Finite Group Databasebeta

← #49123701

Subgroups — #49123701

Order 36224.

696 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×D4×Dic283C211yesmaximal, characteristic
2C2×#22583566C211yesmaximal, characteristic, complemented
3C22×C4×Dic283C211yesmaximal, characteristic, complemented
4#31826359C211yesmaximal, characteristic, complemented
5#31826353C211yesmaximal, characteristic, complemented
6#31826350C211yesmaximal, characteristic, complemented
7#31826348C211yesmaximal, characteristic, complemented
8#31826345C211yesmaximal, characteristic
9#31826338C211yesmaximal, characteristic, complemented
10#31826337C211yesmaximal, characteristic, complemented
11#31826316C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
14#31826310C211yesmaximal, characteristic, complemented
15#386×C283C211yesmaximal, characteristic
16C23×Dic283C2211yescharacteristic
17C23×Dic283C2211yescharacteristic
18C23×Dic283C2211yescharacteristic
19D4×Dic283C418yescomplemented
20#22583566—24no—
21C2×C4⋊Dic283C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×C22⋊Dic283C2211yescharacteristic
27C2×C22⋊Dic283C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic
29C2×C22⋊Dic283C2211yescharacteristic
30C2×C22⋊Dic283C2211yescharacteristic
31C2×C4×Dic283—24no—
32C2×C4×Dic283C2211yescharacteristic
33C2×C4×Dic283C2211yescharacteristic
34C2×C4×Dic283C2211yescharacteristic
35C2×C4×Dic283C2211yescharacteristic
36C2×C4×Dic283C2211yescharacteristic
37C2×C4×Dic283C2211yescharacteristic
38C2×C4×Dic283C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C22×D4×C283C2211yescharacteristic
48C23×C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C22⋊C4×C283C2211yescharacteristic
52#95×C283C2211yescharacteristic
53#95×C283C2211yescharacteristic
54C22×Dic283—22no—
55C22×Dic283—22no—
56C22×Dic283—22no—
57C22×Dic283—22no—
58C22×Dic283—22no—
59C22×Dic283—22no—
60C22×Dic283—22no—
61C22×Dic283C2×C414yes—
62C22×Dic283C2×C414yescomplemented
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C4⋊Dic283C2×C414yescomplemented
72Dic283⋊C4—22no—
73Dic283⋊C4—22no—
74Dic283⋊C4—22no—
75Dic283⋊C4—22no—
76C22⋊Dic283—22no—
77C22⋊Dic283—22no—
78C22⋊Dic283—22no—
79C22⋊Dic283C2×C414yes—
80C22⋊Dic283C2×C414yescomplemented
81C4×Dic283—22no—
82C4×Dic283—22no—
83C4×Dic283—22no—
84C4×Dic283—22no—
85C4×Dic283—22no—
86C4×Dic283C2×C414yescomplemented
87C4×Dic283D414yescomplemented
88C24×C283C2311yescharacteristic
89C24×C283C2311yescharacteristic
90C2×D4×C283—22no—
91C2×D4×C283—22no—
92C2×D4×C283C2×C414yes—
93C22×C4×C283—22no—
94C22×C4×C283—22no—
95C22×C4×C283—22no—
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101C22⋊C4×C283—22no—
102C22⋊C4×C283—22no—
103C22⋊C4×C283—22no—
104C2×Dic283—28no—
105C2×Dic283—21no—
106C2×Dic283—21no—
107C2×Dic283—21no—
108C2×Dic283—21no—
109C2×Dic283—21no—
110C2×Dic283—21no—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—28no—
116C2×Dic283—28no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283C22×C412yes—
124C2×Dic283C22×C412yes—
125C2×Dic283C22×C412yes—
126C2×Dic283C22×C412yes—
127C2×Dic283C2×D412yes—
128C2×Dic283C2×D412yes—
129C2×Dic283#4112yes—
130C2×Dic283#4112yes—
131C23×C283—21no—
132C23×C283—21no—
133C23×C283—21no—
134C23×C283—21no—
135C23×C283—21no—
136C23×C283—21no—
137C23×C283—21no—
138C23×C283—21no—
139C23×C283—21no—
140C23×C283—21no—
141C23×C283C22×C412yes—
142C23×C283C22×C412yes—
143C23×C283#4112yes—
144C23×C283#4112yes—
145C23×C283C2411yescharacteristic
146D4×C283—28no—
147C2×C4×C283—28no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283C22×C412yes—
161C2×C4×C283C2×D412yes—
162C2×C4×C283#4112yes—
163C22×C283—22no—
164C22×C283—22no—
165C22×C283—22no—
166C22×C283—22no—
167C22×C283—22no—
168C22×C283—22no—
169C22×C283—22no—
170C22×C283—22no—
171C22×C283—22no—
172C22×C283—41no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283#11714yescomplemented
177C22×C283C23×C411yescharacteristic
178C22×C283C22×D411yescharacteristic
179C22×C283C2×#4111yescharacteristic
180C22×C283C2×#4111yescharacteristic
181C22×C283C2×#4111yescharacteristic
182C22×C283C2×#4111yescharacteristic
183C22×C283C2×#4111yescharacteristic
184C4×C283—22no—
185C4×C283—22no—
186C4×C283—22no—
187C4×C283—41no—
188C4×C283—41no—
189Dic283—22no—
190Dic283—22no—
191Dic283—22no—
192Dic283—22no—
193Dic283—22no—
194Dic283—41no—
195Dic283—41no—
196Dic283C4×D414yes—
197C2×C283—24no—
198C2×C283—42no—
199C2×C283C2×#11711yescharacteristic
200C2×C283C2×C4×D411yescharacteristic
201C2×C283C4×#4111yescharacteristic
202C2×C283#52511yescharacteristic
203C2×C283#52511yescharacteristic
204C2×C283#52911yescharacteristic
205C2×C283#52911yescharacteristic
206C283#229011yescharacteristic, complemented, Sylow
207#2290—2831nomaximal, Sylow
208C2×C4×D4—2831no—
209C2×#117—2831no—
210C22×C42—2831no—
211#388—2831no—
212#388—2831no—
213#387—2831no—
214#387—2831no—
215#386—2831no—
216#386D28311yescharacteristic
217#385—2831no—
218#385—2831no—
219C4×C4⋊C4—2831no—
220C4×C22⋊C4—2831no—
221C4×C22⋊C4—2831no—
222#376—2831no—
223C22×D4C2×D28311yescharacteristic
224C23×C4—2831no—
225C23×C4—2831no—
226C23×C4—2831no—
227C23×C4C2×D28311yescharacteristic
228C4×D4—2838no—
229#117—5664no—
230C2×C4⋊C4—2831no—
231C2×C4⋊C4—2831no—
232C2×C4⋊C4—2831no—
233C2×C4⋊C4—2831no—
234C2×C4⋊C4—2831no—
235C2×C22⋊C4—2831no—
236C2×C22⋊C4—2831no—
237C2×C22⋊C4—2831no—
238C2×C22⋊C4—2831no—
239C2×C22⋊C4—2831no—
240C2×C22⋊C4C2×D28311yescharacteristic
241C2×C22⋊C4C2×D28311yescharacteristic
242C2×C22⋊C4C2×D28311yescharacteristic
243C2×C42—2831no—
244C2×C42—2831no—
245C2×C42—2831no—
246C2×C42—2831no—
247C2×C42—2831no—
248C2×C42—2831no—
249C2×C42—2831no—
250C2×C42—5664no—
251#95—2831no—
252#95—2831no—
253#95—2831no—
254#95—2831no—
255#95—2831no—
256#95—2831no—
257#95—2831no—
258#95—2831no—
259#95C2×D28311yescharacteristic
260#95C2×D28311yescharacteristic
261C24C22×D28311yescharacteristic
262C24C22×D28311yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C4×D28314yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—2831no—
270C22×C4—2834no—
271C22×C4—2834no—
272C22×C4—2831no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—2831no—
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—5662no—
280C22×C4—5662no—
281C22×C4—5662no—
282C22×C4—5662no—
283C22×C4—5662no—
284C22×C4—5662no—
285C22×C4—5662no—
286C22×C4C22×D28311yescharacteristic
287C22×C4C22×D28311yescharacteristic
288C22×C4C22×D28311yescharacteristic
289C22×C4C22×D28311yescharacteristic
290C22×C4C22×D28311yescharacteristic
291C4⋊C4—2834no—
292C4⋊C4—5662no—
293C4⋊C4—5662no—
294C4⋊C4—5662no—
295C4⋊C4—5662no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—2834no—
300C22⋊C4—2834no—
301C22⋊C4—5662no—
302C22⋊C4—5662no—
303C22⋊C4—5662no—
304C42—2834no—
305C42—2834no—
306C42—5662no—
307C42—5662no—
308C42—5662no—
309C42—5662no—
310C42—5662no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D28312yes—
322C23C2×C4×D28312yes—
323C23#1798539112yes—
324C23#1798539112yes—
325C23C23×D28311yescharacteristic
326D4—28no—
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—2832no—
341C2×C4—2832no—
342C2×C4—2832no—
343C2×C4—2832no—
344C2×C4—2832no—
345C2×C4—2832no—
346C2×C4—2832no—
347C2×C4—2832no—
348C2×C4—5668no—
349C2×C4—5668no—
350C2×C4—5668no—
351C2×C4—5661no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—5661no—
361C2×C4—5661no—
362C2×C4—5661no—
363C2×C4—5661no—
364C2×C4—5661no—
365C2×C4—5661no—
366C2×C4—5661no—
367C2×C4C2×C4×D28312yes—
368C2×C4D4×D28312yes—
369C2×C4#1798539112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#2258356614yescomplemented
384C22C22×C4×D28311yescharacteristic
385C22C2×D4×D28311yescharacteristic
386C22#41×D28311yescharacteristic
387C22#41×D28311yescharacteristic
388C22C2×#1798539111yescharacteristic
389C22C2×#1798539111yescharacteristic
390C22C2×#1798539111yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—2834no—
397C4—5662no—
398C4—5662no—
399C4—5662no—
400C4—5662no—
401C4—5662no—
402C4—11321no—
403C4—11321no—
404C2—24no—
405C2—42no—
406C2C2×#2258356611yescharacteristic
407C2C4×D4×D28311yescharacteristic
408C2C4×#1798539111yescharacteristic
409C2#3182697111yescharacteristic
410C2#3182697511yescharacteristic
411C2#3182699211yescharacteristic
412C2#3182699611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#386×C283C2
socle, cosocleC23×C283C24
prime radicalC22×D4×C283C22
hypercenter#386D283
hypocenterC283#2290
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#22583566C2semidirect
3. C22×C4×Dic283C2semidirect
4. #31826359C2semidirect
5. #31826353C2semidirect
6. #31826350C2semidirect
7. #31826348C2semidirect
9. #31826338C2semidirect
10. #31826337C2semidirect
11. #31826316C2semidirect
12. C22⋊C4×Dic283C2semidirect
13. C22⋊C4×Dic283C2semidirect
14. #31826310C2semidirect
19. D4×Dic283C4semidirect
62. C22×Dic283C2×C4semidirect
71. C4⋊Dic283C2×C4semidirect
80. C22⋊Dic283C2×C4semidirect
86. C4×Dic283C2×C4semidirect
87. C4×Dic283D4semidirect
176. C22×C283#117semidirect
206. C283#2290semidirect
383. C22#22583566semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2832
C2×#225835662
C22×C4×Dic2832
#318263592
#318263532
#318263502
#318263482
#318263452
#318263382
#318263372
#318263162
C22⋊C4×Dic2832
#318263102
#386×C2832
#2290283