Finite Group Databasebeta

← #49097984

Subgroups — #49097984

Order 35968.

556 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582857C211yesmaximal, characteristic
2C2×C4×Dic562C211yesmaximal, characteristic, complemented
3C2×#22582837C211yesmaximal, characteristic
4#31823367C211yesmaximal, characteristic, complemented
5#31823362C211yesmaximal, characteristic, complemented
6#31823360C211yesmaximal, characteristic, complemented
7#31823360C211yesmaximal, characteristic, complemented
8#31823355C211yesmaximal, characteristic
9#31823355C211yesmaximal, characteristic
10#31823354C211yesmaximal, characteristic
11#31823352C211yesmaximal, characteristic
12#31823344C211yesmaximal, characteristic, complemented
13#31823322C211yesmaximal, characteristic
14#31823314C211yesmaximal, characteristic, complemented
15#387×C281C211yesmaximal, characteristic, complemented
16C22×Dic562C2211yescharacteristic
17C22×C4×D281C2211yescharacteristic
18#22582857C418yescomplemented
19C4×Dic562—24no—
20#22582837—24no—
21C2×C4⋊Dic281C2211yescharacteristic
22C2×C4⋊Dic281C2211yescharacteristic
23C2×C4⋊Dic281C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×#17985117C2211yescharacteristic
28C2×#17985117C2211yescharacteristic
29C2×#17985117C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×#17985115C2211yescharacteristic
34C2×#17985115C2211yescharacteristic
35C2×#17985115C2211yescharacteristic
36C2×C4×Dic281C2211yescharacteristic
37C2×C4×Dic281C2211yescharacteristic
38C2×C4×Dic281C2211yescharacteristic
39C2×C4×Dic281C2211yescharacteristic
40C2×C4×Dic281C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46#22582786C2211yescharacteristic
47C2×C4⋊C4×C281C2211yescharacteristic
48C2×C4⋊C4×C281C2211yescharacteristic
49C2×C42×C281C2211yescharacteristic
50#95×C281C2211yescharacteristic
51#95×C281C2211yescharacteristic
52#95×C281C2211yescharacteristic
53#95×C281C2211yescharacteristic
54C23×D281C2311yescharacteristic
55C2×Dic562—22no—
56C2×Dic562—22no—
57C2×Dic562C2×C414yes—
58C22×Dic281C2311yescharacteristic
59C22×Dic281C2311yescharacteristic
60C22×Dic281C2311yescharacteristic
61C22×Dic281C2311yescharacteristic
62C22×Dic281C2311yescharacteristic
63C22×Dic281C2311yescharacteristic
64C22×Dic281C2311yescharacteristic
65C2×C4×D281—22no—
66C2×C4×D281—22no—
67C2×C4×D281C2×C414yes—
68C4⋊Dic281—22no—
69C4⋊Dic281—22no—
70C4⋊Dic281—41no—
71#17985117—22no—
72#17985117—22no—
73#17985117—22no—
74#17985117—41no—
75#17985117C2×C414yes—
76#17985117C2×C414yes—
77#17985115—22no—
78#17985115—22no—
79#17985115—41no—
80#17985115—41no—
81#17985115C2×C414yes—
82#17985115C2×C414yes—
83C4×Dic281—22no—
84C4×Dic281—22no—
85C4×Dic281—41no—
86C4×Dic281—41no—
87C4×Dic281D414yes—
88C22×C4×C281C2311yescharacteristic
89C22×C4×C281C2311yescharacteristic
90C22×C4×C281C2311yescharacteristic
91C22×C4×C281C2311yescharacteristic
92C22×C4×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C22×C4×C281C2311yescharacteristic
95C4⋊C4×C281—22no—
96C4⋊C4×C281C2×C414yes—
97C42×C281—22no—
98C22×D281—21no—
99C22×D281—21no—
100C22×D281—21no—
101C22×D281—21no—
102C22×D281—21no—
103C22×D281—21no—
104C22×D281C22×C412yes—
105Dic562—28no—
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—21no—
115C2×Dic281—21no—
116C2×Dic281—21no—
117C2×Dic281—21no—
118C2×Dic281—21no—
119C2×Dic281—21no—
120C2×Dic281—21no—
121C2×Dic281C22×C412yes—
122C2×Dic281C22×C412yes—
123C2×Dic281C22×C412yes—
124C2×Dic281C2×D412yes—
125C2×Dic281C2×D412yes—
126C2×Dic281#4112yes—
127C4×D281—28no—
128C23×C281C2411yescharacteristic
129C2×C4×C281—21no—
130C2×C4×C281—21no—
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×C281C22×C412yes—
147C2×C4×C281C22×C412yes—
148C2×C4×C281C22×C412yes—
149C2×C4×C281C2×D412yes—
150C22×C281C23×C411yescharacteristic
151C22×C281C22×D411yescharacteristic
152C22×C281C2×#4111yescharacteristic
153C22×C281H(5,𝔽2)11yescharacteristic
154C22×C2812−1+411yescharacteristic
155C22×C2812−1+411yescharacteristic
156C22×C2812−1+411yescharacteristic
157C2×D281—22no—
158C2×D281—22no—
159C2×D281—22no—
160C2×D281—41no—
161C2×D281—41no—
162C2×D281—41no—
163C2×D281—41no—
164C4×C281—22no—
165C4×C281—22no—
166C4×C281—22no—
167C4×C281—22no—
168C4×C281—41no—
169C4×C281—41no—
170C4×C281—41no—
171Dic281—22no—
172Dic281—22no—
173Dic281—22no—
174Dic281—41no—
175Dic281—41no—
176Dic281—41no—
177Dic281C4×D414yes—
178C2×C281C2×C4×D411yescharacteristic
179C2×C281#51911yescharacteristic
180C2×C281#52011yescharacteristic
181C2×C281#53611yescharacteristic
182C2×C281#53711yescharacteristic
183C2×C281#54111yescharacteristic
184C2×C281#54211yescharacteristic
185D281—42no—
186C281#232311yescharacteristic, complemented, Sylow
187#2323—2811nomaximal, Sylow
188C2×C22⋊Q8—2811no—
189C2×C4×Q8—2811no—
190C2×#117—2811no—
191#391—2811no—
192#389—2811no—
193#389—2811no—
194#389—2811no—
195#388—2811no—
196#388—2811no—
197#388—2811no—
198#388—2811no—
199#387—2811no—
200#387D28111yescharacteristic, complemented
201#380—2811no—
202C4×C4⋊C4—2811no—
203C22×Q8—2811no—
204C23×C4—2811no—
205C22⋊Q8—2818no—
206C4×Q8—5624no—
207#117—5624no—
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⋊C4—2811no—
215C2×C4⋊C4—2811no—
216C2×C4⋊C4—2811no—
217C2×C4⋊C4C2×D28111yescharacteristic
218C2×C4⋊C4C2×D28111yescharacteristic
219C2×C22⋊C4—2811no—
220C2×C22⋊C4—2811no—
221C2×C22⋊C4—2811no—
222C2×C22⋊C4—2811no—
223C2×C22⋊C4—2811no—
224C2×C22⋊C4—2811no—
225C2×C42—2811no—
226C2×C42—2811no—
227C2×C42—2811no—
228C2×C42—2811no—
229C2×C42—2811no—
230C2×C42C2×D28111yescharacteristic
231#95—2811no—
232#95—2811no—
233#95—2811no—
234#95—2811no—
235#95—2811no—
236#95—2811no—
237#95C2×D28111yescharacteristic
238#95C2×D28111yescharacteristic
239#95C2×D28111yescharacteristic
240#95C2×D28111yescharacteristic
241C24—2811no—
242C2×Q8—2814no—
243C2×Q8—5622no—
244C2×Q8—5622no—
245C22×C4—2811no—
246C22×C4—2811no—
247C22×C4—2811no—
248C22×C4—2811no—
249C22×C4—2814no—
250C22×C4—2811no—
251C22×C4—2811no—
252C22×C4—2811no—
253C22×C4—5622no—
254C22×C4—5622no—
255C22×C4C22×D28111yescharacteristic
256C22×C4C22×D28111yescharacteristic
257C22×C4C22×D28111yescharacteristic
258C22×C4C22×D28111yescharacteristic
259C22×C4C22×D28111yescharacteristic
260C22×C4C22×D28111yescharacteristic
261C22×C4C22×D28111yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—2814no—
264C4⋊C4—2814no—
265C4⋊C4—5622no—
266C4⋊C4—5622no—
267C4⋊C4—5622no—
268C4⋊C4—5622no—
269C4⋊C4—5622no—
270C4⋊C4—11241no—
271C4⋊C4—11241no—
272C4⋊C4C4×D28114yes—
273C22⋊C4—2814no—
274C22⋊C4—2814no—
275C22⋊C4—5622no—
276C22⋊C4—5622no—
277C22⋊C4—11241no—
278C22⋊C4—11241no—
279C42—22no—
280C42—2814no—
281C42—5622no—
282C42—5622no—
283C42—11241no—
284C42—11241no—
285C23—2812no—
286C23—5621no—
287C23—5621no—
288C23—5621no—
289C23—5621no—
290C23—5621no—
291C23—5621no—
292C23C23×D28111yescharacteristic
293Q8—5628no—
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—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2812no—
312C2×C4—2812no—
313C2×C4—2812no—
314C2×C4—2812no—
315C2×C4—2812no—
316C2×C4—2812no—
317C2×C4—5628no—
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×C4—5621no—
333C2×C4C2×C4×D28112yes—
334C2×C4C2×C4×D28112yes—
335C2×C4C2×C4×D28112yes—
336C2×C4D4×D28112yes—
337C22—5622no—
338C22—5622no—
339C22—5622no—
340C22—11241no—
341C22—11241no—
342C22—11241no—
343C22—11241no—
344C22C22×C4×D28111yescharacteristic
345C22C2×D4×D28111yescharacteristic
346C22#41×D28111yescharacteristic
347C22#2258292511yescharacteristic
348C22#2258292611yescharacteristic
349C22#2258292611yescharacteristic
350C22#2258292711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2814no—
359C4—5622no—
360C4—5622no—
361C4—5622no—
362C4—11241no—
363C4—11241no—
364C4—11241no—
365C2—11242no—
366C2C4×D4×D28111yescharacteristic
367C2#3182393911yescharacteristic
368C2#3182394311yescharacteristic
369C2#3182403511yescharacteristic
370C2#3182404311yescharacteristic
371C2#3182407211yescharacteristic
372C2#3182407911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#387×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenter#387D281
hypocenterC281#2323
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic562C2semidirect
4. #31823367C2semidirect
5. #31823362C2semidirect
6. #31823360C2semidirect
7. #31823360C2semidirect
12. #31823344C2semidirect
14. #31823314C2semidirect
15. #387×C281C2semidirect
18. #22582857C4semidirect
186. C281#2323semidirect
200. #387D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828572
C2×C4×Dic5622
C2×#225828372
#318233672
#318233622
#318233602
#318233552
#318233542
#318233522
#318233442
#318233222
#318233142
#387×C2812
#2323281