Finite Group Databasebeta

← #11779284

Subgroups — #11779284

Order 1152.

496 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593863C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590281C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68433—31nomaximal
9#68201—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63863—21no—
16#63858—22no—
17#63857—21no—
18#63843—21no—
19#63841—21no—
20C2×#3714—21no—
21C32×C4⋊C8C2211yescharacteristic
22#63648—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27#5732—31no—
28#5542—31no—
29#5088—31no—
30#5015—31no—
31#4848—31no—
32#4848—31no—
33#4848—61no—
34#4843—31no—
35#4694—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4484—31no—
40#4483D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54#3744—42no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D412yes—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#3714—42no—
66#1628—91noSylow
67C3×C4⋊Q8—31no—
68C3×C4×D4—31no—
69#947—61no—
70Q8×Dic3—61no—
71#936—61no—
72C2×#213—61no—
73#926—61no—
74#924—61no—
75C2×D24—61no—
76C2×#204—61no—
77C2×#204—61no—
78C2×#204—62no—
79#898—62no—
80#897—61no—
81#892—61no—
82#887—61no—
83#879—62no—
84#874—31no—
85#874—31no—
86#874—61no—
87C4×D12C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C4×Dic6—31no—
90C4×Dic6—31no—
91C4×Dic6—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4×C8—31no—
97#821—61no—
98#821—61no—
99#821—62no—
100#821—62no—
101#821—61no—
102#809—61no—
103#809—62no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊D3—41no—
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118#634—21no—
119#634—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C32×C8—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#556—91no—
132#486—91no—
133#460—91no—
134#459—91no—
135#332—31no—
136Q8⋊C8—91no—
137D4⋊C8—31no—
138C2×C3×Q8—61no—
139C2×C3×D4—31no—
140C22×C3×C4—61no—
141C2×D12—62no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—121no—
149C2×D12—121no—
150C2×D12D1211yescharacteristic
151C2×C4×D3—21no—
152C2×Dic6—21no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—61no—
156C2×C3×C8—22no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—62no—
169#217—62no—
170#213—122no—
171(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174C4⋊Dic3—21no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3—62no—
179C4⋊Dic3D1212yes—
180C4⋊Dic3D1211yescharacteristic
181Dic3⋊C4—62no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—121no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—121no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192D24—122no—
193#204—124no—
194#204—122no—
195#204—122no—
196C22×C32#12011yescharacteristic
197C2×C3⋊D3—81no—
198C2×C3⋊D3—81no—
199C2×C3⋊D3—81no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C32×C4—21no—
204C32×C4#13511yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C3⋊Dic3—41no—
209C3⋊Dic3—41no—
210C3×Dic3—42no—
211C3×Dic3—41no—
212C2×SD16—181no—
213C2×D8—181no—
214C4⋊Q8—31no—
215#127—91no—
216#126—182no—
217#124—181no—
218C22⋊Q8—181no—
219C4×Q8—91no—
220C4×Q8—181no—
221C4×D4—31no—
222#117—181no—
223C4⋊C8—31no—
224C4⋊C8D3211yescharacteristic
225#102—181no—
226#102—182no—
227#102—181no—
228C4×C8—31no—
229C23×C3—61no—
230C22×D3—21no—
231C22×D3—122no—
232C22×D3—121no—
233C22×D3—121no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—61no—
237C3×D4—61no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—22no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259D12—21no—
260D12—21no—
261D12—122no—
262D12—122no—
263D12—122no—
264D12—122no—
265D12—121no—
266D12—121no—
267D12—121no—
268D12—121no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—241no—
274D12—241no—
275D12—242no—
276C4×D3—41no—
277C4×D3—41no—
278Dic6—41no—
279Dic6—41no—
280Dic6—62no—
281Dic6—61no—
282Dic6—61no—
283Dic6—61no—
284Dic6—61no—
285Dic6—121no—
286C3×C8—42no—
287C3×C8—41no—
288C3×C8—41no—
289C3×C8—121no—
290C3×C8—121no—
291C3⋊C8—41no—
292C3⋊C8—41no—
293C2×C32#44911yescharacteristic
294C2×C32#44911yescharacteristic
295C2×C32#45411yescharacteristic
296C3⋊D3—161no—
297C3×D3—81no—
298C2×Q8—61no—
299C2×Q8—91no—
300C2×D4—31no—
301C2×D4—181no—
302C2×D4—181no—
303C2×D4—181no—
304C22×C4—61no—
305SD16—362no—
306D8—362no—
307C2×C8—21no—
308C2×C8—61no—
309C2×C8—61no—
310C4⋊C4—31no—
311C4⋊C4—32no—
312C4⋊C4—61no—
313C4⋊C4—91no—
314C4⋊C4—182no—
315C4⋊C4—181no—
316C22⋊C4—61no—
317C22⋊C4—182no—
318C22⋊C4—182no—
319C42—182no—
320C42—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3#88211yescharacteristic
327C22×C3#88211yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—242no—
332C2×D3—242no—
333C2×D3—242no—
334C2×D3—241no—
335C2×D3—241no—
336C2×D3—241no—
337C2×D3—241no—
338C2×D3—241no—
339C2×D3—241no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—122no—
348C3×C4—121no—
349C3×C4#90411yescharacteristic
350C3×C4#90811yescharacteristic
351C3×C4#91111yescharacteristic
352C3×C4#91111yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91611yescharacteristic
355C3×C4#91611yescharacteristic
356C3×C4#91911yescharacteristic
357Dic3—42no—
358Dic3—41no—
359Dic3—122no—
360Dic3—121no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—241no—
365C32#162811yescharacteristic, complemented, Sylow
366C23—61no—
367C23—361no—
368Q8—121no—
369Q8—121no—
370Q8—181no—
371Q8—181no—
372D4—61no—
373D4—61no—
374D4—362no—
375D4—361no—
376D4—361no—
377D4—361no—
378D4—361no—
379C2×C4—61no—
380C2×C4—62no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4D3×D1211yescharacteristic
386C2×C4D3×D1211yescharacteristic
387C2×C4#381111yescharacteristic
388C8—41no—
389C8—121no—
390C8—121no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—241no—
395C2×C3#473411yescharacteristic
396C2×C3#475311yescharacteristic
397C2×C3#478111yescharacteristic
398C2×C3#478111yescharacteristic
399C2×C3#481011yescharacteristic
400C2×C3#482711yescharacteristic
401D3—81no—
402D3—482no—
403D3—481no—
404D3—481no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—721no—
409C22—721no—
410C22—721no—
411C22#6392311yescharacteristic
412C4—21no—
413C4—121no—
414C4—122no—
415C4—361no—
416C4—361no—
417C4#6379511yescharacteristic
418C4#6380611yescharacteristic
419C4#6393711yescharacteristic
420C4#6395011yescharacteristic
421C3—21no—
422C3#6820111yescharacteristic, complemented
423C3#6843311yescharacteristic, complemented
424C2—241no—
425C2—1441no—
426C2#1059061711yescharacteristic
427C2#1059096811yescharacteristic
428C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590349C2
hypercenterC4⋊C8D32
hypocenterC32#1628
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593863C2semidirect
2. #10592547C2semidirect
4. #10590281C2semidirect
5. C3×#4486C2semidirect
6. C3×#4483C2semidirect
7. #10589085C2semidirect
38. #4486D3semidirect
40. #4483D3semidirect
365. C32#1628semidirect
422. C3#68201semidirect
423. C3#68433semidirect

Maximal subgroups

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

subgroupindex
#105938632
#105925472
#105903492
#105902812
C3×#44862
C3×#44832
#105890852
#684333
#682013