Finite Group Databasebeta

← #11773877

Subgroups — #11773877

Order 1152.

719 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 719 conjugacy classes of subgroups — too many to draw. Only its 102 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×#63883C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4C3×#4469C212yesmaximal, complemented
5#10589147C212yesmaximal, complemented
6#68144—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C411yescharacteristic
9C22×#624C411yescharacteristic
10C2×#3743—21no—
11C2×C3×Dic3⋊C4C2212yes—
12C2×Dic3⋊Dic3C412yes—
13#63883—21no—
14#63883—21no—
15#63883—21no—
16#63883—21no—
17C2×#3712—21no—
18C32×C22⋊C8C2211yescharacteristic
19#63657C2211yescharacteristic
20#63647—21no—
21C3×#830C2212yes—
22#63557—21no—
23C2×D3×C4⋊C4—32no—
24#4726—32no—
25#4726—32no—
26#4726—61no—
27C3×#324—32no—
28#4528—32no—
29#4469—32no—
30#4469D312yescomplemented
31C23×C3⋊D3C2×C411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C2×C4×C3⋊D3—42no—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C22×C3×Dic3C2×C412yes—
40C22×C3×Dic3C2×C412yes—
41C2×#624—21no—
42C2×#624—21no—
43C2×#624—24no—
44C2×#624—21no—
45C2×#624—21no—
46C2×#624—42no—
47C2×C32×C8—21no—
48C2×C3⋊(C3⋊C8)—21no—
49#3743—42no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C2×C3×C3⋊C8—22no—
53Dic3⋊Dic3—22no—
54Dic3⋊Dic3—22no—
55#3712—42no—
56#1463—91noSylow
57C22×C4×D3—32no—
58C22×C4×D3—32no—
59C22×C4×D3—32no—
60C22×C4×D3—61no—
61C2×C3×C4⋊C4—32no—
62C2×C4⋊Dic3—32no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4C2×D312yes—
65C2×ΓL(1,𝔽25)—62no—
66C2×ΓL(1,𝔽25)—62no—
67C2×ΓL(1,𝔽25)—62no—
68D3×C4⋊C4—62no—
69D3×C4⋊C4—62no—
70D3×C4⋊C4—62no—
71D3×C4⋊C4—62no—
72C3×C22⋊C8—21no—
73C3×C22⋊C8—32no—
74C3×C22⋊C8C2×D312yes—
75#830—32no—
76#830—61no—
77#830C2×D312yes—
78(C2×D3)⋊C8—62no—
79(C2×D3)⋊C8—62no—
80(C2×D3)⋊C8—62no—
81C23×C32C22×C411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3—22no—
85C22×C3⋊D3C22⋊C411yescharacteristic
86C22×C3⋊D3C22⋊C411yescharacteristic
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C4×C3⋊D3—22no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—41no—
96C4×C3⋊D3—41no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3M1614yescomplemented
102#624—24no—
103#624—24no—
104#624—42no—
105#624—42no—
106C32×C8—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—42no—
109C22×C4⋊C4—91no—
110#407—91no—
111#407—91no—
112#324—32no—
113#324—92no—
114C23×D3—32no—
115C23×D3—61no—
116C22×C3×C4—21no—
117C22×C3×C4—32no—
118C22×C3×C4—32no—
119C22×C3×C4C22×D312yes—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3C4×D312yes—
123C22×Dic3C4×D312yes—
124C2×C4×D3—32no—
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—64no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—64no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—124no—
139C2×C4×D3—124no—
140C2×C4×D3—124no—
141C2×C3×C8—22no—
142C2×C3×C8—22no—
143C2×C3×C8—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—62no—
146C4⋊Dic3—62no—
147C4⋊Dic3—62no—
148Dic3⋊C4—22no—
149Dic3⋊C4—22no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152C2×C3⋊C8—22no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155ΓL(1,𝔽25)—124no—
156ΓL(1,𝔽25)—124no—
157ΓL(1,𝔽25)—124no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32C2×C22⋊C411yescharacteristic
161C22×C32C2×M1612yes—
162C2×C3⋊D3—28no—
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3#9912yes—
168C2×C3⋊D3#10112yes—
169C32×C4—21no—
170C32×C4—21no—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3×Dic3—24no—
174C3×Dic3—42no—
175C23×C4—91no—
176C23×C4—91no—
177C23×C4—91no—
178C2×M16—181no—
179C2×M16—181no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—92no—
182C2×C4⋊C4—181no—
183C2×C4⋊C4—181no—
184C2×C4⋊C4—181no—
185C2×C4⋊C4—181no—
186C22⋊C8—32no—
187C22⋊C8—91no—
188C22⋊C8—181no—
189C22⋊C8—181no—
190C22⋊C8D3211yescharacteristic
191C23×C3—21no—
192C23×C3C2×C4×D312yes—
193C22×D3—32no—
194C22×D3—32no—
195C22×D3—61no—
196C22×D3—61no—
197C22×D3—64no—
198C22×D3—64no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—122no—
202C22×D3—122no—
203C22×D3—122no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—34no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—122no—
213C2×C3×C4D3×D412yes—
214C2×C3×C4D3×D412yes—
215C2×Dic3—22no—
216C2×Dic3—22no—
217C2×Dic3—22no—
218C2×Dic3—32no—
219C2×Dic3—32no—
220C2×Dic3—42no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3ΓL(1,𝔽25)14yescomplemented
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—64no—
229C4×D3—64no—
230C4×D3—64no—
231C4×D3—122no—
232C4×D3—124no—
233C4×D3—124no—
234C4×D3—122no—
235C4×D3—122no—
236C4×D3—122no—
237C4×D3—122no—
238C3×C8—42no—
239C3×C8—42no—
240C3×C8—122no—
241C3⋊C8—42no—
242C3⋊C8—122no—
243C3⋊C8—122no—
244C2×C32—22no—
245C2×C32#40711yescharacteristic
246C2×C32C2×#9911yescharacteristic
247C2×C32C2×#10111yescharacteristic
248C3⋊D3—22no—
249C3⋊D3—22no—
250C24—91no—
251C22×C4—32no—
252C22×C4—32no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—184no—
259C22×C4—181no—
260C22×C4—181no—
261C22×C4—181no—
262C22×C4—181no—
263C22×C4—362no—
264C22×C4—362no—
265C22×C4C2×D3211yescharacteristic
266M16—362no—
267M16—362no—
268C2×C8—21no—
269C2×C8—62no—
270C2×C8—181no—
271C4⋊C4—62no—
272C4⋊C4—62no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3D3×C22⋊C412yes—
282C22×C3C2×ΓL(1,𝔽25)12yes—
283C22×C3D3×M1612yes—
284C2×D3—34no—
285C2×D3—34no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—68no—
289C2×D3—68no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—121no—
295C2×D3—121no—
296C2×D3—121no—
297C2×D3—121no—
298C2×D3—128no—
299C3×C4—22no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—41no—
303C3×C4—64no—
304C3×C4—122no—
305Dic3—24no—
306Dic3—42no—
307Dic3—62no—
308Dic3—62no—
309Dic3—62no—
310Dic3—121no—
311C32#146311yescharacteristic, complemented, Sylow
312C23—91no—
313C23—91no—
314C23—182no—
315C23—182no—
316C23—182no—
317C23C4×D3211yescharacteristic
318C2×C4—34no—
319C2×C4—41no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—122no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—184no—
329C2×C4—184no—
330C2×C4—361no—
331C2×C4—361no—
332C2×C4—362no—
333C2×C4—362no—
334C2×C4—361no—
335C2×C4#380211yescharacteristic
336C2×C4#381111yescharacteristic
337C8—41no—
338C8—122no—
339C8—361no—
340C2×C3—22no—
341C2×C3—22no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—42no—
346C2×C3#472612yes—
347C2×C3D3×#9912yes—
348C2×C3D3×#10112yes—
349D3—64no—
350D3—64no—
351D3—122no—
352D3—122no—
353C22—21no—
354C22—21no—
355C22—92no—
356C22—92no—
357C22—188no—
358C22—181no—
359C22—181no—
360C22—181no—
361C22—181no—
362C22D3×ΓL(1,𝔽25)12yes—
363C22#6392111yescharacteristic
364C4—21no—
365C4—21no—
366C4—64no—
367C4—122no—
368C4—181no—
369C4—181no—
370C3—21no—
371C3#6814412yescomplemented
372C2—22no—
373C2—182no—
374C2—182no—
375C2#1059040411yescharacteristic
376C2#1059093711yescharacteristic
377C2#1059100311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4469C2semidirect
5. #10589147C2semidirect
30. #4469D3semidirect
101. C2×C3×Dic3M16semidirect
225. C2×Dic3ΓL(1,𝔽25)semidirect
311. C32#1463semidirect
371. C3#68144semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
#105924252
#105911592
C3×#44692
#105891472
#681443