Finite Group Databasebeta

← #11779346

Subgroups — #11779346

Order 1152.

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

normal subgroups only

This group has 471 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#10593951C211yesmaximal, characteristic
2C3×#4693C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic, complemented
4#10590284C211yesmaximal, characteristic, complemented
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic
8#71270—31nomaximal
9#68260—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×#204—22no—
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63898—21no—
16Dic3×D12—21no—
17#63884—22no—
18#63863—21no—
19#63860—21no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63576—21no—
24#63575—21no—
25#63567—21no—
26#63565—21no—
27#5713—31no—
28#5585—31no—
29C3×#492—31no—
30#5091—31no—
31#5091—31no—
32#5021—31no—
33#4850—31no—
34#4693D311yescharacteristic
35C3×Q8⋊C8—31no—
36#4544—31no—
37#4485—31no—
38#4456—31no—
39#4456—31no—
40#4456—61no—
41#4456D311yescharacteristic, complemented
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×D3×Dic3—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C3×#204—44no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#1630—91noSylow
66C2×C3×SD16—62no—
67C3×C4⋊Q8—31no—
68C3×#127—31no—
69C3×C4×Q8—31no—
70#947—61no—
71#936—61no—
72#936—61no—
73#935—62no—
74D4×Dic3—61no—
75D4×Dic3—61no—
76C2×#204—22no—
77#894—62no—
78#893—61no—
79#875—61no—
80#874C2×D311yescharacteristic
81C4×D12—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×C4⋊C8—31no—
88C3×C4×C8—21no—
89C3×C4×C8C2×D311yescharacteristic
90C3×C4×C8C2×D311yescharacteristic
91#835—61no—
92#818—61no—
93#816—61no—
94#810—61no—
95#810—61no—
96#807—61no—
97#807—61no—
98#807—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C22×C3×D3—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109#634—21no—
110#634—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C3×Dic6—42no—
122D3×Dic3—82no—
123C32×C8—22no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—41no—
126#559—91no—
127#492—31no—
128#477—91no—
129#477—91no—
130#331—91no—
131Q8⋊C8—31no—
132Q8⋊C8—91no—
133C2×C3×Q8—31no—
134C2×C3×Q8—61no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×Dic3—62no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12#6712yes—
142C2×C4×D3—62no—
143C2×Dic6—21no—
144C2×Dic6—31no—
145C2×Dic6—31no—
146C2×Dic6—61no—
147C2×Dic6D1211yescharacteristic
148C3×SD16—124no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—41no—
152C2×C3×C8—61no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C42—21no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#217—62no—
162#217—62no—
163#217—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C4⋊Dic3D1211yescharacteristic
173Dic3⋊C4—21no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—121no—
177C4×Dic3—21no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—121no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—121no—
185#204—44no—
186C22×C32#12011yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—21no—
191C32×C4#13511yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4#13711yescharacteristic
194C32×C4#13711yescharacteristic
195C3⋊Dic3—41no—
196C3⋊Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×SD16—62no—
201C4⋊Q8—31no—
202#127—31no—
203#124—181no—
204#124—181no—
205#123—182no—
206C4×Q8—31no—
207C4×Q8—91no—
208C4×D4—181no—
209C4×D4—181no—
210#107—181no—
211#107—181no—
212C4⋊C8—31no—
213C4⋊C8—91no—
214#103—181no—
215#103—181no—
216C4×C8D3211yescharacteristic
217C23×C3—62no—
218C22×D3—22no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—122no—
222C3×D4—122no—
223C3×D4—121no—
224C3×D4—121no—
225C3×D4—121no—
226C3×D4—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—121no—
233C2×C3×C4C2×D1211yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4C2×#6711yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C2×Dic3—242no—
249D12—42no—
250D12—41no—
251D12—41no—
252D12—41no—
253D12—41no—
254C4×D3—242no—
255Dic6—21no—
256Dic6—21no—
257Dic6—42no—
258Dic6—62no—
259Dic6—61no—
260Dic6—61no—
261Dic6—61no—
262Dic6—61no—
263Dic6—121no—
264C3×C8—22no—
265C3×C8—22no—
266C3×C8—42no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—121no—
270C3⋊C8—121no—
271C3⋊C8—241no—
272C2×C32#45211yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45311yescharacteristic
275C3×D3—82no—
276C2×Q8—31no—
277C2×Q8—61no—
278C2×Q8—91no—
279C2×D4—32no—
280C2×D4—61no—
281C2×D4—61no—
282C22×C4—182no—
283SD16—124no—
284C2×C8—21no—
285C2×C8—61no—
286C2×C8—181no—
287C4⋊C4—31no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—91no—
292C4⋊C4—181no—
293C22⋊C4—182no—
294C22⋊C4—182no—
295C22⋊C4—182no—
296C42—61no—
297C42—181no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3#88211yescharacteristic
304C22×C3#93711yescharacteristic
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—121no—
316C3×C4—121no—
317C3×C4—241no—
318C3×C4#90411yescharacteristic
319C3×C4#90911yescharacteristic
320C3×C4#91511yescharacteristic
321C3×C4#91511yescharacteristic
322C3×C4#91611yescharacteristic
323C3×C4#91611yescharacteristic
324C3×C4#91611yescharacteristic
325C3×C4#91811yescharacteristic
326Dic3—41no—
327Dic3—41no—
328Dic3—81no—
329Dic3—122no—
330Dic3—121no—
331Dic3—121no—
332Dic3—121no—
333Dic3—121no—
334Dic3—241no—
335C32#163011yescharacteristic, complemented, Sylow
336C23—62no—
337Q8—61no—
338Q8—61no—
339Q8—122no—
340Q8—181no—
341Q8—181no—
342D4—122no—
343D4—121no—
344D4—121no—
345D4—121no—
346D4—121no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—121no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—722no—
353C2×C4D3×D1211yescharacteristic
354C2×C4#380211yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C8—22no—
357C8—121no—
358C8—361no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—242no—
363C2×C3#473311yescharacteristic
364C2×C3#480811yescharacteristic
365C2×C3#482211yescharacteristic
366C2×C3#507711yescharacteristic
367C2×C3#517311yescharacteristic
368C2×C3#517311yescharacteristic
369D3—82no—
370C22—122no—
371C22—122no—
372C22—122no—
373C22#6392211yescharacteristic
374C4—21no—
375C4—121no—
376C4—121no—
377C4—241no—
378C4—361no—
379C4—361no—
380C4#6380011yescharacteristic
381C4#6380611yescharacteristic
382C4#6380911yescharacteristic
383C4#6381111yescharacteristic
384C3—21no—
385C3#6826011yescharacteristic, complemented
386C3#7127011yescharacteristic, complemented
387C2—242no—
388C2#1059039511yescharacteristic
389C2#1059096011yescharacteristic
390C2#1059096111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#1630
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
3. #10590310C2semidirect
4. #10590284C2semidirect
5. #10589322C2semidirect
6. C3×#4456C2semidirect
41. #4456D3semidirect
335. C32#1630semidirect
385. C3#68260semidirect
386. C3#71270semidirect

Maximal subgroups

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

subgroupindex
#105939512
C3×#46932
#105903102
#105902842
#105893222
C3×#44562
#105890902
#712703
#682603