Finite Group Databasebeta

← #49132821

Subgroups — #49132821

Order 36224.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583643C211yesmaximal, characteristic, complemented
2C2×#22583632C211yesmaximal, characteristic, complemented
3#31827124C211yesmaximal, characteristic, complemented
4#31827120C211yesmaximal, characteristic, complemented
5#31826859C211yesmaximal, characteristic, complemented
6#31826711C211yesmaximal, characteristic, complemented
7#31826706C211yesmaximal, characteristic, complemented
8#31826681C211yesmaximal, characteristic, complemented
9#31826676C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826629C211yesmaximal, characteristic, complemented
12#31826623C211yesmaximal, characteristic, complemented
13#31826612C211yesmaximal, characteristic, complemented
14#31826567C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985392C2211yescharacteristic
18C2×#17985392C2211yescharacteristic
19C22×Dic566C2211yescharacteristic
20#22583643—24no—
21#22583632—24no—
22C2×Dic1132C2211yescharacteristic
23C2×Dic1132C2211yescharacteristic
24C2×Dic1132C2211yescharacteristic
25C2×Dic1132C2211yescharacteristic
26C2×#17985381C2211yescharacteristic
27C2×#17985381C2211yescharacteristic
28C2×#17985381C2211yescharacteristic
29C2×#17985381C2211yescharacteristic
30C2×D2264C2211yescharacteristic
31#22583610C2211yescharacteristic
32#22583598C2211yescharacteristic
33#22583596—21no—
34#22583592—21no—
35#22583592—21no—
36#22583589C2211yescharacteristic
37#22583589C2211yescharacteristic
38#22583589C2211yescharacteristic
39#22583588—21no—
40#22583584C2211yescharacteristic
41#22583582—21no—
42#22583581—21no—
43C4×Dic566C2211yescharacteristic
44C4×D1132C2211yescharacteristic
45(C22⋊D283)⋊C4—21no—
46C4⋊C4×D283—21no—
47#22583544C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583535C2211yescharacteristic
50#22583535C2211yescharacteristic
51#22583535C2211yescharacteristic
52#22583532C2211yescharacteristic
53#22583532C2211yescharacteristic
54C2×M16×C283C2211yescharacteristic
55C22×C8×C283C2211yescharacteristic
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C22⋊C8×C283C2211yescharacteristic
60#97×C283C2211yescharacteristic
61#17985392—22no—
62#17985392—22no—
63#17985392—22no—
64#17985392—41no—
65#17985392—41no—
66#17985392—41no—
67C2×Dic566—22no—
68C2×Dic566—21no—
69C2×Dic566—41no—
70C2×Dic566C2311yescharacteristic
71C2×Dic566C2311yescharacteristic
72C2×Dic566C2311yescharacteristic
73C2×Dic566C2311yescharacteristic
74C2×D1132C2311yescharacteristic
75C2×D1132C2311yescharacteristic
76C2×C22⋊D283—21no—
77C2×C22⋊D283—21no—
78C2×C22⋊D283—21no—
79C2×C22⋊D283—21no—
80C22×Dic283—21no—
81C2×C4×D283—21no—
82C2×C4×D283—21no—
83C2×C4×D283—21no—
84C2×C4×D283—21no—
85Dic1132—22no—
86Dic1132—22no—
87Dic1132—22no—
88Dic1132—41no—
89#17985381—22no—
90#17985381—22no—
91#17985381—41no—
92#17985381D414yescomplemented
93D2264—22no—
94C4⋊Dic283—21no—
95C4⋊Dic283—21no—
96C4⋊Dic283C2311yescharacteristic
97C4⋊Dic283C2311yescharacteristic
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100Dic283⋊C4—21no—
101Dic283⋊C4—21no—
102C22⋊Dic283—21no—
103C22⋊Dic283—21no—
104C22⋊Dic283—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4—21no—
108(C2×D283)⋊C4—21no—
109C4×Dic283—21no—
110C2×D4×C283D411yescharacteristic
111C22×C4×C283C2311yescharacteristic
112C22×C4×C283C2311yescharacteristic
113M16×C283—22no—
114C2×C8×C283—22no—
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C2×C8×C283C2311yescharacteristic
119C4⋊C4×C283D411yescharacteristic
120C22⋊C4×C283D411yescharacteristic
121C22⋊C4×C283D411yescharacteristic
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—21no—
129Dic566—21no—
130Dic566—21no—
131Dic566—21no—
132Dic566—42no—
133Dic566C2×D412yes—
134D1132—21no—
135D1132—21no—
136D1132—21no—
137D1132C2×D412yes—
138C22⋊D283—42no—
139C22⋊D283—42no—
140C22⋊D283—42no—
141C22⋊D283—42no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283—21no—
145C2×Dic283—21no—
146C2×Dic283—21no—
147C2×Dic283—21no—
148C2×Dic283—42no—
149C4×D283—42no—
150C4×D283—42no—
151C4×D283—42no—
152C4×D283—42no—
153C23×C283C2×D411yescharacteristic
154C23×C283C2×D411yescharacteristic
155D4×C283—41no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283C2×D411yescharacteristic
161C2×C4×C283C2×D411yescharacteristic
162C2×C4×C283C2×D411yescharacteristic
163C2×C4×C283C2×D411yescharacteristic
164C2×C4×C283C2411yescharacteristic
165C8×C283—21no—
166C8×C283—21no—
167C8×C283—21no—
168C8×C283C2×D412yes—
169C22×C283—21no—
170C22×C283—21no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283C22×D411yescharacteristic
176C2×D283—22no—
177C2×D283—41no—
178C2×D283—41no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C4×C283—21no—
183C4×C283—21no—
184C4×C283—21no—
185C4×C283—21no—
186C4×C283C22×D411yescharacteristic
187C4×C283H(5,𝔽2)11yescharacteristic
188Dic283—22no—
189Dic283—41no—
190Dic283—41no—
191Dic283—41no—
192Dic283—41no—
193Dic283—41no—
194C2×C283—41no—
195C2×C283—41no—
196C2×C283D4211yescharacteristic
197C2×C283#57511yescharacteristic
198C2×C283#57811yescharacteristic
199D283—42no—
200D283—81no—
201C283#326911yescharacteristic, complemented, Sylow
202#3269—2831nomaximal, Sylow
203C2×#137—2831no—
204C2×#135—2831no—
205#548—2831no—
206#547—2831no—
207#497—2831no—
208#468—2831no—
209#467—2831no—
210#463—2831no—
211#462—2831no—
212#452—2831no—
213#452—2831no—
214#451—2831no—
215#449—2831no—
216#440—2831no—
217#435D28311yescharacteristic, complemented
218C2×#41—2831no—
219C2×#41—2831no—
220C2×#41—2831no—
221C22×Q8—2831no—
222#137—5664no—
223#135—5664no—
224C2×Q16—2831no—
225C2×Q16—2831no—
226C2×Q16—2831no—
227C2×Q16—2831no—
228C2×SD16—2831no—
229C2×SD16—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×D8—2831no—
233C2×M16C2×D28311yescharacteristic
234C22×C8C2×D28311yescharacteristic
235C4⋊Q8—2831no—
236#124—2831no—
237#124—5661no—
238#123—5661no—
239#123—5661no—
240C22⋊Q8—2831no—
241C22⋊Q8—2831no—
242C22⋊Q8—2831no—
243C22⋊Q8—5661no—
244#121—2831no—
245#121—5661no—
246#121—5661no—
247C4×Q8—2831no—
248C4×D4—2831no—
249C4×D4—5661no—
250C4×D4C2×D28311yescharacteristic
251C2×C4⋊C4—5661no—
252#107—2831no—
253C4⋊C8C2×D28311yescharacteristic
254#103—2831no—
255#103—2831no—
256#103—2831no—
257#103—2831no—
258#102—2831no—
259#102—2831no—
260C22⋊C8C2×D28311yescharacteristic
261C22⋊C8C2×D28311yescharacteristic
262#97C2×D28311yescharacteristic
263#41—5662no—
264#41—5662no—
265#41—5662no—
266#41—11321no—
267#41—11321no—
268#41—11321no—
269C2×Q8—2831no—
270C2×Q8—2831no—
271C2×Q8—2831no—
272C2×Q8—2831no—
273C2×Q8—5662no—
274C2×Q8—5661no—
275C2×Q8—11321no—
276C2×D4—2831no—
277C2×D4—2831no—
278C2×D4—5661no—
279C2×D4—5661no—
280C2×D4—5661no—
281C2×D4—5661no—
282C2×D4D113211yescharacteristic
283C22×C4—5661no—
284C22×C4—5661no—
285C22×C4—5661no—
286C22×C4—5661no—
287C22×C4—5661no—
288C22×C4C22×D28311yescharacteristic
289C22×C4C22×D28311yescharacteristic
290Q16—5662no—
291Q16—5662no—
292Q16—5662no—
293Q16—11321no—
294SD16—2834no—
295SD16—5662no—
296SD16—5662no—
297SD16—11321no—
298D8—5662no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D28311yescharacteristic
302C2×C8C22×D28311yescharacteristic
303C2×C8C22×D28311yescharacteristic
304C2×C8C22×D28311yescharacteristic
305C4⋊C4—2831no—
306C4⋊C4—2831no—
307C4⋊C4—5661no—
308C4⋊C4—5661no—
309C4⋊C4—5661no—
310C4⋊C4—5661no—
311C4⋊C4—5661no—
312C4⋊C4—5661no—
313C4⋊C4D113211yescharacteristic
314C22⋊C4—5661no—
315C22⋊C4—5661no—
316C22⋊C4—5661no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4D113211yescharacteristic
322C22⋊C4D113211yescharacteristic
323C42—5661no—
324C42C22×D28311yescharacteristic
325C23—5661no—
326C23—5661no—
327C23C2×D113211yescharacteristic
328C23C2×D113211yescharacteristic
329Q8—2832no—
330Q8—5661no—
331Q8—5661no—
332Q8—5661no—
333Q8—5661no—
334Q8—5661no—
335Q8—5661no—
336Q8—5661no—
337Q8—11322no—
338D4—41no—
339D4—2832no—
340D4—5661no—
341D4—5661no—
342D4—5661no—
343D4—11322no—
344D4—11322no—
345D4—11322no—
346D4—11322no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—5661no—
352C2×C4—5661no—
353C2×C4—5661no—
354C2×C4—5661no—
355C2×C4—5661no—
356C2×C4—5661no—
357C2×C4—11322no—
358C2×C4—11322no—
359C2×C4—11322no—
360C2×C4—11322no—
361C2×C4—11322no—
362C2×C4C2×D113211yescharacteristic
363C2×C4C2×D113211yescharacteristic
364C2×C4C2×D113211yescharacteristic
365C2×C4C2×D113211yescharacteristic
366C2×C4C23×D28311yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D28312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—5662no—
378C22—11321no—
379C22—11321no—
380C22—11321no—
381C22—11321no—
382C22—11321no—
383C22C22×D113211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—5662no—
389C4—11321no—
390C4—11321no—
391C4—11321no—
392C4—11321no—
393C4—11321no—
394C4C2×D4×D28311yescharacteristic
395C4#2258365611yescharacteristic
396C2—41no—
397C2—41no—
398C2—11322no—
399C2—22641no—
400C2D4×D113211yescharacteristic
401C2#3182726511yescharacteristic
402C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
hypercenter#435D283
hypocenterC283#3269
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22583643C2semidirect
2. C2×#22583632C2semidirect
3. #31827124C2semidirect
4. #31827120C2semidirect
5. #31826859C2semidirect
6. #31826711C2semidirect
7. #31826706C2semidirect
8. #31826681C2semidirect
9. #31826676C2semidirect
10. #31826629C2semidirect
11. #31826629C2semidirect
12. #31826623C2semidirect
13. #31826612C2semidirect
14. #31826567C2semidirect
15. #435×C283C2semidirect
92. #17985381D4semidirect
201. C283#3269semidirect
217. #435D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C2×#225836322
#318271242
#318271202
#318268592
#318267112
#318267062
#318266812
#318266762
#318266292
#318266232
#318266122
#318265672
#435×C2832
#3269283