—
225D12—61no—
226D12—62no—
227D12—122no—
228C4×D3—122no—
229C4×D3—121no—
230C4×D3—122no—
231C4×D3—122no—
232C4×D3—121no—
233C4×D3—124no—
234Dic6—42no—
235Dic6—62no—
236Dic6—62no—
237Dic6—61no—
238Dic6—61no—
239Dic6—62no—
240Dic6—122no—
241C3×C8—122no—
242C3⋊C8—42no—
243C3⋊C8—122no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C2×C32—21no—
247C2×C32—81no—
248C2×C32B(4,𝔽2)11yescharacteristic
249C3⋊D3—81no—
250#41—181no—
251#41—182no—
252#41—361no—
253C2×Q8—32no—
254C2×Q8—361no—
255C2×Q8C2×D3211yescharacteristic
256C2×D4#62611yescharacteristic
257C22×C4—61no—
258Q16—362no—
259SD16—362no—
260SD16—361no—
261D8—361no—
262M16—62no—
263M16—181no—
264C4⋊C4—61no—
265C4⋊C4—62no—
266C4⋊C4—61no—
267C4⋊C4—62no—
268C4⋊C4—62no—
269C22⋊C4—22no—
270C22⋊C4—62no—
271C22⋊C4—61no—
272C42—32no—
273C42#62611yescharacteristic
274C22×C3—21no—
275C22×C3—42no—
276C22×C3—42no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—81no—
280C22×C3—82no—
281C22×C3#88211yescharacteristic
282C22×C3#95311yescharacteristic
283C2×D3—122no—
284C2×D3—121no—
285C2×D3—121no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—21no—
291C3×C4—42no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—81no—
295C3×C4—122no—
296C3×C4—122no—
297Dic3—42no—
298Dic3—42no—
299Dic3—122no—
300Dic3—121no—
301Dic3—121no—
302C32#220311yescharacteristic, complemented, Sylow
303C23—21no—
304Q8—41no—
305Q8—122no—
306Q8—181no—
307Q8—182no—
308D4—41no—
309D4—181no—
310D4—182no—
311D4—361no—
312C2×C4—21no—
313C2×C4—62no—
314C2×C4—62no—
315C2×C4—241no—
316C2×C4—362no—
317C2×C4—361no—
318C2×C4C2×#62611yescharacteristic
319C2×C4D3×#6712yes—
320C8—122no—
321C8—361no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—41no—
326C2×C3—81no—
327C2×C3—81no—
328C2×C3—161no—
329C2×C3#474111yescharacteristic
330C2×C3#524411yescharacteristic
331D3—242no—
332D3—241no—
333D3—241no—
334C22—42no—
335C22—41no—
336C22—361no—
337C22#6397711yescharacteristic
338C4—22no—
339C4—21no—
340C4—41no—
341C4—122no—
342C4—122no—
343C4—361no—
344C3—21no—
345C3#6916211yescharacteristic, complemented
346C3#7195911yescharacteristic, complemented
347C2—21no—
348C2—81no—
349C2—721no—
350C2#1059153111yescharacteristic
subgroupG/H
centerC2#10591531
commutator, cosocleC2×C32×Q8C23
FrattiniC2×Q8C2×D32
FittingC32×#124C22
socleC2×C32B(4,𝔽2)
prime radical#10592761C2
hypercenter#124D32
hypocenterC32#2203
LCSG ▷ C2×C32×Q8 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5672C2semidirect
3. #10591650C2semidirect
4. C3×#4542C2semidirect
5. #10589184C2semidirect
22. #5672D3semidirect
30. #4542D3semidirect
302. C32#2203semidirect
345. C3#69162semidirect
346. C3#71959semidirect

Maximal subgroups

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

subgroupindex
C3×#56722
#105927612
#105916502
C3×#45422
#105891842
#719593
#691623