Finite Group Databasebeta

← #49124503

Subgroups — #49124503

Order 36224.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
3C2×#22583569C211yesmaximal, characteristic, complemented
4#31826398C211yesmaximal, characteristic, complemented
5#31826393C211yesmaximal, characteristic, complemented
6#31826388C211yesmaximal, characteristic, complemented
7#31826387C211yesmaximal, characteristic, complemented
8#31826381C211yesmaximal, characteristic, complemented
9#31826380C211yesmaximal, characteristic, complemented
10#31826379C211yesmaximal, characteristic, complemented
11#31826373C211yesmaximal, characteristic
12C4×Dic283⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic283C211yesmaximal, characteristic, complemented
15C2×C4×D4×C283C211yesmaximal, characteristic, complemented
16C22×C22⋊D283C2211yescharacteristic
17C22×C22⋊D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C4×C22⋊D283—24no—
20C4×C22⋊D283—24no—
21#22583569—24no—
22C2×C4⋊Dic283C2211yescharacteristic
23C2×C4⋊Dic283C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×Dic283⋊C4C2211yescharacteristic
27C2×Dic283⋊C4C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic
29C2×C22⋊Dic283C2211yescharacteristic
30C2×C22⋊Dic283C2211yescharacteristic
31C2×C22⋊Dic283C2211yescharacteristic
32C2×C22⋊Dic283C2211yescharacteristic
33C2×C22⋊Dic283C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C2×(C2×D283)⋊C4C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C2×C4×Dic283C2211yescharacteristic
39C2×C4×Dic283C2211yescharacteristic
40C2×C4×Dic283C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C283⋊#95C2211yescharacteristic
46C283⋊#95C2211yescharacteristic
47C22×D4×C283C2211yescharacteristic
48C23×C4×C283C2211yescharacteristic
49C23×C4×C283C2211yescharacteristic
50C4×D4×C283—24no—
51C2×C4⋊C4×C283C2211yescharacteristic
52C2×C22⋊C4×C283C2211yescharacteristic
53C2×C22⋊C4×C283C2211yescharacteristic
54C2×C42×C283C2211yescharacteristic
55C23×D283C2311yescharacteristic
56C2×C22⋊D283—22no—
57C2×C22⋊D283—22no—
58C2×C22⋊D283—22no—
59C2×C22⋊D283—22no—
60C2×C22⋊D283—22no—
61C2×C22⋊D283—22no—
62C22×Dic283C2311yescharacteristic
63C22×Dic283C2311yescharacteristic
64C22×Dic283C2311yescharacteristic
65C22×Dic283C2311yescharacteristic
66C22×Dic283C2311yescharacteristic
67C22×Dic283C2311yescharacteristic
68C22×Dic283C2311yescharacteristic
69C2×C4×D283—22no—
70C2×C4×D283—22no—
71C2×C4×D283—22no—
72C4⋊Dic283—22no—
73C4⋊Dic283—22no—
74Dic283⋊C4—22no—
75Dic283⋊C4—22no—
76Dic283⋊C4—22no—
77Dic283⋊C4—22no—
78C22⋊Dic283—22no—
79C22⋊Dic283—22no—
80C22⋊Dic283—22no—
81C22⋊Dic283—22no—
82C22⋊Dic283—22no—
83C22⋊Dic283—22no—
84(C2×D283)⋊C4—22no—
85(C2×D283)⋊C4—22no—
86(C2×D283)⋊C4—22no—
87(C2×D283)⋊C4—22no—
88C4×Dic283—22no—
89C4×Dic283—22no—
90C4×Dic283D414yescomplemented
91C24×C283C2311yescharacteristic
92C24×C283C2311yescharacteristic
93C2×D4×C283—22no—
94C2×D4×C283—22no—
95C2×D4×C283—22no—
96C22×C4×C283—22no—
97C22×C4×C283—22no—
98C22×C4×C283—22no—
99C22×C4×C283—22no—
100C22×C4×C283—22no—
101C22×C4×C283D414yescomplemented
102C22×C4×C283C2311yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105C22×C4×C283C2311yescharacteristic
106C22×C4×C283C2311yescharacteristic
107C4⋊C4×C283—22no—
108C22⋊C4×C283—22no—
109C22⋊C4×C283—22no—
110C42×C283—22no—
111C22×D283—21no—
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—21no—
116C22×D283—21no—
117C22×D283#4112yes—
118C22⋊D283—28no—
119C22⋊D283—28no—
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×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—21no—
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×C283C2×D412yes—
155C23×C283#4112yes—
156C23×C283C2411yescharacteristic
157D4×C283—28no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—28no—
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—44no—
170C2×C4×C283C2×D412yes—
171C2×C4×C283C2×D412yes—
172C2×C4×C283C2×D412yes—
173C2×C4×C283#4112yes—
174C2×C4×C283#4112yes—
175C22×C283—22no—
176C22×C283—22no—
177C22×C283—22no—
178C22×C283—22no—
179C22×C283—22no—
180C22×C283—22no—
181C22×C283—41no—
182C22×C283—41no—
183C22×C283—41no—
184C22×C283—41no—
185C22×C283—41no—
186C22×C283—41no—
187C22×C283—41no—
188C22×C283—41no—
189C22×C283C22×D411yescharacteristic
190C22×C283C22×D411yescharacteristic
191C22×C283C2×#4111yescharacteristic
192C22×C283C2×#4111yescharacteristic
193C22×C283C2×#4111yescharacteristic
194C22×C283C2×#4111yescharacteristic
195C22×C283C2×#4111yescharacteristic
196C2×D283—22no—
197C2×D283—22no—
198C2×D283—22no—
199C2×D283—41no—
200C2×D283—41no—
201C2×D283—41no—
202C2×D283—41no—
203C4×C283—22no—
204C4×C283—22no—
205C4×C283—41no—
206C4×C283—41no—
207C4×C283#12114yes—
208Dic283—22no—
209Dic283—22no—
210Dic283—22no—
211Dic283—41no—
212Dic283—41no—
213Dic283—41no—
214Dic283—41no—
215C2×C283—42no—
216C2×C283—42no—
217C2×C283C2×#12111yescharacteristic
218C2×C283#52511yescharacteristic
219C2×C283#52511yescharacteristic
220C2×C283#52511yescharacteristic
221C2×C283#52911yescharacteristic
222C2×C283#52911yescharacteristic
223C2×C283#53211yescharacteristic
224D283—42no—
225C283#239211yescharacteristic, complemented, Sylow
226#2392—2831nomaximal, Sylow
227C2×C4×D4—2831no—
228C2×C4×D4—2831no—
229C2×C4×D4D28311yescharacteristic, complemented
230C2×#117—2831no—
231#398—2831no—
232#397—2831no—
233#396—2831no—
234#396—2831no—
235#394—2831no—
236#394—2831no—
237#394—2831no—
238#392—2831no—
239C4×C4⋊C4—2831no—
240C4×C22⋊C4—2831no—
241C4×C22⋊C4—2831no—
242C22×D4—2831no—
243C22×D4—2831no—
244C22×D4C2×D28311yescharacteristic
245C23×C4—2831no—
246C23×C4C2×D28311yescharacteristic
247C23×C4C2×D28311yescharacteristic
248C4×D4—24no—
249C4×D4—5664no—
250C4×D4—5664no—
251#117—5664no—
252C2×C4⋊C4—2831no—
253C2×C4⋊C4—2831no—
254C2×C4⋊C4—2831no—
255C2×C4⋊C4—2831no—
256C2×C4⋊C4—2831no—
257C2×C4⋊C4—2831no—
258C2×C4⋊C4C2×D28311yescharacteristic
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⋊C4—2831no—
267C2×C22⋊C4—2831no—
268C2×C22⋊C4—2831no—
269C2×C22⋊C4C2×D28311yescharacteristic
270C2×C22⋊C4C2×D28311yescharacteristic
271C2×C42—2831no—
272C2×C42—2831no—
273C2×C42—2831no—
274C2×C42C2×D28311yescharacteristic
275#95—2831no—
276#95—2831no—
277#95—2831no—
278#95—2831no—
279#95—2831no—
280#95—2831no—
281C24—2831no—
282C24C22×D28311yescharacteristic
283C24C22×D28311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—5662no—
288C2×D4—5662no—
289C2×D4—5662no—
290C2×D4—5662no—
291C2×D4—5662no—
292C2×D4—5662no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—2831no—
299C22×C4—2831no—
300C22×C4—2831no—
301C22×C4—2831no—
302C22×C4—2831no—
303C22×C4—2831no—
304C22×C4—2831no—
305C22×C4—5662no—
306C22×C4—5662no—
307C22×C4—5662no—
308C22×C4C22⋊D28314yescomplemented
309C22×C4C22×D28311yescharacteristic
310C22×C4C22×D28311yescharacteristic
311C22×C4C22×D28311yescharacteristic
312C22×C4C22×D28311yescharacteristic
313C22×C4C22×D28311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—5662no—
316C4⋊C4—5662no—
317C4⋊C4—5662no—
318C4⋊C4—5662no—
319C4⋊C4—5662no—
320C4⋊C4—5662no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—5662no—
324C22⋊C4—5662no—
325C22⋊C4—5662no—
326C22⋊C4—5662no—
327C22⋊C4—5662no—
328C22⋊C4—5662no—
329C22⋊C4—5662no—
330C22⋊C4—5662no—
331C22⋊C4—5662no—
332C22⋊C4—5662no—
333C42—22no—
334C42—2834no—
335C42—5662no—
336C42—5662no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—2832no—
350C23—5661no—
351C23—5661no—
352C23—5661no—
353C23—5661no—
354C23—5661no—
355C23—5661no—
356C23C2×C22⋊D28312yes—
357C23#1798539212yes—
358C23C23×D28311yescharacteristic
359D4—28no—
360D4—5668no—
361D4—5668no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—28no—
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—5661no—
378C2×C4—5661no—
379C2×C4—5661no—
380C2×C4—5661no—
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—11324no—
396C2×C4D4×D28312yes—
397C2×C4C2×C22⋊D28312yes—
398C2×C4C2×C22⋊D28312yes—
399C2×C4#1798539112yes—
400C2×C4#1798539212yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—5662no—
416C22—5662no—
417C22—5662no—
418C22—11321no—
419C22—11321no—
420C22—11321no—
421C22—11321no—
422C22C2×D4×D28311yescharacteristic
423C22C22×C22⋊D28311yescharacteristic
424C22#41×D28311yescharacteristic
425C22#41×D28311yescharacteristic
426C22C2×#1798539111yescharacteristic
427C22C2×#1798539211yescharacteristic
428C22C2×#1798539211yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—5662no—
434C4—5662no—
435C4—5662no—
436C4—11321no—
437C4—11321no—
438C4—11321no—
439C4—11321no—
440C4#2258358214yes—
441C2—42no—
442C2—42no—
443C2—11322no—
444C2C2×#2258358211yescharacteristic
445C2#3182697211yescharacteristic
446C2#3182697411yescharacteristic
447C2#3182697611yescharacteristic
448C2#3182699511yescharacteristic
449C2#3182699711yescharacteristic
450C2#3182701211yescharacteristic
subgroupG/H
centerC22×C4C22×D283
commutator, socle, cosocleC23×C283C24
FrattiniC23C23×D283
FittingC2×C4×D4×C283C2
prime radical#31826373C2
hypercenterC2×C4×D4D283
hypocenterC283#2392
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D283C2semidirect
2. C2×C4×C22⋊D283C2semidirect
3. C2×#22583569C2semidirect
4. #31826398C2semidirect
5. #31826393C2semidirect
6. #31826388C2semidirect
7. #31826387C2semidirect
8. #31826381C2semidirect
9. #31826380C2semidirect
10. #31826379C2semidirect
12. C4×Dic283⋊C4C2semidirect
13. C4×(C2×D283)⋊C4C2semidirect
14. C4×C22⋊Dic283C2semidirect
15. C2×C4×D4×C283C2semidirect
90. C4×Dic283D4semidirect
101. C22×C4×C283D4semidirect
225. C283#2392semidirect
229. C2×C4×D4D283semidirect
308. C22×C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2832
C2×#225835692
#318263982
#318263932
#318263882
#318263872
#318263812
#318263802
#318263792
#318263732
C4×Dic283⋊C42
C4×(C2×D283)⋊C42
C4×C22⋊Dic2832
C2×C4×D4×C2832
#2392283