Finite Group Databasebeta

← #11870815

Subgroups — #11870815

Order 1152.

879 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 879 conjugacy classes of subgroups — too many to draw. Only its 172 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#10596199C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic
3C3×#5090C212yesmaximal, complemented
4#10591654C212yesmaximal
5#10591581C214yesmaximal, complemented
6#10591555C212yesmaximal
7#10590283C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic
9#80456—32nomaximal
10C2×#3797C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12#64155C2212yes—
13Q8×C3⋊Dic3C2212yes—
14#64106—21no—
15#64101—21no—
16#64099—21no—
17#64096—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2211yescharacteristic
20C2×C3×#216C2214yes—
21C3×C4×Dic6C2212yes—
22C4×#627—21no—
23#63900C2211yescharacteristic
24#63883—21no—
25C4×#624—21no—
26#63843C2212yes—
27#63838—21no—
28C3×#835C2214yes—
29C3×C4⋊(C3⋊C8)C2212yes—
30#63575C2214yes—
31#63566C2214yes—
32#63557C2212yes—
33#63553C2212yes—
34#5728—32no—
35#5728—61no—
36C4×D3×Q8—32no—
37C3×#462—32no—
38#5186—34no—
39Dic3×Q16—34no—
40#5090D312yescomplemented
41#5021—32no—
42#4850—32no—
43#4833—32no—
44#4811—34no—
45#4790—34no—
46C2×C32×Q8C2312yes—
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3C2311yescharacteristic
50C2×#634—21no—
51C2×C3×Dic6C2312yes—
52C2×#627—21no—
53C2×#624—21no—
54C2×#624—21no—
55#3797—24no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C42C2311yescharacteristic
59#3752—22no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—22no—
62C4⋊(C3⋊Dic3)C2312yes—
63#3750—22no—
64C4×C3⋊Dic3—22no—
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3D411yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68C3×#216—28no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3—22no—
72C2×C3×C3⋊C8C2314yes—
73#3724—21no—
74Dic3⋊Dic3—22no—
75Dic32—22no—
76#3104—91noSylow
77C2×D3×Q8—32no—
78C2×C3×Q16—34no—
79C3×C4⋊Q8—21no—
80C3×C4⋊Q8C2×D312yes—
81C3×C4×Q8—32no—
82#946—34no—
83#946—62no—
84Q8×Dic3—34no—
85Q8×Dic3—32no—
86Q8×Dic3—62no—
87C2×#216C2×D314yes—
88#897—62no—
89#897—62no—
90#892—62no—
91#892—62no—
92D3×C4⋊C4—32no—
93D3×C4⋊C4—62no—
94#890—62no—
95#890—62no—
96#887—32no—
97#887—62no—
98#887—62no—
99#887—62no—
100C42×D3—32no—
101C42×D3—61no—
102C42×D3—62no—
103#869—32no—
104#869—61no—
105C4×Dic6—62no—
106C4×Dic6C2×D312yes—
107C3×C4⋊C8—32no—
108C3×#103—34no—
109#835—34no—
110#835C2×D314yes—
111(C2×D3)⋊C8—34no—
112#818—34no—
113#816—34no—
114C8×Dic3—34no—
115#807—34no—
116C4⋊(C3⋊C8)C2×D312yes—
117C22×C3⋊D3C2×D411yescharacteristic
118C32×Q8—24no—
119C2×C32×C4—22no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C4×C3⋊D3—22no—
128C4×C3⋊D3—41no—
129C4×C3⋊D3Q1614yescomplemented
130#634—42no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C3×Dic6—22no—
134C3×Dic6#4114yes—
135#627—24no—
136#624—24no—
137#624—42no—
138C3×C3⋊C8—24no—
139#533—91no—
140C2×C4×Q8—91no—
141#484—92no—
142#477—92no—
143#462—32no—
144#451—92no—
145C4×Q16—94no—
146#431—91no—
147C2×C3×Q8—22no—
148C2×C3×Q8—32no—
149C2×C3×Q8C22×D314yes—
150D3×Q8—64no—
151D3×Q8—64no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×Dic6—62no—
161C2×Dic6—62no—
162C2×Dic6—62no—
163C2×Dic6C22×D312yes—
164C3×Q16—68no—
165C2×C3×C8—34no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—62no—
172C3×C42—21no—
173C3×C42—62no—
174C3×C42C22×D312yes—
175#216—28no—
176(C2×D3)⋊C4—64no—
177(C2×D3)⋊C4—64no—
178C4⋊Dic3—34no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—64no—
182C4⋊Dic3—62no—
183C4⋊Dic3—64no—
184C4⋊Dic3—62no—
185C4⋊Dic3C22×D312yes—
186Dic3⋊C4—22no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—22no—
192C4×Dic3—32no—
193C4×Dic3—32no—
194C4×Dic3—32no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C2×C3⋊C8C22×D314yes—
203C22×C32C22×D411yescharacteristic
204C2×C3⋊D3—21no—
205C2×C3⋊D3—21no—
206C2×C3⋊D3C2×Q1612yes—
207C32×C4—21no—
208C32×C4—42no—
209C32×C4C2×Q1612yes—
210C32×C4C2×#4112yes—
211C3⋊Dic3—21no—
212C3⋊Dic3—21no—
213C3⋊Dic3—42no—
214C3⋊Dic3C2×Q1612yes—
215C3×Dic3—24no—
216C3×Dic3—42no—
217C22×Q8—91no—
218C2×Q16—34no—
219C4⋊Q8—91no—
220C4⋊Q8D3211yescharacteristic
221#125—181no—
222C22⋊Q8—92no—
223C22⋊Q8—181no—
224C4×Q8—32no—
225C4×Q8—92no—
226C4×Q8—92no—
227C4×Q8—181no—
228C4×Q8—181no—
229C4×Q8—181no—
230#117—181no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—181no—
233C2×C42—91no—
234C2×C42—181no—
235#107—94no—
236C4⋊C8—32no—
237#103—34no—
238#103—94no—
239C22⋊C8—92no—
240C4×C8—92no—
241C22×D3—32no—
242C22×D3—61no—
243C3×Q8—24no—
244C3×Q8—24no—
245C3×Q8—34no—
246C3×Q8—44no—
247C3×Q8—62no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—62no—
254C2×C3×C4—62no—
255C2×C3×C4D3×D412yes—
256C2×C3×C4D3×D412yes—
257C2×C3×C4C23×D312yes—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—32no—
261C2×Dic3—32no—
262C2×Dic3—32no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C4×D3—38no—
269C4×D3—64no—
270C4×D3—68no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—122no—
274C4×D3—124no—
275C4×D3—122no—
276C4×D3—122no—
277Dic6—22no—
278Dic6—68no—
279Dic6—124no—
280Dic6—124no—
281Dic6#23714yes—
282C3×C8—64no—
283C3⋊C8—24no—
284C2×C32#52511yescharacteristic
285C2×C32C22×Q1611yescharacteristic
286C2×C32#57511yescharacteristic
287C3⋊D3—22no—
288C2×Q8—32no—
289C2×Q8—181no—
290C2×Q8—184no—
291C2×Q8—181no—
292C2×Q8C2×D3212yes—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—181no—
297C22×C4—181no—
298Q16—68no—
299C2×C8—34no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—32no—
303C4⋊C4—62no—
304C4⋊C4—92no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—181no—
308C4⋊C4—182no—
309C4⋊C4—181no—
310C22⋊C4—182no—
311C42—62no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—182no—
316C42—182no—
317C42C2×D3211yescharacteristic
318C22×C3—21no—
319C22×C3C2×D3×D412yes—
320C2×D3—34no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—121no—
325C2×D3—121no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—44no—
331C3×C4—44no—
332C3×C4—64no—
333C3×C4—122no—
334C3×C4D3×Q1614yes—
335C3×C4C2×#23712yes—
336C3×C4D3×#4112yes—
337Dic3—24no—
338Dic3—34no—
339Dic3—42no—
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343Dic3—121no—
344Dic3—121no—
345Dic3—124no—
346Dic3—124no—
347C32#310411yescharacteristic, complemented, Sylow
348C23—91no—
349Q8—24no—
350Q8—34no—
351Q8—62no—
352Q8—184no—
353Q8—362no—
354C2×C4—22no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—91no—
358C2×C4—94no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—184no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—361no—
365C2×C4—362no—
366C2×C4#381111yescharacteristic
367C2×C4#381111yescharacteristic
368C2×C4C22×D3211yescharacteristic
369C8—64no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3#560612yes—
374C2×C3C2×D3×Q1612yes—
375C2×C3#577712yes—
376D3—64no—
377D3—122no—
378C22—92no—
379C22—181no—
380C22—181no—
381C22C2×#381111yescharacteristic
382C4—21no—
383C4—42no—
384C4—64no—
385C4—92no—
386C4—122no—
387C4—181no—
388C4—181no—
389C4—362no—
390C4#6394412yes—
391C4D3×#23712yes—
392C3—21no—
393C3#8045612yescomplemented
394C2—182no—
395C2#1059530611yescharacteristic
396C2#1059532311yescharacteristic
397C2C2×#6394411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5090C2semidirect
5. #10591581C2semidirect
7. #10590283C2semidirect
40. #5090D3semidirect
129. C4×C3⋊D3Q16semidirect
347. C32#3104semidirect
393. C3#80456semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×#37972
C3×#50902
#105916542
#105915812
#105915552
#105902832
#105902562
#804563