Finite Group Databasebeta

← #49098604

Subgroups — #49098604

Order 35968.

432 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C281⋊#401C211yesmaximal, characteristic, complemented
2#31823405C211yesmaximal, characteristic, complemented
3#31823402C211yesmaximal, characteristic, complemented
4#31823401C211yesmaximal, characteristic, complemented
5#31823392C211yesmaximal, characteristic
6#31823390C211yesmaximal, characteristic
7#31823389C211yesmaximal, characteristic
8#31823385C211yesmaximal, characteristic
9C4×#17985117C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic281C211yesmaximal, characteristic, complemented
11C4×#17985115C211yesmaximal, characteristic
12C4×#17985115C211yesmaximal, characteristic
13C4×#17985115C211yesmaximal, characteristic
14#31823309C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C281C211yesmaximal, characteristic, complemented
16C22×C4×D281C2211yescharacteristic
17C2×C4⋊Dic281C2211yescharacteristic
18C2×C4⋊Dic281C2211yescharacteristic
19C2×#17985117C2211yescharacteristic
20C2×#17985117C2211yescharacteristic
21C2×#17985115C2211yescharacteristic
22C2×#17985115C2211yescharacteristic
23C2×#17985115C2211yescharacteristic
24C2×#17985115C2211yescharacteristic
25C2×#17985115C2211yescharacteristic
26C2×#17985115C2211yescharacteristic
27C2×C4×Dic281C2211yescharacteristic
28C2×C4×Dic281C2211yescharacteristic
29C2×C4×Dic281C2211yescharacteristic
30#22582786C2211yescharacteristic
31#22582786C2211yescharacteristic
32#22582786C2211yescharacteristic
33#22582786C2211yescharacteristic
34#22582786C2211yescharacteristic
35#22582786C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44C2×C4⋊C4×C281C2211yescharacteristic
45C2×C4⋊C4×C281C2211yescharacteristic
46C2×C42×C281C2211yescharacteristic
47C2×C42×C281C2211yescharacteristic
48C2×C42×C281C2211yescharacteristic
49#95×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51C23×D281C2311yescharacteristic
52C22×Dic281C2311yescharacteristic
53C22×Dic281C2311yescharacteristic
54C22×Dic281C2311yescharacteristic
55C22×Dic281C2311yescharacteristic
56C22×Dic281C2311yescharacteristic
57C22×Dic281C2311yescharacteristic
58C22×Dic281C2311yescharacteristic
59C2×C4×D281—22no—
60C2×C4×D281—22no—
61C2×C4×D281—22no—
62C4⋊Dic281—22no—
63C4⋊Dic281—22no—
64#17985117—22no—
65#17985117—22no—
66#17985115—22no—
67#17985115—22no—
68#17985115—22no—
69#17985115—22no—
70#17985115—22no—
71#17985115—22no—
72C4×Dic281—22no—
73C4×Dic281—22no—
74C4×Dic281—22no—
75C22×C4×C281C2311yescharacteristic
76C22×C4×C281C2311yescharacteristic
77C22×C4×C281C2311yescharacteristic
78C22×C4×C281C2311yescharacteristic
79C22×C4×C281C2311yescharacteristic
80C22×C4×C281C2311yescharacteristic
81C22×C4×C281C2311yescharacteristic
82C4⋊C4×C281—22no—
83C4⋊C4×C281—22no—
84C42×C281—22no—
85C42×C281—22no—
86C42×C281—22no—
87C22×D281—21no—
88C22×D281—21no—
89C22×D281—21no—
90C22×D281—21no—
91C22×D281—21no—
92C22×D281—21no—
93C22×D281#4112yes—
94C2×Dic281—21no—
95C2×Dic281—21no—
96C2×Dic281—21no—
97C2×Dic281—21no—
98C2×Dic281—21no—
99C2×Dic281—21no—
100C2×Dic281—21no—
101C2×Dic281—21no—
102C2×Dic281—21no—
103C2×Dic281—21no—
104C2×Dic281—21no—
105C2×Dic281—21no—
106C2×Dic281—21no—
107C2×Dic281—21no—
108C2×Dic281—21no—
109C2×Dic281—21no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281—21no—
113C2×Dic281—21no—
114C2×Dic281#4112yes—
115C4×D281—44no—
116C23×C281C2411yescharacteristic
117C2×C4×C281—21no—
118C2×C4×C281—21no—
119C2×C4×C281—21no—
120C2×C4×C281—21no—
121C2×C4×C281—21no—
122C2×C4×C281—21no—
123C2×C4×C281—21no—
124C2×C4×C281—21no—
125C2×C4×C281—21no—
126C2×C4×C281—21no—
127C2×C4×C281—21no—
128C2×C4×C281—21no—
129C2×C4×C281—21no—
130C2×C4×C281—21no—
131C2×C4×C281—21no—
132C2×C4×C281—21no—
133C2×C4×C281#4112yes—
134C2×C4×C281#4112yes—
135C2×C4×C281#4112yes—
136C2×C4×C281#4112yes—
137C2×C4×C281#4112yes—
138C22×C281C2×#4111yescharacteristic
139C22×C281C2×#4111yescharacteristic
140C22×C281C2×#4111yescharacteristic
141C22×C281C2×#4111yescharacteristic
142C22×C281C2×#4111yescharacteristic
143C22×C281C2×#4111yescharacteristic
144C22×C281C2×#4111yescharacteristic
145C2×D281—22no—
146C2×D281—22no—
147C2×D281—22no—
148C2×D281—41no—
149C2×D281—41no—
150C2×D281—41no—
151C2×D281—41no—
152C4×C281—22no—
153C4×C281—22no—
154C4×C281—41no—
155C4×C281—41no—
156C4×C281—41no—
157C4×C281—41no—
158C4×C281#12614yes—
159Dic281—22no—
160Dic281—41no—
161Dic281—41no—
162Dic281—41no—
163Dic281—41no—
164Dic281—41no—
165Dic281—41no—
166C2×C281C2×#12611yescharacteristic
167C2×C281#52911yescharacteristic
168C2×C281#52911yescharacteristic
169C2×C281#52911yescharacteristic
170C2×C281#52911yescharacteristic
171C2×C281#52911yescharacteristic
172C2×C281#52911yescharacteristic
173D281—42no—
174C281#240111yescharacteristic, complemented, Sylow
175#2401—2811nomaximal, Sylow
176#401—2811no—
177#400—2811no—
178#400—2811no—
179#400—2811no—
180#397—2811no—
181#397—2811no—
182#397—2811no—
183#396—2811no—
184C4×C4⋊C4—2811no—
185C4×C4⋊C4—2811no—
186C4×C4⋊C4D28111yescharacteristic, complemented
187C4×C22⋊C4—2811no—
188C4×C22⋊C4—2811no—
189C4×C22⋊C4—2811no—
190#376—2811no—
191C23×C4—2811no—
192C2×C4⋊C4—2811no—
193C2×C4⋊C4—2811no—
194C2×C4⋊C4—2811no—
195C2×C4⋊C4—2811no—
196C2×C4⋊C4C2×D28111yescharacteristic
197C2×C4⋊C4C2×D28111yescharacteristic
198C2×C22⋊C4—2811no—
199C2×C22⋊C4—2811no—
200C2×C22⋊C4—2811no—
201C2×C22⋊C4—2811no—
202C2×C22⋊C4—2811no—
203C2×C22⋊C4—2811no—
204C2×C42—2811no—
205C2×C42—2811no—
206C2×C42—2811no—
207C2×C42C2×D28111yescharacteristic
208C2×C42C2×D28111yescharacteristic
209C2×C42C2×D28111yescharacteristic
210#95—2811no—
211#95—2811no—
212#95—2811no—
213#95—2811no—
214#95—2811no—
215#95—2811no—
216#95—2811no—
217#95—2811no—
218#95—2811no—
219#95—2811no—
220#95—2811no—
221#95—2811no—
222#95—2811no—
223#95—2811no—
224#95C2×D28111yescharacteristic
225#95C2×D28111yescharacteristic
226C24—2811no—
227C22×C4—2811no—
228C22×C4—2811no—
229C22×C4—2811no—
230C22×C4—2811no—
231C22×C4—2811no—
232C22×C4—2811no—
233C22×C4—2811no—
234C22×C4—5622no—
235C22×C4—5622no—
236C22×C4—5622no—
237C22×C4C22×D28111yescharacteristic
238C22×C4C22×D28111yescharacteristic
239C22×C4C22×D28111yescharacteristic
240C22×C4C22×D28111yescharacteristic
241C22×C4C22×D28111yescharacteristic
242C22×C4C22×D28111yescharacteristic
243C22×C4C22×D28111yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—5622no—
247C4⋊C4—5622no—
248C4⋊C4—5622no—
249C4⋊C4—5622no—
250C22⋊C4—5622no—
251C22⋊C4—5622no—
252C22⋊C4—5622no—
253C22⋊C4—5622no—
254C22⋊C4—5622no—
255C22⋊C4—5622no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—5622no—
260C42—5622no—
261C42—5622no—
262C23—2812no—
263C23—5621no—
264C23—5621no—
265C23—5621no—
266C23—5621no—
267C23—5621no—
268C23—5621no—
269C23C23×D28111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—2812no—
287C2×C4—5621no—
288C2×C4—5621no—
289C2×C4—5621no—
290C2×C4—5621no—
291C2×C4—5621no—
292C2×C4—5621no—
293C2×C4—5621no—
294C2×C4—5621no—
295C2×C4—5621no—
296C2×C4—5621no—
297C2×C4—5621no—
298C2×C4—5621no—
299C2×C4—5621no—
300C2×C4—5621no—
301C2×C4—5621no—
302C2×C4—5621no—
303C2×C4—5621no—
304C2×C4—5621no—
305C2×C4—5621no—
306C2×C4—5621no—
307C2×C4—11244no—
308C2×C4#1798513712yes—
309C2×C4#1798513812yes—
310C2×C4#1798513812yes—
311C2×C4#1798513812yes—
312C2×C4#1798513912yes—
313C22—5622no—
314C22—5622no—
315C22—5622no—
316C22—11241no—
317C22—11241no—
318C22—11241no—
319C22—11241no—
320C22#41×D28111yescharacteristic
321C22#41×D28111yescharacteristic
322C22C2×#1798513711yescharacteristic
323C22C2×#1798513811yescharacteristic
324C22C2×#1798513811yescharacteristic
325C22C2×#1798513811yescharacteristic
326C22C2×#1798513911yescharacteristic
327C4—22no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—5622no—
334C4—11241no—
335C4—11241no—
336C4—11241no—
337C4—11241no—
338C4—11241no—
339C4—11241no—
340C4#2258287414yes—
341C2—11242no—
342C2C2×#2258287411yescharacteristic
343C2#3182399111yescharacteristic
344C2#3182399311yescharacteristic
345C2#3182399511yescharacteristic
346C2#3182399711yescharacteristic
347C2#3182400011yescharacteristic
348C2#3182400011yescharacteristic
subgroupG/H
centerC22×C4C22×D281
commutator, socle, cosocleC23×C281C24
FrattiniC23C23×D281
FittingC4×C4⋊C4×C281C2
prime radicalC23×D281C23
hypercenterC4×C4⋊C4D281
hypocenterC281#2401
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C281⋊#401C2semidirect
2. #31823405C2semidirect
3. #31823402C2semidirect
4. #31823401C2semidirect
9. C4×#17985117C2semidirect
10. C4×C4⋊Dic281C2semidirect
14. #31823309C2semidirect
15. C4×C4⋊C4×C281C2semidirect
174. C281#2401semidirect
186. C4×C4⋊C4D281semidirect

Maximal subgroups

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

subgroupindex
C281⋊#4012
#318234052
#318234022
#318234012
#318233922
#318233902
#318233892
#318233852
C4×#179851172
C4×C4⋊Dic2812
C4×#179851152
#318233092
C4×C4⋊C4×C2812
#2401281