Finite Group Databasebeta

← #11870728

Subgroups — #11870728

Order 1152.

1005 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1005 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, complemented
2#10594929C211yesmaximal, characteristic
3C3×#5227C212yesmaximal, complemented
4#10591630C212yesmaximal, complemented
5#10591622C212yesmaximal, complemented
6#10591571C214yesmaximal, complemented
7#10591092C212yesmaximal, complemented
8#10591061C211yesmaximal, characteristic, complemented
9#80028—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3805—21no—
12Q8×C3⋊Dic3—21no—
13Q8×C3⋊Dic3—21no—
14Q8×C3⋊Dic3C2212yes—
15Q8×C3⋊Dic3C2212yes—
16C2×C4⋊(C3⋊Dic3)—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#215C2214yes—
21C3×#930C2212yes—
22#63980—21no—
23#63919C2211yescharacteristic
24#63915—21no—
25#63914C2211yescharacteristic
26#63902—21no—
27#63898C2212yes—
28C3×#835C2214yes—
29C3×#830C2212yes—
30#63573C2214yes—
31#63572C2212yes—
32#63563C2214yes—
33#63553C2212yes—
34C2×Q8×Dic3—32no—
35C2×Q8×Dic3—61no—
36#5596—32no—
37C3×#448—32no—
38#5227D312yescomplemented
39#5163—34no—
40Dic3×SD16—34no—
41#5034—32no—
42#4791—34no—
43#4788—34no—
44#4735—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×#67—22no—
55C2×C3×D12C2312yes—
56C2×#627—21no—
57C2×#625—21no—
58C2×#625—21no—
59#3805—44no—
60C2×D3×Dic3—22no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—22no—
63C4⋊(C3⋊Dic3)—22no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4×C3⋊Dic3—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3D411yescharacteristic
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3C2311yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C3×#215—28no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77#3103—91noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8C2×D312yes—
80C2×#237—62no—
81C2×C3×SD16—34no—
82C3×#121—32no—
83Q8×Dic3—34no—
84Q8×Dic3—34no—
85Q8×Dic3—62no—
86Q8×Dic3—62no—
87Q8×Dic3—62no—
88Q8×Dic3—62no—
89Q8×Dic3—62no—
90Q8×Dic3—62no—
91C2×#215C2×D314yes—
92#940—32no—
93#939—62no—
94D4×Dic3—32no—
95#930C2×D312yes—
96C2×C4⋊Dic3—32no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—62no—
99C2×C4⋊Dic3—62no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3—62no—
103C2×C4×Dic3—62no—
104#893—32no—
105#888—32no—
106#885—62no—
107#67⋊C4—62no—
108C3×#103—34no—
109C3×C22⋊C8—32no—
110#835C2×D314yes—
111#832—34no—
112#830C2×D312yes—
113#821—34no—
114#817—34no—
115Dic3⋊C8—34no—
116C8×Dic3—34no—
117#808—34no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C32×Q8—24no—
121C32×Q8—22no—
122C32×Q8#4114yescomplemented
123C2×C32×C4—24no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—42no—
131C2×C3⋊Dic3SD1614yescomplemented
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C2×C3⋊Dic3C2×D411yescharacteristic
136C3×#67—44no—
137C2×C3×Dic3—22no—
138C3×D12—24no—
139#627—42no—
140#625—42no—
141#625—42no—
142D3×Dic3—44no—
143C3×C3⋊C8—24no—
144#532—91no—
145C2×C4×Q8—91no—
146#481—92no—
147#475—92no—
148#460—92no—
149#448—32no—
150C4×SD16—94no—
151#431—91no—
152C2×C3×Q8—22no—
153C2×C3×Q8—28no—
154C2×C3×Q8—28no—
155C2×C3×Q8—22no—
156C2×C3×Q8—22no—
157C2×C3×Q8C22×D314yes—
158C2×C3×D4—32no—
159C2×C3×D4—62no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D312yes—
164C2×#67—22no—
165C2×#67—62no—
166C2×#67—62no—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174#237—128no—
175C2×D12C22×D312yes—
176C2×C4×D3—62no—
177C2×Dic6—62no—
178C3×SD16—68no—
179C2×C3×C8—34no—
180C3×C4⋊C4—32no—
181C3×C22⋊C4—62no—
182#217—62no—
183#215—28no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—34no—
187C4⋊Dic3—62no—
188C4⋊Dic3—64no—
189C4⋊Dic3—64no—
190C4⋊Dic3—64no—
191C4⋊Dic3—64no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194C4⋊Dic3C22×D312yes—
195Dic3⋊C4—62no—
196C4×Dic3—32no—
197C4×Dic3—32no—
198C4×Dic3—32no—
199C4×Dic3—32no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—64no—
205C4×Dic3—64no—
206C4×Dic3—64no—
207C4×Dic3—64no—
208C2×C3⋊C8C22×D314yes—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C2×SD1612yes—
212C22×C32C22×D411yescharacteristic
213C2×C3×D3—42no—
214C2×C3×D3—42no—
215C2×C3×D3—42no—
216C32×C4—24no—
217C32×C4—21no—
218C32×C4C2×#4112yes—
219C3⋊Dic3—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—42no—
222C3⋊Dic3C2×SD1612yes—
223C3⋊Dic3C2×SD1612yes—
224C3×Dic3—42no—
225C2×#41—181no—
226C22×Q8D3211yescharacteristic
227C2×SD16—34no—
228C4⋊Q8—91no—
229#127—91no—
230#124—181no—
231#121—32no—
232#121—181no—
233C4×Q8—92no—
234C4×Q8—92no—
235C4×Q8—181no—
236C4×Q8—181no—
237C4×D4—92no—
238C4×D4—181no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—181no—
241C2×C42—91no—
242C2×C42—181no—
243#106—94no—
244C4⋊C8—92no—
245#103—34no—
246#102—94no—
247C22⋊C8—32no—
248C4×C8—92no—
249C23×C3—21no—
250C23×C3—62no—
251C23×C3D3×D412yes—
252C22×D3—22no—
253C3×Q8—28no—
254C3×Q8—28no—
255C3×Q8—24no—
256C3×Q8—24no—
257C3×Q8—24no—
258C3×Q8#23718yescomplemented
259C3×D4—64no—
260C3×D4—124no—
261C2×C3×C4—24no—
262C2×C3×C4—28no—
263C2×C3×C4—28no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—62no—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C23×D312yes—
272#67—44no—
273#67—124no—
274#67—124no—
275C2×Dic3—22no—
276C2×Dic3—38no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—64no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—124no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—124no—
292C2×Dic3—124no—
293D12—24no—
294C4×D3—124no—
295Dic6—124no—
296C3×C8—64no—
297C3⋊C8—24no—
298C2×C32—22no—
299C2×C32#52511yescharacteristic
300C2×C32C22×SD1611yescharacteristic
301C2×C32#57511yescharacteristic
302C3×D3—82no—
303#41—364no—
304C2×Q8—24no—
305C2×Q8—21no—
306C2×Q8—181no—
307C2×Q8C2×D3212yes—
308C2×D4—32no—
309C2×D4—62no—
310C2×D4—181no—
311C2×D4—181no—
312C22×C4—21no—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—182no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318SD16—68no—
319C2×C8—34no—
320C4⋊C4—32no—
321C4⋊C4—92no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C22⋊C4—62no—
327C22⋊C4—182no—
328C42—91no—
329C42—91no—
330C42—91no—
331C42—91no—
332C42—182no—
333C42—182no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—122no—
341C22×C3—122no—
342C22×C3—122no—
343C22×C3D3×SD1614yes—
344C22×C3C2×D3×D412yes—
345C2×D3—42no—
346C2×D3—42no—
347C2×D3—42no—
348C3×C4—28no—
349C3×C4—22no—
350C3×C4—28no—
351C3×C4—22no—
352C3×C4—22no—
353C3×C4—122no—
354C3×C4C2×#23714yes—
355Dic3—34no—
356Dic3—34no—
357Dic3—42no—
358Dic3—62no—
359Dic3—62no—
360Dic3—62no—
361Dic3—62no—
362Dic3—121no—
363Dic3—121no—
364Dic3—124no—
365Dic3—124no—
366C32#310311yescharacteristic, complemented, Sylow
367C23—62no—
368C23#381111yescharacteristic
369Q8—24no—
370Q8—22no—
371Q8—362no—
372Q8#380514yescomplemented
373D4—64no—
374D4—124no—
375D4—362no—
376D4—362no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—62no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—94no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—182no—
387C2×C4—364no—
388C2×C4—361no—
389C2×C4—362no—
390C2×C4#381111yescharacteristic
391C2×C4C22×D3211yescharacteristic
392C8—64no—
393C2×C3—24no—
394C2×C3—24no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—242no—
399C2×C3#558612yes—
400C2×C3C2×D3×SD1612yes—
401C2×C3#577712yes—
402D3—82no—
403C22—21no—
404C22—21no—
405C22—122no—
406C22—122no—
407C22—122no—
408C22#6394012yes—
409C22C2×#381111yescharacteristic
410C4—24no—
411C4—21no—
412C4—92no—
413C4—92no—
414C4—122no—
415C4—181no—
416C4—181no—
417C4—362no—
418C4C2×#380512yes—
419C3—21no—
420C3#8002812yescomplemented
421C2—22no—
422C2—242no—
423C2C2×#6394011yescharacteristic
424C2#1059532311yescharacteristic
425C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594929C2
hypercenterC22×Q8D32
hypocenterC32#3103
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
1. C2×Q8×C3⋊Dic3C2semidirect
3. C3×#5227C2semidirect
4. #10591630C2semidirect
5. #10591622C2semidirect
6. #10591571C2semidirect
7. #10591092C2semidirect
8. #10591061C2semidirect
38. #5227D3semidirect
122. C32×Q8#41semidirect
131. C2×C3⋊Dic3SD16semidirect
258. C3×Q8#237semidirect
366. C32#3103semidirect
372. Q8#3805semidirect
420. C3#80028semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
#105949292
C3×#52272
#105916302
#105916222
#105915712
#105910922
#105910612
#800283