Finite Group Databasebeta

← #11779382

Subgroups — #11779382

Order 1152.

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

normal subgroups only

This group has 547 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×#5577C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71919—31nomaximal
9#71160—31nomaximal
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12C3×#895—22no—
13C3×#895—21no—
14C3×#874—21no—
15C3×#874C2211yescharacteristic
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3715—22no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63574—21no—
26#63562—21no—
27C3×#550—31no—
28#5577D311yescharacteristic
29C3×#477—31no—
30#5085—31no—
31#5084—31no—
32#5076—31no—
33#5021D311yescharacteristic, complemented
34#5008—31no—
35#4544—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4485—31no—
41#4483—31no—
42C2×C32×Q8D411yescharacteristic
43C3×#239—42no—
44C3×#239—42no—
45C2×C3×D12—22no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—22no—
49C2×C3×D12D411yescharacteristic
50C2×C3×D12D412yes—
51C2×C3×C4×D3—22no—
52C2×C3×C4×D3—21no—
53C2×C3×Dic6—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66#3715—44no—
67#1631—91noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C3×C4⋊Q8—31no—
71C3×#127—31no—
72C3×#127—61no—
73C3×#121—62no—
74C3×#121—61no—
75C3×C4×Q8—21no—
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×D4—31no—
79C3×C4×D4—61no—
80C2×#215—62no—
81C2×#214—62no—
82#895—22no—
83#895—21no—
84#874—21no—
85#874C2×D311yescharacteristic
86C4×D12—21no—
87C4×D12C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C3×#107—61no—
90C3×C4⋊C8—31no—
91C3×#103—61no—
92#835—21no—
93#832—61no—
94#809—61no—
95#808—61no—
96#808—61no—
97#807—21no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C32×Q8—21no—
108C32×Q8SD1612yescomplemented
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—44no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—82no—
125C3×C4×D3—44no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—42no—
129C3⋊(C3⋊C8)—22no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#550—31no—
133#492—91no—
134#477—31no—
135#476—91no—
136#331—91no—
137Q8⋊C8—91no—
138D4⋊C8—91no—
139C3×#41—122no—
140C3×#41—122no—
141C2×C3×Q8—21no—
142C2×C3×Q8—61no—
143C2×C3×Q8#6711yescharacteristic
144C2×C3×Q8#6711yescharacteristic
145C2×C3×D4—31no—
146C2×C3×D4—32no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153#239—42no—
154#239—42no—
155C2×D12—22no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12—22no—
159C2×D12#6711yescharacteristic
160C2×D12#6712yes—
161C2×C4×D3—22no—
162C2×C4×D3—21no—
163C2×Dic6—21no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4#6711yescharacteristic
173C3×C4⋊C4#6711yescharacteristic
174C3×C22⋊C4—62no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—41no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#215—124no—
183#214—124no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3#6711yescharacteristic
189C2×C3⋊C8—21no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C22×C32#12011yescharacteristic
197C2×C3×D3—42no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—41no—
203C32×C4—22no—
204C32×C4—21no—
205C32×C4—41no—
206C32×C4C2×SD1611yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4#13711yescharacteristic
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—61no—
213C2×SD16—182no—
214C4⋊Q8—31no—
215#127—31no—
216#127—61no—
217#121—62no—
218#121—61no—
219C4×Q8D3211yescharacteristic
220C4×D4—31no—
221C4×D4—61no—
222#107—61no—
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226#103—61no—
227#102—181no—
228C4×C8—91no—
229C23×C3—61no—
230C23×C3—62no—
231C22×D3—21no—
232C22×D3—22no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—22no—
236C3×Q8—41no—
237C3×Q8—122no—
238C3×Q8#21412yescomplemented
239C3×Q8#21512yescomplemented
240C3×D4—61no—
241C3×D4—61no—
242C3×D4—122no—
243C3×D4—124no—
244C3×D4—121no—
245C3×D4—121no—
246C3×D4—121no—
247C3×D4—121no—
248C3×D4—242no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—61no—
259C2×C3×C4—124no—
260C2×C3×C4—121no—
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—41no—
271D12—21no—
272D12—21no—
273D12—42no—
274D12—44no—
275D12—41no—
276D12—41no—
277D12—41no—
278D12—41no—
279D12—82no—
280C4×D3—44no—
281C4×D3—41no—
282C4×D3—41no—
283Dic6—42no—
284C3×C8—121no—
285C3⋊C8—41no—
286C3⋊C8—62no—
287C3⋊C8—62no—
288C3⋊C8—122no—
289C3⋊C8—121no—
290C3⋊C8—121no—
291C3⋊C8—241no—
292C2×C32#45011yescharacteristic
293C2×C32#45211yescharacteristic
294C2×C32#45311yescharacteristic
295C3×D3—81no—
296C3×D3—82no—
297#41—122no—
298#41—122no—
299C2×Q8—61no—
300C2×Q8#62511yescharacteristic
301C2×D4—31no—
302C2×D4—32no—
303C2×D4—62no—
304C2×D4—62no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—62no—
308C22×C4—61no—
309SD16—364no—
310C2×C8—61no—
311C2×C8—181no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—31no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4#62511yescharacteristic
318C22⋊C4—62no—
319C22⋊C4—61no—
320C42—21no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—121no—
327C22×C3—122no—
328C22×C3—121no—
329C22×C3#93711yescharacteristic
330C22×C3#95311yescharacteristic
331C2×D3—42no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—42no—
335C2×D3—42no—
336C2×D3—41no—
337C3×C4—21no—
338C3×C4—22no—
339C3×C4—21no—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—42no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—81no—
350C3×C4—121no—
351C3×C4—241no—
352C3×C4#91811yescharacteristic
353C3×C4#91911yescharacteristic
354C3×C4#93211yescharacteristic
355C3×C4C2×#21411yescharacteristic
356C3×C4C2×#21511yescharacteristic
357C3×C4#94911yescharacteristic
358C3×C4#95011yescharacteristic
359C3×C4#95111yescharacteristic
360Dic3—41no—
361Dic3—81no—
362C32#163111yescharacteristic, complemented, Sylow
363C23—61no—
364C23—62no—
365Q8—21no—
366Q8—122no—
367Q8#371512yescomplemented
368D4—61no—
369D4—61no—
370D4—122no—
371D4—124no—
372D4—121no—
373D4—121no—
374D4—121no—
375D4—121no—
376D4—242no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—61no—
380C2×C4—124no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4C2×#62511yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C8—121no—
388C8—182no—
389C8—361no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—241no—
394C2×C3—242no—
395C2×C3#504611yescharacteristic
396C2×C3#518711yescharacteristic
397C2×C3#519811yescharacteristic
398C2×C3#521811yescharacteristic
399C2×C3#523911yescharacteristic
400C2×C3#524111yescharacteristic
401D3—81no—
402D3—82no—
403C22—121no—
404C22—122no—
405C22—122no—
406C22—121no—
407C22—122no—
408C22—121no—
409C22#6397611yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—121no—
414C4—241no—
415C4#6382311yescharacteristic
416C4C2×#371511yescharacteristic
417C4#6394311yescharacteristic
418C4#6394911yescharacteristic
419C3—21no—
420C3#7116011yescharacteristic, complemented
421C3#7191911yescharacteristic, complemented
422C2—241no—
423C2—242no—
424C2#1059116911yescharacteristic
425C2#1059159711yescharacteristic
426C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#1631
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
2. C3×#5021C2semidirect
3. #10590375C2semidirect
4. #10590266C2semidirect
5. #10589401C2semidirect
6. #10589090C2semidirect
7. #10589080C2semidirect
33. #5021D3semidirect
108. C32×Q8SD16semidirect
238. C3×Q8#214semidirect
239. C3×Q8#215semidirect
362. C32#1631semidirect
367. Q8#3715semidirect
420. C3#71160semidirect
421. C3#71919semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#50212
#105903752
#105902662
#105894012
#105890902
#105890802
#719193
#711603