Finite Group Databasebeta

← #11779221

Subgroups — #11779221

Order 1152.

532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5727C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic, complemented
3#10590364C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71914—31nomaximal
9#71205—31nomaximal
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#946—21no—
13C3×#896—22no—
14C3×#893—21no—
15C3×#888—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3715—21no—
20C2×#3713—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#809—22no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63562—21no—
26#63562—21no—
27C3×D4×Q8—31no—
28#5727D311yescharacteristic, complemented
29C3×#486—31no—
30#5088D311yescharacteristic, complemented
31#5075—31no—
32#5072—31no—
33#5027—31no—
34#5015—31no—
35#4547—31no—
36#4547—31no—
37#4547—61no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8—21no—
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—22no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4D412yes—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66#3715—42no—
67#3713—42no—
68#1627—91noSylow
69C22×C3×Q8—61no—
70C2×D3×Q8—21no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×#127—31no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#946—21no—
82C2×#215—61no—
83C2×#214—61no—
84C2×#213—61no—
85C2×#213—61no—
86#896—22no—
87#893—21no—
88#888—21no—
89#874C2×D311yescharacteristic
90C4×D12C2×D311yescharacteristic
91C4×Dic6C2×D311yescharacteristic
92C3×#102—62no—
93C3×C4×C8—31no—
94#832—61no—
95#832—61no—
96#809—22no—
97#809—61no—
98#809—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)—61no—
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C32×Q8—41no—
109C32×Q8—41no—
110C2×C32×C4—22no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—44no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6—44no—
129C3×Dic6D812yescomplemented
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—31no—
134#486—31no—
135#460—91no—
136#459—91no—
137#332—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C2×C3×Q8—21no—
141C2×C3×Q8—21no—
142C2×C3×Q8—31no—
143C2×C3×Q8—41no—
144C2×C3×Q8—62no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153D3×Q8—42no—
154D3×Q8—42no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12#6711yescharacteristic
159C2×C4×D3—22no—
160C2×C4×D3—21no—
161C2×Dic6—22no—
162C2×Dic6#6711yescharacteristic
163C2×C3×C8—61no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4#6712yes—
173C3×C4⋊C4#6712yes—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#215—122no—
181#214—122no—
182#213—122no—
183#213—122no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—21no—
186C4⋊Dic3#6711yescharacteristic
187C4⋊Dic3#6711yescharacteristic
188Dic3⋊C4—22no—
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—121no—
197C2×C3⋊C8—121no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C32×C4—21no—
206C32×C4—42no—
207C32×C4C2×D811yescharacteristic
208C32×C4C2×SD1611yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C22×Q8—61no—
215C2×SD16—181no—
216C2×D8—181no—
217C4⋊Q8—61no—
218C4⋊Q8D3211yescharacteristic
219#127—31no—
220C22⋊Q8—61no—
221C22⋊Q8—62no—
222C4×Q8—31no—
223C4×D4—31no—
224C4×D4—61no—
225C4⋊C8—91no—
226C4⋊C8—91no—
227#102—62no—
228#102—181no—
229#102—181no—
230C4×C8—31no—
231C23×C3—61no—
232C23×C3—121no—
233C22×D3—21no—
234C22×D3—41no—
235C3×Q8—32no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—61no—
241C3×Q8—81no—
242C3×Q8—81no—
243C3×Q8—124no—
244C3×D4—32no—
245C3×D4—61no—
246C3×D4—122no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—42no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—124no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272D12—21no—
273D12—42no—
274D12—41no—
275D12—41no—
276D12—41no—
277D12—41no—
278D12#21512yescomplemented
279C4×D3—44no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—21no—
283Dic6—44no—
284Dic6#21312yescomplemented
285C3×C8—121no—
286C3⋊C8—41no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C3⋊C8—121no—
291C3⋊C8—241no—
292C3⋊C8—241no—
293C2×C32#44711yescharacteristic
294C2×C32#44811yescharacteristic
295C2×C32#45411yescharacteristic
296C3×D3—42no—
297C3×D3—161no—
298C2×Q8—21no—
299C2×Q8—31no—
300C2×Q8—62no—
301C2×Q8—122no—
302C2×Q8—122no—
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—62no—
308C22×C4—61no—
309SD16—362no—
310D8—362no—
311C2×C8—61no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—21no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—62no—
318C4⋊C4—61no—
319C4⋊C4#62512yes—
320C22⋊C4—62no—
321C22⋊C4—61no—
322C42—61no—
323C42C2×D3211yescharacteristic
324C22×C3—21no—
325C22×C3—62no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—241no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3#93711yescharacteristic
332C22×C3#95311yescharacteristic
333C2×D3—22no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—81no—
337C2×D3—81no—
338C2×D3—81no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—42no—
347C3×C4—42no—
348C3×C4—62no—
349C3×C4—82no—
350C3×C4—121no—
351C3×C4—121no—
352C3×C4D3×D811yescharacteristic
353C3×C4#91111yescharacteristic
354C3×C4D3×SD1611yescharacteristic
355C3×C4#91511yescharacteristic
356C3×C4C2×#21311yescharacteristic
357C3×C4#93211yescharacteristic
358C3×C4C2×#21511yescharacteristic
359C3×C4#94211yescharacteristic
360Dic3—22no—
361Dic3—41no—
362Dic3—41no—
363C32#162711yescharacteristic, complemented, Sylow
364C23—61no—
365C23—121no—
366Q8—32no—
367Q8—41no—
368Q8—41no—
369Q8—61no—
370Q8—124no—
371D4—32no—
372D4—61no—
373D4—122no—
374D4—121no—
375D4—121no—
376D4—121no—
377D4—121no—
378C2×C4—22no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—124no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4C2×#62511yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C8—121no—
389C8—361no—
390C8—361no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—122no—
395C2×C3—481no—
396C2×C3#506211yescharacteristic
397C2×C3#515611yescharacteristic
398C2×C3#517011yescharacteristic
399C2×C3#521711yescharacteristic
400C2×C3#522711yescharacteristic
401C2×C3#524511yescharacteristic
402D3—42no—
403D3—161no—
404C22—62no—
405C22—121no—
406C22—121no—
407C22—241no—
408C22—241no—
409C22—241no—
410C22#6397611yescharacteristic
411C4—21no—
412C4—42no—
413C4—62no—
414C4—121no—
415C4—121no—
416C4D3×#21311yescharacteristic
417C4#6393211yescharacteristic
418C4D3×#21511yescharacteristic
419C4#6394611yescharacteristic
420C3—21no—
421C3#7120511yescharacteristic, complemented
422C3#7191411yescharacteristic, complemented
423C2—122no—
424C2—481no—
425C2#1059144711yescharacteristic
426C2#1059158311yescharacteristic
427C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4⋊Q8D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5727C2semidirect
2. C3×#5088C2semidirect
3. #10590364C2semidirect
5. #10589413C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
28. #5727D3semidirect
30. #5088D3semidirect
123. C3×D12SD16semidirect
129. C3×Dic6D8semidirect
278. D12#215semidirect
284. Dic6#213semidirect
363. C32#1627semidirect
421. C3#71205semidirect
422. C3#71914semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C3×#50882
#105903642
#105903472
#105894132
#105890842
#105890812
#719143
#712053