Finite Group Databasebeta

← #11870798

Subgroups — #11870798

Order 1152.

917 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 917 conjugacy classes of subgroups — too many to draw. Only its 180 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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic
3C3×#5228C212yesmaximal
4#10591633C212yesmaximal, complemented
5#10591631C212yesmaximal, complemented
6#10591581C214yesmaximal, complemented
7#10591103C212yesmaximal
8#10591061C211yesmaximal, characteristic
9#80172—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12Q8×C3⋊Dic3—21no—
13Q8×C3⋊Dic3C2212yes—
14Q8×C3⋊Dic3C2212yes—
15C2×C4⋊(C3⋊Dic3)—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#216C2214yes—
20C3×#924C2212yes—
21#63982—21no—
22#63957—21no—
23#63919C2211yescharacteristic
24#63873C2211yescharacteristic
25#63870—21no—
26#63843C2212yes—
27#63838—21no—
28C3×#835C2214yes—
29C3×#830C2212yes—
30#63575C2214yes—
31#63572C2212yes—
32#63566C2214yes—
33#63553C2212yes—
34C2×Q8×Dic3—32no—
35C2×Q8×Dic3—61no—
36#5622—32no—
37C3×#451—32no—
38#5228D312yes—
39#5182—34no—
40Dic3×Q16—34no—
41#5044—32no—
42#4793—34no—
43#4790—34no—
44#4722—32no—
45#4718—32no—
46C2×C32×Q8—24no—
47C2×C32×Q8—21no—
48C2×C32×Q8C2312yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×C3×Dic6C2312yes—
55C2×#627—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—22no—
58C4⋊(C3⋊Dic3)—22no—
59C4⋊(C3⋊Dic3)C2312yes—
60C4×C3⋊Dic3—22no—
61C4×C3⋊Dic3—22no—
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C3×#217—22no—
67C3×#216—28no—
68C3×C4⋊Dic3C2312yes—
69C3×Dic3⋊C4—22no—
70C2×C3×C3⋊C8C2314yes—
71#3724—21no—
72#3724—21no—
73#3724—21no—
74Dic3⋊Dic3—22no—
75Dic32—22no—
76#3104—91noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D312yes—
79C2×C3×Q16—34no—
80C3×C22⋊Q8—32no—
81Q8×Dic3—34no—
82Q8×Dic3—34no—
83Q8×Dic3—32no—
84Q8×Dic3—62no—
85Q8×Dic3—62no—
86Q8×Dic3—62no—
87Q8×Dic3—62no—
88Q8×Dic3—62no—
89Q8×Dic3—62no—
90#944—32no—
91C2×#216C2×D314yes—
92C2×C4⋊Dic3—32no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—62no—
95C2×C4⋊Dic3—62no—
96#924C2×D312yes—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—61no—
99C2×C4×Dic3—62no—
100C2×C4×Dic3—62no—
101#889—62no—
102#888—32no—
103#887—32no—
104#887—62no—
105#878—62no—
106#877—62no—
107C3×#103—34no—
108C3×C22⋊C8—32no—
109#835—34no—
110#835C2×D314yes—
111#830C2×D312yes—
112#818—34no—
113#816—34no—
114Dic3⋊C8—34no—
115C8×Dic3—34no—
116#807—34no—
117C23×C32C2×D411yescharacteristic
118C32×Q8—24no—
119C32×Q8—22no—
120C32×Q8#4114yes—
121C2×C32×C4—24no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—42no—
129C2×C3⋊Dic3Q1614yescomplemented
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C3×Dic6—24no—
137#627—42no—
138C3×C3⋊C8—24no—
139#533—91no—
140C2×C4×Q8—91no—
141#484—92no—
142#477—92no—
143#462—92no—
144#451—32no—
145C4×Q16—94no—
146#431—91no—
147C2×C3×Q8—22no—
148C2×C3×Q8—28no—
149C2×C3×Q8—28no—
150C2×C3×Q8—22no—
151C2×C3×Q8—22no—
152C2×C3×Q8—32no—
153C2×C3×Q8C22×D314yes—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—21no—
157C22×C3×C4C22×D312yes—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—62no—
163C22×Dic3—62no—
164C2×Dic6—62no—
165C2×Dic6C22×D312yes—
166C3×Q16—68no—
167C2×C3×C8—34no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—62no—
170C3×C22⋊C4—62no—
171#217—22no—
172#216—28no—
173C4⋊Dic3—34no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176C4⋊Dic3—64no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4⋊Dic3—64no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3C22×D312yes—
183Dic3⋊C4—22no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—32no—
191C4×Dic3—32no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C4×Dic3—64no—
202C2×C3⋊C8C22×D314yes—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32C2×Q1612yes—
206C22×C32C22×D411yescharacteristic
207C32×C4—24no—
208C32×C4—21no—
209C32×C4C2×#4112yes—
210C3⋊Dic3—21no—
211C3⋊Dic3—21no—
212C3⋊Dic3—42no—
213C3⋊Dic3C2×Q1612yes—
214C3⋊Dic3C2×Q1612yes—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C22×Q8D3211yescharacteristic
218C2×Q16—34no—
219C4⋊Q8—91no—
220C4⋊Q8—91no—
221#125—181no—
222C22⋊Q8—32no—
223C22⋊Q8—181no—
224C4×Q8—92no—
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—92no—
237#103—34no—
238#103—94no—
239C22⋊C8—32no—
240C4×C8—92no—
241C23×C3—21no—
242C23×C3D3×D412yes—
243C3×Q8—28no—
244C3×Q8—28no—
245C3×Q8—24no—
246C3×Q8—24no—
247C3×Q8—24no—
248C3×Q8—64no—
249C3×Q8#23718yes—
250C2×C3×C4—24no—
251C2×C3×C4—28no—
252C2×C3×C4—28no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4D3×D412yes—
261C2×C3×C4C23×D312yes—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—38no—
265C2×Dic3—32no—
266C2×Dic3—32no—
267C2×Dic3—32no—
268C2×Dic3—32no—
269C2×Dic3—64no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—64no—
275C2×Dic3—64no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—124no—
279C2×Dic3—124no—
280Dic6—24no—
281Dic6—124no—
282C3×C8—64no—
283C3⋊C8—24no—
284C2×C32—22no—
285C2×C32#52511yescharacteristic
286C2×C32C22×Q1611yescharacteristic
287C2×C32#57511yescharacteristic
288C2×Q8—24no—
289C2×Q8—21no—
290C2×Q8—32no—
291C2×Q8—181no—
292C2×Q8C2×D3212yes—
293C22×C4—21no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—181no—
297C22×C4C2×D3211yescharacteristic
298Q16—68no—
299C2×C8—34no—
300C4⋊C4—32no—
301C4⋊C4—62no—
302C4⋊C4—92no—
303C4⋊C4—182no—
304C4⋊C4—182no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—182no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C22⋊C4—62no—
311C42—91no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—182no—
316C42—182no—
317C42—182no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—22no—
324C22×C3D3×Q1614yes—
325C22×C3C2×D3×D412yes—
326C3×C4—28no—
327C3×C4—22no—
328C3×C4—28no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—122no—
332C3×C4—122no—
333C3×C4C2×#23714yes—
334Dic3—34no—
335Dic3—34no—
336Dic3—42no—
337Dic3—42no—
338Dic3—62no—
339Dic3—62no—
340Dic3—62no—
341Dic3—62no—
342Dic3—121no—
343Dic3—121no—
344Dic3—124no—
345Dic3—124no—
346C32#310411yescharacteristic, complemented, Sylow
347C23#381111yescharacteristic
348Q8—24no—
349Q8—22no—
350Q8—64no—
351Q8—362no—
352Q8#380514yes—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—94no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—182no—
364C2×C4—361no—
365C2×C4—362no—
366C2×C4#381111yescharacteristic
367C2×C4C22×D3211yescharacteristic
368C8—64no—
369C2×C3—24no—
370C2×C3—24no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3#558612yes—
375C2×C3C2×D3×Q1612yes—
376C2×C3#577712yes—
377C22—21no—
378C22—21no—
379C22#6394412yes—
380C22C2×#381111yescharacteristic
381C4—24no—
382C4—21no—
383C4—92no—
384C4—92no—
385C4—122no—
386C4—122no—
387C4—181no—
388C4—181no—
389C4—362no—
390C4C2×#380512yes—
391C3—21no—
392C3#8017212yescomplemented
393C2—22no—
394C2#1059532311yescharacteristic
395C2C2×#6394411yescharacteristic
396C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591633C2semidirect
5. #10591631C2semidirect
6. #10591581C2semidirect
129. C2×C3⋊Dic3Q16semidirect
346. C32#3104semidirect
392. C3#80172semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
#105948102
C3×#52282
#105916332
#105916312
#105915812
#105911032
#105910612
#801723