Finite Group Databasebeta

← #11776223

Subgroups — #11776223

Order 1152.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593897C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589347C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#70773—31nomaximal
9#68382—31nomaximal
10C2×#3795C412yes—
11#64078C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14#63908—21no—
15#63908—21no—
16Dic3×D12—21no—
17Dic3×D12—21no—
18#63860C412yes—
19C32×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×(C2×D3)⋊C8—21no—
22C3×C8×Dic3—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27#5716—31no—
28#5477—31no—
29C3×#431—31no—
30#4925—31no—
31#4833—31no—
32#4833D311yescharacteristic, complemented
33C3×#331—31no—
34#4544—31no—
35#4485—31no—
36#4485D311yescharacteristic, complemented
37#4481—31no—
38#4481—31no—
39#4481—31no—
40#4481—31no—
41#4481—61no—
42C2×#634C2×C412yes—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12C2×C412yes—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×#625—22no—
50C2×D3×Dic3—22no—
51#3795—44no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×C4×Dic3C2×C411yescharacteristic
58C3×C4×Dic3D411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#1543—91noSylow
65C2×#237—32no—
66C2×#235—32no—
67C3×#127—31no—
68C2×C3×C42—31no—
69#938—61no—
70#938—61no—
71#936—32no—
72D4×Dic3—61no—
73D4×Dic3—61no—
74#930—61no—
75#930—61no—
76#875—32no—
77#874C2×D311yescharacteristic
78C4×D12—61no—
79C4×D12—61no—
80C42×D3C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—61no—
84C3×C4⋊C8—21no—
85C3×C4⋊C8—31no—
86C3×C4⋊C8—31no—
87C3×C4⋊C8C2×D311yescharacteristic
88C3×C4⋊C8C2×D311yescharacteristic
89C3×C22⋊C8—61no—
90C3×C4×C8—61no—
91#830—61no—
92(C2×D3)⋊C8—21no—
93(C2×D3)⋊C8—61no—
94C8×Dic3—21no—
95C8×Dic3—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4×C3⋊C8—61no—
102C22×C3×D3—22no—
103C22×C3×D3C22⋊C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108#634—42no—
109C2×C3×Dic3C22⋊C411yescharacteristic
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C3×D12—42no—
113C3×D12—41no—
114C3×D12—41no—
115C3×D12—41no—
116C3×D12—41no—
117C3×C4×D3—21no—
118C3×C4×D3—21no—
119C3×C4×D3—21no—
120C3×C4×D3—21no—
121C3×C4×D3—22no—
122#625—44no—
123D3×Dic3—44no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128#532—91no—
129#431—31no—
130#431—91no—
131#333—91no—
132#333—91no—
133#331—31no—
134#331—91no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C2×#67—62no—
142C2×#67—62no—
143C22×Dic3—62no—
144#237—124no—
145#235—124no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12C4×D312yes—
149C2×C4×D3—62no—
150C2×C4×D3C4×D311yescharacteristic
151C2×C4×D3D1211yescharacteristic
152C2×C4×D3#6711yescharacteristic
153C2×Dic6—32no—
154C2×Dic6—32no—
155C2×Dic6—62no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—41no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C42—21no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42—31no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167#217—62no—
168#217—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—121no—
176C4⋊Dic3—121no—
177C4×Dic3C4×D311yescharacteristic
178C4×Dic3D1211yescharacteristic
179C4×Dic3#6711yescharacteristic
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—121no—
185C22×C32C2×C22⋊C411yescharacteristic
186C2×C3×D3—21no—
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3—42no—
190C2×C3×D3—42no—
191C2×C3×D3—42no—
192C32×C4—21no—
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4#13511yescharacteristic
196C32×C4#13511yescharacteristic
197C3⋊Dic3—42no—
198C3×Dic3—21no—
199C3×Dic3—21no—
200C3×Dic3#10012yes—
201C2×#41—92no—
202C4⋊Q8—91no—
203#127—31no—
204#124—92no—
205#121—181no—
206#121—181no—
207C4×D4—181no—
208C4×D4—181no—
209C2×C42—31no—
210C4⋊C8—31no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213C4⋊C8D3211yescharacteristic
214C22⋊C8—61no—
215C22⋊C8—181no—
216C4×C8—61no—
217C4×C8—181no—
218C23×C3—31no—
219C23×C3—62no—
220C22×D3—22no—
221C22×D3(C2×D3)⋊C411yescharacteristic
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—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—62no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244#67—124no—
245#67—124no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—122no—
249C2×Dic3—124no—
250C2×Dic3(C2×D3)⋊C411yescharacteristic
251C2×Dic3(C2×D3)⋊C411yescharacteristic
252C2×Dic3(C2×D3)⋊C411yescharacteristic
253D12—42no—
254D12—41no—
255D12—41no—
256D12—41no—
257D12—41no—
258C4×D3—21no—
259C4×D3—21no—
260C4×D3—21no—
261C4×D3—21no—
262C4×D3—22no—
263C4×D3—124no—
264Dic6—122no—
265Dic6—122no—
266Dic6—242no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3×C8—121no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C3⋊C8—121no—
275C3⋊C8—121no—
276C3⋊C8—241no—
277C2×C32C2×#10011yescharacteristic
278C2×C32#41611yescharacteristic
279C2×C32#41611yescharacteristic
280C3×D3—41no—
281C3×D3—82no—
282#41—364no—
283C2×Q8—92no—
284C2×D4—32no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—182no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—31no—
291C22×C4—182no—
292C2×C8—21no—
293C2×C8—61no—
294C2×C8—61no—
295C2×C8—181no—
296C4⋊C4—181no—
297C4⋊C4—181no—
298C22⋊C4—182no—
299C22⋊C4—182no—
300C42—31no—
301C42—31no—
302C42—31no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—61no—
306C22×C3—61no—
307C22×C3—61no—
308C22×C3—122no—
309C22×C3—122no—
310C22×C3—122no—
311C22×C3D3×C22⋊C411yescharacteristic
312C22×C3C2×(C2×D3)⋊C411yescharacteristic
313C2×D3—21no—
314C2×D3—21no—
315C2×D3—21no—
316C2×D3—42no—
317C2×D3—42no—
318C2×D3—42no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—32no—
326C3×C4—41no—
327C3×C4—61no—
328C3×C4—61no—
329C3×C4#90411yescharacteristic
330C3×C4#90411yescharacteristic
331C3×C4#91211yescharacteristic
332C3×C4#91211yescharacteristic
333C3×C4#91611yescharacteristic
334C3×C4#91611yescharacteristic
335C3×C4#95011yescharacteristic
336C3×C4#95011yescharacteristic
337Dic3—21no—
338Dic3—21no—
339Dic3—122no—
340Dic3—122no—
341Dic3—242no—
342Dic3#82312yes—
343C32#154311yescharacteristic, complemented, Sylow
344C23—31no—
345C23—62no—
346Q8—362no—
347D4—122no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—121no—
352D4—364no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—62no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—182no—
362C2×C4—364no—
363C2×C4C4×D3211yescharacteristic
364C2×C4D3×D1211yescharacteristic
365C2×C4D3×#6711yescharacteristic
366C8—41no—
367C8—121no—
368C8—121no—
369C8—361no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—121no—
374C2×C3—242no—
375C2×C3D3×#10011yescharacteristic
376C2×C3#477211yescharacteristic
377C2×C3#477211yescharacteristic
378C2×C3#500211yescharacteristic
379C2×C3#511311yescharacteristic
380C2×C3C2×#82311yescharacteristic
381D3—41no—
382D3—82no—
383C22—61no—
384C22—61no—
385C22—61no—
386C22—122no—
387C22—122no—
388C22—122no—
389C22D3×(C2×D3)⋊C411yescharacteristic
390C4—21no—
391C4—32no—
392C4—61no—
393C4—61no—
394C4—362no—
395C4#6380611yescharacteristic
396C4#6380711yescharacteristic
397C4#6393311yescharacteristic
398C4#6394711yescharacteristic
399C3—21no—
400C3#6838211yescharacteristic, complemented
401C3#7077311yescharacteristic, complemented
402C2—121no—
403C2—242no—
404C2#1059060811yescharacteristic
405C2#1059095411yescharacteristic
406C2D3×#82311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593897C2
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1543
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4833C2semidirect
3. #10590248C2semidirect
4. #10589347C2semidirect
5. C3×#4485C2semidirect
6. #10589096C2semidirect
7. #10589090C2semidirect
32. #4833D3semidirect
36. #4485D3semidirect
343. C32#1543semidirect
400. C3#68382semidirect
401. C3#70773semidirect

Maximal subgroups

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

subgroupindex
#105938972
C3×#48332
#105902482
#105893472
C3×#44852
#105890962
#105890902
#707733
#683823