Finite Group Databasebeta

← #11775745

Subgroups — #11775745

Order 1152.

575 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 575 conjugacy classes of subgroups — too many to draw. Only its 112 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×#5668C211yesmaximal, characteristic
2#10590334C212yesmaximal, complemented
3#10589406C211yesmaximal, characteristic, complemented
4C3×#4540C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71797—31nomaximal
7#68342—31nomaximal
8C2×C3×#239C411yescharacteristic
9C2×C3×#237C411yescharacteristic
10C32×#124C2211yescharacteristic
11C3×#944C411yescharacteristic
12C3×#940C411yescharacteristic
13C3×#884—22no—
14C3×#67⋊C4—22no—
15C3×#875C2211yescharacteristic
16C3×C42×D3C2211yescharacteristic
17C2×#3711—22no—
18#63630C2212yes—
19C3×#803C2212yes—
20Dic3×C3⋊C8—22no—
21C3×#532—31no—
22#5668D311yescharacteristic
23C4×#208—32no—
24#4707—32no—
25C3×#329—31no—
26#4540—31no—
27#4540—31no—
28#4540—32no—
29#4540—61no—
30#4540D311yescharacteristic, complemented
31#4464—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×D4C2×C411yescharacteristic
34C2×C3×#67—21no—
35C2×C3×#67—22no—
36C22×C3×Dic3—21no—
37C3×#239—42no—
38C3×#237—42no—
39C2×C3×D12—21no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×C4×D3C2×C411yescharacteristic
43C2×C3×C4×D3D412yes—
44C2×C3×Dic6C2×C411yescharacteristic
45C32×C22⋊C4—22no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×C4×Dic3C2×C411yescharacteristic
51C3×C4×Dic3D412yes—
52C2×C3×C3⋊C8—22no—
53#3711—28no—
54#1525—91noSylow
55C2×C3×#41—31no—
56C2×C3×#41—31no—
57C2×#239Dic311yescharacteristic
58C2×#237Dic311yescharacteristic
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C3×#124—21no—
62C3×#124—31no—
63C3×#124C2×D311yescharacteristic
64C3×#124C2×D311yescharacteristic
65C3×#121—62no—
66C3×C4×D4—62no—
67C2×C3×C42—31no—
68#944Dic311yescharacteristic
69#940Dic311yescharacteristic
70C2×#208—62no—
71C2×ΓL(1,𝔽25)—62no—
72#884—22no—
73#67⋊C4—22no—
74#875C2×D311yescharacteristic
75C42×D3C2×D311yescharacteristic
76C3×#97—32no—
77C8×Dic3—62no—
78#803—32no—
79#803—32no—
80#803—62no—
81#803C2×D312yes—
82C4×C3⋊C8—62no—
83C23×C32—21no—
84C22×C3×D3—21no—
85C22×C3×D3C22⋊C411yescharacteristic
86C32×Q8—41no—
87C32×D4—41no—
88C2×C32×C4—21no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D412yes—
91C3×#67—42no—
92C3×#67—44no—
93C2×C3×Dic3—21no—
94C2×C3×Dic3—42no—
95C2×C3×Dic3C22⋊C411yescharacteristic
96C2×C3×Dic3C22⋊C412yes—
97C3×D12—41no—
98C3×D12—42no—
99C3×C4×D3—22no—
100C3×C4×D3—24no—
101C3×C4×D3—42no—
102C3×Dic6—41no—
103C3⋊(C3⋊C8)—24no—
104C3×C3⋊C8—24no—
105#532—31no—
106C4×M16—92no—
107#329—31no—
108#329—92no—
109#329—91no—
110C3×#41—122no—
111C3×#41—122no—
112C2×C3×Q8—21no—
113C2×C3×Q8—31no—
114C2×C3×Q8C4×D311yescharacteristic
115C2×C3×Q8C2×Dic311yescharacteristic
116C2×C3×D4—21no—
117C2×C3×D4—31no—
118C2×C3×D4—61no—
119C2×C3×D4—62no—
120C2×C3×D4—61no—
121C2×C3×D4C4×D311yescharacteristic
122C2×C3×D4C2×Dic311yescharacteristic
123C22×C3×C4—31no—
124C22×C3×C4—32no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C2×#67—21no—
128C2×#67—22no—
129C22×Dic3—21no—
130#239—42no—
131#237—42no—
132C2×D12—21no—
133C2×D12C2×Dic311yescharacteristic
134C2×C4×D3—21no—
135C2×C4×D3C2×Dic311yescharacteristic
136C2×C4×D3#6712yes—
137C2×Dic6C2×Dic311yescharacteristic
138C2×C3×C8—62no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—22no—
142C3×C22⋊C4—42no—
143C3×C22⋊C4—62no—
144C3×C42—21no—
145C3×C42—31no—
146C3×C42—32no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149(C2×D3)⋊C4—22no—
150Dic3⋊C4—22no—
151C4×Dic3C2×Dic311yescharacteristic
152C4×Dic3#6712yes—
153#208—68no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—122no—
158ΓL(1,𝔽25)—68no—
159C22×C32—41no—
160C22×C32—42no—
161C22×C32C2×C22⋊C411yescharacteristic
162C2×C3×D3—21no—
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—42no—
166C32×C4—21no—
167C32×C4—22no—
168C32×C4—41no—
169C3×Dic3—41no—
170C3×Dic3#10012yes—
171C3×Dic3#10414yes—
172C2×#41—31no—
173C2×#41—31no—
174C2×M16—182no—
175C4⋊Q8—31no—
176#127—31no—
177#124—31no—
178#124D3211yescharacteristic
179#121—62no—
180C4×D4—62no—
181C2×C42—31no—
182#97—32no—
183#97—92no—
184C4×C8—182no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—31no—
188C23×C3—41no—
189C23×C3—61no—
190C22×D3—21no—
191C22×D3#21711yescharacteristic
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—81no—
195C3×Q8—121no—
196C3×D4—41no—
197C3×D4—41no—
198C3×D4—81no—
199C3×D4—121no—
200C3×D4—124no—
201C3×D4—122no—
202C3×D4—122no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—22no—
207C2×C3×C4—32no—
208C2×C3×C4—31no—
209C2×C3×C4—41no—
210C2×C3×C4—64no—
211C2×C3×C4—62no—
212C2×C3×C4—61no—
213C2×C3×C4—122no—
214C2×C3×C4—122no—
215C2×C3×C4C2×C4×D311yescharacteristic
216C2×C3×C4D3×D412yes—
217C2×C3×C4C22×Dic311yescharacteristic
218C2×C3×C4C2×#6712yes—
219#67—42no—
220#67—44no—
221C2×Dic3—21no—
222C2×Dic3—42no—
223C2×Dic3#21711yescharacteristic
224C2×Dic3#21712yes—
225D12—41no—
226D12—42no—
227C4×D3—22no—
228C4×D3—24no—
229C4×D3—42no—
230Dic6—41no—
231C3×C8—64no—
232C3⋊C8—24no—
233C3⋊C8—64no—
234C3⋊C8—64no—
235C3⋊C8—124no—
236C2×C32—81no—
237C2×C32C2×#10011yescharacteristic
238C2×C32C2×#10412yes—
239C3×D3—41no—
240C3×D3—81no—
241#41—122no—
242#41—122no—
243C2×Q8—31no—
244C2×Q8D3×Dic311yescharacteristic
245C2×D4—31no—
246C2×D4—61no—
247C2×D4—62no—
248C2×D4—61no—
249C2×D4D3×Dic311yescharacteristic
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—61no—
253C22×C4—61no—
254M16—188no—
255C2×C8—62no—
256C2×C8—182no—
257C4⋊C4—62no—
258C22⋊C4—22no—
259C22⋊C4—62no—
260C42—31no—
261C42—32no—
262C42C2×D3211yescharacteristic
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—42no—
268C22×C3—61no—
269C22×C3—62no—
270C22×C3—81no—
271C22×C3—82no—
272C22×C3—121no—
273C22×C3—122no—
274C22×C3D3×C22⋊C411yescharacteristic
275C22×C3C2×#21711yescharacteristic
276C2×D3—21no—
277C2×D3—22no—
278C2×D3—41no—
279C2×D3—42no—
280C3×C4—21no—
281C3×C4—22no—
282C3×C4—21no—
283C3×C4—22no—
284C3×C4—32no—
285C3×C4—34no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—81no—
291C3×C4—121no—
292Dic3—41no—
293Dic3#83312yes—
294Dic3#83714yes—
295C32#152511yescharacteristic, complemented, Sylow
296C23—21no—
297C23—31no—
298C23—61no—
299Q8—41no—
300Q8—121no—
301D4—41no—
302D4—121no—
303D4—124no—
304D4—122no—
305D4—122no—
306C2×C4—21no—
307C2×C4—32no—
308C2×C4—31no—
309C2×C4—64no—
310C2×C4—62no—
311C2×C4—61no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4C2×D3×Dic311yescharacteristic
315C2×C4D3×#6712yes—
316C8—64no—
317C8—184no—
318C2×C3—21no—
319C2×C3—22no—
320C2×C3—81no—
321C2×C3—81no—
322C2×C3—121no—
323C2×C3—161no—
324C2×C3—241no—
325C2×C3D3×#10011yescharacteristic
326C2×C3D3×#10412yes—
327C2×C3C2×#83311yescharacteristic
328C2×C3C2×#83712yes—
329D3—41no—
330D3—81no—
331C22—41no—
332C22—42no—
333C22—61no—
334C22—62no—
335C22—121no—
336C22—122no—
337C22D3×#21711yescharacteristic
338C4—21no—
339C4—22no—
340C4—32no—
341C4—34no—
342C4—41no—
343C4—121no—
344C3—21no—
345C3#6834211yescharacteristic, complemented
346C3#7179711yescharacteristic, complemented
347C2—81no—
348C2—121no—
349C2—241no—
350C2D3×#83311yescharacteristic
351C2D3×#83712yes—
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5668C2
cosocleC32×C42C23
hypercenter#124D32
hypocenterC32#1525
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10590334C2semidirect
3. #10589406C2semidirect
4. C3×#4540C2semidirect
5. #10589086C2semidirect
30. #4540D3semidirect
295. C32#1525semidirect
345. C3#68342semidirect
346. C3#71797semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
#105903342
#105894062
C3×#45402
#105890862
#717973
#683423