Finite Group Databasebeta

← #11870825

Subgroups — #11870825

Order 1152.

917 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 917 conjugacy classes of subgroups — too many to draw. Only its 168 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×#64096C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic
3C3×#4970C212yesmaximal
4#10591190C212yesmaximal
5#10591061C211yesmaximal, characteristic
6#10590566C212yesmaximal, complemented
7#10590482C214yesmaximal, complemented
8#10590432C212yesmaximal, complemented
9#81452—32nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64096—21no—
16#64096—21no—
17#64096C2212yes—
18#64096C2212yes—
19C3×#924C2212yes—
20#63982—21no—
21#63957—21no—
22#63919C2211yescharacteristic
23#63873C2211yescharacteristic
24#63870—21no—
25#63843C2212yes—
26#63838—21no—
27C2×#3719C2214yes—
28C3×#830C2212yes—
29C3×#810C2214yes—
30C3×#807C2214yes—
31#63572C2212yes—
32#63567C2214yes—
33#63553C2212yes—
34#5622—32no—
35C2×#887—32no—
36C2×#887—61no—
37C3×#484—32no—
38#5050—32no—
39#4970D312yes—
40#4875—34no—
41#4873—34no—
42#4795—34no—
43#4790—34no—
44#4739—32no—
45#4718—32no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×#634—21no—
52C2×#634—24no—
53C2×#634C2312yes—
54C2×C3×Dic6C2312yes—
55C2×#627—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2312yes—
58#3750—22no—
59#3750—22no—
60C4×C3⋊Dic3—22no—
61C4×C3⋊Dic3—22no—
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C3×#217—22no—
67C3×C4⋊Dic3C2312yes—
68C3×Dic3⋊C4—22no—
69C2×C3×C3⋊C8C2314yes—
70#3724—21no—
71#3724—21no—
72#3724—21no—
73Dic3⋊Dic3—22no—
74Dic32—22no—
75#3719—28no—
76#3104—91noSylow
77C22×Dic6—32no—
78C22×Dic6—61no—
79C3×C22⋊Q8—32no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4C2×D312yes—
82Q8×Dic3—32no—
83#944—32no—
84C2×#216—34no—
85#924C2×D312yes—
86C2×Dic3⋊C4—62no—
87C2×Dic3⋊C4—62no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—61no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3—62no—
92C2×Dic12—34no—
93#889—62no—
94#888—32no—
95#887—32no—
96#887—34no—
97#887—34no—
98#887—62no—
99#887—62no—
100#887—62no—
101#887—62no—
102#887—62no—
103#887—62no—
104#887—62no—
105#878—62no—
106#877—62no—
107C3×#107—34no—
108C3×#103—34no—
109C3×C22⋊C8—32no—
110#830C2×D312yes—
111#816—34no—
112Dic3⋊C8—34no—
113C8×Dic3—34no—
114#810—34no—
115#810C2×D314yes—
116#807C2×D314yes—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—42no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—24no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3Q1614yescomplemented
127C2×C3⋊Dic3C2×D411yescharacteristic
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131#634—24no—
132#634—22no—
133#634#4114yes—
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—32no—
142#477—92no—
143#462—92no—
144#451—92no—
145C4×Q16—94no—
146#431—91no—
147C2×C3×Q8—32no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4C22×D312yes—
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C2×Dic6—34no—
159C2×Dic6—62no—
160C2×Dic6—68no—
161C2×Dic6—62no—
162C2×Dic6—68no—
163C2×Dic6—62no—
164C2×Dic6—62no—
165C2×Dic6C22×D312yes—
166C2×C3×C8—34no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4C22×D314yes—
173C3×C22⋊C4—62no—
174#217—22no—
175#216—68no—
176C4⋊Dic3—62no—
177C4⋊Dic3C22×D312yes—
178Dic3⋊C4—22no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—62no—
183Dic3⋊C4—64no—
184Dic3⋊C4—64no—
185Dic3⋊C4—64no—
186Dic3⋊C4—64no—
187C4×Dic3—32no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—32no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—62no—
196C4×Dic3—62no—
197C4×Dic3—64no—
198C4×Dic3—64no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C2×C3⋊C8C22×D314yes—
202Dic12—68no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32C2×Q1612yes—
206C22×C32C22×D411yescharacteristic
207C32×C4—21no—
208C32×C4—42no—
209C32×C4C2×#4112yes—
210C3⋊Dic3—24no—
211C3⋊Dic3—21no—
212C3⋊Dic3—21no—
213C3⋊Dic3C2×Q1612yes—
214C3⋊Dic3C2×Q1612yes—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C22×Q8—91no—
218C2×Q16—94no—
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—181no—
232C2×C4⋊C4D3211yescharacteristic
233C2×C42—91no—
234C2×C42—181no—
235#107—34no—
236C4⋊C8—92no—
237#103—34no—
238#103—94no—
239C22⋊C8—32no—
240C4×C8—92no—
241C23×C3—21no—
242C23×C3D3×D412yes—
243C3×Q8—64no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—44no—
251C2×C3×C4—44no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4D3×D412yes—
255C2×C3×C4C23×D312yes—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—38no—
259C2×Dic3—32no—
260C2×Dic3—32no—
261C2×Dic3—32no—
262C2×Dic3—32no—
263C2×Dic3—64no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—64no—
269C2×Dic3—68no—
270C2×Dic3—68no—
271C2×Dic3—64no—
272C2×Dic3—122no—
273C2×Dic3—122no—
274Dic6—24no—
275Dic6—38no—
276Dic6—64no—
277Dic6—68no—
278Dic6—68no—
279Dic6—64no—
280Dic6—64no—
281Dic6—124no—
282C3×C8—64no—
283C3⋊C8—24no—
284C2×C32—22no—
285C2×C32#52511yescharacteristic
286C2×C32C22×Q1611yescharacteristic
287C2×C32#57511yescharacteristic
288C2×Q8—32no—
289C2×Q8—92no—
290C2×Q8—184no—
291C2×Q8—181no—
292C2×Q8—181no—
293C22×C4—21no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—181no—
297C22×C4C2×D3211yescharacteristic
298Q16—188no—
299C2×C8—34no—
300C4⋊C4—21no—
301C4⋊C4—32no—
302C4⋊C4—62no—
303C4⋊C4—182no—
304C4⋊C4—182no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—182no—
308C4⋊C4—181no—
309C4⋊C4C2×D3212yes—
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—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—44no—
330C3×C4—44no—
331C3×C4—122no—
332C3×C4—122no—
333C3×C4D3×#4114yes—
334Dic3—34no—
335Dic3—34no—
336Dic3—42no—
337Dic3—42no—
338Dic3—62no—
339Dic3—62no—
340Dic3—68no—
341Dic3—68no—
342Dic3—62no—
343Dic3—62no—
344Dic3—121no—
345Dic3—121no—
346C32#310411yescharacteristic, complemented, Sylow
347C23#381111yescharacteristic
348Q8—64no—
349Q8—94no—
350Q8—184no—
351Q8—182no—
352Q8—362no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—94no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—184no—
364C2×C4—182no—
365C2×C4—361no—
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#565612yes—
375C2×C3C2×D3×Q1612yes—
376C2×C3#577312yes—
377C22—21no—
378C22—21no—
379C22#6394412yes—
380C22C2×#381111yescharacteristic
381C4—21no—
382C4—42no—
383C4—92no—
384C4—92no—
385C4—122no—
386C4—122no—
387C4—181no—
388C4—181no—
389C4—184no—
390C4#6430612yes—
391C3—21no—
392C3#8145212yescomplemented
393C2—22no—
394C2#1059492011yescharacteristic
395C2#1059510111yescharacteristic
396C2C2×#6394411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10590566C2semidirect
7. #10590482C2semidirect
8. #10590432C2semidirect
126. C2×C3⋊Dic3Q16semidirect
346. C32#3104semidirect
392. C3#81452semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105948102
C3×#49702
#105911902
#105910612
#105905662
#105904822
#105904322
#814523