Finite Group Databasebeta

← #11781717

Subgroups — #11781717

Order 1152.

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

normal subgroups only

This group has 466 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#10592542C211yesmaximal, characteristic, complemented
2#10590355C211yesmaximal, characteristic, complemented
3#10590350C211yesmaximal, characteristic, complemented
4#10590338C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#68540—31nomaximal
9#68399—31nomaximal
10C2×#3745—21no—
11#64083C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C2×#3714—21no—
15C2×#3714—21no—
16C2×#3714—21no—
17C2×#3712—21no—
18C32×C4⋊C8C2211yescharacteristic
19#63648—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63557—21no—
25#5073—31no—
26#5072—31no—
27#4843—31no—
28#4843—31no—
29#4843—31no—
30#4843—61no—
31#4838—31no—
32#4695—31no—
33#4688—31no—
34C3×#334—31no—
35C3×#331—31no—
36#4485—31no—
37#4485—31no—
38#4485D311yescharacteristic, complemented
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50#3752—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3745—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3714—42no—
58#3714—42no—
59#3714—42no—
60#3712—42no—
61#1687—91noSylow
62C3×#127—31no—
63C2×#213—61no—
64C2×#213—61no—
65C2×#213—61no—
66C2×D24—61no—
67C2×D24—61no—
68C2×D24—62no—
69C2×D24—61no—
70C2×D24—61no—
71C2×D24—61no—
72C2×ΓL(1,𝔽25)—61no—
73C2×ΓL(1,𝔽25)—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77#874C2×D311yescharacteristic
78C4×D12—31no—
79C4×D12—31no—
80C4×D12—61no—
81C3×C4⋊C8—21no—
82C3×C4⋊C8—31no—
83C3×C4⋊C8—31no—
84C3×C4⋊C8C2×D311yescharacteristic
85C3×C4⋊C8C2×D311yescharacteristic
86C3×C4×C8—31no—
87#832—61no—
88#821—61no—
89#821—61no—
90#821—61no—
91#821—62no—
92(C2×D3)⋊C8—61no—
93(C2×D3)⋊C8—61no—
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4⋊(C3⋊C8)C2×D311yescharacteristic
96C4×C3⋊C8C2×D311yescharacteristic
97C22×C3⋊D3—21no—
98C22×C3⋊D3—41no—
99C22×C3×D3—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—21no—
104C4⋊(C3⋊D3)—21no—
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—81no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113C3×D12—41no—
114C3×D12—41no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—81no—
118C32×C8—41no—
119C3×C3⋊C8—21no—
120C3×C3⋊C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8D812yescomplemented
123#493—91no—
124#459—91no—
125#459—91no—
126#436—91no—
127#334—31no—
128#331—31no—
129#331—91no—
130C2×C3×D4—61no—
131C2×C3×D4—61no—
132C2×C3×D4—61no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—31no—
137C2×D12—31no—
138C2×D12—61no—
139C2×D12—62no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—121no—
147C2×D12—121no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—121no—
151C2×C3×C8—22no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—31no—
155C2×C3×C8—31no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C42—21no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#213—122no—
162#213—122no—
163#213—122no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—121no—
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169C4⋊Dic3—61no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8D1211yescharacteristic
173C2×C3⋊C8D1211yescharacteristic
174D24—122no—
175D24—124no—
176D24—122no—
177D24—122no—
178D24—122no—
179D24—122no—
180ΓL(1,𝔽25)—122no—
181ΓL(1,𝔽25)—122no—
182C22×C32#12111yescharacteristic
183C2×C3⋊D3—41no—
184C2×C3⋊D3—41no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—81no—
187C2×C3⋊D3—81no—
188C2×C3⋊D3—81no—
189C2×C3×D3—81no—
190C2×C3×D3—81no—
191C2×C3×D3—81no—
192C32×C4—21no—
193C32×C4C2×D811yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C3⋊Dic3—41no—
198C2×D8—181no—
199C2×D8—181no—
200C2×D8—181no—
201C2×D8—181no—
202C2×M16—181no—
203#127—31no—
204#127—91no—
205C4×D4—91no—
206C4⋊C8—31no—
207C4⋊C8—31no—
208C4⋊C8D3211yescharacteristic
209#102—181no—
210#102—181no—
211C22⋊C8—181no—
212C4×C8—31no—
213C23×C3—121no—
214C22×D3—41no—
215C22×D3—61no—
216C22×D3—61no—
217C22×D3—121no—
218C22×D3—122no—
219C22×D3—121no—
220C22×D3—121no—
221C3×D4—121no—
222C3×D4—121no—
223C3×D4—121no—
224C3×D4—121no—
225C3×D4—241no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4#23511yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23911yescharacteristic
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—121no—
238D12—41no—
239D12—41no—
240D12—41no—
241D12—41no—
242D12—62no—
243D12—61no—
244D12—61no—
245D12—61no—
246D12—61no—
247D12—81no—
248D12—121no—
249D12—122no—
250D12—122no—
251D12—121no—
252D12—121no—
253D12—121no—
254D12—121no—
255D12—121no—
256D12—121no—
257D12—121no—
258D12—121no—
259D12—241no—
260D12—241no—
261D12—241no—
262D12—241no—
263D12—242no—
264C4×D3—121no—
265C4×D3—121no—
266C4×D3—121no—
267C4×D3—121no—
268C4×D3—241no—
269C4×D3—241no—
270C3×C8—32no—
271C3×C8—42no—
272C3×C8—41no—
273C3×C8—41no—
274C3×C8—61no—
275C3×C8—121no—
276C3×C8—121no—
277C3⋊C8—21no—
278C3⋊C8—41no—
279C3⋊C8—41no—
280C3⋊C8D2412yescomplemented
281C2×C32#45911yescharacteristic
282C2×C32#46911yescharacteristic
283C2×C32#47211yescharacteristic
284C3⋊D3—81no—
285C3⋊D3—161no—
286C3×D3—161no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—91no—
291C2×D4—181no—
292C2×D4—181no—
293C2×D4—181no—
294C22×C4—181no—
295D8—362no—
296D8—362no—
297D8—362no—
298D8—362no—
299M16—362no—
300C2×C8—21no—
301C2×C8—31no—
302C2×C8—31no—
303C2×C8—61no—
304C2×C8—61no—
305C4⋊C4—91no—
306C22⋊C4—181no—
307C42C2×D3211yescharacteristic
308C22×C3—21no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3—241no—
312C22×C3#88411yescharacteristic
313C22×C3#89511yescharacteristic
314C2×D3—81no—
315C2×D3—81no—
316C2×D3—81no—
317C2×D3—122no—
318C2×D3—121no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—241no—
325C2×D3—241no—
326C2×D3—242no—
327C2×D3—242no—
328C2×D3—242no—
329C2×D3—241no—
330C2×D3—241no—
331C2×D3—241no—
332C2×D3—241no—
333C2×D3—241no—
334C2×D3—241no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4C2×D2411yescharacteristic
343C3×C4#90811yescharacteristic
344C3×C4D3×D811yescharacteristic
345C3×C4#91111yescharacteristic
346C3×C4#91411yescharacteristic
347C3×C4#91411yescharacteristic
348C3×C4#91411yescharacteristic
349C3×C4#91411yescharacteristic
350Dic3—121no—
351Dic3—121no—
352Dic3—241no—
353C32#168711yescharacteristic, complemented, Sylow
354C23—121no—
355C23—181no—
356C23—361no—
357D4—121no—
358D4—121no—
359D4—121no—
360D4—121no—
361D4—181no—
362D4—181no—
363D4—241no—
364D4—361no—
365D4—361no—
366D4—361no—
367D4—361no—
368D4—721no—
369C2×C4—181no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4#379911yescharacteristic
373C2×C4D3×D1211yescharacteristic
374C2×C4#381111yescharacteristic
375C8—32no—
376C8—41no—
377C8—61no—
378C8—121no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—481no—
384C2×C3#474911yescharacteristic
385C2×C3#478211yescharacteristic
386C2×C3#478611yescharacteristic
387C2×C3#484311yescharacteristic
388C2×C3#486511yescharacteristic
389C2×C3#489711yescharacteristic
390D3—161no—
391D3—242no—
392D3—241no—
393D3—241no—
394D3—482no—
395D3—481no—
396D3—481no—
397C22—241no—
398C22—241no—
399C22—241no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22—721no—
404C22—721no—
405C22—721no—
406C22#6391011yescharacteristic
407C4—21no—
408C4—361no—
409C4D3×D2411yescharacteristic
410C4#6379411yescharacteristic
411C4#6393711yescharacteristic
412C4#6394111yescharacteristic
413C3—21no—
414C3#6839911yescharacteristic, complemented
415C3#6854011yescharacteristic, complemented
416C2—481no—
417C2—721no—
418C2—1441no—
419C2#1059050811yescharacteristic
420C2#1059076511yescharacteristic
421C2#1059098711yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1687
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. #10592542C2semidirect
2. #10590355C2semidirect
3. #10590350C2semidirect
4. #10590338C2semidirect
5. C3×#4485C2semidirect
6. C3×#4480C2semidirect
7. #10589091C2semidirect
38. #4485D3semidirect
39. #4480D3semidirect
122. C3×C3⋊C8D8semidirect
280. C3⋊C8D24semidirect
353. C32#1687semidirect
414. C3#68399semidirect
415. C3#68540semidirect

Maximal subgroups

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

subgroupindex
#105925422
#105903552
#105903502
#105903382
C3×#44852
C3×#44802
#105890912
#685403
#683993