Finite Group Databasebeta

← #49098295

Subgroups — #49098295

Order 35968.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22582862C211yesmaximal, characteristic
2C2×#22582839C211yesmaximal, characteristic
3#31823358C211yesmaximal, characteristic, complemented
4#31823354C211yesmaximal, characteristic, complemented
5#31823353C211yesmaximal, characteristic, complemented
6#31823347C211yesmaximal, characteristic, complemented
7#31823344C211yesmaximal, characteristic, complemented
8#31823340C211yesmaximal, characteristic
9#31823335C211yesmaximal, characteristic, complemented
10#31823334C211yesmaximal, characteristic, complemented
11C4×#17985117C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic281C211yesmaximal, characteristic, complemented
13C4×#17985115C211yesmaximal, characteristic, complemented
14C2×#22582786C211yesmaximal, characteristic, complemented
15C2×#117×C281C211yesmaximal, characteristic, complemented
16C22×C22⋊D281C2211yescharacteristic
17C23×Dic281C2211yescharacteristic
18C23×Dic281C2211yescharacteristic
19C22×C4×D281C2211yescharacteristic
20#22582862C418yescomplemented
21#22582839—24no—
22C2×#17985117C2211yescharacteristic
23C2×#17985117C2211yescharacteristic
24C2×#17985117C2211yescharacteristic
25C2×#17985117C2211yescharacteristic
26C2×#17985117C2211yescharacteristic
27C2×C22⋊Dic281C2211yescharacteristic
28C2×#17985115C2211yescharacteristic
29C2×#17985115C2211yescharacteristic
30C2×#17985115C2211yescharacteristic
31C2×#17985115C2211yescharacteristic
32C2×#17985115C2211yescharacteristic
33C2×C4×Dic281C2211yescharacteristic
34C2×C4×Dic281C2211yescharacteristic
35C2×C4×Dic281C2211yescharacteristic
36#22582786C2211yescharacteristic
37#22582786C2211yescharacteristic
38#22582786C2211yescharacteristic
39#22582786C2211yescharacteristic
40#22582786C2211yescharacteristic
41#22582786C2211yescharacteristic
42#22582786C2211yescharacteristic
43#22582786C2211yescharacteristic
44#22582786C2211yescharacteristic
45#22582786C2211yescharacteristic
46C23×C4×C281C2211yescharacteristic
47#117×C281—24no—
48C2×C4⋊C4×C281C2211yescharacteristic
49C2×C4⋊C4×C281C2211yescharacteristic
50C2×C22⋊C4×C281C2211yescharacteristic
51C2×C22⋊C4×C281C2211yescharacteristic
52C2×C42×C281C2211yescharacteristic
53C2×C42×C281C2211yescharacteristic
54C23×D281C2311yescharacteristic
55C2×C22⋊D281—22no—
56C2×C22⋊D281—22no—
57C2×C22⋊D281C2×C414yes—
58C22×Dic281—22no—
59C22×Dic281—22no—
60C22×Dic281—22no—
61C22×Dic281—22no—
62C22×Dic281—41no—
63C22×Dic281—41no—
64C22×Dic281C2311yescharacteristic
65C22×Dic281C2311yescharacteristic
66C22×Dic281C2311yescharacteristic
67C22×Dic281C2311yescharacteristic
68C22×Dic281C2311yescharacteristic
69C22×Dic281C2311yescharacteristic
70C22×Dic281C2311yescharacteristic
71C2×C4×D281—22no—
72C2×C4×D281—22no—
73C2×C4×D281—41no—
74#17985117—22no—
75#17985117—22no—
76#17985117—41no—
77#17985117C2×C414yescomplemented
78#17985117C2×C414yescomplemented
79C22⋊Dic281C2×C414yescomplemented
80#17985115—22no—
81#17985115—22no—
82#17985115—41no—
83#17985115C2×C414yescomplemented
84#17985115C2×C414yescomplemented
85C4×Dic281—22no—
86C4×Dic281—22no—
87C4×Dic281—41no—
88C24×C281C2311yescharacteristic
89C22×C4×C281—22no—
90C22×C4×C281—22no—
91C22×C4×C281C2×C414yescomplemented
92C22×C4×C281C2311yescharacteristic
93C22×C4×C281C2311yescharacteristic
94C22×C4×C281C2311yescharacteristic
95C22×C4×C281C2311yescharacteristic
96C22×C4×C281C2311yescharacteristic
97C22×C4×C281C2311yescharacteristic
98C4⋊C4×C281—22no—
99C4⋊C4×C281—22no—
100C22⋊C4×C281—22no—
101C22⋊C4×C281D414yes—
102C42×C281—22no—
103C42×C281—22no—
104C22×D281—21no—
105C22×D281—21no—
106C22×D281—21no—
107C22×D281—21no—
108C22×D281—21no—
109C22×D281—21no—
110C22×D281C22×C412yes—
111C22⋊D281—28no—
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×Dic281—21no—
122C2×Dic281—21no—
123C2×Dic281—21no—
124C2×Dic281—21no—
125C2×Dic281—21no—
126C2×Dic281—21no—
127C2×Dic281—21no—
128C2×Dic281—44no—
129C2×Dic281—44no—
130C2×Dic281C22×C412yes—
131C2×Dic281C22×C412yes—
132C2×Dic281C22×C412yes—
133C2×Dic281#4112yes—
134C2×Dic281#4112yes—
135C4×D281—44no—
136C23×C281—21no—
137C23×C281—21no—
138C23×C281—21no—
139C23×C281—21no—
140C23×C281C22×C412yes—
141C23×C281C2×D412yes—
142C23×C281#4112yes—
143C23×C281C2411yescharacteristic
144C2×C4×C281—28no—
145C2×C4×C281—21no—
146C2×C4×C281—21no—
147C2×C4×C281—21no—
148C2×C4×C281—21no—
149C2×C4×C281—21no—
150C2×C4×C281—21no—
151C2×C4×C281—21no—
152C2×C4×C281—21no—
153C2×C4×C281—21no—
154C2×C4×C281—21no—
155C2×C4×C281—21no—
156C2×C4×C281—21no—
157C2×C4×C281—21no—
158C2×C4×C281—21no—
159C2×C4×C281C22×C412yes—
160C2×C4×C281C22×C412yes—
161C2×C4×C281C2×D412yes—
162C2×C4×C281C2×D412yes—
163C22×C281—22no—
164C22×C281—22no—
165C22×C281—22no—
166C22×C281—22no—
167C22×C281—22no—
168C22×C281—22no—
169C22×C281C4×D414yes—
170C22×C281C23×C411yescharacteristic
171C22×C281C22×D411yescharacteristic
172C22×C281C2×#4111yescharacteristic
173C22×C281C2×#4111yescharacteristic
174C22×C281C2×#4111yescharacteristic
175C22×C281H(5,𝔽2)11yescharacteristic
176C22×C2812−1+411yescharacteristic
177C2×D281—22no—
178C2×D281—22no—
179C2×D281—22no—
180C2×D281—41no—
181C2×D281—41no—
182C2×D281—41no—
183C2×D281—41no—
184C4×C281—22no—
185C4×C281—22no—
186C4×C281—22no—
187C4×C281—22no—
188C4×C281—41no—
189C4×C281—41no—
190Dic281—22no—
191Dic281—22no—
192Dic281—22no—
193Dic281—22no—
194Dic281—22no—
195Dic281—41no—
196Dic281—41no—
197C2×C281—24no—
198C2×C281C2×C4×D411yescharacteristic
199C2×C281C4×#4111yescharacteristic
200C2×C281#52011yescharacteristic
201C2×C281#54611yescharacteristic
202C2×C281#54711yescharacteristic
203C2×C281#55111yescharacteristic
204C2×C281#55211yescharacteristic
205D281—42no—
206C281#235911yescharacteristic, complemented, Sylow
207#2359—2811nomaximal, Sylow
208C2×#123—2811no—
209C2×C4×D4—2811no—
210C2×#117D28111yescharacteristic, complemented
211#389—2811no—
212#388—2811no—
213#388—2811no—
214#387—2811no—
215#387—2811no—
216#386—2811no—
217#385—2811no—
218#385—2811no—
219C4×C4⋊C4—2811no—
220C4×C22⋊C4—2811no—
221C4×C22⋊C4—2811no—
222C2×#95—2811no—
223C22×D4—2811no—
224C23×C4—2811no—
225C23×C4—2811no—
226C23×C4—2811no—
227C23×C4C2×D28111yescharacteristic
228#123—2818no—
229C4×D4—5624no—
230#117—24no—
231C2×C4⋊C4—2811no—
232C2×C4⋊C4—2811no—
233C2×C4⋊C4—2811no—
234C2×C4⋊C4—2811no—
235C2×C4⋊C4—2811no—
236C2×C4⋊C4C2×D28111yescharacteristic
237C2×C4⋊C4C2×D28111yescharacteristic
238C2×C22⋊C4—2811no—
239C2×C22⋊C4—2811no—
240C2×C22⋊C4—2811no—
241C2×C22⋊C4—2811no—
242C2×C22⋊C4—2811no—
243C2×C22⋊C4—2811no—
244C2×C22⋊C4C2×D28111yescharacteristic
245C2×C22⋊C4C2×D28111yescharacteristic
246C2×C42—2811no—
247C2×C42—2811no—
248C2×C42—2811no—
249C2×C42C2×D28111yescharacteristic
250C2×C42C2×D28111yescharacteristic
251#95—2811no—
252#95—2811no—
253#95—2811no—
254#95—2811no—
255#95—2811no—
256#95—2811no—
257#95—2811no—
258#95—2811no—
259#95—2811no—
260#95—2811no—
261C24—2811no—
262C24C22×D28111yescharacteristic
263C2×D4—2814no—
264C2×D4—5622no—
265C2×D4—5622no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—2811no—
269C22×C4—2811no—
270C22×C4—2811no—
271C22×C4—2811no—
272C22×C4—2811no—
273C22×C4—2811no—
274C22×C4—2811no—
275C22×C4—5622no—
276C22×C4—5622no—
277C22×C4—5622no—
278C22×C4—5622no—
279C22×C4—5622no—
280C22×C4—5622no—
281C22×C4—11241no—
282C22×C4—11241no—
283C22×C4—11241no—
284C22×C4C4×D28114yescomplemented
285C22×C4C22×D28111yescharacteristic
286C22×C4C22×D28111yescharacteristic
287C22×C4C22×D28111yescharacteristic
288C22×C4C22×D28111yescharacteristic
289C22×C4C22×D28111yescharacteristic
290C22×C4C22×D28111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—2814no—
294C4⋊C4—2814no—
295C4⋊C4—5622no—
296C4⋊C4—5622no—
297C4⋊C4—11241no—
298C22⋊C4—22no—
299C22⋊C4—2814no—
300C22⋊C4—2814no—
301C22⋊C4—2814no—
302C22⋊C4—5622no—
303C22⋊C4—5622no—
304C22⋊C4—11241no—
305C22⋊C4C22⋊D28114yes—
306C42—22no—
307C42—22no—
308C42—5622no—
309C42—5622no—
310C42—11241no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—2812no—
316C23—5621no—
317C23—5621no—
318C23—5621no—
319C23—5621no—
320C23—5621no—
321C23—5621no—
322C23C2×C4×D28112yes—
323C23C2×C22⋊D28112yes—
324C23#1798513812yes—
325C23C23×D28111yescharacteristic
326D4—5628no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2812no—
343C2×C4—2812no—
344C2×C4—2812no—
345C2×C4—2812no—
346C2×C4—2812no—
347C2×C4—5621no—
348C2×C4—5621no—
349C2×C4—5621no—
350C2×C4—5621no—
351C2×C4—5621no—
352C2×C4—5621no—
353C2×C4—5621no—
354C2×C4—5621no—
355C2×C4—5621no—
356C2×C4—5621no—
357C2×C4—5621no—
358C2×C4—5621no—
359C2×C4—5621no—
360C2×C4—5621no—
361C2×C4—5621no—
362C2×C4—5621no—
363C2×C4—11244no—
364C2×C4—11244no—
365C2×C4—11244no—
366C2×C4C2×C4×D28112yes—
367C2×C4C2×C4×D28112yes—
368C2×C4C2×C22⋊D28112yes—
369C2×C4C2×C22⋊D28112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—5622no—
377C22—5622no—
378C22—5622no—
379C22—11241no—
380C22—11241no—
381C22—11241no—
382C22—11241no—
383C22C4×C22⋊D28114yes—
384C22C22×C4×D28111yescharacteristic
385C22C22×C22⋊D28111yescharacteristic
386C22#41×D28111yescharacteristic
387C22#41×D28111yescharacteristic
388C22C2×#1798513811yescharacteristic
389C22#2258292511yescharacteristic
390C22#2258292611yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—5622no—
398C4—5622no—
399C4—5622no—
400C4—5622no—
401C4—5622no—
402C4—11241no—
403C4—11241no—
404C2—24no—
405C2—11242no—
406C2C2×C4×C22⋊D28111yescharacteristic
407C2#3182393111yescharacteristic
408C2#3182394311yescharacteristic
409C2#3182410111yescharacteristic
410C2#3182411211yescharacteristic
411C2#3182413711yescharacteristic
412C2#3182414611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
FittingC2×#117×C281C2
socle, cosocleC23×C281C24
prime radicalC22×C22⋊D281C22
hypercenterC2×#117D281
hypocenterC281#2359
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #31823358C2semidirect
4. #31823354C2semidirect
5. #31823353C2semidirect
6. #31823347C2semidirect
7. #31823344C2semidirect
9. #31823335C2semidirect
10. #31823334C2semidirect
11. C4×#17985117C2semidirect
12. C22⋊C4×Dic281C2semidirect
13. C4×#17985115C2semidirect
14. C2×#22582786C2semidirect
15. C2×#117×C281C2semidirect
20. #22582862C4semidirect
77. #17985117C2×C4semidirect
78. #17985117C2×C4semidirect
79. C22⋊Dic281C2×C4semidirect
83. #17985115C2×C4semidirect
84. #17985115C2×C4semidirect
91. C22×C4×C281C2×C4semidirect
206. C281#2359semidirect
210. C2×#117D281semidirect
284. C22×C4C4×D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828622
C2×#225828392
#318233582
#318233542
#318233532
#318233472
#318233442
#318233402
#318233352
#318233342
C4×#179851172
C22⋊C4×Dic2812
C4×#179851152
C2×#225827862
C2×#117×C2812
#2359281