Finite Group Databasebeta

← #11780259

Subgroups — #11780259

Order 1152.

435 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5584C211yesmaximal, characteristic
2C3×#5020C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic
8#71933—31nomaximal
9#71126—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C3×#898—22no—
13C3×#892—21no—
14C3×#875—21no—
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6—21no—
19C2×#3715—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#808—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—22no—
26#63565—21no—
27C3×#556—31no—
28#5584D311yescharacteristic
29C3×#475—31no—
30#5083—31no—
31#5078—31no—
32#5078—31no—
33#5020D311yescharacteristic, complemented
34#5019—31no—
35#4547—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4486—31no—
41#4483—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—22no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D412yes—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64#3715—42no—
65#1650—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×#126—62no—
69C3×#124—61no—
70C3×C22⋊Q8—61no—
71C3×C4×Q8—21no—
72C3×C4×Q8—61no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×D4—31no—
76C3×#117—61no—
77#946—21no—
78C2×#215—61no—
79C2×#214—61no—
80#898—22no—
81#892—21no—
82#875—21no—
83C4×D12C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6—21no—
87C3×#106—61no—
88C3×C4⋊C8—31no—
89C3×#103—61no—
90#835—21no—
91#835—61no—
92#810—61no—
93#808—21no—
94#807—62no—
95#807—62no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3×D3—21no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#556—31no—
126#500—91no—
127#475—31no—
128#461—91no—
129#332—91no—
130Q8⋊C8—91no—
131D4⋊C8—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8—61no—
134C2×C3×Q8—61no—
135C2×C3×Q8#6711yescharacteristic
136C2×C3×Q8#6711yescharacteristic
137C2×C3×D4—31no—
138C22×C3×C4—61no—
139C2×D12#6711yescharacteristic
140C2×C4×D3—21no—
141C2×Dic6—21no—
142C2×Dic6—21no—
143C2×C3×C8—61no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—32no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4#6711yescharacteristic
155C3×C4⋊C4#6711yescharacteristic
156C3×C22⋊C4—62no—
157C3×C22⋊C4—62no—
158C3×C22⋊C4—61no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—41no—
163C3×C42—62no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#215—122no—
167#214—122no—
168(C2×D3)⋊C4—22no—
169(C2×D3)⋊C4—22no—
170(C2×D3)⋊C4—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3#6712yes—
175C4⋊Dic3#6711yescharacteristic
176Dic3⋊C4—22no—
177C4×Dic3—22no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C2×C3⋊C8—121no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4#13511yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×SD16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#126—62no—
203#124—61no—
204C22⋊Q8—61no—
205C4×Q8—61no—
206C4×Q8D3211yescharacteristic
207C4×D4—31no—
208#117—61no—
209#107—182no—
210#106—61no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213#103—61no—
214#103—181no—
215C4×C8—91no—
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—22no—
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—41no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×Q8—121no—
227C3×Q8—121no—
228C3×D4—61no—
229C3×D4—61no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—61no—
240C2×C3×C4—62no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—41no—
253D12—21no—
254D12—21no—
255C4×D3—41no—
256C4×D3—41no—
257Dic6—41no—
258Dic6—41no—
259Dic6—41no—
260Dic6—41no—
261C3×C8—121no—
262C3⋊C8—41no—
263C3⋊C8—62no—
264C3⋊C8—62no—
265C3⋊C8—122no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C3⋊C8—241no—
269C2×C32#44911yescharacteristic
270C2×C32#45211yescharacteristic
271C2×C32#45611yescharacteristic
272C3×D3—81no—
273C2×Q8—61no—
274C2×Q8—61no—
275C2×Q8#62511yescharacteristic
276C2×D4—31no—
277C22×C4—61no—
278SD16—362no—
279C2×C8—61no—
280C2×C8—181no—
281C2×C8—181no—
282C4⋊C4—21no—
283C4⋊C4—31no—
284C4⋊C4—32no—
285C4⋊C4—62no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4#62511yescharacteristic
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—61no—
293C42—21no—
294C42—62no—
295C42C2×D3211yescharacteristic
296C22×C3—21no—
297C22×C3—121no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#93711yescharacteristic
301C22×C3#95311yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—122no—
319C3×C4—121no—
320C3×C4—241no—
321C3×C4#91411yescharacteristic
322C3×C4#91611yescharacteristic
323C3×C4#94211yescharacteristic
324C3×C4#94911yescharacteristic
325C3×C4#95011yescharacteristic
326C3×C4#95011yescharacteristic
327C3×C4#95011yescharacteristic
328C3×C4#95111yescharacteristic
329Dic3—42no—
330Dic3—41no—
331Dic3—81no—
332C32#165011yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—21no—
335Q8—21no—
336Q8—121no—
337Q8—121no—
338Q8—121no—
339Q8—121no—
340D4—61no—
341D4—61no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4C2×#62511yescharacteristic
350C2×C4D3×#6711yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—121no—
353C8—182no—
354C8—361no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—241no—
359C2×C3#504711yescharacteristic
360C2×C3#517211yescharacteristic
361C2×C3#520511yescharacteristic
362C2×C3#523811yescharacteristic
363C2×C3#523911yescharacteristic
364C2×C3#524611yescharacteristic
365D3—81no—
366C22—121no—
367C22—121no—
368C22—121no—
369C22#6397611yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—122no—
374C4—121no—
375C4—241no—
376C4#6382211yescharacteristic
377C4#6382711yescharacteristic
378C4#6393911yescharacteristic
379C4#6394711yescharacteristic
380C3—21no—
381C3#7112611yescharacteristic, complemented
382C3#7193311yescharacteristic, complemented
383C2—241no—
384C2#1059117011yescharacteristic
385C2#1059158611yescharacteristic
386C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#1650
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×#5020C2semidirect
4. #10590312C2semidirect
5. #10589401C2semidirect
6. #10589092C2semidirect
33. #5020D3semidirect
332. C32#1650semidirect
381. C3#71126semidirect
382. C3#71933semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×#50202
#105903632
#105903122
#105894012
#105890922
#105890802
#719333
#711263