Finite Group Databasebeta

← #11779549

Subgroups — #11779549

Order 1152.

500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593895C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic, complemented
3#10590287C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589352C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71140—31nomaximal
9#68204—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63908—21no—
16#63891—22no—
17D3×C4⋊Dic3—21no—
18#63857—21no—
19C32×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×#821—21no—
22C3×#817—21no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63574—21no—
25#63566—22no—
26#63562—21no—
27#5555—31no—
28#5551—31no—
29C3×#476—31no—
30#5084—31no—
31#5079—31no—
32#5008—31no—
33#4842D311yescharacteristic, complemented
34#4681—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4486—31no—
38#4486—31no—
39#4486—61no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C2×#634—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×#625—22no—
49C2×D3×Dic3—22no—
50#3795—42no—
51#3795—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#1635—91noSylow
67C2×#237—61no—
68C2×#235—61no—
69C3×C4⋊Q8—31no—
70C3×C4×D4—31no—
71C3×C4×D4—31no—
72#938—61no—
73#930—61no—
74C2×C4⋊Dic3—61no—
75#924—61no—
76#897—61no—
77D3×C4⋊C4—61no—
78#886—62no—
79#883—62no—
80C4×D12C2×D311yescharacteristic
81C4×D12C2×D311yescharacteristic
82#869—31no—
83#869—31no—
84#869—61no—
85#869C2×D311yescharacteristic
86C3×#106—61no—
87C3×C4⋊C8—21no—
88C3×C4⋊C8C2×D311yescharacteristic
89C3×C4⋊C8C2×D311yescharacteristic
90C3×#102—61no—
91C3×C4×C8—31no—
92#835—62no—
93#832—61no—
94#821—21no—
95#817—21no—
96#816—62no—
97#809—61no—
98#808—61no—
99#808—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4×C3⋊C8C2×D311yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110#634—41no—
111#634—41no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—41no—
115C3×D12—21no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12SD1612yes—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—42no—
124#625—44no—
125D3×Dic3—44no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129#547—91no—
130#487—91no—
131#476—31no—
132#476—91no—
133#332—91no—
134D4⋊C8—31no—
135D4⋊C8—91no—
136C2×C3×Q8—61no—
137C2×C3×D4—31no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C2×#67—62no—
142C2×#67—62no—
143C22×Dic3—62no—
144#237—122no—
145#237—122no—
146#235—122no—
147#235—122no—
148C2×D12D1211yescharacteristic
149C2×D12#6711yescharacteristic
150C2×C4×D3—21no—
151C2×C4×D3—21no—
152C2×C4×D3—62no—
153C2×Dic6—21no—
154C2×Dic6—61no—
155C2×Dic6—61no—
156C2×Dic6—121no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—41no—
160C2×C3×C8—61no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171(C2×D3)⋊C4—21no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—62no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—32no—
177C4⋊Dic3—32no—
178C4⋊Dic3—62no—
179C4⋊Dic3—62no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—121no—
183C4⋊Dic3D1211yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—62no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—121no—
190C22×C32#12011yescharacteristic
191C2×C3×D3—22no—
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4C2×SD1611yescharacteristic
199C32×C4#13511yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3⋊Dic3—42no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—81no—
206C2×#41—181no—
207C4⋊Q8—31no—
208C4⋊Q8—91no—
209#123—182no—
210C22⋊Q8—181no—
211#121—181no—
212C4×D4—31no—
213C4×D4—31no—
214C2×C4⋊C4—181no—
215#106—61no—
216#106—181no—
217C4⋊C8—91no—
218C4⋊C8D3211yescharacteristic
219#103—182no—
220#102—61no—
221#102—181no—
222C4×C8—31no—
223C23×C3—61no—
224C23×C3—61no—
225C22×D3—21no—
226C22×D3—21no—
227C3×Q8—122no—
228C3×D4—32no—
229C3×D4—61no—
230C3×D4—61no—
231C3×D4—61no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248#67—124no—
249#67—124no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—41no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—124no—
257D12—21no—
258D12—21no—
259D12—21no—
260D12#20412yes—
261C4×D3—41no—
262C4×D3—41no—
263C4×D3—41no—
264C4×D3—41no—
265C4×D3—124no—
266Dic6—42no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271Dic6—241no—
272Dic6—241no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—81no—
276C3×C8—121no—
277C3⋊C8—41no—
278C3⋊C8—121no—
279C3⋊C8—121no—
280C3⋊C8—241no—
281C2×C32#45011yescharacteristic
282C2×C32#45211yescharacteristic
283C2×C32#45411yescharacteristic
284C3×D3—42no—
285C3×D3—81no—
286#41—362no—
287#41—362no—
288C2×Q8—61no—
289C2×Q8—181no—
290C2×D4—31no—
291C2×D4—31no—
292C2×D4—182no—
293C22×C4—61no—
294C22×C4—61no—
295C22×C4—182no—
296C2×C8—21no—
297C2×C8—61no—
298C2×C8—181no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4—92no—
304C4⋊C4—182no—
305C4⋊C4—181no—
306C22⋊C4—61no—
307C22⋊C4—61no—
308C22⋊C4—182no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—62no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#88211yescharacteristic
318C22×C3#93711yescharacteristic
319C2×D3—22no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—121no—
333C3×C4—121no—
334C3×C4—241no—
335C3×C4C2×#20411yescharacteristic
336C3×C4#90811yescharacteristic
337C3×C4#91211yescharacteristic
338C3×C4D3×SD1611yescharacteristic
339C3×C4#91411yescharacteristic
340C3×C4#91511yescharacteristic
341C3×C4#94211yescharacteristic
342C3×C4#95011yescharacteristic
343Dic3—41no—
344Dic3—41no—
345Dic3—81no—
346Dic3—122no—
347Dic3—122no—
348Dic3—242no—
349C32#163511yescharacteristic, complemented, Sylow
350C23—61no—
351C23—61no—
352Q8—122no—
353Q8—361no—
354Q8—361no—
355D4—32no—
356D4—61no—
357D4—61no—
358D4—61no—
359D4—364no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—121no—
367C2×C4—182no—
368C2×C4—364no—
369C2×C4D3×D1211yescharacteristic
370C2×C4#380211yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C8—41no—
373C8—121no—
374C8—361no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—122no—
379C2×C3—241no—
380C2×C3#473111yescharacteristic
381C2×C3#478311yescharacteristic
382C2×C3#482711yescharacteristic
383C2×C3#504711yescharacteristic
384C2×C3#516911yescharacteristic
385C2×C3#520111yescharacteristic
386D3—42no—
387D3—81no—
388C22—62no—
389C22—121no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22#6392211yescharacteristic
395C4—21no—
396C4—121no—
397C4—121no—
398C4—241no—
399C4—362no—
400C4D3×#20411yescharacteristic
401C4#6379411yescharacteristic
402C4#6393311yescharacteristic
403C4#6394611yescharacteristic
404C3—21no—
405C3#6820411yescharacteristic, complemented
406C3#7114011yescharacteristic, complemented
407C2—122no—
408C2—241no—
409C2#1059061411yescharacteristic
410C2#1059094211yescharacteristic
411C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593895C2
hypercenterC4⋊C8D32
hypocenterC32#1635
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
2. C3×#4842C2semidirect
3. #10590287C2semidirect
4. #10590266C2semidirect
5. #10589352C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
33. #4842D3semidirect
40. #4483D3semidirect
349. C32#1635semidirect
405. C3#68204semidirect
406. C3#71140semidirect

Maximal subgroups

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

subgroupindex
#105938952
C3×#48422
#105902872
#105902662
#105893522
C3×#44832
#105890812
#711403
#682043