Finite Group Databasebeta

← #11775281

Subgroups — #11775281

Order 1152.

456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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#10595033C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic, complemented
3#10591274C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×C4×#67—21no—
8C2×C3×C4⋊Dic3—21no—
9#63982C2211yescharacteristic
10#63980C2211yescharacteristic
11#63962—21no—
12C2×Dic32—21no—
13C4×#627C411yescharacteristic, complemented
14#63915C411yescharacteristic, complemented
15C4×#625C411yescharacteristic, complemented
16#63870C411yescharacteristic, complemented
17#63862—21no—
18#63855—21no—
19C22⋊#622C2212yes—
20#63777—21no—
21C4⋊#622—21no—
22#63579C2212yes—
23#5538—61no—
24Dic3×C4⋊C4—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C3×#67—21no—
29C22×C3×Dic3—22no—
30C2×C3×C4×D3—21no—
31C2×#627C2×C411yescharacteristic
32C2×#625C2×C411yescharacteristic
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×#217—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×C4⋊Dic3—24no—
41C3×Dic3⋊C4—21no—
42C3×C4×Dic3—21no—
43#3724C2×C411yescharacteristic
44#3724C2×C411yescharacteristic
45Dic3⋊Dic3—21no—
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48(C2×D3)⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—42no—
52#1509—91nomaximal, Sylow
53C3×C4×D4—61no—
54C2×C3×C4⋊C4—61no—
55#939—61no—
56#935—61no—
57C4×#67—21no—
58C4×#67—61no—
59#926—61no—
60C2×C4⋊Dic3—21no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—62no—
64#898—61no—
65#889—61no—
66#886—61no—
67#885—61no—
68#879—61no—
69#878—61no—
70#872—61no—
71C4×Dic6—61no—
72C3⋊#95—62no—
73C23×C32C2×D411yescharacteristic
74C22×C3×D3—21no—
75C2×C32×C4—22no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C3×#67—41no—
86C3×#67—41no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C3×C4×D3—42no—
94#627—41no—
95#625—41no—
96#622—42no—
97#529—91no—
98#432—91no—
99C4×C4⋊C4—91no—
100#328—92no—
101#327—92no—
102C2×C3×D4—61no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—61no—
106C22×C3×C4—62no—
107C2×#67—21no—
108C2×#67—61no—
109C22×Dic3—22no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C2×C4×D3—21no—
115C2×Dic6—61no—
116C3×C4⋊C4—61no—
117C3×C4⋊C4—64no—
118C3×C22⋊C4—61no—
119C3×C22⋊C4—61no—
120C3×C42—61no—
121#217—21no—
122#217—61no—
123#217—61no—
124#217—61no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4—61no—
127(C2×D3)⋊C4—61no—
128(C2×D3)⋊C4—61no—
129C4⋊Dic3—24no—
130C4⋊Dic3—61no—
131C4⋊Dic3—61no—
132C4⋊Dic3—61no—
133Dic3⋊C4—21no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139C4×Dic3—21no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—124no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32C2×C22⋊C411yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C22×C32#13711yescharacteristic
154C2×C3×D3—41no—
155C2×C3×D3—41no—
156C2×C3×D3—41no—
157C32×C4—21no—
158C32×C4#10412yes—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3×Dic3—44no—
164C3×Dic3—41no—
165C3×Dic3—41no—
166C3×Dic3—41no—
167#126—181no—
168#125—91no—
169#124—91no—
170#123—181no—
171C22⋊Q8—91no—
172#121—91no—
173C4×Q8—91no—
174C4×D4—61no—
175C4×D4—91no—
176#117—181no—
177C2×C4⋊C4—61no—
178C2×C42—91no—
179C2×C42—181no—
180C4⋊C8—181no—
181C22⋊C8—92no—
182#97—181no—
183#95—92no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—61no—
187C22×D3—21no—
188C3×D4—121no—
189C3×D4—121no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—61no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4—64no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4—122no—
204#67—41no—
205#67—41no—
206#67—122no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—24no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—121no—
224C2×Dic3—121no—
225C2×Dic3—122no—
226C2×Dic3—121no—
227C2×Dic3—121no—
228C4×D3—42no—
229Dic6—122no—
230C2×C32—21no—
231C2×C32—21no—
232C2×C32#41011yescharacteristic
233C2×C32#41711yescharacteristic
234C2×C32C2×#10411yescharacteristic
235C3×D3—81no—
236C2×Q8—91no—
237C2×D4—61no—
238C2×D4—91no—
239C22×C4—62no—
240C22×C4—61no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4GO+(4,𝔽2)11yescharacteristic
244C2×C8—182no—
245C4⋊C4—64no—
246C4⋊C4—61no—
247C4⋊C4—91no—
248C4⋊C4—91no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—181no—
255C22⋊C4—181no—
256C22⋊C4—181no—
257C42—61no—
258C42—91no—
259C42—91no—
260C42—91no—
261C42—91no—
262C42—362no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—121no—
276C22×C3—121no—
277C22×C3—121no—
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—41no—
285C3×C4—121no—
286C3×C4—124no—
287C3×C4—121no—
288C3×C4—121no—
289Dic3—41no—
290Dic3—41no—
291Dic3—44no—
292Dic3—41no—
293Dic3—62no—
294Dic3—62no—
295Dic3—62no—
296Dic3—121no—
297Dic3—121no—
298Dic3—121no—
299Dic3—121no—
300Dic3—121no—
301C32#150911yescharacteristic, complemented, Sylow
302C23—61no—
303C23C2×GO+(4,𝔽2)11yescharacteristic
304Q8—361no—
305D4—121no—
306D4—121no—
307D4—361no—
308C2×C4—22no—
309C2×C4—64no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—361no—
323C2×C4D32⋊C411yescharacteristic
324C2×C4D32⋊C411yescharacteristic
325C8—362no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—41no—
337C2×C3—41no—
338C2×C3—241no—
339D3—81no—
340C22—21no—
341C22—21no—
342C22—121no—
343C22—121no—
344C22—121no—
345C22#6422411yescharacteristic
346C22#6422611yescharacteristic
347C22C2×D32⋊C411yescharacteristic
348C4—21no—
349C4—124no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4—181no—
354C4—181no—
355C4—181no—
356C4—181no—
357C4#6374112yes—
358C3—21no—
359C3—21no—
360C2—21no—
361C2—21no—
362C2—241no—
363C2#1059334611yescharacteristic
364C2#1059336011yescharacteristic
365C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1509
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593806C2semidirect
3. #10591274C2semidirect
4. #10590072C2semidirect
13. C4×#627C4semidirect
14. #63915C4semidirect
15. C4×#625C4semidirect
16. #63870C4semidirect
301. C32#1509semidirect

Maximal subgroups

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

subgroupindex
#105950332
#105938062
#105912742
#105900722
#105900712
#15099