Finite Group Databasebeta

← #11878925

Subgroups — #11878925

Order 1152.

827 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 827 conjugacy classes of subgroups — too many to draw. Only its 166 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#10593909C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4C3×#4849C212yesmaximal, complemented
5#10590950C214yesmaximal
6#10590905C212yesmaximal, complemented
7#10590901C212yesmaximal, complemented
8#10590384C212yesmaximal, complemented
9#80480—32nomaximal
10C2×#3797C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12C2×C3×Dic12C2214yes—
13C3×#869C2212yes—
14C3×C4×Dic6C2212yes—
15#63919—21no—
16#63919—21no—
17#63919C2211yescharacteristic
18C4×#627—21no—
19#63900—21no—
20#63900—21no—
21#63874—21no—
22#63873C2211yescharacteristic
23#63873C2212yes—
24#63871C2212yes—
25#63870—21no—
26#63865—21no—
27C2×#3718C2214yes—
28C32×C4⋊C8C2211yescharacteristic
29#63647C2212yes—
30C8×C3⋊Dic3C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C3×#816C2214yes—
33#63565C2214yes—
34D3×C4⋊Q8—32no—
35#5578—32no—
36C3×#462—32no—
37#5186—34no—
38#5183—34no—
39#5090—32no—
40#5031—32no—
41#4849D312yescomplemented
42#4833—32no—
43#4833—61no—
44#4809—34no—
45#4792—34no—
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C3×Dic6C2312yes—
50C2×C3×Dic6C2314yes—
51C2×#627—22no—
52C2×#627—21no—
53C2×#624—22no—
54#3797—42no—
55#3797—42no—
56C2×C32×C8C2312yes—
57C32×C42C2311yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3C2311yescharacteristic
61C2×C3⋊(C3⋊C8)C2312yes—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3C2312yes—
65C3×Dic3⋊C4—22no—
66C3×C4×Dic3—22no—
67C3×Dic12—44no—
68#3724—21no—
69#3724—21no—
70#3724—21no—
71#3724—22no—
72#3724—22no—
73Dic3⋊Dic3—22no—
74#3722—22no—
75#3718—44no—
76#3209—91noSylow
77C2×D3×Q8—34no—
78C2×C3×Q16—34no—
79C3×C4⋊Q8—32no—
80C3×C4×Q8—32no—
81#946—32no—
82#944—32no—
83#944—34no—
84C2×#216—34no—
85C2×#216—34no—
86C2×Dic12C2×D314yes—
87#897—32no—
88#896—62no—
89D3×C4⋊C4—62no—
90D3×C4⋊C4—62no—
91#889—62no—
92#888—32no—
93#888—62no—
94#888—62no—
95#872—62no—
96C42×D3—32no—
97C42×D3—61no—
98#869C2×D312yes—
99C4×Dic6—62no—
100C4×Dic6C2×D312yes—
101C3×C4⋊C8—21no—
102C3×C4⋊C8C2×D312yes—
103C3×#103—34no—
104#835—34no—
105(C2×D3)⋊C8—34no—
106(C2×D3)⋊C8—62no—
107#816C2×D314yes—
108C8×Dic3—34no—
109C8×Dic3—62no—
110#810—34no—
111C4⋊(C3⋊C8)—32no—
112C4⋊(C3⋊C8)—61no—
113C22×C3⋊D3C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C4×C3⋊D3—21no—
121C4×C3⋊D3—21no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3Q1614yescomplemented
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C3×Dic6—22no—
128C3×Dic6—24no—
129C3×Dic6—22no—
130C3×Dic6—24no—
131#627—44no—
132#627—42no—
133#624—44no—
134C32×C8—22no—
135C3⋊(C3⋊C8)—22no—
136#533—91no—
137C2×C4⋊Q8—91no—
138#494—92no—
139#487—92no—
140#462—32no—
141#462—92no—
142#451—94no—
143#431—91no—
144C2×C3×Q8—34no—
145C2×C3×Q8—32no—
146D3×Q8—124no—
147D3×Q8—124no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—32no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—64no—
155C2×Dic6—62no—
156C2×Dic6—64no—
157C2×Dic6C22×D314yes—
158C2×Dic6C22×D312yes—
159C3×Q16—124no—
160C2×C3×C8—22no—
161C2×C3×C8C22×D314yes—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—62no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—62no—
166C3×C42—21no—
167C3×C42—62no—
168C3×C42C22×D312yes—
169#216—124no—
170#216—124no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173C4⋊Dic3—22no—
174C4⋊Dic3—22no—
175C4⋊Dic3—62no—
176C4⋊Dic3C22×D312yes—
177Dic3⋊C4—22no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—64no—
183Dic3⋊C4—64no—
184C4×Dic3—22no—
185C4×Dic3—32no—
186C4×Dic3—32no—
187C4×Dic3—32no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C2×C3⋊C8—34no—
192C2×C3⋊C8—62no—
193Dic12—44no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3C2×Q1612yes—
198C32×C4—21no—
199C32×C4C2×Q1612yes—
200C32×C4H(5,𝔽2)11yescharacteristic
201C32×C4H(5,𝔽2)11yescharacteristic
202C3⋊Dic3—21no—
203C3⋊Dic3C2×Q1612yes—
204C3⋊Dic3#13712yes—
205C3×Dic3—44no—
206C3×Dic3—42no—
207C3×Dic3—42no—
208C22×Q8—92no—
209C2×Q16—34no—
210C2×Q16—94no—
211C4⋊Q8—32no—
212C4⋊Q8—91no—
213C4⋊Q8—92no—
214C4⋊Q8—91no—
215C4⋊Q8—181no—
216C4⋊Q8—181no—
217#125—181no—
218C22⋊Q8—92no—
219C22⋊Q8—181no—
220C4×Q8—32no—
221C4×Q8—181no—
222#117—181no—
223C2×C4⋊C4—181no—
224C2×C4⋊C4—181no—
225C2×C42—91no—
226C4⋊C8—91no—
227C4⋊C8D3211yescharacteristic
228#103—34no—
229#103—94no—
230C22⋊C8—92no—
231C4×C8—92no—
232C22×D3—32no—
233C22×D3—61no—
234C3×Q8—62no—
235C3×Q8—64no—
236C3×Q8—62no—
237C3×Q8—64no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—62no—
244C2×C3×C4D3×D412yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4C23×D312yes—
247C2×Dic3—22no—
248C2×Dic3—22no—
249C2×Dic3—24no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—32no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C4×D3—38no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—122no—
262C4×D3—121no—
263C4×D3—121no—
264C4×D3—128no—
265Dic6—22no—
266Dic6—24no—
267Dic6—22no—
268Dic6—24no—
269Dic6—124no—
270Dic6—128no—
271C3×C8—24no—
272C3×C8—42no—
273C3⋊C8—64no—
274C3⋊C8—122no—
275C2×C32#53511yescharacteristic
276C2×C32C22×Q1611yescharacteristic
277C2×C32C2×#13711yescharacteristic
278C3⋊D3—22no—
279C2×Q8—34no—
280C2×Q8—32no—
281C2×Q8—181no—
282C2×Q8—182no—
283C2×Q8—362no—
284C2×Q8—362no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—182no—
289Q16—124no—
290Q16—364no—
291C2×C8—92no—
292C2×C8C2×D3212yes—
293C4⋊C4—32no—
294C4⋊C4—62no—
295C4⋊C4—62no—
296C4⋊C4—62no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4—182no—
302C4⋊C4—181no—
303C22⋊C4—182no—
304C42—62no—
305C42—91no—
306C42—91no—
307C42—91no—
308C42C2×D3211yescharacteristic
309C22×C3—21no—
310C22×C3C2×D3×D412yes—
311C2×D3—34no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—121no—
316C2×D3—121no—
317C3×C4—22no—
318C3×C4—21no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—122no—
323C3×C4—124no—
324C3×C4—122no—
325C3×C4D3×Q1614yes—
326C3×C4#100412yes—
327C3×C4#100912yes—
328Dic3—34no—
329Dic3—34no—
330Dic3—42no—
331Dic3—44no—
332Dic3—42no—
333Dic3—62no—
334Dic3—62no—
335Dic3—62no—
336Dic3—121no—
337C32#320911yescharacteristic, complemented, Sylow
338C23—91no—
339Q8—62no—
340Q8—64no—
341Q8—62no—
342Q8—64no—
343Q8—362no—
344Q8—364no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—64no—
348C2×C4—91no—
349C2×C4—91no—
350C2×C4—94no—
351C2×C4—91no—
352C2×C4—182no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—364no—
356C2×C4#380211yescharacteristic
357C2×C4#380211yescharacteristic
358C2×C4C22×D3211yescharacteristic
359C8—22no—
360C8—182no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3#560712yes—
365C2×C3C2×D3×Q1612yes—
366C2×C3D3×#13712yes—
367D3—64no—
368D3—122no—
369C22—92no—
370C22—181no—
371C22—181no—
372C22C2×#380211yescharacteristic
373C4—21no—
374C4—92no—
375C4—92no—
376C4—124no—
377C4—122no—
378C4—122no—
379C4—181no—
380C4#6380212yes—
381C4#6431311yescharacteristic
382C4#6432011yescharacteristic
383C3—21no—
384C3#8048012yescomplemented
385C2—182no—
386C2#1059463411yescharacteristic
387C2C2×#6380211yescharacteristic
388C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4849C2semidirect
6. #10590905C2semidirect
7. #10590901C2semidirect
8. #10590384C2semidirect
41. #4849D3semidirect
123. C4×C3⋊D3Q16semidirect
337. C32#3209semidirect
384. C3#80480semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105938822
#105925322
C3×#48492
#105909502
#105909052
#105909012
#105903842
#804803