Finite Group Databasebeta

← #49133309

Subgroups — #49133309

Order 36224.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827153C211yesmaximal, characteristic
2Q8×D1132C211yesmaximal, characteristic
3#31826835C211yesmaximal, characteristic, complemented
4#31826808C211yesmaximal, characteristic, complemented
5#31826797C211yesmaximal, characteristic, complemented
6#31826724C211yesmaximal, characteristic, complemented
7#31826707C211yesmaximal, characteristic, complemented
8#31826676C211yesmaximal, characteristic, complemented
9#31826622C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826570C211yesmaximal, characteristic, complemented
12#31826535C211yesmaximal, characteristic
13#31826472C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#479×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583610—21no—
24#22583610C2211yescharacteristic
25#22583605—21no—
26#22583601—21no—
27#22583595—21no—
28#22583590—21no—
29#22583590—21no—
30#22583590C2211yescharacteristic
31#22583590C2211yescharacteristic
32#22583590C2211yescharacteristic
33#22583590C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35C4×D1132—21no—
36C4×D1132C2211yescharacteristic
37#22583568—21no—
38#22583568C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583535C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—22no—
66Q8×D283—41no—
67Q8×D283—41no—
68C2×D1132D411yescharacteristic
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73C2×C4×D283C2311yescharacteristic
74Dic1132—41no—
75Dic1132—41no—
76#17985382—22no—
77#17985375—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283—21no—
84C4⋊Dic283—21no—
85C4⋊Dic283—21no—
86C4⋊Dic283—21no—
87C4⋊Dic283D411yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C4×Dic283—21no—
100C2×Q8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—21no—
119Dic566—42no—
120Dic566—42no—
121D1132—22no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—42no—
134C4×D283—42no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137Q8×C283—21no—
138Q8×C283#4112yes—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283C22×D411yescharacteristic
149C2×D283—21no—
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—21no—
153C2×D283—21no—
154C2×D283#13712yes—
155C4×C283—22no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283H(5,𝔽2)11yescharacteristic
163Dic283—21no—
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169C2×C283#54611yescharacteristic
170C2×C283C2×#13711yescharacteristic
171C2×C283#57811yescharacteristic
172D283—22no—
173D283—41no—
174C283#331211yescharacteristic, complemented, Sylow
175#3312—2831nomaximal, Sylow
176#552—2831no—
177D4×Q8—2831no—
178#491—2831no—
179#485—2831no—
180#483—2831no—
181#479D28311yescharacteristic, complemented
182#470—2831no—
183#467—2831no—
184#462—2831no—
185#451—2831no—
186#451—2831no—
187#441—2831no—
188#435—2831no—
189#419—2831no—
190C2×#103—2831no—
191C22×Q8—2831no—
192C22×Q8—2831no—
193C2×Q16—2831no—
194C2×Q16—2831no—
195C2×Q16—2831no—
196C2×M16—2831no—
197C22×C8—2831no—
198C4⋊Q8—2831no—
199C4⋊Q8—5661no—
200#126—5661no—
201#125—5661no—
202#125C2×D28311yescharacteristic
203#123—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—2831no—
208C22⋊Q8—5661no—
209C22⋊Q8—5661no—
210C4×Q8—2831no—
211C4×Q8C2×D28311yescharacteristic
212C4×D4—2831no—
213C4×D4—5661no—
214#117—2831no—
215#117—5661no—
216C2×C4⋊C4—2831no—
217#107C2×D28311yescharacteristic
218#106—2831no—
219#106C2×D28311yescharacteristic
220C4⋊C8C2×D28311yescharacteristic
221#103—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103C2×D28311yescharacteristic
230#103C2×D28311yescharacteristic
231C22⋊C8—2831no—
232C22⋊C8—2831no—
233#97—2831no—
234C2×Q8—2831no—
235C2×Q8—2831no—
236C2×Q8—2831no—
237C2×Q8—5661no—
238C2×Q8—5661no—
239C2×Q8—5662no—
240C2×Q8—5662no—
241C2×Q8—11321no—
242C2×Q8—11321no—
243C2×Q8C22×D28311yescharacteristic
244C2×D4—2831no—
245C22×C4—2831no—
246C22×C4—2831no—
247C22×C4—5661no—
248C22×C4—5661no—
249C22×C4—5661no—
250Q16—5662no—
251Q16—11321no—
252Q16—11321no—
253M16—11321no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—11321no—
257C2×C8C22×D28311yescharacteristic
258C2×C8C22×D28311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—2831no—
276C22⋊C4—2831no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C42—21no—
283C42—5661no—
284C42—5661no—
285C42C22×D28311yescharacteristic
286C23—2831no—
287C23—2831no—
288Q8—21no—
289Q8—5661no—
290Q8—5661no—
291Q8—5661no—
292Q8—5661no—
293Q8—5661no—
294Q8—5661no—
295Q8—11322no—
296Q8—11322no—
297Q8#1798539312yes—
298D4—5662no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—11322no—
314C2×C4—11322no—
315C2×C4—11322no—
316C2×C4D4×D28311yescharacteristic
317C2×C4D4×D28311yescharacteristic
318C2×C4C23×D28311yescharacteristic
319C8—21no—
320C8—21no—
321C8—5661no—
322C8—5661no—
323C22—2832no—
324C22—5661no—
325C22—5661no—
326C22—5661no—
327C22—5661no—
328C22—5661no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5661no—
337C4—5661no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4—11321no—
342C4C2×#1798539311yescharacteristic
343C4#2258365611yescharacteristic
344C2—5662no—
345C2—11321no—
346C2#3182710611yescharacteristic
347C2#137×D28311yescharacteristic
348C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#479×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132D4
hypercenter#479D283
hypocenterC283#3312
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #31826835C2semidirect
4. #31826808C2semidirect
5. #31826797C2semidirect
6. #31826724C2semidirect
7. #31826707C2semidirect
8. #31826676C2semidirect
9. #31826622C2semidirect
10. #31826622C2semidirect
11. #31826570C2semidirect
13. #31826472C2semidirect
14. #103×D283C2semidirect
15. #479×C283C2semidirect
174. C283#3312semidirect
181. #479D283semidirect

Maximal subgroups

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

subgroupindex
#318271532
Q8×D11322
#318268352
#318268082
#318267972
#318267242
#318267072
#318266762
#318266222
#318265702
#318265352
#318264722
#103×D2832
#479×C2832
#3312283