Finite Group Databasebeta

← #11781708

Subgroups — #11781708

Order 1152.

477 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 477 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592772C211yesmaximal, characteristic, complemented
2C3×#5072C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic, complemented
4#10590339C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71009—31nomaximal
9#68399—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3753—21no—
12C2×#3753—21no—
13#64083C2211yescharacteristic
14C2×C3×#213—21no—
15C3×C4×D12C2211yescharacteristic
16C2×#3714—21no—
17C2×#3711—21no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#832—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63564—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#459—31no—
26#5073—31no—
27#5073—31no—
28#5073—61no—
29#5072D311yescharacteristic, complemented
30#5015—31no—
31#5012—31no—
32#4843—31no—
33#4838—31no—
34C3×#331—31no—
35#4544D311yescharacteristic, complemented
36#4485—31no—
37#4485—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C32×C42C2311yescharacteristic
49#3753—42no—
50#3753—42no—
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×#213—42no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59#3714—42no—
60#3711—42no—
61#1687—91noSylow
62C2×C3×D8—61no—
63C3×#127—21no—
64C3×#127C2×D311yescharacteristic
65C3×#127C2×D311yescharacteristic
66C3×C4×D4—31no—
67C2×#213—21no—
68C2×#213—61no—
69C2×#213—61no—
70C2×#213—61no—
71C2×#213—61no—
72C2×#213—61no—
73C2×#213—62no—
74C2×#213—62no—
75C2×#208—61no—
76C2×D24—61no—
77C2×ΓL(1,𝔽25)—61no—
78#874—31no—
79#874—31no—
80#874—61no—
81C4×D12C2×D311yescharacteristic
82C3×C4⋊C8—31no—
83C3×C4⋊C8—31no—
84C3×C4⋊C8—31no—
85C3×#102—61no—
86#832—21no—
87#830—61no—
88#821—61no—
89(C2×D3)⋊C8—61no—
90#809—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8—31no—
95C4×C3⋊C8—31no—
96C4×C3⋊C8—61no—
97C23×C32—41no—
98C22×C3⋊D3—41no—
99C22×C3×D3—21no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—81no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—81no—
113C2×C3×Dic3—21no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3⋊(C3⋊C8)—21no—
119C3⋊(C3⋊C8)D812yescomplemented
120C3×C3⋊C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8—41no—
123#493—91no—
124#459—31no—
125#459—91no—
126#436—91no—
127#334—91no—
128#331—31no—
129#331—91no—
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—31no—
138C2×C3×D4—41no—
139C2×C3×D4—41no—
140C22×C3×C4—61no—
141C2×D12—62no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—121no—
149C2×D12—121no—
150C2×D12#6711yescharacteristic
151C2×C4×D3—21no—
152C3×D8—122no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C2×C3×C8—61no—
156C3×C4⋊C4—31no—
157C3×C22⋊C4—61no—
158C3×C42—21no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#213—42no—
162#213—122no—
163#213—122no—
164#213—122no—
165#213—124no—
166#213—124no—
167#213—122no—
168#213—122no—
169(C2×D3)⋊C4—21no—
170C4⋊Dic3#6711yescharacteristic
171#208—122no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—21no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—31no—
176C2×C3⋊C8—31no—
177C2×C3⋊C8—31no—
178C2×C3⋊C8—31no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181D24—122no—
182ΓL(1,𝔽25)—122no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32—81no—
186C22×C32#12111yescharacteristic
187C2×C3⋊D3—81no—
188C2×C3⋊D3—81no—
189C2×C3⋊D3—81no—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4C2×D811yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4AGL(1,ℤ/8)11yescharacteristic
198C3×Dic3—41no—
199C2×D8—61no—
200C2×D8—181no—
201C2×D8—181no—
202C2×D8—181no—
203C2×M16—181no—
204#127—91no—
205#127D3211yescharacteristic
206C4×D4—31no—
207C4⋊C8—31no—
208C4⋊C8—31no—
209C4⋊C8—31no—
210#102—61no—
211#102—181no—
212C22⋊C8—181no—
213C4×C8—91no—
214C23×C3—42no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—61no—
218C22×D3—21no—
219C22×D3—122no—
220C22×D3—121no—
221C22×D3—121no—
222C3×D4—42no—
223C3×D4—42no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—61no—
233C3×D4—61no—
234C3×D4—81no—
235C3×D4—81no—
236C3×D4—81no—
237C3×D4—81no—
238C3×D4—82no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—61no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4#23711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×Dic3—21no—
252D12—21no—
253D12—21no—
254D12—122no—
255D12—122no—
256D12—121no—
257D12—121no—
258D12—121no—
259D12—121no—
260D12—121no—
261D12—121no—
262D12—121no—
263D12—121no—
264D12—241no—
265D12—241no—
266D12—241no—
267D12—241no—
268D12—242no—
269C4×D3—41no—
270C4×D3—41no—
271C3×C8—121no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—32no—
275C3⋊C8—32no—
276C3⋊C8—41no—
277C3⋊C8—41no—
278C3⋊C8—41no—
279C3⋊C8—62no—
280C3⋊C8—62no—
281C3⋊C8—61no—
282C3⋊C8—61no—
283C2×C32—161no—
284C2×C32#45911yescharacteristic
285C2×C32#46911yescharacteristic
286C2×C32#47211yescharacteristic
287C3⋊D3—161no—
288C3×D3—81no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—31no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4—181no—
296C22×C4—61no—
297D8—122no—
298D8—362no—
299D8—362no—
300D8—362no—
301M16—362no—
302C2×C8—61no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—91no—
306C2×C8—91no—
307C4⋊C4—31no—
308C22⋊C4—61no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—82no—
312C22×C3—82no—
313C22×C3—82no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—81no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3#88411yescharacteristic
324C22×C3#93911yescharacteristic
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—242no—
329C2×D3—242no—
330C2×D3—242no—
331C2×D3—241no—
332C2×D3—241no—
333C2×D3—241no—
334C2×D3—241no—
335C2×D3—241no—
336C2×D3—241no—
337C3×C4—22no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—121no—
345C3×C4D3×D811yescharacteristic
346C3×C4D3×D811yescharacteristic
347C3×C4#91111yescharacteristic
348C3×C4#91111yescharacteristic
349C3×C4#91411yescharacteristic
350C3×C4#91411yescharacteristic
351C3×C4#93211yescharacteristic
352C3×C4#94911yescharacteristic
353Dic3—41no—
354C32#168711yescharacteristic, complemented, Sylow
355C23—41no—
356C23—61no—
357C23—361no—
358D4—41no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—61no—
363D4—61no—
364D4—81no—
365D4—361no—
366D4—361no—
367D4—361no—
368D4—361no—
369D4—721no—
370C2×C4—61no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4#380411yescharacteristic
374C2×C4D3×#6711yescharacteristic
375C2×C4#381111yescharacteristic
376C8—92no—
377C8—121no—
378C8—121no—
379C8—121no—
380C8—181no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—162no—
385C2×C3—161no—
386C2×C3—161no—
387C2×C3—241no—
388C2×C3#474911yescharacteristic
389C2×C3#478211yescharacteristic
390C2×C3#478611yescharacteristic
391C2×C3#503911yescharacteristic
392C2×C3#515011yescharacteristic
393C2×C3#519911yescharacteristic
394D3—81no—
395D3—482no—
396D3—481no—
397D3—481no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—121no—
402C22—121no—
403C22—121no—
404C22—721no—
405C22—721no—
406C22—721no—
407C22#6397111yescharacteristic
408C4—21no—
409C4—121no—
410C4#6392511yescharacteristic
411C4#6392611yescharacteristic
412C4#6393411yescharacteristic
413C4#6393711yescharacteristic
414C3—21no—
415C3#6839911yescharacteristic, complemented
416C3#7100911yescharacteristic, complemented
417C2—161no—
418C2—241no—
419C2—1441no—
420C2#1059143311yescharacteristic
421C2#1059145311yescharacteristic
422C2#1059150811yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#121
hypercenter#127D32
hypocenterC32#1687
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10592772C2semidirect
2. C3×#5072C2semidirect
3. #10590349C2semidirect
4. #10590339C2semidirect
5. C3×#4544C2semidirect
6. #10589098C2semidirect
7. #10589091C2semidirect
29. #5072D3semidirect
35. #4544D3semidirect
119. C3⋊(C3⋊C8)D8semidirect
354. C32#1687semidirect
415. C3#68399semidirect
416. C3#71009semidirect

Maximal subgroups

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

subgroupindex
#105927722
C3×#50722
#105903492
#105903392
C3×#45442
#105890982
#105890912
#710093
#683993