Finite Group Databasebeta

← #49132674

Subgroups — #49132674

Order 36224.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827086C211yesmaximal, characteristic, complemented
2#31827070C211yesmaximal, characteristic, complemented
3#31826773C211yesmaximal, characteristic, complemented
4#31826766C211yesmaximal, characteristic, complemented
5#31826756C211yesmaximal, characteristic, complemented
6#31826746C211yesmaximal, characteristic, complemented
7#31826718C211yesmaximal, characteristic, complemented
8#31826711C211yesmaximal, characteristic, complemented
9#31826701C211yesmaximal, characteristic, complemented
10#31826694C211yesmaximal, characteristic, complemented
11#31826681C211yesmaximal, characteristic, complemented
12#31826681C211yesmaximal, characteristic, complemented
13#31826666C211yesmaximal, characteristic, complemented
14#31826661C211yesmaximal, characteristic, complemented
15#424×C283C211yesmaximal, characteristic, complemented
16C2×#17985381C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19C2×D2264C2211yescharacteristic
20#22583610C2211yescharacteristic
21#22583607C2211yescharacteristic
22#22583605—21no—
23#22583602C2211yescharacteristic
24#22583598C2211yescharacteristic
25#22583596—21no—
26#22583595—21no—
27#22583595—21no—
28#22583592—21no—
29#22583589C2211yescharacteristic
30#22583588—21no—
31#22583584C2211yescharacteristic
32#22583584C2211yescharacteristic
33#22583584C2211yescharacteristic
34#22583583—21no—
35#22583583—21no—
36C4×Dic566C2211yescharacteristic
37C4×D1132C2211yescharacteristic
38C4×D1132C2211yescharacteristic
39C4×D1132C2211yescharacteristic
40#22583544C2211yescharacteristic
41#22583544C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583542C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54#117×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic
58C4⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72#17985381—41no—
73#17985381—41no—
74D2264—41no—
75D2264—41no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85C22⋊Dic283—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C22×C4×C283C2311yescharacteristic
96M16×C283—41no—
97C2×C8×C283—41no—
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283D411yescharacteristic
103C4⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C22⋊C4×C283D411yescharacteristic
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—81no—
114D1132—21no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—81no—
121D1132—81no—
122C22⋊D283—81no—
123C22⋊D283—81no—
124C22⋊D283—81no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C4×D283—81no—
131C4×D283—81no—
132C4×D283—81no—
133C23×C283C2×D411yescharacteristic
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2411yescharacteristic
142C8×C283—21no—
143C8×C283—21no—
144C8×C283—21no—
145C8×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283C22×D411yescharacteristic
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283H(5,𝔽2)11yescharacteristic
165C4×C2832−1+411yescharacteristic
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283—41no—
172C2×C283#53711yescharacteristic
173C2×C283#57611yescharacteristic
174C2×C283#57711yescharacteristic
175D283—81no—
176D283—81no—
177D283—81no—
178C283#325711yescharacteristic, complemented, Sylow
179#3257—2831nomaximal, Sylow
180#542—2831no—
181#540—2831no—
182#479—2831no—
183#478—2831no—
184#476—2831no—
185#474—2831no—
186#469—2831no—
187#468—2831no—
188#466—2831no—
189#465—2831no—
190#463—2831no—
191#463—2831no—
192#460—2831no—
193#459—2831no—
194#424D28311yescharacteristic, complemented
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×D8—2831no—
198C2×D8—2831no—
199C2×M16C2×D28311yescharacteristic
200C22×C8C2×D28311yescharacteristic
201C4⋊Q8—2831no—
202#127—2831no—
203#126—5661no—
204#125—2831no—
205#124—2831no—
206#124—5661no—
207#123—5661no—
208#123—5661no—
209#123—5661no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—2831no—
214#121—2831no—
215#121—5661no—
216#121—5661no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—2831no—
220C4×D4—2831no—
221#117C2×D28311yescharacteristic
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8C2×D28311yescharacteristic
227C4⋊C8C2×D28311yescharacteristic
228C4⋊C8C2×D28311yescharacteristic
229C4⋊C8C2×D28311yescharacteristic
230#103—2831no—
231#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237#102—2831no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×D4—2831no—
241C2×D4—2831no—
242C2×D4—2831no—
243C2×D4—5661no—
244C2×D4—5661no—
245C2×D4—5661no—
246C2×D4—5661no—
247C2×D4—5661no—
248C22×C4—5661no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4C22×D28311yescharacteristic
252SD16—11321no—
253SD16—11321no—
254D8—11321no—
255D8—11321no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D28311yescharacteristic
259C2×C8C22×D28311yescharacteristic
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4D113211yescharacteristic
272C4⋊C4D113211yescharacteristic
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4D113211yescharacteristic
283C22⋊C4D113211yescharacteristic
284C42—5661no—
285C42C22×D28311yescharacteristic
286C42C22×D28311yescharacteristic
287C23—5661no—
288C23—5661no—
289C23—5661no—
290C23C2×D113211yescharacteristic
291Q8—5661no—
292Q8—5661no—
293Q8—22641no—
294D4—5661no—
295D4—5661no—
296D4—5661no—
297D4—5661no—
298D4—5661no—
299D4—5661no—
300D4—22641no—
301D4—22641no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—22641no—
313C2×C4—22641no—
314C2×C4—22641no—
315C2×C4C2×D113211yescharacteristic
316C2×C4C2×D113211yescharacteristic
317C2×C4C2×D113211yescharacteristic
318C2×C4C2×D113211yescharacteristic
319C2×C4C2×D113211yescharacteristic
320C2×C4C23×D28311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—11321no—
329C22—11321no—
330C22—11321no—
331C22—11321no—
332C22—11321no—
333C22—11321no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C22×D113211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—11321no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4#2258365511yescharacteristic
349C4#2258365811yescharacteristic
350C2—41no—
351C2—22641no—
352C2—22641no—
353C2—22641no—
354C2#3182704611yescharacteristic
355C2#3182727011yescharacteristic
356C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#424×C283C2
socleC22×C283C22×D4
hypercenter#424D283
hypocenterC283#3257
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #31827086C2semidirect
2. #31827070C2semidirect
3. #31826773C2semidirect
4. #31826766C2semidirect
5. #31826756C2semidirect
6. #31826746C2semidirect
7. #31826718C2semidirect
8. #31826711C2semidirect
9. #31826701C2semidirect
10. #31826694C2semidirect
11. #31826681C2semidirect
12. #31826681C2semidirect
13. #31826666C2semidirect
14. #31826661C2semidirect
15. #424×C283C2semidirect
178. C283#3257semidirect
194. #424D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318270702
#318267732
#318267662
#318267562
#318267462
#318267182
#318267112
#318267012
#318266942
#318266812
#318266662
#318266612
#424×C2832
#3257283