Finite Group Databasebeta

← #11775857

Subgroups — #11775857

Order 1152.

549 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 86 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#10596162C211yesmaximal, characteristic
2#10590299C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4C3×#4543C212yesmaximal, complemented
5#10589087C212yesmaximal, complemented
6#68364—32nomaximal
7C32×#125C2211yescharacteristic
8#64107—21no—
9#64106C411yescharacteristic
10#64104C411yescharacteristic
11#64103—21no—
12#64102—21no—
13#64102C411yescharacteristic
14#64101—21no—
15#64096C411yescharacteristic
16#64084C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×#3712—21no—
19C3×#803C2212yes—
20C3×#803C2212yes—
21#63572—21no—
22#63557—21no—
23#63553—21no—
24#5691—32no—
25#5691—61no—
26#4707—32no—
27#4705—32no—
28C3×#330—32no—
29#4543D312yescomplemented
30#4464—32no—
31#4464—32no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×#634C2×C411yescharacteristic
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C4⋊C4C2×C411yescharacteristic
43C32×C42C2311yescharacteristic
44#3752—21no—
45#3752—21no—
46#3752—21no—
47#3752—21no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#3712—24no—
58#1529—91noSylow
59C3×#125—21no—
60C3×#125C2×D312yes—
61C2×ΓL(1,𝔽25)—62no—
62#898—62no—
63#898—62no—
64#897—32no—
65#897—61no—
66#895—32no—
67#895—61no—
68#894—62no—
69#894—62no—
70#893—32no—
71#893—61no—
72#893—62no—
73#893—62no—
74#892—62no—
75#892—62no—
76#887—32no—
77#887—61no—
78#875—32no—
79#875—61no—
80C42×D3—32no—
81C42×D3—61no—
82C3×#97—32no—
83C3×#97—32no—
84(C2×D3)⋊C8—62no—
85Dic3⋊C8—62no—
86C8×Dic3—62no—
87#803C2×D312yes—
88#803C2×D312yes—
89C22×C3⋊D3—21no—
90C22×C3⋊D3C22⋊C411yescharacteristic
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—42no—
102C4×C3⋊D3—22no—
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—42no—
106#634—41no—
107C3×C3⋊C8—24no—
108C3×C3⋊C8—42no—
109#529—91no—
110#432—91no—
111C4×M16—91no—
112#330—32no—
113#329—92no—
114C2×D12—32no—
115C2×D12—61no—
116C2×D12—62no—
117C2×D12—62no—
118C2×C4×D3—32no—
119C2×C4×D3—32no—
120C2×C4×D3—32no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×Dic6—32no—
127C2×Dic6—61no—
128C2×C3×C8—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4C4×D312yes—
137C3×C4⋊C4C4×D312yes—
138C3×C42—21no—
139C3×C42C22×D312yes—
140(C2×D3)⋊C4—62no—
141(C2×D3)⋊C4—62no—
142(C2×D3)⋊C4—62no—
143(C2×D3)⋊C4—62no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147(C2×D3)⋊C4—62no—
148(C2×D3)⋊C4—62no—
149(C2×D3)⋊C4—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154C4×Dic3—32no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8—22no—
164ΓL(1,𝔽25)—68no—
165C22×C32C2×C22⋊C411yescharacteristic
166C2×C3⋊D3—21no—
167C2×C3⋊D3—21no—
168C2×C3⋊D3—21no—
169C2×C3⋊D3—41no—
170C2×C3⋊D3—41no—
171C2×C3⋊D3—41no—
172C32×C4—21no—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—41no—
176C32×C4—41no—
177C3⋊Dic3—21no—
178C3⋊Dic3—21no—
179C3⋊Dic3—41no—
180C3⋊Dic3#10412yes—
181C2×M16—181no—
182#126—181no—
183#125D3211yescharacteristic
184#124—91no—
185#123—181no—
186C22⋊Q8—91no—
187#121—91no—
188C4×Q8—91no—
189C4×D4—91no—
190C4×D4—181no—
191#117—181no—
192C2×C42—91no—
193C4⋊C8—181no—
194C22⋊C8—181no—
195#97—32no—
196#97—32no—
197C4×C8—181no—
198C22×D3—32no—
199C22×D3—61no—
200C22×D3—62no—
201C22×D3—62no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4D3×D412yes—
211C2×C3×C4D3×D412yes—
212C2×Dic3—32no—
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220D12—122no—
221D12—122no—
222D12—124no—
223D12—124no—
224C4×D3—64no—
225C4×D3—122no—
226C4×D3—124no—
227C4×D3—122no—
228C4×D3—122no—
229C4×D3—124no—
230C4×D3—122no—
231C4×D3—122no—
232Dic6—122no—
233Dic6—122no—
234C3×C8—64no—
235C3×C8—122no—
236C3⋊C8—24no—
237C3⋊C8—42no—
238C2×C32#41311yescharacteristic
239C2×C32C2×#10411yescharacteristic
240C2×C32#42111yescharacteristic
241C3⋊D3—41no—
242C3⋊D3—81no—
243C2×Q8—91no—
244C2×D4—91no—
245C2×D4—181no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—181no—
250M16—184no—
251C2×C8—62no—
252C2×C8—62no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4#62411yescharacteristic
258C4⋊C4#62411yescharacteristic
259C22⋊C4—181no—
260C22⋊C4—181no—
261C22⋊C4—181no—
262C22⋊C4—181no—
263C22⋊C4—181no—
264C42—91no—
265C42—91no—
266C42—91no—
267C42—181no—
268C42C2×D3211yescharacteristic
269C22×C3—21no—
270C22×C3D3×C22⋊C412yes—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—122no—
278C2×D3—122no—
279C2×D3—122no—
280C2×D3—122no—
281C2×D3—122no—
282C2×D3—122no—
283C3×C4—22no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—42no—
290C3×C4—42no—
291C3×C4—42no—
292C3×C4—42no—
293Dic3—34no—
294Dic3—62no—
295Dic3—62no—
296Dic3—62no—
297Dic3—121no—
298Dic3—121no—
299Dic3—122no—
300Dic3—122no—
301C32#152911yescharacteristic, complemented, Sylow
302C23—91no—
303C23—181no—
304Q8—361no—
305D4—361no—
306D4—362no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—91no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—182no—
313C2×C4—181no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4—362no—
317C2×C4C2×#62411yescharacteristic
318C2×C4#381111yescharacteristic
319C2×C4#381111yescharacteristic
320C8—64no—
321C8—122no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3#475112yes—
326C2×C3D3×#10412yes—
327C2×C3#482112yes—
328D3—122no—
329D3—122no—
330D3—242no—
331D3—242no—
332C22—181no—
333C22—181no—
334C22—181no—
335C22—361no—
336C22—361no—
337C22—361no—
338C22#6397411yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—92no—
345C4—181no—
346C4—181no—
347C4—361no—
348C3—21no—
349C3#6836412yescomplemented
350C2—361no—
351C2—721no—
352C2#1059164011yescharacteristic
353C2#1059167111yescharacteristic
354C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32C2×C22⋊C4
prime radical#64104C4
cosocleC32×C42C23
hypercenter#125D32
hypocenterC32#1529
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10590299C2semidirect
3. #10590247C2semidirect
4. C3×#4543C2semidirect
5. #10589087C2semidirect
29. #4543D3semidirect
301. C32#1529semidirect
349. C3#68364semidirect

Maximal subgroups

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

subgroupindex
#105961622
#105902992
#105902472
C3×#45432
#105890872
#683643