Finite Group Databasebeta

← #11773909

Subgroups — #11773909

Order 1152.

472 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593992C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590028C212yesmaximal, complemented
5#10590027C212yesmaximal
6C2×C4×D32C411yescharacteristic
7C42×C3⋊D3C2211yescharacteristic
8C3×#872—21no—
9#63921C411yescharacteristic
10#63921C2211yescharacteristic
11#63883C411yescharacteristic
12#63883C2211yescharacteristic
13C4×#624C411yescharacteristic
14#63878—21no—
15#63878—21no—
16#63855—21no—
17#63778C2212yes—
18#63777—21no—
19C4⋊#622—21no—
20C3×#803—21no—
21#63572—21no—
22#63557C2212yes—
23D3×#117—61no—
24#4705—61no—
25C22×D32C2×C411yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×C4×D3—21no—
30C2×#624C2×C411yescharacteristic
31C2×#624C2×C411yescharacteristic
32C2×#624C2×C411yescharacteristic
33C2×D3×Dic3—21no—
34C4×D32—22no—
35C4×D32—22no—
36C2×#622—22no—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×(C2×D3)⋊C4—21no—
42C3×(C2×D3)⋊C4—21no—
43C3×Dic3⋊C4—21no—
44C3×Dic3⋊C4—21no—
45C3×C4×Dic3—21no—
46C2×C3×C3⋊C8—22no—
47Dic3⋊Dic3—21no—
48Dic3⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—21no—
52#1464—91nomaximal, Sylow
53C22×C4×D3—61no—
54C3×#117—61no—
55#926—61no—
56#892—61no—
57#892—61no—
58D3×C4⋊C4—61no—
59D3×C4⋊C4—61no—
60D3×C22⋊C4—61no—
61D3×C22⋊C4—61no—
62#877—61no—
63#877—61no—
64#872—21no—
65#872—61no—
66C42×D3—61no—
67C42×D3—61no—
68C42×D3—61no—
69C3×#97—61no—
70(C2×D3)⋊C8—62no—
71Dic3⋊C8—62no—
72#803—21no—
73C22×C3⋊D3C22×C411yescharacteristic
74C22×C3×D3—21no—
75C2×D32—21no—
76C2×D32—41no—
77C2×D32—41no—
78C2×D32M1612yes—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4×C3⋊D3—21no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3—41no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—21no—
92C3×C4×D3—24no—
93#624—21no—
94#624—41no—
95#624—41no—
96#624M1612yes—
97D3×Dic3—24no—
98#622—42no—
99C3×C3⋊C8—42no—
100C2×#117—91no—
101#432—91no—
102#432—91no—
103#324—92no—
104#323—92no—
105C23×D3—61no—
106C22×C3×C4—61no—
107C22×Dic3—61no—
108C2×C4×D3—21no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—64no—
119C2×C4×D3—64no—
120C2×C4×D3—61no—
121C2×C3×C8—62no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C22⋊C4—61no—
125C3×C22⋊C4—61no—
126C3×C42—21no—
127C3×C42—21no—
128C3×C42—61no—
129#217—61no—
130#217—61no—
131(C2×D3)⋊C4—21no—
132(C2×D3)⋊C4—21no—
133(C2×D3)⋊C4—61no—
134(C2×D3)⋊C4—61no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137Dic3⋊C4—21no—
138Dic3⋊C4—21no—
139Dic3⋊C4—61no—
140Dic3⋊C4—61no—
141C4×Dic3—21no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C2×C3⋊C8—22no—
151C22×C32C2×C22⋊C411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3C2×M1611yescharacteristic
155C2×C3⋊D3C2×M1611yescharacteristic
156C2×C3×D3—22no—
157C2×C3×D3—41no—
158C2×C3×D3—41no—
159D32—42no—
160D32—42no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—21no—
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3—21no—
167C3×Dic3—22no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C23×C4—91no—
171#117—61no—
172#117—181no—
173#117—181no—
174#117—181no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C2×C22⋊C4—91no—
178C2×C22⋊C4—91no—
179C2×C42—91no—
180C2×C42—91no—
181C4⋊C8—181no—
182C4⋊C8—181no—
183C22⋊C8—92no—
184C22⋊C8—92no—
185#97—61no—
186#97—181no—
187C23×C3—61no—
188C22×D3—21no—
189C22×D3—62no—
190C22×D3—61no—
191C22×D3—61no—
192C22×D3—62no—
193C22×D3—122no—
194C22×D3—122no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—64no—
202C2×C3×C4—61no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—64no—
215C4×D3—24no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—62no—
220C4×D3—64no—
221C4×D3—121no—
222C4×D3—121no—
223C4×D3—122no—
224C4×D3—122no—
225C4×D3—122no—
226C4×D3—122no—
227C4×D3—122no—
228C4×D3—122no—
229C3×C8—122no—
230C3⋊C8—42no—
231C2×C32#40711yescharacteristic
232C2×C32#41011yescharacteristic
233C2×C32#41311yescharacteristic
234C3⋊D3—21no—
235C3⋊D3—21no—
236C3×D3—42no—
237C24—91no—
238C22×C4—61no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—182no—
246C22×C4—182no—
247C22×C4—181no—
248C2×C8—62no—
249C2×C8—182no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—181no—
257C22⋊C4—181no—
258C42—61no—
259C42—91no—
260C42—91no—
261C42—91no—
262C42—181no—
263C42GO+(4,𝔽2)11yescharacteristic
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—62no—
267C22×C3—121no—
268C22×C3—121no—
269C2×D3—22no—
270C2×D3—41no—
271C2×D3—41no—
272C2×D3—61no—
273C2×D3—61no—
274C2×D3—61no—
275C2×D3—61no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—124no—
281C2×D3—124no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—62no—
289C3×C4—121no—
290C3×C4—121no—
291Dic3—22no—
292Dic3—41no—
293Dic3—41no—
294Dic3—62no—
295Dic3—62no—
296Dic3—121no—
297Dic3—121no—
298Dic3—121no—
299Dic3—121no—
300C32#146411yescharacteristic, complemented, Sylow
301C23—61no—
302C23—92no—
303C23—91no—
304C23—181no—
305C23—361no—
306C23—361no—
307C2×C4—64no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—92no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—184no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4D32⋊C411yescharacteristic
324C2×C4D32⋊C411yescharacteristic
325C2×C4C2×GO+(4,𝔽2)11yescharacteristic
326C8—122no—
327C8—362no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—122no—
335D3—42no—
336D3—62no—
337D3—62no—
338D3—121no—
339D3—121no—
340C22—62no—
341C22—91no—
342C22—91no—
343C22—121no—
344C22—121no—
345C22—181no—
346C22—181no—
347C22—362no—
348C22—362no—
349C22C2×D32⋊C411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—62no—
354C4—121no—
355C4—121no—
356C4—181no—
357C4—181no—
358C4—181no—
359C3—21no—
360C3—21no—
361C2—122no—
362C2—181no—
363C2—181no—
364C2#1059330711yescharacteristic
365C2#1059331311yescharacteristic
366C2#1059334511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×D32C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1464
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593730C2semidirect
3. #10590299C2semidirect
4. #10590028C2semidirect
300. C32#1464semidirect

Maximal subgroups

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

subgroupindex
#105939922
#105937302
#105902992
#105900282
#105900272
#14649