Finite Group Databasebeta

← #49124524

Subgroups — #49124524

Order 36224.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D1132C211yesmaximal, characteristic
2C2×#22583567C211yesmaximal, characteristic, complemented
3#31826407C211yesmaximal, characteristic, complemented
4#31826400C211yesmaximal, characteristic, complemented
5#31826398C211yesmaximal, characteristic, complemented
6#31826394C211yesmaximal, characteristic, complemented
7#31826394C211yesmaximal, characteristic, complemented
8#31826391C211yesmaximal, characteristic, complemented
9#31826383C211yesmaximal, characteristic
10#31826382C211yesmaximal, characteristic
11C4×Dic283⋊C4C211yesmaximal, characteristic, complemented
12C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
14C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C4×D1132—24no—
20#22583567—24no—
21C2×C4⋊Dic283C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C2×C4×Dic283C2211yescharacteristic
37C2×C4×Dic283C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C2×C4⋊C4×C283C2211yescharacteristic
47C2×C4⋊C4×C283C2211yescharacteristic
48C2×C42×C283C2211yescharacteristic
49C2×C42×C283C2211yescharacteristic
50C2×C42×C283C2211yescharacteristic
51#95×C283C2211yescharacteristic
52#95×C283C2211yescharacteristic
53C23×D283C2311yescharacteristic
54C23×D283C2311yescharacteristic
55C2×D1132—22no—
56C2×D1132—22no—
57C2×D1132—22no—
58C22×Dic283C2311yescharacteristic
59C22×Dic283C2311yescharacteristic
60C22×Dic283C2311yescharacteristic
61C22×Dic283C2311yescharacteristic
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C2×C4×D283—22no—
65C2×C4×D283—22no—
66C2×C4×D283—22no—
67C2×C4×D283—22no—
68C2×C4×D283—22no—
69C2×C4×D283D414yes—
70C4⋊Dic283—22no—
71Dic283⋊C4—22no—
72Dic283⋊C4—22no—
73Dic283⋊C4—22no—
74Dic283⋊C4—22no—
75(C2×D283)⋊C4—22no—
76(C2×D283)⋊C4—22no—
77(C2×D283)⋊C4—22no—
78(C2×D283)⋊C4—22no—
79(C2×D283)⋊C4—22no—
80(C2×D283)⋊C4—22no—
81(C2×D283)⋊C4—22no—
82(C2×D283)⋊C4—22no—
83(C2×D283)⋊C4—22no—
84(C2×D283)⋊C4—22no—
85C4×Dic283—22no—
86C4×Dic283—22no—
87C22×C4×C283C2311yescharacteristic
88C22×C4×C283C2311yescharacteristic
89C22×C4×C283C2311yescharacteristic
90C22×C4×C283C2311yescharacteristic
91C22×C4×C283C2311yescharacteristic
92C22×C4×C283C2311yescharacteristic
93C22×C4×C283C2311yescharacteristic
94C4⋊C4×C283—22no—
95C4⋊C4×C283—22no—
96C42×C283—22no—
97C42×C283—22no—
98C42×C283—22no—
99C22×D283—21no—
100C22×D283—21no—
101C22×D283—21no—
102C22×D283—21no—
103C22×D283—21no—
104C22×D283—21no—
105C22×D283—21no—
106C22×D283—21no—
107C22×D283—21no—
108C22×D283—21no—
109C22×D283—21no—
110C22×D283—21no—
111C22×D283C2×D412yes—
112C22×D283#4112yes—
113D1132—28no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283C2×D412yes—
131C2×Dic283#4112yes—
132C4×D283—28no—
133C4×D283—44no—
134C23×C283C2411yescharacteristic
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×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—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283C2×D412yes—
152C2×C4×C283#4112yes—
153C2×C4×C283#4112yes—
154C2×C4×C283#4112yes—
155C2×C4×C283#4112yes—
156C22×C283C22×D411yescharacteristic
157C22×C283C2×#4111yescharacteristic
158C22×C283C2×#4111yescharacteristic
159C22×C283C2×#4111yescharacteristic
160C22×C283C2×#4111yescharacteristic
161C22×C283C2×#4111yescharacteristic
162C22×C283C2×#4111yescharacteristic
163C2×D283—22no—
164C2×D283—22no—
165C2×D283—22no—
166C2×D283—22no—
167C2×D283—22no—
168C2×D283—22no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—41no—
176C2×D283—41no—
177C4×C283—22no—
178C4×C283—22no—
179C4×C283—41no—
180C4×C283—41no—
181C4×C283—41no—
182C4×C283—41no—
183C4×C283#12314yes—
184Dic283—22no—
185Dic283—22no—
186Dic283—41no—
187Dic283—41no—
188Dic283—41no—
189Dic283—41no—
190C2×C283C2×#12311yescharacteristic
191C2×C283#52511yescharacteristic
192C2×C283#52911yescharacteristic
193C2×C283#52911yescharacteristic
194C2×C283#52911yescharacteristic
195C2×C283#52911yescharacteristic
196C2×C283#53211yescharacteristic
197D283—42no—
198D283—42no—
199C283#239511yescharacteristic, complemented, Sylow
200#2395—2831nomaximal, Sylow
201C2×C4×D4—2831no—
202C2×#117—2831no—
203#400—2831no—
204#399—2831no—
205#398—2831no—
206#397—2831no—
207#397—2831no—
208#397—2831no—
209#394—2831no—
210#394—2831no—
211C4×C4⋊C4—2831no—
212C4×C4⋊C4D28311yescharacteristic, complemented
213C4×C22⋊C4—2831no—
214C4×C22⋊C4—2831no—
215C4×C22⋊C4—2831no—
216C22×D4—2831no—
217C23×C4—2831no—
218C23×C4—2831no—
219C4×D4—5664no—
220#117—5664no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4—2831no—
223C2×C4⋊C4—2831no—
224C2×C4⋊C4—2831no—
225C2×C4⋊C4—2831no—
226C2×C4⋊C4C2×D28311yescharacteristic
227C2×C4⋊C4C2×D28311yescharacteristic
228C2×C22⋊C4—2831no—
229C2×C22⋊C4—2831no—
230C2×C22⋊C4—2831no—
231C2×C22⋊C4—2831no—
232C2×C22⋊C4—2831no—
233C2×C22⋊C4—2831no—
234C2×C22⋊C4—2831no—
235C2×C22⋊C4—2831no—
236C2×C22⋊C4—2831no—
237C2×C22⋊C4—2831no—
238C2×C42—2831no—
239C2×C42—2831no—
240C2×C42C2×D28311yescharacteristic
241C2×C42C2×D28311yescharacteristic
242C2×C42C2×D28311yescharacteristic
243#95—2831no—
244#95—2831no—
245#95—2831no—
246#95—2831no—
247#95—2831no—
248#95—2831no—
249#95—2831no—
250#95—2831no—
251#95C2×D28311yescharacteristic
252#95C2×D28311yescharacteristic
253C24—2831no—
254C24—2831no—
255C2×D4—5662no—
256C2×D4—5662no—
257C2×D4—5662no—
258C22×C4—2831no—
259C22×C4—2831no—
260C22×C4—2834no—
261C22×C4—2831no—
262C22×C4—2831no—
263C22×C4—2831no—
264C22×C4—2831no—
265C22×C4—5662no—
266C22×C4—5662no—
267C22×C4—5662no—
268C22×C4—5662no—
269C22×C4—5662no—
270C22×C4C22×D28311yescharacteristic
271C22×C4C22×D28311yescharacteristic
272C22×C4C22×D28311yescharacteristic
273C22×C4C22×D28311yescharacteristic
274C22×C4C22×D28311yescharacteristic
275C22×C4C22×D28311yescharacteristic
276C22×C4C22×D28311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—5662no—
280C4⋊C4—5662no—
281C4⋊C4—5662no—
282C4⋊C4—5662no—
283C4⋊C4—5662no—
284C22⋊C4—5662no—
285C22⋊C4—5662no—
286C22⋊C4—5662no—
287C22⋊C4—5662no—
288C22⋊C4—5662no—
289C22⋊C4—5662no—
290C22⋊C4—5662no—
291C22⋊C4—5662no—
292C22⋊C4—5662no—
293C22⋊C4—5662no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—5662no—
298C42—5662no—
299C23—2832no—
300C23—2832no—
301C23—5661no—
302C23—5661no—
303C23—5661no—
304C23—5661no—
305C23—5661no—
306C23—5661no—
307C23—5661no—
308C23—5661no—
309C23—5661no—
310C23—5661no—
311C23—5661no—
312C23—5661no—
313C23C23×D28311yescharacteristic
314D4—5668no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—2832no—
332C2×C4—2832no—
333C2×C4—5661no—
334C2×C4—5661no—
335C2×C4—5661no—
336C2×C4—5661no—
337C2×C4—5668no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4—5661no—
346C2×C4—5661no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—11324no—
351C2×C4D4×D28312yes—
352C2×C4#1798539212yes—
353C2×C4#1798539212yes—
354C2×C4#1798539212yes—
355C2×C4#1798539312yes—
356C22—5662no—
357C22—5662no—
358C22—5662no—
359C22—5662no—
360C22—5662no—
361C22—5662no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—11321no—
368C22—11321no—
369C22—11321no—
370C22C2×D4×D28311yescharacteristic
371C22#41×D28311yescharacteristic
372C22#41×D28311yescharacteristic
373C22C2×#1798539211yescharacteristic
374C22C2×#1798539211yescharacteristic
375C22C2×#1798539211yescharacteristic
376C22C2×#1798539311yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—5662no—
384C4—5662no—
385C4—11321no—
386C4—11321no—
387C4—11321no—
388C4—11321no—
389C4#2258359514yes—
390C2—11322no—
391C2—11322no—
392C2C2×#2258359511yescharacteristic
393C2#3182697411yescharacteristic
394C2#3182699311yescharacteristic
395C2#3182699911yescharacteristic
396C2#3182700211yescharacteristic
397C2#3182700211yescharacteristic
398C2#3182701211yescharacteristic
subgroupG/H
centerC22×C4C22×D283
commutator, socle, cosocleC23×C283C24
FrattiniC23C23×D283
FittingC4×C4⋊C4×C283C2
prime radicalC22×D1132C22
hypercenterC4×C4⋊C4D283
hypocenterC283#2395
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#22583567C2semidirect
3. #31826407C2semidirect
4. #31826400C2semidirect
5. #31826398C2semidirect
6. #31826394C2semidirect
7. #31826394C2semidirect
8. #31826391C2semidirect
11. C4×Dic283⋊C4C2semidirect
12. C4×(C2×D283)⋊C4C2semidirect
13. C4×(C2×D283)⋊C4C2semidirect
14. C4×(C2×D283)⋊C4C2semidirect
15. C4×C4⋊C4×C283C2semidirect
199. C283#2395semidirect
212. C4×C4⋊C4D283semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D11322
C2×#225835672
#318264072
#318264002
#318263982
#318263942
#318263912
#318263832
#318263822
C4×Dic283⋊C42
C4×(C2×D283)⋊C42
C4×C4⋊C4×C2832
#2395283