Finite Group Databasebeta

← #11774773

Subgroups — #11774773

Order 1152.

575 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 575 conjugacy classes of subgroups — too many to draw. Only its 110 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#10596049C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3C4×#3710C211yesmaximal, characteristic
4C3×#4535C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68240—32nomaximal
7C32×C4×Q8C2211yescharacteristic
8#64155C411yescharacteristic
9#64153C411yescharacteristic
10#64106C411yescharacteristic
11#64105—21no—
12#64098—21no—
13#64097C411yescharacteristic
14#64081—21no—
15C42×C3⋊D3C2211yescharacteristic
16C4×#634—21no—
17C4×#634C2211yescharacteristic
18C2×#3712—21no—
19C2×#3710—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4×C3⋊C8C2212yes—
22#63572—21no—
23#63553—21no—
24#5578—32no—
25#5578—61no—
26#4837—32no—
27C4×D3×C8—32no—
28C3×Q8⋊C8—32no—
29#4535D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×#634—21no—
37C2×#634C2×C411yescharacteristic
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C42—21no—
41C32×C42C2311yescharacteristic
42#3752—21no—
43#3752—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—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—42no—
58#3710—24no—
59#1493—91noSylow
60C3×C4×Q8—21no—
61C3×C4×Q8C2×D312yes—
62#946—32no—
63#946—61no—
64#944—32no—
65#944—61no—
66C2×ΓL(1,𝔽25)—62no—
67C2×D3×C8—62no—
68#897—32no—
69#897—61no—
70#896—62no—
71#896—62no—
72#889—62no—
73#889—62no—
74#888—32no—
75#888—61no—
76#872—62no—
77#872—62no—
78C42×D3—32no—
79C42×D3—61no—
80C4×Dic6—32no—
81C4×Dic6—61no—
82C4×Dic6—62no—
83C4×Dic6—62no—
84C3×C4⋊C8—32no—
85C3×C4×C8—32no—
86Dic3⋊C8—62no—
87C8×Dic3—62no—
88C4⋊(C3⋊C8)C2×D312yes—
89C4×C3⋊C8C2×D312yes—
90C22×C3⋊D3C22⋊C411yescharacteristic
91C32×Q8—22no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C4×C3⋊D3—22no—
103C4×C3⋊D3—22no—
104C4×C3⋊D3SD1612yes—
105C4×C3⋊D3Q1612yes—
106#634—22no—
107#634—42no—
108C3×C3⋊C8—24no—
109C3×C3⋊C8—42no—
110#533—91no—
111#423—91no—
112C2×C4×C8—91no—
113Q8⋊C8—32no—
114Q8⋊C8—92no—
115C2×C3×Q8—21no—
116C2×C3×Q8C4×D312yes—
117C2×C4×D3—32no—
118C2×C4×D3—32no—
119C2×C4×D3—32no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×Dic6—32no—
124C2×Dic6—61no—
125C2×Dic6—62no—
126C2×Dic6—62no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4C4×D312yes—
133C3×C42—22no—
134C3×C42—22no—
135C3×C42—21no—
136C3×C42C22×D312yes—
137(C2×D3)⋊C4—62no—
138(C2×D3)⋊C4—62no—
139(C2×D3)⋊C4—62no—
140(C2×D3)⋊C4—62no—
141C4⋊Dic3—32no—
142C4⋊Dic3—61no—
143C4⋊Dic3—62no—
144C4⋊Dic3—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—32no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—22no—
165ΓL(1,𝔽25)—124no—
166D3×C8—68no—
167C22×C32C2×C22⋊C411yescharacteristic
168C2×C3⋊D3—21no—
169C2×C3⋊D3—21no—
170C2×C3⋊D3#10312yes—
171C32×C4—21no—
172C32×C4—41no—
173C32×C4—41no—
174C32×C4#13112yes—
175C32×C4C2×SD1611yescharacteristic
176C32×C4C2×Q1611yescharacteristic
177C3⋊Dic3—21no—
178C3⋊Dic3—41no—
179C3⋊Dic3—41no—
180C3⋊Dic3#10312yes—
181C3⋊Dic3#10412yes—
182C2×M16—181no—
183C22×C8—181no—
184C4⋊Q8—91no—
185C4⋊Q8—91no—
186#125—181no—
187C22⋊Q8—91no—
188C22⋊Q8—91no—
189C22⋊Q8—181no—
190C4×Q8—91no—
191C4×Q8—181no—
192C4×Q8D3211yescharacteristic
193#117—181no—
194C2×C42—91no—
195C4⋊C8—32no—
196C4⋊C8—181no—
197C4×C8—32no—
198C4×C8—181no—
199C22×D3—32no—
200C22×D3—61no—
201C3×Q8—22no—
202C3×Q8—22no—
203C3×Q8—42no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4C2×C4×D312yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4D3×D412yes—
214C2×Dic3—32no—
215C2×Dic3—32no—
216C2×Dic3—32no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C4×D3—34no—
225C4×D3—34no—
226C4×D3—62no—
227C4×D3—62no—
228C4×D3—64no—
229C4×D3—62no—
230C4×D3—62no—
231C4×D3—122no—
232C4×D3—122no—
233Dic6—62no—
234Dic6—62no—
235Dic6—122no—
236Dic6—124no—
237Dic6—124no—
238C3×C8—64no—
239C3×C8—122no—
240C3⋊C8—24no—
241C3⋊C8—42no—
242C2×C32#40811yescharacteristic
243C2×C32C2×#10311yescharacteristic
244C2×C32C2×#10411yescharacteristic
245C3⋊D3—22no—
246C2×Q8—91no—
247C2×Q8—181no—
248C2×Q8#62411yescharacteristic
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252M16—362no—
253C2×C8—62no—
254C2×C8—62no—
255C2×C8—184no—
256C4⋊C4—21no—
257C4⋊C4—91no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4#62411yescharacteristic
265C22⋊C4—181no—
266C22⋊C4—181no—
267C42—21no—
268C42—91no—
269C42—91no—
270C42—91no—
271C42—181no—
272C42C2×D3211yescharacteristic
273C22×C3—21no—
274C22×C3D3×C22⋊C412yes—
275C2×D3—34no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—121no—
280C2×D3—121no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—42no—
287C3×C4—42no—
288C3×C4—42no—
289C3×C4—42no—
290C3×C4#90112yes—
291C3×C4#90712yes—
292C3×C4D3×SD1612yes—
293C3×C4D3×Q1612yes—
294Dic3—34no—
295Dic3—34no—
296Dic3—62no—
297Dic3—62no—
298Dic3—62no—
299Dic3—121no—
300Dic3—122no—
301Dic3—122no—
302Dic3—122no—
303Dic3—122no—
304C32#149311yescharacteristic, complemented, Sylow
305C23—91no—
306Q8—22no—
307Q8—182no—
308Q8—362no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—91no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4C2×#62411yescharacteristic
321C2×C4#381111yescharacteristic
322C2×C4#381111yescharacteristic
323C8—64no—
324C8—122no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3#472712yes—
329C2×C3D3×#10312yes—
330C2×C3D3×#10412yes—
331D3—64no—
332D3—122no—
333C22—92no—
334C22—181no—
335C22—181no—
336C22#6397411yescharacteristic
337C4—21no—
338C4—41no—
339C4—41no—
340C4—92no—
341C4—92no—
342C4—181no—
343C4—361no—
344C4—361no—
345C4#6381712yes—
346C4#6394011yescharacteristic
347C4#6394411yescharacteristic
348C3—21no—
349C3#6824012yescomplemented
350C2—182no—
351C2#1059115311yescharacteristic
352C2#1059155211yescharacteristic
353C2#1059167111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1493
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4535C2semidirect
5. #10589085C2semidirect
29. #4535D3semidirect
304. C32#1493semidirect
349. C3#68240semidirect

Maximal subgroups

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

subgroupindex
#105960492
#105903402
C4×#37102
C3×#45352
#105890852
#682403