Finite Group Databasebeta

← #11878735

Subgroups — #11878735

Order 1152.

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

normal subgroups only

This group has 915 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#10593972C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3#10592532C211yesmaximal, characteristic, complemented
4C3×#4841C212yesmaximal, complemented
5#10590901C212yesmaximal, complemented
6#10590884C212yesmaximal, complemented
7#10590824C214yesmaximal, complemented
8#10590363C212yesmaximal, complemented
9#80432—32nomaximal
10C2×#3798—21no—
11C2×#3797C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C2×C3×#204C2214yes—
14C3×C4×D12C2212yes—
15C3×#869C2212yes—
16#63919—21no—
17#63919—21no—
18#63919C2211yescharacteristic
19#63916C2212yes—
20#63915—21no—
21#63914C2211yescharacteristic
22#63912—21no—
23C4×#625—21no—
24#63900—21no—
25#63900—21no—
26#63873C2212yes—
27C2×#3715C2214yes—
28C32×C4⋊C8C2211yescharacteristic
29#63647C2212yes—
30C8×C3⋊Dic3C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C3×#816C2214yes—
33#63565C2214yes—
34D3×C4⋊Q8—32no—
35#5548—32no—
36C3×#461—32no—
37#5175—34no—
38#5170—34no—
39#5083—32no—
40#5019—32no—
41#4841D312yescomplemented
42#4833—32no—
43#4833—61no—
44#4806—34no—
45#4792—34no—
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C3×D12C2312yes—
50C2×C3×C4×D3—22no—
51C2×C3×Dic6C2314yes—
52C2×#627—22no—
53C2×#627—21no—
54C2×#626—22no—
55C2×#625—21no—
56C2×#625—21no—
57C2×#624—22no—
58#3798—44no—
59#3797—42no—
60#3797—42no—
61C2×C32×C8C2312yes—
62C32×C42C2311yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×(C2×D3)⋊C4—22no—
68C3×C4⋊Dic3—22no—
69C3×C4⋊Dic3—22no—
70C3×C4⋊Dic3C2312yes—
71C3×#204—44no—
72#3724—22no—
73#3724—22no—
74#3724—21no—
75(C2×D3)⋊Dic3—22no—
76#3715—44no—
77#3206—91noSylow
78C2×D3×Q8—34no—
79C2×#235—62no—
80C2×C3×SD16—34no—
81C3×C4⋊Q8—32no—
82C3×C4×D4—32no—
83#944—34no—
84C2×#215—34no—
85#940—32no—
86#938—32no—
87C2×#214—34no—
88C4×#67—62no—
89C2×#204C2×D314yes—
90#895—32no—
91D3×C4⋊C4—62no—
92D3×C4⋊C4—62no—
93#888—32no—
94#888—62no—
95#888—62no—
96#885—62no—
97#884—62no—
98C4×D12C2×D312yes—
99C42×D3—32no—
100C42×D3—61no—
101#869C2×D312yes—
102C3×C4⋊C8—21no—
103C3×C4⋊C8C2×D312yes—
104C3×#103—34no—
105#835—34no—
106(C2×D3)⋊C8—34no—
107(C2×D3)⋊C8—62no—
108#816C2×D314yes—
109C8×Dic3—34no—
110C8×Dic3—62no—
111#810—34no—
112C4⋊(C3⋊C8)—32no—
113C4⋊(C3⋊C8)—61no—
114C22×C3⋊D3C2×D411yescharacteristic
115C22×C3×D3—22no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C4×C3⋊D3—21no—
123C4×C3⋊D3—21no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3SD1614yescomplemented
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C3×D12—22no—
129C3×D12—22no—
130C3×C4×D3—44no—
131C3×Dic6—24no—
132C3×Dic6—24no—
133#627—44no—
134#627—42no—
135#626—44no—
136#625—42no—
137#625—42no—
138#624—44no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—22no—
141#532—91no—
142C2×C4⋊Q8—91no—
143#492—92no—
144#487—92no—
145#461—32no—
146#461—92no—
147#448—94no—
148#431—91no—
149C2×C3×Q8—34no—
150C2×C3×D4—32no—
151C22×C3×C4—62no—
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—62no—
155D3×Q8—124no—
156D3×Q8—124no—
157#235—128no—
158C2×D12—62no—
159C2×D12C22×D312yes—
160C2×C4×D3—22no—
161C2×C4×D3—32no—
162C2×C4×D3—32no—
163C2×C4×D3—32no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—64no—
168C2×Dic6—62no—
169C2×Dic6—64no—
170C2×Dic6C22×D314yes—
171C3×SD16—124no—
172C2×C3×C8—22no—
173C2×C3×C8C22×D314yes—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4—62no—
177C3×C22⋊C4—62no—
178C3×C42—21no—
179C3×C42C22×D312yes—
180#217—62no—
181#215—124no—
182#214—124no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—22no—
186C4⋊Dic3—22no—
187C4⋊Dic3C22×D312yes—
188Dic3⋊C4—62no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—32no—
192C4×Dic3—32no—
193C4×Dic3—32no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C2×C3⋊C8—34no—
198C2×C3⋊C8—62no—
199#204—44no—
200C22×C32C22×D411yescharacteristic
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3C2×SD1612yes—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C32×C4—21no—
208C32×C4C2×SD1612yes—
209C32×C4H(5,𝔽2)11yescharacteristic
210C32×C4H(5,𝔽2)11yescharacteristic
211C3⋊Dic3—21no—
212C3⋊Dic3C2×SD1612yes—
213C3⋊Dic3#13712yes—
214C3×Dic3—44no—
215C3×Dic3—42no—
216C2×#41—181no—
217C22×Q8—92no—
218C2×SD16—34no—
219C2×SD16—94no—
220C4⋊Q8—32no—
221C4⋊Q8—91no—
222C4⋊Q8—92no—
223C4⋊Q8—181no—
224C4⋊Q8—181no—
225#127—91no—
226#124—181no—
227#121—92no—
228#121—181no—
229C4×D4—32no—
230C4×D4—181no—
231C2×C4⋊C4—181no—
232C2×C4⋊C4—181no—
233C2×C42—91no—
234C4⋊C8—91no—
235C4⋊C8D3211yescharacteristic
236#103—34no—
237#103—94no—
238C22⋊C8—92no—
239C4×C8—92no—
240C23×C3—62no—
241C22×D3—22no—
242C22×D3—32no—
243C22×D3—61no—
244C3×Q8—64no—
245C3×Q8—64no—
246C3×D4—62no—
247C3×D4—62no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—64no—
252C2×C3×C4—62no—
253C2×C3×C4—124no—
254C2×C3×C4D3×D412yes—
255C2×C3×C4D3×D412yes—
256C2×C3×C4C23×D312yes—
257#67—124no—
258#67—124no—
259#67—124no—
260C2×Dic3—24no—
261C2×Dic3—22no—
262C2×Dic3—32no—
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268D12—22no—
269D12—22no—
270D12—124no—
271C4×D3—38no—
272C4×D3—44no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—122no—
278C4×D3—121no—
279C4×D3—121no—
280C4×D3—128no—
281Dic6—24no—
282Dic6—24no—
283Dic6—124no—
284Dic6—128no—
285C3×C8—24no—
286C3×C8—42no—
287C3⋊C8—64no—
288C3⋊C8—122no—
289C2×C32#53511yescharacteristic
290C2×C32C22×SD1611yescharacteristic
291C2×C32C2×#13711yescharacteristic
292C3⋊D3—22no—
293C3×D3—82no—
294#41—364no—
295C2×Q8—34no—
296C2×Q8—181no—
297C2×Q8—182no—
298C2×Q8—362no—
299C2×Q8—362no—
300C2×D4—32no—
301C2×D4—182no—
302C2×D4—181no—
303C2×D4—181no—
304C22×C4—62no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—182no—
309SD16—124no—
310SD16—364no—
311C2×C8—92no—
312C2×C8C2×D3212yes—
313C4⋊C4—32no—
314C4⋊C4—62no—
315C4⋊C4—62no—
316C4⋊C4—182no—
317C4⋊C4—182no—
318C4⋊C4—181no—
319C22⋊C4—62no—
320C22⋊C4—182no—
321C42—91no—
322C42—91no—
323C42—91no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—122no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3C2×D3×D412yes—
330C2×D3—34no—
331C2×D3—42no—
332C2×D3—42no—
333C2×D3—42no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—121no—
338C2×D3—121no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—41no—
344C3×C4—122no—
345C3×C4—124no—
346C3×C4D3×SD1614yes—
347C3×C4#100412yes—
348C3×C4#100912yes—
349Dic3—34no—
350Dic3—34no—
351Dic3—42no—
352Dic3—44no—
353Dic3—62no—
354Dic3—62no—
355Dic3—62no—
356Dic3—121no—
357C32#320611yescharacteristic, complemented, Sylow
358C23—62no—
359C23—91no—
360Q8—64no—
361Q8—64no—
362Q8—362no—
363Q8—364no—
364D4—62no—
365D4—62no—
366D4—362no—
367D4—362no—
368D4—364no—
369C2×C4—62no—
370C2×C4—64no—
371C2×C4—91no—
372C2×C4—91no—
373C2×C4—94no—
374C2×C4—91no—
375C2×C4—124no—
376C2×C4—182no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—364no—
380C2×C4#380211yescharacteristic
381C2×C4#380211yescharacteristic
382C2×C4C22×D3211yescharacteristic
383C8—22no—
384C8—182no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—242no—
389C2×C3#560712yes—
390C2×C3C2×D3×SD1612yes—
391C2×C3D3×#13712yes—
392D3—64no—
393D3—82no—
394D3—122no—
395C22—92no—
396C22—122no—
397C22—122no—
398C22—122no—
399C22—181no—
400C22—181no—
401C22C2×#380211yescharacteristic
402C4—21no—
403C4—92no—
404C4—92no—
405C4—124no—
406C4—122no—
407C4—181no—
408C4#6379612yes—
409C4#6431311yescharacteristic
410C4#6432011yescharacteristic
411C3—21no—
412C3#8043212yescomplemented
413C2—182no—
414C2—242no—
415C2#1059463411yescharacteristic
416C2C2×#6379611yescharacteristic
417C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593972C2
hypercenterC4⋊C8D32
hypocenterC32#3206
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
2. #10593909C2semidirect
3. #10592532C2semidirect
4. C3×#4841C2semidirect
5. #10590901C2semidirect
6. #10590884C2semidirect
7. #10590824C2semidirect
8. #10590363C2semidirect
41. #4841D3semidirect
125. C4×C3⋊D3SD16semidirect
357. C32#3206semidirect
412. C3#80432semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105939092
#105925322
C3×#48412
#105909012
#105908842
#105908242
#105903632
#804323