Finite Group Databasebeta

← #11795174

Subgroups — #11795174

Order 1152.

376 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#63743C211yesmaximal, characteristic
2C2×#63742C211yesmaximal, characteristic
3#10591360C211yesmaximal, characteristic
4#10591337C211yesmaximal, characteristic
5#10590207C211yesmaximal, characteristic
6#10590075C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×Dic3⋊C4—21no—
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16#63743—22no—
17#63742—22no—
18C3×C3⋊#95—21no—
19#63579—21no—
20#63579—21no—
21#4976—61no—
22#4650—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C22×C3×Dic3—21no—
27C22×C3×Dic3—21no—
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C2×#622—21no—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622—21no—
34C2×#622Q812yes—
35C2×#622Q812yes—
36C4×C3⋊Dic3—21no—
37C4×C3⋊Dic3—21no—
38C3×Dic3⋊C4—42no—
39#3724—21no—
40#3724—21no—
41#3724—21no—
42#3724—21no—
43#3724—21no—
44#3724—21no—
45#3724—21no—
46#3724D412yes—
47#2085—91nomaximal, Sylow
48C2×C3×C4⋊C4—61no—
49C2×Dic3⋊C4—21no—
50C2×Dic3⋊C4—61no—
51C2×Dic3⋊C4—61no—
52C2×Dic3⋊C4—61no—
53C2×Dic3⋊C4—61no—
54C2×C4×Dic3—61no—
55C2×C4×Dic3—61no—
56C3×#95—61no—
57C3⋊#95—21no—
58C3⋊#95—61no—
59C3⋊#95—61no—
60C3⋊#95—61no—
61C3⋊#95—61no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×Q811yescharacteristic
71C2×C3⋊Dic3C2×Q811yescharacteristic
72C2×C3⋊Dic3#4111yescharacteristic
73C2×C3⋊Dic3#4111yescharacteristic
74C2×C3⋊Dic3#4111yescharacteristic
75C2×C3×Dic3—22no—
76C2×C3×Dic3—41no—
77C2×C3×Dic3—41no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87#622—22no—
88#622—22no—
89C2×#107—91no—
90C2×#106—91no—
91#389—91no—
92#382—91no—
93#340—91no—
94#340—91no—
95#336—91no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102C22×Dic3—21no—
103C22×Dic3—21no—
104C22×Dic3—21no—
105C22×Dic3—21no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C3×C4⋊C4—122no—
111Dic3⋊C4—42no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114Dic3⋊C4—121no—
115Dic3⋊C4—121no—
116Dic3⋊C4—121no—
117Dic3⋊C4—121no—
118Dic3⋊C4—121no—
119Dic3⋊C4—121no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C4×Dic3—121no—
123C4×Dic3—121no—
124C22×C32#12111yescharacteristic
125C22×C32#12311yescharacteristic
126C22×C32C4⋊Q811yescharacteristic
127C22×C32#13511yescharacteristic
128C22×C32#13511yescharacteristic
129C22×C32AGL(1,ℤ/8)11yescharacteristic
130C22×C32#13711yescharacteristic
131C32×C4—41no—
132C3⋊Dic3—41no—
133C3⋊Dic3C22⋊Q811yescharacteristic
134C3⋊Dic3C22⋊Q811yescharacteristic
135C3⋊Dic3#12511yescharacteristic
136C3⋊Dic3#12511yescharacteristic
137C3×Dic3—42no—
138C3×Dic3—81no—
139C3×Dic3—81no—
140C3×Dic3—81no—
141C22×C8—91no—
142C22×C8—91no—
143C2×C4⋊C4—61no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C2×C42—91no—
149#107—182no—
150#106—182no—
151#95—61no—
152#95—181no—
153#95—181no—
154C23×C3—21no—
155C23×C3—21no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—62no—
163C2×C3×C4—121no—
164C2×C3×C4—121no—
165C2×C3×C4—121no—
166C2×C3×C4—121no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174C2×Dic3—22no—
175C2×Dic3—41no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204C2×C32#39811yescharacteristic
205C2×C32#46311yescharacteristic
206C2×C32#46411yescharacteristic
207C2×C32#48211yescharacteristic
208C2×C32#48511yescharacteristic
209C2×C32#49911yescharacteristic
210C2×C32#50111yescharacteristic
211C22×C4—61no—
212C22×C4—61no—
213C22×C4—61no—
214C22×C4—61no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4GO+(4,𝔽2)11yescharacteristic
218C2×C8—92no—
219C2×C8—92no—
220C2×C8—181no—
221C2×C8—181no—
222C2×C8—181no—
223C2×C8—181no—
224C4⋊C4—92no—
225C4⋊C4—122no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C42—181no—
234C42—181no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C3×C4—42no—
250C3×C4—42no—
251C3×C4—122no—
252C3×C4—241no—
253C3×C4—241no—
254C3×C4—241no—
255Dic3—42no—
256Dic3—61no—
257Dic3—61no—
258Dic3—61no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—81no—
265Dic3—81no—
266Dic3—81no—
267Dic3—122no—
268Dic3—122no—
269C32#208511yescharacteristic, complemented, Sylow
270C23C2×GO+(4,𝔽2)11yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—121no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4—121no—
285C2×C4—121no—
286C2×C4—121no—
287C2×C4—121no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C8—182no—
296C8—182no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C22#6422211yescharacteristic
312C22#6422311yescharacteristic
313C22#6422611yescharacteristic
314C22#6423011yescharacteristic
315C22#6423311yescharacteristic
316C22#6423611yescharacteristic
317C22#6423711yescharacteristic
318C4—41no—
319C4—91no—
320C4—91no—
321C4—91no—
322C4—91no—
323C4—122no—
324C4—241no—
325C4—241no—
326C4—241no—
327C4—361no—
328C3—21no—
329C3—21no—
330C2#1059333911yescharacteristic
331C2#1059337011yescharacteristic
332C2#1059339011yescharacteristic
333C2#1059339211yescharacteristic
334C2#1059342211yescharacteristic
335C2#1059344011yescharacteristic
336C2#1059349411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2085
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
269. C32#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#637432
C2×#637422
#105913602
#105913372
#105902072
#105900752
#20859