Finite Group Databasebeta

← #11775215

Subgroups — #11775215

Order 1152.

787 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 94 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#10595081C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic, complemented
3#10591260C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal, complemented
5#10589149C212yesmaximal, complemented
6#68303—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3811—21no—
9C2×#3802C411yescharacteristic, complemented
10C2×#3743—21no—
11C3×#930C2212yes—
12#63980—21no—
13C2×#3722—21no—
14C2×Dic32—21no—
15#63921—21no—
16#63916C412yescomplemented
17#63912—21no—
18#63900C411yescharacteristic, complemented
19C32×C22⋊C8C2211yescharacteristic, complemented
20#63657C2211yescharacteristic, complemented
21#63647—21no—
22C3×C3⋊#95C2212yescomplemented
23D3×#121—32no—
24#4726—32no—
25#4726—61no—
26#4666—32no—
27C3×#327—32no—
28#4537—32no—
29#4470D312yescomplemented
30#4451—32no—
31C23×C3⋊D3D411yescharacteristic
32C22×D32—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3—42no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C3×#67—22no—
41C22×C3×Dic3—22no—
42C2×C3×D12C2×C412yes—
43#3811—44no—
44C2×#626—22no—
45C2×#625—21no—
46C2×#624—21no—
47#3802—42no—
48C2×C32×C8—21no—
49C2×C3⋊(C3⋊C8)—21no—
50#3743—42no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3C2×C412yes—
53#3724—21no—
54#3722—24no—
55(C2×D3)⋊Dic3—22no—
56Dic32—42no—
57#1507—91noSylow
58C2×D3×D4—32no—
59C2×D3×D4—62no—
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C3×#121—32no—
63#939—62no—
64#938—32no—
65#930C2×D312yes—
66C2×(C2×D3)⋊C4—62no—
67C2×C4×Dic3—62no—
68C2×ΓL(1,𝔽25)—62no—
69C2×ΓL(1,𝔽25)—62no—
70#895—32no—
71D3×C4⋊C4—32no—
72#884—62no—
73D3×C22⋊C4—62no—
74C3×C22⋊C8—21no—
75C3×C22⋊C8C2×D312yescomplemented
76C3×#95—32no—
77C3⋊#95C2×D312yescomplemented
78#830—32no—
79#830—61no—
80(C2×D3)⋊C8—62no—
81(C2×D3)⋊C8—62no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—22no—
84C22×C3⋊D3—22no—
85C22×C3⋊D3—41no—
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3×D3—22no—
89C2×D32—42no—
90C2×D32—42no—
91C2×D32—42no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C4×C3⋊D3—22no—
99C4×C3⋊D3—22no—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—41no—
102C3×#67—42no—
103C3×#67—42no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—42no—
108C3×D12—42no—
109#626—44no—
110#625—42no—
111#624—42no—
112C32×C8—41no—
113C3⋊(C3⋊C8)—41no—
114C2×#121—91no—
115#407—91no—
116C4×C22⋊C4—91no—
117#327—32no—
118#327—92no—
119C23×D3—32no—
120C23×D3—61no—
121C23×D3—62no—
122C2×C3×D4—32no—
123C2×C3×D4—62no—
124C22×C3×C4—21no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D312yes—
127C2×#67—22no—
128C2×#67—62no—
129C2×#67—62no—
130C22×Dic3—22no—
131C22×Dic3—32no—
132C22×Dic3—61no—
133D3×D4—124no—
134D3×D4—124no—
135D3×D4—124no—
136C2×D12—62no—
137C2×D12C4×D312yes—
138C2×C4×D3—32no—
139C2×C4×D3—32no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—62no—
147C2×C4×D3—124no—
148C2×C4×D3—124no—
149C2×C3×C8—22no—
150C2×C3×C8—22no—
151C3×C4⋊C4—32no—
152C3×C22⋊C4—62no—
153#217—62no—
154(C2×D3)⋊C4—22no—
155(C2×D3)⋊C4—68no—
156(C2×D3)⋊C4—62no—
157C4⋊Dic3C4×D312yes—
158Dic3⋊C4—62no—
159C4×Dic3—124no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—62no—
162ΓL(1,𝔽25)—124no—
163ΓL(1,𝔽25)—124no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32AGL(1,ℤ/8)12yes—
168C2×C3⋊D3—21no—
169C2×C3⋊D3—21no—
170C2×C3⋊D3—21no—
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—44no—
174C2×C3⋊D3#10412yes—
175C2×C3×D3—42no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178D32—84no—
179C32×C4—21no—
180C32×C4—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3#9912yes—
183C3×Dic3—44no—
184C3×Dic3—42no—
185C22×D4—91no—
186C22×D4—181no—
187C23×C4—91no—
188C2×M16—181no—
189#121—32no—
190#121—92no—
191#121—181no—
192#121—181no—
193C2×C4⋊C4—91no—
194C2×C22⋊C4—181no—
195C2×C22⋊C4—181no—
196C2×C42—181no—
197C22⋊C8—91no—
198C22⋊C8—181no—
199C22⋊C8D3211yescharacteristic, complemented
200#95—32no—
201C23×C3—21no—
202C23×C3—62no—
203C23×C3D3×D412yes—
204C22×D3—22no—
205C22×D3—32no—
206C22×D3—32no—
207C22×D3—61no—
208C22×D3—61no—
209C22×D3—64no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—122no—
213C22×D3—122no—
214C22×D3—124no—
215C22×D3—124no—
216C22×D3—124no—
217C22×D3—122no—
218C22×D3—122no—
219C3×D4—122no—
220C3×D4—122no—
221C3×D4—122no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—64no—
227C2×C3×C4—62no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230C2×C3×C4C2×C4×D312yes—
231C2×C3×C4D3×D412yes—
232#67—42no—
233#67—42no—
234#67—124no—
235#67—124no—
236C2×Dic3—24no—
237C2×Dic3—22no—
238C2×Dic3—32no—
239C2×Dic3—32no—
240C2×Dic3—42no—
241C2×Dic3—42no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—64no—
245C2×Dic3—122no—
246D12—42no—
247D12—124no—
248C4×D3—64no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—122no—
252C4×D3—124no—
253C4×D3—122no—
254C4×D3—122no—
255C4×D3—122no—
256C4×D3—122no—
257C3×C8—42no—
258C3×C8—42no—
259C3⋊C8—122no—
260C3⋊C8—122no—
261C2×C32—22no—
262C2×C32C2×#9911yescharacteristic
263C2×C32#41811yescharacteristic
264C2×C32C2×#10411yescharacteristic
265C3⋊D3—22no—
266C3⋊D3—41no—
267C3×D3—82no—
268C24—91no—
269C24—181no—
270C2×D4—32no—
271C2×D4—62no—
272C2×D4—182no—
273C2×D4—181no—
274C2×D4—362no—
275C2×D4—364no—
276C22×C4—62no—
277C22×C4—91no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—91no—
282C22×C4—181no—
283C22×C4—362no—
284C22×C4C2×D3211yescharacteristic
285M16—362no—
286C2×C8—21no—
287C2×C8—181no—
288C4⋊C4—32no—
289C4⋊C4—181no—
290C22⋊C4—62no—
291C22⋊C4—184no—
292C22⋊C4—182no—
293C42—362no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3D3×C22⋊C412yes—
304C22×C3#91112yes—
305C22×C3#91412yes—
306C2×D3—34no—
307C2×D3—42no—
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—62no—
311C2×D3—62no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—121no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—128no—
324C2×D3—248no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—124no—
330C3×C4—122no—
331Dic3—34no—
332Dic3—44no—
333Dic3—42no—
334Dic3—62no—
335Dic3—62no—
336Dic3—121no—
337C32#150711yescharacteristic, complemented, Sylow
338C23—62no—
339C23—91no—
340C23—91no—
341C23—182no—
342C23—182no—
343C23—361no—
344C23—362no—
345C23—362no—
346C23—362no—
347C23#380211yescharacteristic
348D4—122no—
349D4—122no—
350D4—122no—
351D4—362no—
352D4—364no—
353C2×C4—41no—
354C2×C4—64no—
355C2×C4—62no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—122no—
359C2×C4—122no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—361no—
364C2×C4—361no—
365C2×C4—362no—
366C2×C4C4×D3211yescharacteristic
367C2×C4#381111yescharacteristic
368C8—41no—
369C8—361no—
370C2×C3—22no—
371C2×C3—22no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—42no—
376C2×C3—242no—
377C2×C3D3×#9912yes—
378C2×C3#477012yes—
379C2×C3D3×#10412yes—
380D3—64no—
381D3—82no—
382D3—122no—
383D3—122no—
384D3—122no—
385C22—21no—
386C22—21no—
387C22—92no—
388C22—122no—
389C22—122no—
390C22—122no—
391C22—181no—
392C22—181no—
393C22—181no—
394C22—181no—
395C22—181no—
396C22—364no—
397C22—724no—
398C22#6379812yes—
399C22#6392111yescharacteristic
400C4—21no—
401C4—21no—
402C4—92no—
403C4—124no—
404C4—122no—
405C4—181no—
406C3—21no—
407C3#6830312yescomplemented
408C2—22no—
409C2—182no—
410C2—242no—
411C2—361no—
412C2#1059040411yescharacteristic
413C2#1059094111yescharacteristic
414C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1507
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. #10591260C2semidirect
4. C3×#4470C2semidirect
5. #10589149C2semidirect
9. C2×#3802C4semidirect
16. #63916C4semidirect
18. #63900C4semidirect
19. C32×C22⋊C8C22semidirect
20. #63657C22semidirect
22. C3×C3⋊#95C22semidirect
29. #4470D3semidirect
75. C3×C22⋊C8C2×D3semidirect
77. C3⋊#95C2×D3semidirect
199. C22⋊C8D32semidirect
337. C32#1507semidirect
407. C3#68303semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105924252
#105912602
C3×#44702
#105891492
#683033