Finite Group Databasebeta

← #49131462

Subgroups — #49131462

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#31827070C211yesmaximal, characteristic, complemented
2#31826945C211yesmaximal, characteristic, complemented
3#31826784C211yesmaximal, characteristic, complemented
4#31826779C211yesmaximal, characteristic, complemented
5#31826773C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826666C211yesmaximal, characteristic, complemented
8#31826661C211yesmaximal, characteristic, complemented
9#31826612C211yesmaximal, characteristic, complemented
10#31826612C211yesmaximal, characteristic, complemented
11#31826578C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13C4×#17985381C211yesmaximal, characteristic, complemented
14C4×D2264C211yesmaximal, characteristic, complemented
15#433×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×D2264C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21#22583607C2211yescharacteristic
22#22583602C2211yescharacteristic
23#22583595—21no—
24#22583595—21no—
25#22583584C2211yescharacteristic
26#22583584C2211yescharacteristic
27#22583583—21no—
28#22583583—21no—
29C4×Dic566C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31C4×D1132C2211yescharacteristic
32C4×D1132C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34C4×D1132C2211yescharacteristic
35(C22⋊D283)⋊C4—21no—
36(C22⋊D283)⋊C4—21no—
37#22583568—21no—
38C2×C4⋊Dic283C2211yescharacteristic
39C4⋊C4×D283—21no—
40#22583544C2211yescharacteristic
41#22583544C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583542C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52#117×C283C2211yescharacteristic
53C4⋊C8×C283C2211yescharacteristic
54C4⋊C8×C283C2211yescharacteristic
55C22⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57#97×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—21no—
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×D1132C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76#17985381—22no—
77#17985381—22no—
78D2264—22no—
79D2264—22no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊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—
94(C2×D283)⋊C4—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C22×C4×C283C2311yescharacteristic
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#4112yes—
113D1132—21no—
114D1132—21no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—81no—
119D1132—81no—
120D1132#4112yes—
121C22⋊D283—24no—
122C22⋊D283—81no—
123C22⋊D283—81no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—81no—
130C4×D283—24no—
131C4×D283—81no—
132C4×D283—81no—
133C4×D283—81no—
134C4×D283—81no—
135C23×C283C2×D411yescharacteristic
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C8×C283—21no—
147C8×C283—21no—
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283C22×D411yescharacteristic
152C2×D283—22no—
153C2×D283—41no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283—21no—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—22no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173C2×C283—41no—
174C2×C283#52511yescharacteristic
175C2×C283#57611yescharacteristic
176C2×C283#57711yescharacteristic
177D283—42no—
178D283—81no—
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#442—2831no—
193#440—2831no—
194C4×SD16—2831no—
195C4×D8—2831no—
196#433D28311yescharacteristic, complemented
197C2×#41—2831no—
198C2×SD16—2831no—
199C2×SD16—2831no—
200C2×D8—2831no—
201C2×D8—2831no—
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—2831no—
215C4×D4—2831no—
216C4×D4—5661no—
217C4×D4—5661no—
218#117—5661no—
219#117C2×D28311yescharacteristic
220C2×C4⋊C4—2831no—
221C2×C4⋊C4—5661no—
222#107—2831no—
223#107—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8C2×D28311yescharacteristic
227C4⋊C8C2×D28311yescharacteristic
228#103—2831no—
229#103—2831no—
230#102—2831no—
231#102—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235#102—2831no—
236C22⋊C8C2×D28311yescharacteristic
237C22⋊C8C2×D28311yescharacteristic
238#97C2×D28311yescharacteristic
239C4×C8C2×D28311yescharacteristic
240#41—5662no—
241#41—5662no—
242C2×Q8—2831no—
243C2×D4—2831no—
244C2×D4—2831no—
245C2×D4—2831no—
246C2×D4—5661no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4—5661no—
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258SD16—5662no—
259SD16—5662no—
260D8—5662no—
261D8—5662no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
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⋊C4D113211yescharacteristic
276C4⋊C4D113211yescharacteristic
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4D113211yescharacteristic
284C22⋊C4D113211yescharacteristic
285C42—5661no—
286C42—5661no—
287C42C22×D28311yescharacteristic
288C42C22×D28311yescharacteristic
289C23—5661no—
290C23—5661no—
291C23—5661no—
292C23C2×D113211yescharacteristic
293Q8—2832no—
294Q8—5661no—
295D4—2832no—
296D4—5664no—
297D4—5661no—
298D4—5661no—
299D4—5661no—
300D4—5661no—
301D4—5661no—
302D4—22641no—
303D4—22641no—
304D4—22641no—
305D4—22641no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—5664no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—22641no—
315C2×C4—22641no—
316C2×C4—22641no—
317C2×C4—22641no—
318C2×C4—22641no—
319C2×C4C2×D113211yescharacteristic
320C2×C4C2×D113211yescharacteristic
321C2×C4C2×D113211yescharacteristic
322C2×C4C2×D113211yescharacteristic
323C2×C4C2×D113211yescharacteristic
324C2×C4C23×D28311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—5662no—
333C22—11321no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22C22×D113211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—5662no—
348C4—11321no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4#41×D28311yescharacteristic
353C4#41×D28311yescharacteristic
354C2—41no—
355C2—11322no—
356C2—22641no—
357C2—22641no—
358C2#3182697711yescharacteristic
359C2#3182727011yescharacteristic
360C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
hypercenter#433D283
hypocenterC283#3119
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31827070C2semidirect
2. #31826945C2semidirect
3. #31826784C2semidirect
4. #31826779C2semidirect
5. #31826773C2semidirect
6. #31826766C2semidirect
7. #31826666C2semidirect
8. #31826661C2semidirect
9. #31826612C2semidirect
10. #31826612C2semidirect
11. #31826578C2semidirect
12. #31826567C2semidirect
13. C4×#17985381C2semidirect
14. C4×D2264C2semidirect
15. #433×C283C2semidirect
180. C283#3119semidirect
196. #433D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318269452
#318267842
#318267792
#318267732
#318267662
#318266662
#318266612
#318266122
#318265782
#318265672
C4×#179853812
C4×D22642
#433×C2832
#3119283