Finite Group Databasebeta

← #11799388

Subgroups — #11799388

Order 1152.

350 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 68 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#10592859C211yesmaximal, characteristic, complemented
2C2×C3×#826C211yesmaximal, characteristic, complemented
3#10590929C211yesmaximal, characteristic, complemented
4#10590624C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6#10589143C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#71472—31nomaximal
9#69260—31nomaximal
10C2×C32×D8C2211yescharacteristic
11#64141—21no—
12#64110C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14#63830—21no—
15#63660—21no—
16#63646C2211yescharacteristic
17C3×#826—21no—
18C3×#826—21no—
19C3×#819C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22#63558—21no—
23#63544—21no—
24#63542—21no—
25C2×C3×D16—31no—
26#5160—31no—
27#5160—31no—
28#5160—31no—
29#5160—61no—
30C2×#826D311yescharacteristic, complemented
31#4907—31no—
32#4901—31no—
33#4897—31no—
34C3×#361—31no—
35#4563—31no—
36#4563D311yescharacteristic, complemented
37#4516—31no—
38#4506—31no—
39#4493—31no—
40C2×C32×D4—21no—
41#3828D411yescharacteristic
42C2×C3×D12—21no—
43C32×D8—21no—
44C32×D8—21no—
45C2×C32×C8C2311yescharacteristic
46#3754—41no—
47#3753—41no—
48#3748—21no—
49#3748D411yescharacteristic
50#3743—21no—
51C8×C3⋊D3—21no—
52C3×#208—21no—
53C3×D24—21no—
54C3×D24—21no—
55#3716—41no—
56#3714—41no—
57C3×C3⋊C16—21no—
58C3×C3⋊C16D411yescharacteristic
59C3×C3⋊C16D411yescharacteristic
60#2221—91noSylow
61C2×C3×D8—21no—
62C2×C3×D8—31no—
63C2×C3×D8C2×D311yescharacteristic
64C2×C3×D8C2×D311yescharacteristic
65#932—61no—
66#932—61no—
67#932—61no—
68#932—62no—
69#908—61no—
70C2×D24C2×D311yescharacteristic
71#901—31no—
72#901—31no—
73#901—61no—
74C3×D16—61no—
75C3×D16—61no—
76C3×M32—31no—
77C2×C3×C16—31no—
78C3×#108—31no—
79#833—61no—
80#833—61no—
81#833—61no—
82#833—62no—
83#826—21no—
84#826—21no—
85#823—61no—
86#819—31no—
87#819—31no—
88#819—61no—
89#819C2×D311yescharacteristic
90#812C2×D311yescharacteristic
91C2×C3⋊C16C2×D311yescharacteristic
92#798—61no—
93#798—61no—
94D3×C16—61no—
95D3×C16—61no—
96C23×C32—41no—
97C22×C3×D3—41no—
98C32×D4—41no—
99C32×D4—41no—
100C2×C32×C4C2×D411yescharacteristic
101#638—21no—
102C4⋊(C3⋊D3)D811yescharacteristic
103C4×C3⋊D3—21no—
104#634D811yescharacteristic
105C3×D12—41no—
106C3×D12—41no—
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—41no—
112C2×D16—31no—
113#504—91no—
114#472—91no—
115#472—91no—
116#368—91no—
117#361—31no—
118#361—91no—
119C2×C3×D4—22no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4—61no—
123#235—31no—
124#235—31no—
125#235—61no—
126C2×D12—21no—
127C3×D8—21no—
128C3×D8—21no—
129C3×D8—21no—
130C3×D8—21no—
131C3×D8—41no—
132C3×D8—41no—
133C3×D8—61no—
134C3×D8—61no—
135C3×M16—61no—
136C2×C3×C8—21no—
137C2×C3×C8C22×D311yescharacteristic
138C2×C3×C8C22×D311yescharacteristic
139#214—121no—
140#214—121no—
141#214—121no—
142#214—122no—
143#213—121no—
144#213—121no—
145#213—121no—
146#213—122no—
147#208—21no—
148#208—31no—
149#208—31no—
150#208—61no—
151#208—62no—
152#208—61no—
153#208—61no—
154D24—21no—
155D24—21no—
156D24—121no—
157#204—121no—
158ΓL(1,𝔽25)—61no—
159ΓL(1,𝔽25)—61no—
160ΓL(1,𝔽25)—121no—
161D3×C8—61no—
162D3×C8—61no—
163D3×C8—121no—
164C3×C16—31no—
165C3×C16—31no—
166C3×C16—61no—
167C3⋊C16—21no—
168C3⋊C16#6711yescharacteristic
169C3⋊C16#6711yescharacteristic
170C22×C32—81no—
171C22×C32—161no—
172C22×C32#13511yescharacteristic
173C2×C3⋊D3—21no—
174C2×C3×D3—81no—
175C2×C3×D3—161no—
176C32×C4#12111yescharacteristic
177C32×C4C2×D811yescharacteristic
178C3⋊Dic3—21no—
179AGL(1,ℤ/8)—181no—
180AGL(1,ℤ/8)—181no—
181C2×D8—31no—
182C2×D8D3211yescharacteristic
183#131—91no—
184D16—61no—
185D16—61no—
186M32—31no—
187M32—181no—
188C2×C16—31no—
189C2×C16—181no—
190#108—31no—
191#108—91no—
192#100—181no—
193#100—181no—
194C23×C3—42no—
195C23×C3—41no—
196C23×C3—41no—
197C23×C3—121no—
198C22×D3—41no—
199C3×D4—42no—
200C3×D4—42no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—121no—
206C3×D4—121no—
207C2×C3×C4—21no—
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210#67—61no—
211#67—61no—
212#67—121no—
213D12—31no—
214D12—31no—
215D12—41no—
216D12—41no—
217D12—61no—
218C4×D3—61no—
219C4×D3—61no—
220C4×D3—121no—
221Dic6—31no—
222Dic6—31no—
223Dic6—61no—
224C3×C8—21no—
225C3×C8—21no—
226C3×C8—121no—
227C3×C8#23511yescharacteristic
228C3×C8D3×D411yescharacteristic
229C3×C8#23711yescharacteristic
230C3×C8C2×#6711yescharacteristic
231C3⋊C8—41no—
232C3⋊C8—61no—
233C3⋊C8—61no—
234C3⋊C8—121no—
235C3⋊C8—122no—
236C3⋊C8—121no—
237C3⋊C8—121no—
238C2×C32—21no—
239C2×C32—161no—
240C2×C32#46611yescharacteristic
241C3⋊D3—41no—
242C3×D3—161no—
243#41—91no—
244C2×D4—21no—
245C2×D4—61no—
246SD16—361no—
247SD16—361no—
248D8—21no—
249D8—21no—
250D8—61no—
251D8—61no—
252D8—361no—
253D8—361no—
254M16—61no—
255M16—91no—
256M16—181no—
257M16—181no—
258C2×C8—181no—
259C2×C8C2×D3211yescharacteristic
260C16—31no—
261C16—31no—
262C16—61no—
263C22×C3—21no—
264C22×C3—82no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3—161no—
268C22×C3—161no—
269C22×C3—162no—
270C22×C3—241no—
271C22×C3—481no—
272C22×C3#91211yescharacteristic
273C22×C3#91611yescharacteristic
274C2×D3—61no—
275C2×D3—61no—
276C2×D3—81no—
277C2×D3—121no—
278C2×D3—161no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4#88411yescharacteristic
282C3×C4D3×D811yescharacteristic
283C3×C4D3×D811yescharacteristic
284C3×C4#93811yescharacteristic
285Dic3—61no—
286Dic3—61no—
287Dic3—121no—
288C32#222111yescharacteristic, complemented, Sylow
289C23—41no—
290C23—121no—
291Q8—91no—
292D4—41no—
293D4—41no—
294D4—91no—
295D4—121no—
296D4—121no—
297D4—181no—
298C2×C4—181no—
299C2×C4#381111yescharacteristic
300C8—121no—
301C8—181no—
302C8—361no—
303C8#380411yescharacteristic
304C8D3×#6711yescharacteristic
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—41no—
309C2×C3—162no—
310C2×C3—161no—
311C2×C3—161no—
312C2×C3—481no—
313C2×C3#477511yescharacteristic
314C2×C3#515711yescharacteristic
315D3—121no—
316D3—121no—
317D3—161no—
318D3—241no—
319C22—81no—
320C22—161no—
321C22—181no—
322C22—241no—
323C22—481no—
324C22#6393611yescharacteristic
325C4—181no—
326C4#6392611yescharacteristic
327C4#6395811yescharacteristic
328C3—21no—
329C3#6926011yescharacteristic, complemented
330C3#7147211yescharacteristic, complemented
331C2—21no—
332C2—161no—
333C2—361no—
334C2—481no—
335C2#1059145511yescharacteristic
subgroupG/H
centerC2#10591455
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#466
hypercenterC2×D8D32
hypocenterC32#2221
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10592859C2semidirect
2. C2×C3×#826C2semidirect
3. #10590929C2semidirect
4. #10590624C2semidirect
5. C3×#4563C2semidirect
6. #10589143C2semidirect
7. #10589127C2semidirect
30. C2×#826D3semidirect
36. #4563D3semidirect
288. C32#2221semidirect
329. C3#69260semidirect
330. C3#71472semidirect

Maximal subgroups

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

subgroupindex
#105928592
C2×C3×#8262
#105909292
#105906242
C3×#45632
#105891432
#105891272
#714723
#692603