Finite Group Databasebeta

← #49098578

Subgroups — #49098578

Order 35968.

528 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582844C211yesmaximal, characteristic, complemented
2C2×#22582835C211yesmaximal, characteristic
3#31823404C211yesmaximal, characteristic, complemented
4#31823399C211yesmaximal, characteristic
5#31823396C211yesmaximal, characteristic, complemented
6#31823393C211yesmaximal, characteristic, complemented
7#31823386C211yesmaximal, characteristic
8#31823383C211yesmaximal, characteristic, complemented
9#31823375C211yesmaximal, characteristic
10C4⋊C4×Dic281C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic281C211yesmaximal, characteristic, complemented
12#31823314C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic281C211yesmaximal, characteristic
14C22⋊C4×Dic281C211yesmaximal, characteristic
15#396×C281C211yesmaximal, characteristic
16C22×Dic562C2211yescharacteristic
17C23×Dic281C2211yescharacteristic
18#22582844—24no—
19#22582835—24no—
20C2×C4⋊Dic281C2211yescharacteristic
21C2×C4⋊Dic281C2211yescharacteristic
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×#17985117C2211yescharacteristic
28C2×C22⋊Dic281C2211yescharacteristic
29C2×C22⋊Dic281C2211yescharacteristic
30C2×C22⋊Dic281C2211yescharacteristic
31C2×C4×Dic281C2211yescharacteristic
32C2×C4×Dic281C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35C2×C4×Dic281C2211yescharacteristic
36C2×C4×Dic281C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46C2×C4⋊C4×C281C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C4⋊C4×C281C2211yescharacteristic
49C2×C22⋊C4×C281C2211yescharacteristic
50C2×C22⋊C4×C281C2211yescharacteristic
51C2×C22⋊C4×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53C2×Dic562—22no—
54C2×Dic562—22no—
55C2×Dic562—22no—
56C22×Dic281—22no—
57C22×Dic281—22no—
58C22×Dic281Q814yescomplemented
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C4⋊Dic281—22no—
68C4⋊Dic281—22no—
69#17985117—22no—
70#17985117—22no—
71#17985117—22no—
72#17985117—22no—
73#17985117—22no—
74#17985117—22no—
75C22⋊Dic281—22no—
76C22⋊Dic281—22no—
77C22⋊Dic281—22no—
78C4×Dic281—22no—
79C4×Dic281—22no—
80C4×Dic281—22no—
81C4×Dic281—22no—
82C4×Dic281—22no—
83C4×Dic281D414yes—
84C24×C281C2311yescharacteristic
85C22×C4×C281C2311yescharacteristic
86C22×C4×C281C2311yescharacteristic
87C22×C4×C281C2311yescharacteristic
88C22×C4×C281C2311yescharacteristic
89C22×C4×C281C2311yescharacteristic
90C22×C4×C281C2311yescharacteristic
91C4⋊C4×C281—22no—
92C4⋊C4×C281—22no—
93C4⋊C4×C281—22no—
94C22⋊C4×C281—22no—
95C22⋊C4×C281—22no—
96C22⋊C4×C281—22no—
97Dic562—28no—
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—28no—
107C2×Dic281—21no—
108C2×Dic281—21no—
109C2×Dic281—21no—
110C2×Dic281—21no—
111C2×Dic281—21no—
112C2×Dic281—21no—
113C2×Dic281—21no—
114C2×Dic281—21no—
115C2×Dic281—21no—
116C2×Dic281C2×D412yes—
117C2×Dic281C2×D412yes—
118C2×Dic281C2×Q812yes—
119C2×Dic281C2×Q812yes—
120C2×Dic281#4112yes—
121C2×Dic281#4112yes—
122C2×Dic281#4112yes—
123C23×C281—21no—
124C23×C281—21no—
125C23×C281—21no—
126C23×C281—21no—
127C23×C281—21no—
128C23×C281—21no—
129C23×C281C2×Q812yes—
130C23×C281C2411yescharacteristic
131C2×C4×C281—21no—
132C2×C4×C281—21no—
133C2×C4×C281—21no—
134C2×C4×C281—21no—
135C2×C4×C281—21no—
136C2×C4×C281—21no—
137C2×C4×C281—21no—
138C2×C4×C281—21no—
139C2×C4×C281—21no—
140C2×C4×C281—21no—
141C2×C4×C281—21no—
142C2×C4×C281—21no—
143C2×C4×C281—21no—
144C2×C4×C281—21no—
145C2×C4×C281—21no—
146C2×C4×C281C2×D412yes—
147C2×C4×C281#4112yes—
148C2×C4×C281#4112yes—
149C22×C281—22no—
150C22×C281—22no—
151C22×C281—22no—
152C22×C281—41no—
153C22×C281—41no—
154C22×C281—41no—
155C22×C281—41no—
156C22×C281C22×D411yescharacteristic
157C22×C281C22×Q811yescharacteristic
158C22×C281C2×#4111yescharacteristic
159C22×C281C2×#4111yescharacteristic
160C22×C281C2×#4111yescharacteristic
161C22×C281C2×#4111yescharacteristic
162C22×C281C2×#4111yescharacteristic
163C4×C281—22no—
164C4×C281—22no—
165C4×C281—22no—
166C4×C281—41no—
167C4×C281—41no—
168C4×C281—41no—
169Dic281—22no—
170Dic281—22no—
171Dic281—22no—
172Dic281—22no—
173Dic281—41no—
174Dic281—41no—
175Dic281—41no—
176Dic281C22⋊Q814yes—
177C2×C281—42no—
178C2×C281C2×C22⋊Q811yescharacteristic
179C2×C281#52511yescharacteristic
180C2×C281#52911yescharacteristic
181C2×C281#52911yescharacteristic
182C2×C281#53211yescharacteristic
183C2×C281#53311yescharacteristic
184C2×C281#53311yescharacteristic
185C281#239611yescharacteristic, complemented, Sylow
186#2396—2811nomaximal, Sylow
187C2×C4×Q8—2811no—
188C2×#117—2811no—
189#400—2811no—
190#399—2811no—
191#398—2811no—
192#398—2811no—
193#396—2811no—
194#396D28111yescharacteristic
195#395—2811no—
196#393—2811no—
197C4×C4⋊C4—2811no—
198C4×C4⋊C4—2811no—
199C4×C4⋊C4—2811no—
200C4×C22⋊C4—2811no—
201C4×C22⋊C4—2811no—
202C22×Q8—2811no—
203C23×C4—2811no—
204C4×Q8—5624no—
205#117—5624no—
206C2×C4⋊C4—2811no—
207C2×C4⋊C4—2811no—
208C2×C4⋊C4—2811no—
209C2×C4⋊C4—2811no—
210C2×C4⋊C4—2811no—
211C2×C4⋊C4—2811no—
212C2×C4⋊C4—2811no—
213C2×C4⋊C4—2811no—
214C2×C4⋊C4C2×D28111yescharacteristic
215C2×C4⋊C4C2×D28111yescharacteristic
216C2×C4⋊C4C2×D28111yescharacteristic
217C2×C22⋊C4—2811no—
218C2×C22⋊C4—2811no—
219C2×C22⋊C4—2811no—
220C2×C22⋊C4C2×D28111yescharacteristic
221C2×C22⋊C4C2×D28111yescharacteristic
222C2×C22⋊C4C2×D28111yescharacteristic
223C2×C42—2811no—
224C2×C42—2811no—
225C2×C42—2811no—
226C2×C42—2811no—
227C2×C42—2811no—
228C2×C42—2811no—
229#95—2811no—
230#95—2811no—
231#95—2811no—
232#95—2811no—
233#95—2811no—
234#95—2811no—
235#95—2811no—
236#95—2811no—
237#95—2811no—
238#95C2×D28111yescharacteristic
239C24C22×D28111yescharacteristic
240C2×Q8—5622no—
241C2×Q8—5622no—
242C2×Q8—5622no—
243C22×C4—2811no—
244C22×C4—2814no—
245C22×C4—2811no—
246C22×C4—2811no—
247C22×C4—2811no—
248C22×C4—2811no—
249C22×C4—2811no—
250C22×C4—2811no—
251C22×C4—2811no—
252C22×C4—5622no—
253C22×C4—5622no—
254C22×C4C22×D28111yescharacteristic
255C22×C4C22×D28111yescharacteristic
256C22×C4C22×D28111yescharacteristic
257C22×C4C22×D28111yescharacteristic
258C22×C4C22×D28111yescharacteristic
259C22×C4C22×D28111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—5622no—
264C4⋊C4—5622no—
265C4⋊C4—5622no—
266C4⋊C4—5622no—
267C4⋊C4—5622no—
268C4⋊C4—5622no—
269C4⋊C4—5622no—
270C4⋊C4—5622no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—5622no—
275C22⋊C4—5622no—
276C22⋊C4—5622no—
277C42—2814no—
278C42—5622no—
279C42—5622no—
280C42—5622no—
281C42—5622no—
282C42—5622no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23Q8×D28112yes—
290C23C23×D28111yescharacteristic
291Q8—5628no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2812no—
308C2×C4—2812no—
309C2×C4—2812no—
310C2×C4—2812no—
311C2×C4—2812no—
312C2×C4—2812no—
313C2×C4—2812no—
314C2×C4—5628no—
315C2×C4—5621no—
316C2×C4—5621no—
317C2×C4—5621no—
318C2×C4—5621no—
319C2×C4—5621no—
320C2×C4—5621no—
321C2×C4—5621no—
322C2×C4—5621no—
323C2×C4—5621no—
324C2×C4—5621no—
325C2×C4—5621no—
326C2×C4—5621no—
327C2×C4—5621no—
328C2×C4—5621no—
329C2×C4—5621no—
330C2×C4—5621no—
331C2×C4—5621no—
332C2×C4D4×D28112yes—
333C2×C4#1798513712yes—
334C2×C4#1798513712yes—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C2×D4×D28111yescharacteristic
343C22C2×Q8×D28111yescharacteristic
344C22#41×D28111yescharacteristic
345C22#41×D28111yescharacteristic
346C22#41×D28111yescharacteristic
347C22C2×#1798513711yescharacteristic
348C22C2×#1798513711yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2814no—
356C4—5622no—
357C4—5622no—
358C4—5622no—
359C4—5622no—
360C4—11241no—
361C4—11241no—
362C4—11241no—
363C2—42no—
364C2C22⋊Q8×D28111yescharacteristic
365C2#3182397311yescharacteristic
366C2#3182399411yescharacteristic
367C2#3182399611yescharacteristic
368C2#3182400811yescharacteristic
369C2#3182401511yescharacteristic
370C2#3182401511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#396×C281C2
prime radicalC24×C281C23
hypercenter#396D281
hypocenterC281#2396
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#22582844C2semidirect
3. #31823404C2semidirect
5. #31823396C2semidirect
6. #31823393C2semidirect
8. #31823383C2semidirect
10. C4⋊C4×Dic281C2semidirect
11. C4⋊C4×Dic281C2semidirect
12. #31823314C2semidirect
58. C22×Dic281Q8semidirect
185. C281#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#225828442
C2×#225828352
#318234042
#318233992
#318233962
#318233932
#318233862
#318233832
#318233752
C4⋊C4×Dic2812
#318233142
C22⋊C4×Dic2812
#396×C2812
#2396281