Finite Group Databasebeta

← #49130712

Subgroups — #49130712

Order 36224.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583630C211yesmaximal, characteristic, complemented
2#31827011C211yesmaximal, characteristic, complemented
3#41×Dic283C211yesmaximal, characteristic, complemented
4#31826689C211yesmaximal, characteristic, complemented
5#31826685C211yesmaximal, characteristic, complemented
6#31826682C211yesmaximal, characteristic, complemented
7#31826678C211yesmaximal, characteristic, complemented
8#31826673C211yesmaximal, characteristic, complemented
9#31826668C211yesmaximal, characteristic, complemented
10#31826663C211yesmaximal, characteristic, complemented
11#31826658C211yesmaximal, characteristic, complemented
12C2×Dic283⋊C8C211yesmaximal, characteristic, complemented
13#31826462C211yesmaximal, characteristic, complemented
14#31826461C211yesmaximal, characteristic, complemented
15C2×#135×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17#22583630—24no—
18C2×#17985382C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21C2×#17985377C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583608C2211yescharacteristic
24#22583606C2211yescharacteristic
25#22583599C2211yescharacteristic
26#22583597C2211yescharacteristic
27#22583582—21no—
28#22583582—21no—
29Q8×Dic283C2211yescharacteristic
30Q8×Dic283C2211yescharacteristic
31D4×Dic283—21no—
32D4×Dic283—21no—
33D4×Dic283C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35C4×C22⋊D283—21no—
36C4×C22⋊D283—21no—
37#22583569—21no—
38#22583569C2211yescharacteristic
39C2×C4×Dic283—21no—
40C2×C4×Dic283C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583534C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583531C2211yescharacteristic
52#22583531C2211yescharacteristic
53C2×#41×C283C2211yescharacteristic
54C2×#41×C283C2211yescharacteristic
55#135×C283—24no—
56C2×Q16×C283C2211yescharacteristic
57C2×SD16×C283C2211yescharacteristic
58C2×SD16×C283C2211yescharacteristic
59C2×D8×C283C2211yescharacteristic
60C22×C8×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—22no—
63C2×Dic566C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C22×Dic283D411yescharacteristic
71C22×Dic283D411yescharacteristic
72C2×C4×D283—21no—
73#17985382—22no—
74#17985380—22no—
75#17985379—22no—
76#17985377—22no—
77C2×C283⋊C8—22no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C4⋊Dic283—21no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283D411yescharacteristic
97C4×Dic283D411yescharacteristic
98C4×Dic283C2311yescharacteristic
99C4×Dic283C2311yescharacteristic
100#41×C283—22no—
101#41×C283—22no—
102#41×C283—22no—
103#41×C283D414yescomplemented
104C2×Q8×C283C2311yescharacteristic
105C2×Q8×C283C2311yescharacteristic
106C2×D4×C283—21no—
107C2×D4×C283—21no—
108C2×D4×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283—21no—
111C22×C4×C283—21no—
112C22×C4×C283C2311yescharacteristic
113Q16×C283—22no—
114SD16×C283—22no—
115SD16×C283—22no—
116D8×C283—22no—
117C2×C8×C283—22no—
118C2×C8×C283C2311yescharacteristic
119C2×C8×C283C2311yescharacteristic
120C22×D283—21no—
121Dic566—21no—
122Dic566—21no—
123D1132—21no—
124D1132—21no—
125C22⋊D283—42no—
126C22⋊D283—42no—
127C22⋊D283—42no—
128C2×Dic283—22no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—41no—
133C2×Dic283—42no—
134C2×Dic283—42no—
135C2×Dic283C2×D411yescharacteristic
136C2×Dic283C2×D411yescharacteristic
137C2×Dic283C2×D411yescharacteristic
138C2×Dic283C2×D411yescharacteristic
139C4×D283—42no—
140C283⋊C8—21no—
141C283⋊C8—21no—
142C23×C283—21no—
143C23×C283—21no—
144C23×C283C2×D411yescharacteristic
145Q8×C283—21no—
146Q8×C283—21no—
147Q8×C283—21no—
148Q8×C283C2×D412yes—
149D4×C283—24no—
150D4×C283—21no—
151D4×C283—21no—
152D4×C283—21no—
153D4×C283—42no—
154D4×C283C2×D412yes—
155C2×C4×C283—21no—
156C2×C4×C283—24no—
157C2×C4×C283—21no—
158C2×C4×C283—42no—
159C2×C4×C283C2×D411yescharacteristic
160C2×C4×C283C2×D412yes—
161C2×C4×C283#4112yes—
162C2×C4×C283C2411yescharacteristic
163C8×C283—21no—
164C8×C283—21no—
165C22×C283—21no—
166C22×C283—21no—
167C22×C283—22no—
168C22×C283—41no—
169C22×C283—41no—
170C22×C283—41no—
171C22×C283—41no—
172C22×C283—41no—
173C22×C283#12112yes—
174C22×C283C22×D411yescharacteristic
175C2×D283—41no—
176C2×D283—41no—
177C2×D283—41no—
178C4×C283—22no—
179C4×C283—41no—
180C4×C283#12112yes—
181C4×C283C22×D411yescharacteristic
182C4×C283C2×#4111yescharacteristic
183Dic283—21no—
184Dic283—21no—
185Dic283—21no—
186Dic283—41no—
187Dic283—41no—
188Dic283—41no—
189Dic283#13512yescomplemented
190C2×C283—22no—
191C2×C283—42no—
192C2×C283—81no—
193C2×C283C2×#12111yescharacteristic
194C2×C283C2×#13511yescharacteristic
195C2×C283#57511yescharacteristic
196D283—81no—
197C283#303511yescharacteristic, complemented, Sylow
198#3035—2831nomaximal, Sylow
199C2×#135—2831no—
200C2×#135D28311yescharacteristic, complemented
201#532—2831no—
202C4×#41—2831no—
203#464—2831no—
204#464—2831no—
205#463—2831no—
206#463—2831no—
207#462—2831no—
208#461—2831no—
209#460—2831no—
210#459—2831no—
211C2×C4⋊C8—2831no—
212#416—2831no—
213#416—2831no—
214C2×#41—2831no—
215C2×#41C2×D28311yescharacteristic
216C2×#41C2×D28311yescharacteristic
217#135—24no—
218#135—5664no—
219C2×Q16—2831no—
220C2×Q16C2×D28311yescharacteristic
221C2×SD16—2831no—
222C2×SD16—2831no—
223C2×SD16C2×D28311yescharacteristic
224C2×SD16C2×D28311yescharacteristic
225C2×D8—2831no—
226C2×D8C2×D28311yescharacteristic
227C22×C8—2831no—
228C22×C8C2×D28311yescharacteristic
229C4⋊Q8—2831no—
230#127—2831no—
231#124—2831no—
232#124—2831no—
233#121—5661no—
234#121—5661no—
235C4×Q8—2831no—
236C4×Q8—2831no—
237C4×D4—2831no—
238C4×D4—2831no—
239C4×D4—5661no—
240C4×D4—5661no—
241C4×D4—5661no—
242C4×D4—5661no—
243#117—2831no—
244#117—5661no—
245C2×C42—2831no—
246C2×C42—5661no—
247C4⋊C8—2831no—
248C4⋊C8—2831no—
249C4⋊C8—2831no—
250C4⋊C8—2831no—
251#103—2831no—
252#103—2831no—
253#103—2831no—
254#103—2831no—
255#102—2831no—
256#102—2831no—
257#102—2831no—
258#102—2831no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—5662no—
263#41—5662no—
264#41C22⋊D28314yescomplemented
265C2×Q8—2831no—
266C2×Q8C22×D28311yescharacteristic
267C2×Q8C22×D28311yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—2831no—
271C2×D4—5661no—
272C2×D4—5661no—
273C2×D4—5661no—
274C2×D4C22×D28311yescharacteristic
275C2×D4C22×D28311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—5661no—
281C22×C4—5661no—
282C22×C4—5661no—
283C22×C4C22×D28311yescharacteristic
284Q16—22no—
285Q16—5662no—
286SD16—22no—
287SD16—22no—
288SD16—5662no—
289SD16—5662no—
290D8—22no—
291D8—5662no—
292C2×C8—22no—
293C2×C8—2831no—
294C2×C8—2831no—
295C2×C8—5662no—
296C2×C8C22×D28311yescharacteristic
297C2×C8C22×D28311yescharacteristic
298C4⋊C4—2831no—
299C4⋊C4—2831no—
300C4⋊C4—5661no—
301C4⋊C4—5661no—
302C4⋊C4—5661no—
303C4⋊C4—5661no—
304C22⋊C4—5661no—
305C22⋊C4—5661no—
306C22⋊C4—5661no—
307C22⋊C4—5661no—
308C22⋊C4—5661no—
309C22⋊C4—5661no—
310C22⋊C4—5661no—
311C42—2831no—
312C42—2831no—
313C42—2831no—
314C42—2831no—
315C42—5661no—
316C42—5661no—
317C42—5661no—
318C23—21no—
319C23—21no—
320C23—5661no—
321C23D4×D28311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—5661no—
326Q8—5661no—
327Q8C2×C22⋊D28312yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—5661no—
334D4—5661no—
335D4—11322no—
336D4—11322no—
337D4—11322no—
338D4C2×C22⋊D28312yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2831no—
344C2×C4—2831no—
345C2×C4—2831no—
346C2×C4—2831no—
347C2×C4—5662no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—5661no—
351C2×C4—11322no—
352C2×C4—11321no—
353C2×C4—11322no—
354C2×C4—11322no—
355C2×C4D4×D28311yescharacteristic
356C2×C4C2×C22⋊D28312yes—
357C2×C4#1798539112yes—
358C2×C4C23×D28311yescharacteristic
359C8—21no—
360C8—21no—
361C8—5661no—
362C8—5661no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—11321no—
372C22—11321no—
373C22—11321no—
374C22#2258358212yes—
375C22C2×D4×D28311yescharacteristic
376C4—22no—
377C4—41no—
378C4—2832no—
379C4—5661no—
380C4—5661no—
381C4—5661no—
382C4—11321no—
383C4—11321no—
384C4—11321no—
385C4#2258358212yes—
386C4C22×C22⋊D28311yescharacteristic
387C4C2×#1798539111yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—22641no—
392C2C2×#2258358211yescharacteristic
393C2#135×D28311yescharacteristic
394C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3035
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22583630C2semidirect
2. #31827011C2semidirect
3. #41×Dic283C2semidirect
4. #31826689C2semidirect
5. #31826685C2semidirect
6. #31826682C2semidirect
7. #31826678C2semidirect
8. #31826673C2semidirect
9. #31826668C2semidirect
10. #31826663C2semidirect
11. #31826658C2semidirect
12. C2×Dic283⋊C8C2semidirect
13. #31826462C2semidirect
14. #31826461C2semidirect
15. C2×#135×C283C2semidirect
103. #41×C283D4semidirect
189. Dic283#135semidirect
197. C283#3035semidirect
200. C2×#135D283semidirect
264. #41C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836302
#318270112
#41×Dic2832
#318266892
#318266852
#318266822
#318266782
#318266732
#318266682
#318266632
#318266582
C2×Dic283⋊C82
#318264622
#318264612
C2×#135×C2832
#3035283