Finite Group Databasebeta

← #11778936

Subgroups — #11778936

Order 1152.

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

normal subgroups only

This group has 522 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#10593963C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic, complemented
3#10590364C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71031—31nomaximal
9#68258—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63897—22no—
16#63894—21no—
17#63894—21no—
18#63864—21no—
19#63864—21no—
20C2×#3715—21no—
21C2×#3714—22no—
22C32×C4⋊C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#821—21no—
25C3×C4×C3⋊C8C2211yescharacteristic
26#63562—21no—
27#5585—31no—
28#5585—31no—
29C3×#460—31no—
30#5075—31no—
31#5073—31no—
32#5027—31no—
33#4848D311yescharacteristic, complemented
34#4695—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4485—31no—
38#4485—31no—
39#4485—61no—
40#4484D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)D412yes—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×C3×Dic6D411yescharacteristic
50C2×#624—22no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C3×#204—42no—
62#3722—22no—
63#3722—22no—
64#3722—22no—
65#3715—42no—
66#3714—44no—
67#1620—91noSylow
68C2×C3×SD16—61no—
69C3×#127—31no—
70C3×C4×Q8—31no—
71C3×C4×Q8—31no—
72#947—61no—
73#947—61no—
74C2×#215—61no—
75C2×#214—61no—
76C2×#213—62no—
77C2×D24—62no—
78C2×#204—21no—
79#894—62no—
80#894—62no—
81#893—61no—
82#893—61no—
83#875—61no—
84#875—61no—
85#874—31no—
86#874—31no—
87#874—61no—
88#874C2×D311yescharacteristic
89C4×D12—61no—
90C4×D12—61no—
91C4×Dic6C2×D311yescharacteristic
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×#102—61no—
97C3×C4×C8—31no—
98#832—61no—
99#821—21no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—22no—
106C22×C3×D3—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C4⋊(C3⋊D3)—42no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C3×D12—42no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×Dic6—21no—
125C3×Dic6—21no—
126C3×Dic6—21no—
127C3×Dic6—21no—
128#624—82no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132#559—91no—
133#493—91no—
134#460—31no—
135#460—91no—
136#331—91no—
137Q8⋊C8—31no—
138Q8⋊C8—91no—
139C2×C3×Q8—31no—
140C2×C3×Q8—31no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12—21no—
147C2×D12—32no—
148C2×D12—32no—
149C2×D12—62no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—121no—
155C2×D12—121no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×Dic6D1211yescharacteristic
159C2×Dic6#6711yescharacteristic
160C3×SD16—122no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C42—21no—
170C3×C42—61no—
171C3×C42—61no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#215—122no—
175#214—122no—
176#213—124no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183C4⋊Dic3D1211yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—121no—
193D24—124no—
194#204—42no—
195C22×C32#12011yescharacteristic
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C2×C3×D3—81no—
202C32×C4—21no—
203C32×C4#13511yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C2×SD16—61no—
212C2×SD16—181no—
213C2×D8—182no—
214#127—31no—
215#127—91no—
216#124—181no—
217#124—181no—
218#123—182no—
219C4×Q8—31no—
220C4×Q8—31no—
221C4×D4—181no—
222C4×D4—181no—
223C4⋊C8—91no—
224C4⋊C8D3211yescharacteristic
225#102—61no—
226#102—181no—
227C4×C8—31no—
228C23×C3—121no—
229C22×D3—41no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—122no—
233C3×Q8—61no—
234C3×Q8—61no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×D4—122no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259D12—42no—
260D12—41no—
261D12—41no—
262D12—41no—
263D12—41no—
264D12—122no—
265D12—122no—
266D12—121no—
267D12—121no—
268D12—121no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—241no—
275D12—241no—
276D12—241no—
277D12—241no—
278D12—242no—
279C4×D3—242no—
280C4×D3—242no—
281Dic6—21no—
282Dic6—21no—
283Dic6—21no—
284Dic6—21no—
285C3×C8—41no—
286C3×C8—41no—
287C3×C8—62no—
288C3×C8—81no—
289C3⋊C8—22no—
290C3⋊C8—121no—
291C3⋊C8—121no—
292C3⋊C8—241no—
293C2×C32#44911yescharacteristic
294C2×C32#44911yescharacteristic
295C2×C32#45311yescharacteristic
296C3⋊D3—82no—
297C3×D3—161no—
298C2×Q8—31no—
299C2×Q8—31no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—92no—
304C2×D4—181no—
305C2×D4—181no—
306C22×C4—182no—
307SD16—122no—
308SD16—362no—
309D8—364no—
310C2×C8—21no—
311C2×C8—61no—
312C2×C8—181no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C22⋊C4—182no—
318C22⋊C4—182no—
319C22⋊C4—182no—
320C42—61no—
321C42—61no—
322C42C2×D3211yescharacteristic
323C22×C3—21no—
324C22×C3—241no—
325C22×C3—241no—
326C22×C3—241no—
327C22×C3#88211yescharacteristic
328C22×C3#93711yescharacteristic
329C2×D3—81no—
330C2×D3—81no—
331C2×D3—81no—
332C2×D3—122no—
333C2×D3—122no—
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—242no—
339C2×D3—242no—
340C2×D3—242no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4—121no—
351C3×C4—121no—
352C3×C4#90411yescharacteristic
353C3×C4#90811yescharacteristic
354C3×C4#91411yescharacteristic
355C3×C4#91411yescharacteristic
356C3×C4#91611yescharacteristic
357C3×C4#91911yescharacteristic
358C3×C4#93211yescharacteristic
359C3×C4#95011yescharacteristic
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3—41no—
364C32#162011yescharacteristic, complemented, Sylow
365C23—121no—
366C23—182no—
367Q8—61no—
368Q8—61no—
369Q8—61no—
370Q8—61no—
371D4—122no—
372D4—121no—
373D4—121no—
374D4—121no—
375D4—121no—
376D4—362no—
377D4—361no—
378D4—361no—
379D4—361no—
380D4—361no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—722no—
386C2×C4D3×D1211yescharacteristic
387C2×C4#380211yescharacteristic
388C2×C4D3×#6711yescharacteristic
389C8—41no—
390C8—62no—
391C8—361no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—481no—
396C2×C3#473411yescharacteristic
397C2×C3#481011yescharacteristic
398C2×C3#482211yescharacteristic
399C2×C3#503711yescharacteristic
400C2×C3#517211yescharacteristic
401C2×C3#519811yescharacteristic
402D3—161no—
403D3—242no—
404D3—242no—
405D3—482no—
406C22—241no—
407C22—241no—
408C22—241no—
409C22—362no—
410C22—362no—
411C22—362no—
412C22#6392211yescharacteristic
413C4—21no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4—121no—
418C4#6379411yescharacteristic
419C4#6380611yescharacteristic
420C4#6393411yescharacteristic
421C4#6394911yescharacteristic
422C3—21no—
423C3#6825811yescharacteristic, complemented
424C3#7103111yescharacteristic, complemented
425C2—481no—
426C2—722no—
427C2#1059061511yescharacteristic
428C2#1059082311yescharacteristic
429C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590350C2
hypercenterC4⋊C8D32
hypocenterC32#1620
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. #10593963C2semidirect
2. C3×#4848C2semidirect
3. #10590364C2semidirect
5. #10589351C2semidirect
6. C3×#4484C2semidirect
7. #10589084C2semidirect
33. #4848D3semidirect
40. #4484D3semidirect
364. C32#1620semidirect
423. C3#68258semidirect
424. C3#71031semidirect

Maximal subgroups

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

subgroupindex
#105939632
C3×#48482
#105903642
#105903502
#105893512
C3×#44842
#105890842
#710313
#682583