Finite Group Databasebeta

← #49131464

Subgroups — #49131464

Order 36224.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827066C211yesmaximal, characteristic, complemented
2#31826944C211yesmaximal, characteristic, complemented
3#31826785C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826775C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826664C211yesmaximal, characteristic, complemented
8#31826658C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826567C211yesmaximal, characteristic, complemented
12C4×#17985380C211yesmaximal, characteristic, complemented
13C4×#17985377C211yesmaximal, characteristic, complemented
14#31826527C211yesmaximal, characteristic, complemented
15#442×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985377C2211yescharacteristic
20#22583606C2211yescharacteristic
21#22583601C2211yescharacteristic
22#22583593—21no—
23#22583592—21no—
24#22583585C2211yescharacteristic
25#22583584—21no—
26#22583583—21no—
27#22583581C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29#22583575C2211yescharacteristic
30C4×D1132C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583567C2211yescharacteristic
35#22583566—21no—
36C2×Dic283⋊C4—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C22×Dic283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73#17985381—22no—
74#17985380—22no—
75#17985377—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86Dic283⋊C4D411yescharacteristic
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×D4×C283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99C22×C4×C283—21no—
100D8×C283—22no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566#4112yes—
112D1132—21no—
113D1132—21no—
114D1132—81no—
115C22⋊D283—24no—
116C22⋊D283—81no—
117C22⋊D283—81no—
118C22⋊D283—81no—
119C2×Dic283—24no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—81no—
130C4×D283—81no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134C23×C283—21no—
135D4×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283#4112yes—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—81no—
142C2×C4×C283—81no—
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—22no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283C22×D411yescharacteristic
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283C2×#4111yescharacteristic
166C4×C283C2×#4111yescharacteristic
167Dic283—21no—
168Dic283—22no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173C2×C283—42no—
174C2×C283—81no—
175C2×C283#52511yescharacteristic
176C2×C283#57611yescharacteristic
177C2×C283#57711yescharacteristic
178D283—41no—
179D283—81no—
180C283#311911yescharacteristic, complemented, Sylow
181#3119—2831nomaximal, Sylow
182#540—2831no—
183#520—2831no—
184#481—2831no—
185#480—2831no—
186#479—2831no—
187#478—2831no—
188#460—2831no—
189#459—2831no—
190#449—2831no—
191#449—2831no—
192#442D28311yescharacteristic, complemented
193#440—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196#433—2831no—
197C2×#41—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×D8—2831no—
201C2×D8C2×D28311yescharacteristic
202#127—2831no—
203#125—2831no—
204#123—5661no—
205#123—5661no—
206#121—2831no—
207#121—2831no—
208#121—5661no—
209#121—5661no—
210C4×Q8—2831no—
211C4×Q8—2831no—
212C4×D4—2831no—
213C4×D4—2831no—
214C4×D4—5661no—
215C4×D4—5661no—
216C4×D4C2×D28311yescharacteristic
217C4×D4C2×D28311yescharacteristic
218#117—2831no—
219#117—5661no—
220C2×C4⋊C4—2831no—
221C2×C4⋊C4—5661no—
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106C2×D28311yescharacteristic
226C4⋊C8—2831no—
227C4⋊C8—2831no—
228#103—2831no—
229#103—2831no—
230#102—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102C2×D28311yescharacteristic
235#102C2×D28311yescharacteristic
236C22⋊C8—2831no—
237C22⋊C8—2831no—
238#97C2×D28311yescharacteristic
239C4×C8—2831no—
240#41—5662no—
241#41—5662no—
242C2×Q8—2831no—
243C2×D4—2831no—
244C2×D4—5661no—
245C2×D4—5661no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—2831no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258SD16—5662no—
259SD16—5662no—
260D8—22no—
261D8—5662no—
262C2×C8—2831no—
263C2×C8—2831no—
264C2×C8C22×D28311yescharacteristic
265C2×C8C22×D28311yescharacteristic
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2831no—
280C22⋊C4—2831no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C42—2831no—
286C42—5661no—
287C42—5661no—
288C42C22×D28311yescharacteristic
289C23—21no—
290C23—21no—
291C23—2831no—
292C23—5661no—
293Q8—2832no—
294Q8—5661no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—5664no—
299D4—5661no—
300D4—5661no—
301D4—22641no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305D4#1798539212yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—5664no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—22641no—
320C2×C4—22641no—
321C2×C4—22641no—
322C2×C4D4×D28311yescharacteristic
323C2×C4D4×D28311yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—21no—
326C8—21no—
327C8—5661no—
328C8—5661no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—5661no—
336C22—5661no—
337C22—5661no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—5661no—
347C4—5662no—
348C4—5661no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4#41×D28311yescharacteristic
353C4C2×#1798539211yescharacteristic
354C2—42no—
355C2—81no—
356C2—11321no—
357C2—22641no—
358C2#3182697411yescharacteristic
359C2#3182726911yescharacteristic
360C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
hypercenter#442D283
hypocenterC283#3119
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31827066C2semidirect
2. #31826944C2semidirect
3. #31826785C2semidirect
4. #31826777C2semidirect
5. #31826775C2semidirect
6. #31826763C2semidirect
7. #31826664C2semidirect
8. #31826658C2semidirect
9. #31826611C2semidirect
10. #31826607C2semidirect
11. #31826567C2semidirect
12. C4×#17985380C2semidirect
13. C4×#17985377C2semidirect
14. #31826527C2semidirect
15. #442×C283C2semidirect
180. C283#3119semidirect
192. #442D283semidirect

Maximal subgroups

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

subgroupindex
#318270662
#318269442
#318267852
#318267772
#318267752
#318267632
#318266642
#318266582
#318266112
#318266072
#318265672
C4×#179853802
C4×#179853772
#318265272
#442×C2832
#3119283