Finite Group Databasebeta

← #49133135

Subgroups — #49133135

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic
2#31827128C211yesmaximal, characteristic
3#31826814C211yesmaximal, characteristic, complemented
4#31826802C211yesmaximal, characteristic, complemented
5#31826759C211yesmaximal, characteristic, complemented
6#31826707C211yesmaximal, characteristic, complemented
7#31826704C211yesmaximal, characteristic, complemented
8#31826674C211yesmaximal, characteristic, complemented
9#31826623C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826559C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic
13C2×#22583533C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#484×C283C211yesmaximal, characteristic, complemented
16C22×Dic566C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583609—21no—
24#22583609C2211yescharacteristic
25#22583608C2211yescharacteristic
26#22583600—21no—
27#22583590C2211yescharacteristic
28#22583590C2211yescharacteristic
29#22583589—21no—
30#22583589C2211yescharacteristic
31#22583588—21no—
32#22583588—21no—
33#22583587—21no—
34#22583575C2211yescharacteristic
35#22583575C2211yescharacteristic
36C4×C22⋊D283—21no—
37C4×C22⋊D283C2211yescharacteristic
38(C22⋊D283)⋊C4—21no—
39C4⋊C4×D283C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583533C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C22⋊Q8×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566—22no—
62C2×Dic566—21no—
63C2×Dic566—41no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×Dic566C2311yescharacteristic
67Q8×D283—22no—
68Q8×D283—41no—
69C2×C22⋊D283D411yescharacteristic
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74Dic1132—22no—
75Dic1132—41no—
76#17985382—41no—
77C2×C283⋊C8—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4D411yescharacteristic
92C22⋊Dic283—21no—
93C22⋊Dic283D411yescharacteristic
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C22×C4×C283—21no—
102C22×C4×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—42no—
118Dic566—42no—
119Dic566—81no—
120Dic566#4112yes—
121C22⋊D283Q1614yescomplemented
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—42no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—81no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283C2×D411yescharacteristic
137Q8×C283—21no—
138Q8×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—81no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2411yescharacteristic
148C8×C283—21no—
149C8×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283C2×Q1612yes—
153C22×C283C22×D411yescharacteristic
154C2×D283—21no—
155C2×D283—21no—
156C2×D283C2×Q1612yes—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283C2×#4111yescharacteristic
163C4×C283H(5,𝔽2)11yescharacteristic
164Dic283—21no—
165Dic283—22no—
166Dic283—21no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283C2×Q1612yes—
171C2×C283—22no—
172C2×C283#54611yescharacteristic
173C2×C283C22×Q1611yescharacteristic
174C2×C283#57711yescharacteristic
175D283—22no—
176C283#329911yescharacteristic, complemented, Sylow
177#3299—2831nomaximal, Sylow
178#554—2831no—
179D4×Q8—2831no—
180#487—2831no—
181#484—2831no—
182#484D28311yescharacteristic, complemented
183#477—2831no—
184#467—2831no—
185#467—2831no—
186#462—2831no—
187#451—2831no—
188#451—2831no—
189C4×Q16—2831no—
190C8×D4—2831no—
191C2×#103—2831no—
192C2×#103—2831no—
193C22×Q8—2831no—
194C22×Q8—2831no—
195C2×Q16—2831no—
196C2×Q16—2831no—
197C2×Q16—2831no—
198C22×C8—2831no—
199C22×C8—2831no—
200C4⋊Q8—2831no—
201C4⋊Q8—2831no—
202C4⋊Q8—5661no—
203#125—5661no—
204C22⋊Q8—2831no—
205C22⋊Q8—2831no—
206C22⋊Q8—2831no—
207C22⋊Q8—5661no—
208C22⋊Q8—5661no—
209C22⋊Q8—5661no—
210C22⋊Q8—5661no—
211C22⋊Q8C2×D28311yescharacteristic
212C4×Q8—2831no—
213C4×Q8—2831no—
214C4×D4—2831no—
215C4×D4—5661no—
216C4×D4—5661no—
217C2×C4⋊C4—2831no—
218C2×C4⋊C4C2×D28311yescharacteristic
219#107—2831no—
220#107C2×D28311yescharacteristic
221#107C2×D28311yescharacteristic
222C4⋊C8—2831no—
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103C2×D28311yescharacteristic
232#103C2×D28311yescharacteristic
233C22⋊C8—2831no—
234C22⋊C8C2×D28311yescharacteristic
235C4×C8—2831no—
236C2×Q8—2831no—
237C2×Q8—2831no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×Q8—5661no—
241C2×Q8—5662no—
242C2×Q8—5661no—
243C2×Q8—5662no—
244C2×Q8—11321no—
245C2×Q8—11321no—
246C2×Q8C22×D28311yescharacteristic
247C2×D4—2831no—
248C22×C4—21no—
249C22×C4—2831no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4C22×D28311yescharacteristic
254Q16—5662no—
255Q16—11321no—
256Q16—11321no—
257C2×C8—2831no—
258C2×C8—2831no—
259C2×C8—11321no—
260C2×C8—11321no—
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4C22×D28311yescharacteristic
277C4⋊C4C22×D28311yescharacteristic
278C4⋊C4C22×D28311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—2831no—
281C22⋊C4—2831no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C42—2831no—
286C42—5661no—
287C42—5661no—
288C23—2831no—
289C23D4×D28311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2832no—
293Q8—5661no—
294Q8—5661no—
295Q8—5661no—
296Q8—5661no—
297Q8—5661no—
298Q8—11322no—
299Q8—11322no—
300Q8—22641no—
301D4—2834no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—2831no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—11322no—
319C2×C4—11322no—
320C2×C4—22641no—
321C2×C4D4×D28311yescharacteristic
322C2×C4C23×D28311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5661no—
326C8—5661no—
327C22—21no—
328C22—21no—
329C22—2832no—
330C22—5661no—
331C22—5661no—
332C22Q16×D28312yes—
333C22C2×D4×D28311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—2832no—
340C4—5661no—
341C4—5661no—
342C4—5662no—
343C4—11321no—
344C4—11321no—
345C4—11321no—
346C4#41×D28311yescharacteristic
347C4#2258365611yescharacteristic
348C2—22no—
349C2—5662no—
350C2#3182710711yescharacteristic
351C2C2×Q16×D28311yescharacteristic
352C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#484×C283C2
socleC22×C283C22×D4
prime radicalC2×C22⋊D283D4
hypercenter#484D283
hypocenterC283#3299
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #31826814C2semidirect
4. #31826802C2semidirect
5. #31826759C2semidirect
6. #31826707C2semidirect
7. #31826704C2semidirect
8. #31826674C2semidirect
9. #31826623C2semidirect
10. #31826622C2semidirect
11. #31826559C2semidirect
13. C2×#22583533C2semidirect
14. #103×D283C2semidirect
15. #484×C283C2semidirect
121. C22⋊D283Q16semidirect
176. C283#3299semidirect
182. #484D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318271282
#318268142
#318268022
#318267592
#318267072
#318267042
#318266742
#318266232
#318266222
#318265592
(C22⋊D283)⋊C82
C2×#225835332
#103×D2832
#484×C2832
#3299283