Finite Group Databasebeta

← #49130812

Subgroups — #49130812

Order 36224.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583639C211yesmaximal, characteristic, complemented
2C2×#22583629C211yesmaximal, characteristic
3#31827035C211yesmaximal, characteristic, complemented
4#31826944C211yesmaximal, characteristic, complemented
5#31826686C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826678C211yesmaximal, characteristic, complemented
8#31826676C211yesmaximal, characteristic, complemented
9#31826674C211yesmaximal, characteristic, complemented
10#31826670C211yesmaximal, characteristic, complemented
11#31826668C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×Q8×D283C2211yescharacteristic
19#22583639—24no—
20#22583629—24no—
21C2×Dic1132C2211yescharacteristic
22C2×Dic1132C2211yescharacteristic
23C2×#17985382C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985380C2211yescharacteristic
26C2×#17985380C2211yescharacteristic
27C2×#17985375C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583610C2211yescharacteristic
30#22583608C2211yescharacteristic
31#22583597C2211yescharacteristic
32#22583592—21no—
33#22583592—21no—
34#22583587—21no—
35#22583587—21no—
36C4×Dic566C2211yescharacteristic
37#22583575C2211yescharacteristic
38D4×Dic283C2211yescharacteristic
39C4×C22⋊D283—21no—
40(C22⋊D283)⋊C4—21no—
41#22583567C2211yescharacteristic
42#22583566—21no—
43C2×Dic283⋊C4—21no—
44C4⋊C4×D283C2211yescharacteristic
45C4⋊(C283⋊C8)C2211yescharacteristic
46Dic283⋊C8C2211yescharacteristic
47Dic283⋊C8C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583535C2211yescharacteristic
50#22583534C2211yescharacteristic
51#22583533C2211yescharacteristic
52#22583533C2211yescharacteristic
53#22583531C2211yescharacteristic
54C2×SD16×C283C2211yescharacteristic
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic
57C4×D4×C283C2211yescharacteristic
58C4⋊C8×C283C2211yescharacteristic
59#103×C283C2211yescharacteristic
60#102×C283C2211yescharacteristic
61#17985391—22no—
62#17985391—22no—
63#17985391—22no—
64#17985391D414yes—
65C2×Dic566—21no—
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×Dic566C2311yescharacteristic
69Q8×D283—22no—
70Q8×D283—22no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C22×Dic283—21no—
74C22×Dic283—21no—
75C22×Dic283—21no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283C2311yescharacteristic
79Dic1132—22no—
80Dic1132—22no—
81#17985382—22no—
82#17985380—22no—
83#17985380—22no—
84#17985380—22no—
85#17985375—22no—
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C8×D283—22no—
89C4⋊Dic283—21no—
90C4⋊Dic283—21no—
91C4⋊Dic283C2311yescharacteristic
92Dic283⋊C4—21no—
93Dic283⋊C4—21no—
94Dic283⋊C4—21no—
95Dic283⋊C4—21no—
96Dic283⋊C4—21no—
97Dic283⋊C4D411yescharacteristic
98Dic283⋊C4D411yescharacteristic
99C22⋊Dic283—21no—
100C22⋊Dic283—21no—
101C22⋊Dic283—21no—
102(C2×D283)⋊C4D411yescharacteristic
103(C2×D283)⋊C4D411yescharacteristic
104C4×Dic283—21no—
105C4×Dic283—21no—
106C4×Dic283C2311yescharacteristic
107C2×Q8×C283C2311yescharacteristic
108C2×D4×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283—21no—
111SD16×C283—22no—
112D8×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C4⋊C4×C283C2311yescharacteristic
116C22⋊C4×C283—21no—
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C42×C283C2311yescharacteristic
120C22×D283C2×D411yescharacteristic
121Dic566—21no—
122Dic566—21no—
123Dic566—21no—
124Dic566—21no—
125Dic566—21no—
126Dic566—42no—
127Dic566C2×D412yes—
128C22⋊D283—24no—
129C22⋊D283—42no—
130C2×Dic283—21no—
131C2×Dic283—24no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—42no—
136C2×Dic283—81no—
137C2×Dic283C2×D411yescharacteristic
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C4×D283—42no—
141C4×D283—81no—
142C4×D283C2×D412yes—
143C4×D283#4112yes—
144C283⋊C8—21no—
145C283⋊C8—21no—
146C23×C283—21no—
147C23×C283—21no—
148Q8×C283—21no—
149Q8×C283—21no—
150D4×C283—21no—
151D4×C283—21no—
152D4×C283—21no—
153D4×C283C2×D412yes—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—81no—
157C2×C4×C283C2×D411yescharacteristic
158C2×C4×C283C2×D411yescharacteristic
159C2×C4×C283C2411yescharacteristic
160C8×C283—21no—
161C8×C283—21no—
162C22×C283—22no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283—41no—
166C22×C283—41no—
167C22×C283—41no—
168C22×C283C22×D411yescharacteristic
169C2×D283—21no—
170C2×D283—21no—
171C2×D283#12112yes—
172C4×C283—21no—
173C4×C283—21no—
174C4×C283—41no—
175C4×C283—41no—
176C4×C283C22×D411yescharacteristic
177C4×C283C2×#4111yescharacteristic
178Dic283—22no—
179Dic283—21no—
180Dic283—21no—
181Dic283—41no—
182Dic283—41no—
183Dic283—41no—
184Dic283#12112yes—
185C2×C283—42no—
186C2×C283—81no—
187C2×C283C2×#12111yescharacteristic
188C2×C283#57711yescharacteristic
189C2×C283#57811yescharacteristic
190D283—22no—
191C283#304611yescharacteristic, complemented, Sylow
192#3046—2831nomaximal, Sylow
193C2×#137—2831no—
194C2×#135—2831no—
195#536—2831no—
196#520—2831no—
197#464—2831no—
198#464—2831no—
199#463—2831no—
200#463D28311yescharacteristic, complemented
201#462—2831no—
202#462—2831no—
203#461—2831no—
204#461—2831no—
205#424—2831no—
206#417—2831no—
207C2×#103—2831no—
208C2×#41—2831no—
209C2×#41—2831no—
210C22×Q8—2831no—
211#137—5664no—
212#135—5664no—
213C2×Q16—2831no—
214C2×Q16—2831no—
215C2×Q16—2831no—
216C2×SD16—2831no—
217C2×SD16—2831no—
218C2×SD16—2831no—
219C2×SD16C2×D28311yescharacteristic
220C2×D8C2×D28311yescharacteristic
221C2×M16—2831no—
222C22×C8—2831no—
223C4⋊Q8—2831no—
224C4⋊Q8—2831no—
225#124—2831no—
226#124C2×D28311yescharacteristic
227#123—5661no—
228#123—5661no—
229C22⋊Q8—5661no—
230C22⋊Q8—5661no—
231C4×Q8—2831no—
232C4×Q8—2831no—
233C4×D4—2831no—
234C4×D4—5661no—
235C4×D4—5661no—
236C4×D4C2×D28311yescharacteristic
237#117—2831no—
238#117—5661no—
239C2×C4⋊C4—2831no—
240C2×C4⋊C4—5661no—
241C4⋊C8—2831no—
242C4⋊C8—2831no—
243C4⋊C8—2831no—
244C4⋊C8C2×D28311yescharacteristic
245#103—2831no—
246#103—2831no—
247#103—2831no—
248#103—2831no—
249#103—2831no—
250#103C2×D28311yescharacteristic
251#102—2831no—
252#102C2×D28311yescharacteristic
253#41—2834no—
254#41—5662no—
255#41—5662no—
256#41—5662no—
257C2×Q8—2831no—
258C2×Q8—2831no—
259C2×Q8—2831no—
260C2×Q8—5661no—
261C2×Q8—5662no—
262C2×Q8—5662no—
263C2×Q8C22×D28311yescharacteristic
264C2×D4—5661no—
265C2×D4—5661no—
266C2×D4C22×D28311yescharacteristic
267C2×D4C22×D28311yescharacteristic
268C22×C4—21no—
269C22×C4—2831no—
270C22×C4—5661no—
271C22×C4—5661no—
272C22×C4—5661no—
273C22×C4—5661no—
274C22×C4—5661no—
275Q16—5662no—
276Q16—5662no—
277Q16—5662no—
278SD16—22no—
279SD16—5662no—
280SD16—5662no—
281SD16—5662no—
282D8—22no—
283M16—5662no—
284C2×C8—2831no—
285C2×C8—2831no—
286C2×C8—5662no—
287C2×C8C22×D28311yescharacteristic
288C2×C8C22×D28311yescharacteristic
289C4⋊C4—2831no—
290C4⋊C4—2831no—
291C4⋊C4—2831no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4—5661no—
296C4⋊C4—5661no—
297C4⋊C4—5661no—
298C4⋊C4—5661no—
299C4⋊C4C22×D28311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—2831no—
304C22⋊C4—2831no—
305C22⋊C4—5661no—
306C22⋊C4—5661no—
307C22⋊C4—5661no—
308C42—2831no—
309C42—5661no—
310C42—5661no—
311C42C22×D28311yescharacteristic
312C23—21no—
313C23—21no—
314C23—2831no—
315Q8—21no—
316Q8—21no—
317Q8—2832no—
318Q8—5661no—
319Q8—5661no—
320Q8—5661no—
321Q8—5661no—
322Q8—5661no—
323Q8—11322no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—5664no—
328D4—11322no—
329D4D4×D28312yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—2831no—
334C2×C4—2832no—
335C2×C4—2832no—
336C2×C4—2831no—
337C2×C4—2831no—
338C2×C4—5664no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—11322no—
344C2×C4—11322no—
345C2×C4—22641no—
346C2×C4—22641no—
347C2×C4D4×D28311yescharacteristic
348C2×C4D4×D28311yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—21no—
351C8—21no—
352C8—5661no—
353C8—5661no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2832no—
361C22—5661no—
362C22—5661no—
363C22C2×D4×D28311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—2832no—
369C4—5662no—
370C4—5661no—
371C4—5661no—
372C4—11321no—
373C4—11321no—
374C4—11321no—
375C4C2×D4×D28311yescharacteristic
376C4#41×D28311yescharacteristic
377C2—42no—
378C2—81no—
379C2—5662no—
380C2#121×D28311yescharacteristic
381C2#3182727511yescharacteristic
382C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583629C2
hypercenter#463D283
hypocenterC283#3046
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22583639C2semidirect
3. #31827035C2semidirect
4. #31826944C2semidirect
5. #31826686C2semidirect
6. #31826684C2semidirect
7. #31826678C2semidirect
8. #31826676C2semidirect
9. #31826674C2semidirect
10. #31826670C2semidirect
11. #31826668C2semidirect
12. #31826490C2semidirect
13. #31826463C2semidirect
14. #103×D283C2semidirect
15. #463×C283C2semidirect
191. C283#3046semidirect
200. #463D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
C2×#225836292
#318270352
#318269442
#318266862
#318266842
#318266782
#318266762
#318266742
#318266702
#318266682
#318264902
#318264632
#103×D2832
#463×C2832
#3046283