Finite Group Databasebeta

← #49123951

Subgroups — #49123951

Order 36224.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583582C211yesmaximal, characteristic
2C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
3C2×#22583566C211yesmaximal, characteristic, complemented
4#31826368C211yesmaximal, characteristic, complemented
5#31826365C211yesmaximal, characteristic, complemented
6#31826365C211yesmaximal, characteristic, complemented
7#31826362C211yesmaximal, characteristic, complemented
8#31826354C211yesmaximal, characteristic, complemented
9#31826353C211yesmaximal, characteristic, complemented
10#31826341C211yesmaximal, characteristic, complemented
11#31826339C211yesmaximal, characteristic, complemented
12#31826338C211yesmaximal, characteristic, complemented
13#31826323C211yesmaximal, characteristic, complemented
14#31826316C211yesmaximal, characteristic, complemented
15#386×C283C211yesmaximal, characteristic, complemented
16C22×C22⋊D283C2211yescharacteristic
17C22×C22⋊D283C2211yescharacteristic
18C23×Dic283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20#22583582C418yescomplemented
21C4×C22⋊D283—24no—
22#22583566—24no—
23C2×C4⋊Dic283C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×Dic283⋊C4C2211yescharacteristic
29C2×Dic283⋊C4C2211yescharacteristic
30C2×C22⋊Dic283C2211yescharacteristic
31C2×C22⋊Dic283C2211yescharacteristic
32C2×C22⋊Dic283C2211yescharacteristic
33C2×C22⋊Dic283C2211yescharacteristic
34C2×C22⋊Dic283C2211yescharacteristic
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C2×(C2×D283)⋊C4C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C2×(C2×D283)⋊C4C2211yescharacteristic
39C2×C4×Dic283C2211yescharacteristic
40C2×C4×Dic283C2211yescharacteristic
41C2×C4×Dic283C2211yescharacteristic
42C2×C4×Dic283C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C22×D4×C283C2211yescharacteristic
48C23×C4×C283C2211yescharacteristic
49C2×C22⋊C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C22⋊C4×C283C2211yescharacteristic
52#95×C283C2211yescharacteristic
53#95×C283C2211yescharacteristic
54C23×D283C2311yescharacteristic
55C2×C22⋊D283—22no—
56C2×C22⋊D283—22no—
57C2×C22⋊D283—41no—
58C2×C22⋊D283—41no—
59C2×C22⋊D283C2×C414yes—
60C2×C22⋊D283C2×C414yescomplemented
61C22×Dic283—22no—
62C22×Dic283—22no—
63C22×Dic283C2×C414yescomplemented
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C22×Dic283C2311yescharacteristic
70C22×Dic283C2311yescharacteristic
71C2×C4×D283—22no—
72C2×C4×D283—41no—
73C2×C4×D283—41no—
74C4⋊Dic283—41no—
75Dic283⋊C4—22no—
76Dic283⋊C4—22no—
77Dic283⋊C4—22no—
78Dic283⋊C4—22no—
79Dic283⋊C4—41no—
80Dic283⋊C4C2×C414yescomplemented
81C22⋊Dic283—22no—
82C22⋊Dic283—22no—
83C22⋊Dic283—41no—
84C22⋊Dic283—41no—
85C22⋊Dic283C2×C414yescomplemented
86(C2×D283)⋊C4—22no—
87(C2×D283)⋊C4—41no—
88(C2×D283)⋊C4—41no—
89(C2×D283)⋊C4C2×C414yescomplemented
90C4×Dic283—22no—
91C4×Dic283—41no—
92C4×Dic283—41no—
93C4×Dic283D414yescomplemented
94C24×C283C2311yescharacteristic
95C24×C283C2311yescharacteristic
96C2×D4×C283—41no—
97C2×D4×C283—41no—
98C2×D4×C283C2×C414yescomplemented
99C22×C4×C283—22no—
100C22×C4×C283—41no—
101C22×C4×C283—41no—
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105C22×C4×C283C2311yescharacteristic
106C22×C4×C283C2311yescharacteristic
107C22⋊C4×C283—22no—
108C22⋊C4×C283—41no—
109C22⋊C4×C283—41no—
110C22×D283—21no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—21no—
116C22×D283C22×C412yes—
117C22⋊D283—28no—
118C22⋊D283—44no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—28no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283C22×C412yes—
136C2×Dic283C22×C412yes—
137C2×Dic283C22×C412yes—
138C2×Dic283C2×D412yes—
139C2×Dic283C2×D412yes—
140C2×Dic283#4112yes—
141C4×D283—44no—
142C23×C283—21no—
143C23×C283—21no—
144C23×C283—21no—
145C23×C283—21no—
146C23×C283—21no—
147C23×C283—21no—
148C23×C283—21no—
149C23×C283—21no—
150C23×C283—21no—
151C23×C283—21no—
152C23×C283—21no—
153C23×C283—21no—
154C23×C283C22×C412yes—
155C23×C283C22×C412yes—
156C23×C283C2411yescharacteristic
157D4×C283—44no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—21no—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283—21no—
167C2×C4×C283—21no—
168C2×C4×C283—21no—
169C2×C4×C283—21no—
170C2×C4×C283—21no—
171C2×C4×C283—44no—
172C2×C4×C283C22×C412yes—
173C2×C4×C283C2×D412yes—
174C22×C283—22no—
175C22×C283—22no—
176C22×C283—22no—
177C22×C283—22no—
178C22×C283—22no—
179C22×C283—22no—
180C22×C283—41no—
181C22×C283—41no—
182C22×C283—41no—
183C22×C283—41no—
184C22×C283—41no—
185C22×C283—41no—
186C22×C283—41no—
187C22×C283—41no—
188C22×C283C23×C411yescharacteristic
189C22×C283C22×D411yescharacteristic
190C22×C283C2×#4111yescharacteristic
191C22×C283H(5,𝔽2)11yescharacteristic
192C22×C283H(5,𝔽2)11yescharacteristic
193C22×C283H(5,𝔽2)11yescharacteristic
194C22×C2832−1+411yescharacteristic
195C2×D283—22no—
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—41no—
199C2×D283—41no—
200C2×D283—41no—
201C2×D283—41no—
202C4×C283—22no—
203C4×C283—22no—
204C4×C283—41no—
205C4×C283—41no—
206C4×C283—41no—
207Dic283—22no—
208Dic283—22no—
209Dic283—22no—
210Dic283—41no—
211Dic283—41no—
212Dic283—41no—
213Dic283C4×D414yes—
214C2×C283—42no—
215C2×C283—42no—
216C2×C283C2×C4×D411yescharacteristic
217C2×C283#51811yescharacteristic
218C2×C283#52011yescharacteristic
219C2×C283#53511yescharacteristic
220C2×C283#53711yescharacteristic
221C2×C283#54011yescharacteristic
222C2×C283#54211yescharacteristic
223D283—42no—
224C283#232411yescharacteristic, complemented, Sylow
225#2324—2831nomaximal, Sylow
226C2×#121—2831no—
227C2×C4×D4—2831no—
228C2×#117—2831no—
229#390—2831no—
230#390—2831no—
231#390—2831no—
232#389—2831no—
233#388—2831no—
234#388—2831no—
235#386—2831no—
236#386D28311yescharacteristic, complemented
237#385—2831no—
238#385—2831no—
239#380—2831no—
240C4×C4⋊C4—2831no—
241C22×D4—2831no—
242C22×D4—2831no—
243C22×D4C2×D28311yescharacteristic
244C23×C4—2831no—
245C23×C4—2831no—
246C23×C4C2×D28311yescharacteristic
247#121—2838no—
248C4×D4—5664no—
249#117—5664no—
250C2×C4⋊C4—2831no—
251C2×C4⋊C4—2831no—
252C2×C4⋊C4—2831no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4—2831no—
257C2×C22⋊C4—2831no—
258C2×C22⋊C4—2831no—
259C2×C22⋊C4—2831no—
260C2×C22⋊C4—2831no—
261C2×C22⋊C4—2831no—
262C2×C22⋊C4—2831no—
263C2×C22⋊C4—2831no—
264C2×C22⋊C4—2831no—
265C2×C22⋊C4—2831no—
266C2×C22⋊C4C2×D28311yescharacteristic
267C2×C22⋊C4C2×D28311yescharacteristic
268C2×C22⋊C4C2×D28311yescharacteristic
269C2×C42—2831no—
270C2×C42—2831no—
271C2×C42—2831no—
272C2×C42—2831no—
273#95—2831no—
274#95—2831no—
275#95—2831no—
276#95—2831no—
277#95C2×D28311yescharacteristic
278#95C2×D28311yescharacteristic
279C24—2831no—
280C24C22×D28311yescharacteristic
281C24C22×D28311yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—2834no—
285C2×D4—2834no—
286C2×D4—5662no—
287C2×D4—5662no—
288C2×D4—11321no—
289C2×D4—11321no—
290C2×D4C4×D28314yescomplemented
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—2831no—
295C22×C4—2834no—
296C22×C4—2831no—
297C22×C4—2831no—
298C22×C4—2831no—
299C22×C4—2831no—
300C22×C4—2831no—
301C22×C4—2831no—
302C22×C4—5662no—
303C22×C4—5662no—
304C22×C4—5662no—
305C22×C4—11321no—
306C22×C4—11321no—
307C22×C4C22×D28311yescharacteristic
308C22×C4C22×D28311yescharacteristic
309C22×C4C22×D28311yescharacteristic
310C22×C4C22×D28311yescharacteristic
311C22×C4C22×D28311yescharacteristic
312C4⋊C4—2834no—
313C4⋊C4—5662no—
314C4⋊C4—5662no—
315C4⋊C4—5662no—
316C4⋊C4—5662no—
317C4⋊C4—11321no—
318C4⋊C4—11321no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—2834no—
323C22⋊C4—2834no—
324C22⋊C4—5662no—
325C22⋊C4—5662no—
326C22⋊C4—5662no—
327C22⋊C4—11321no—
328C22⋊C4—11321no—
329C22⋊C4—11321no—
330C22⋊C4—11321no—
331C42—2834no—
332C42—5662no—
333C42—11321no—
334C42—11321no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—2832no—
348C23—5661no—
349C23—5661no—
350C23—5661no—
351C23—5661no—
352C23—5661no—
353C23—5661no—
354C23C2×C4×D28312yes—
355C23C2×C4×D28312yes—
356C23C23×D28311yescharacteristic
357D4—44no—
358D4—5668no—
359D4—11324no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—2832no—
375C2×C4—2832no—
376C2×C4—2832no—
377C2×C4—2832no—
378C2×C4—2832no—
379C2×C4—2832no—
380C2×C4—5668no—
381C2×C4—5661no—
382C2×C4—5661no—
383C2×C4—5661no—
384C2×C4—5661no—
385C2×C4—5661no—
386C2×C4—5661no—
387C2×C4—5661no—
388C2×C4—5661no—
389C2×C4—5661no—
390C2×C4—5661no—
391C2×C4—5661no—
392C2×C4—5661no—
393C2×C4—5661no—
394C2×C4—5661no—
395C2×C4—5661no—
396C2×C4—11324no—
397C2×C4C2×C4×D28312yes—
398C2×C4D4×D28312yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—5662no—
414C22—5662no—
415C22—5662no—
416C22—11321no—
417C22—11321no—
418C22—11321no—
419C22—11321no—
420C22C22×C4×D28311yescharacteristic
421C22C2×D4×D28311yescharacteristic
422C22#41×D28311yescharacteristic
423C22#2258365511yescharacteristic
424C22#2258365511yescharacteristic
425C22#2258365511yescharacteristic
426C22#2258365711yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—2834no—
433C4—5662no—
434C4—5662no—
435C4—5662no—
436C4—11321no—
437C4—11321no—
438C4—11321no—
439C2—42no—
440C2—42no—
441C2—11322no—
442C2C4×D4×D28311yescharacteristic
443C2#3182693811yescharacteristic
444C2#3182694411yescharacteristic
445C2#3182703011yescharacteristic
446C2#3182704411yescharacteristic
447C2#3182706511yescharacteristic
448C2#3182708311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#386×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583582C2
hypercenter#386D283
hypocenterC283#2324
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D283C2semidirect
3. C2×#22583566C2semidirect
4. #31826368C2semidirect
5. #31826365C2semidirect
6. #31826365C2semidirect
7. #31826362C2semidirect
8. #31826354C2semidirect
9. #31826353C2semidirect
10. #31826341C2semidirect
11. #31826339C2semidirect
12. #31826338C2semidirect
13. #31826323C2semidirect
14. #31826316C2semidirect
15. #386×C283C2semidirect
20. #22583582C4semidirect
60. C2×C22⋊D283C2×C4semidirect
63. C22×Dic283C2×C4semidirect
80. Dic283⋊C4C2×C4semidirect
85. C22⋊Dic283C2×C4semidirect
89. (C2×D283)⋊C4C2×C4semidirect
93. C4×Dic283D4semidirect
98. C2×D4×C283C2×C4semidirect
224. C283#2324semidirect
236. #386D283semidirect
290. C2×D4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835822
C2×C4×C22⋊D2832
C2×#225835662
#318263682
#318263652
#318263622
#318263542
#318263532
#318263412
#318263392
#318263382
#318263232
#318263162
#386×C2832
#2324283