Finite Group Databasebeta

← #44509957

Subgroups — #44509957

Order 30848.

824 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21440615C211yesmaximal, characteristic
2C2×#21440604C211yesmaximal, characteristic, complemented
3C2×#21440602C211yesmaximal, characteristic, complemented
4C2×#21440602C211yesmaximal, characteristic, complemented
5C2×C42×D241C211yesmaximal, characteristic, complemented
6#29507617C211yesmaximal, characteristic, complemented
7#29507612C211yesmaximal, characteristic, complemented
8#29507608C211yesmaximal, characteristic, complemented
9#29507595C211yesmaximal, characteristic, complemented
10#29507593C211yesmaximal, characteristic, complemented
11#29507576C211yesmaximal, characteristic, complemented
12#29507568C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic241C211yesmaximal, characteristic, complemented
14#29507564C211yesmaximal, characteristic, complemented
15#388×C241C211yesmaximal, characteristic, complemented
16C22×D964C2211yescharacteristic
17C22×C22⋊D241C2211yescharacteristic
18C22×C22⋊D241C2211yescharacteristic
19C23×Dic241C2211yescharacteristic
20C22×C4×D241C2211yescharacteristic
21C22×C4×D241C2211yescharacteristic
22C22×C4×D241C2211yescharacteristic
23C22×C4×D241C2211yescharacteristic
24#21440615C418yescomplemented
25#21440604—24no—
26#21440602—24no—
27#21440602—24no—
28C2×#16838749C2211yescharacteristic
29C2×#16838749C2211yescharacteristic
30C2×#16838749C2211yescharacteristic
31C2×#16838749C2211yescharacteristic
32C2×C22⋊Dic241C2211yescharacteristic
33C2×#16838747C2211yescharacteristic
34C2×#16838747C2211yescharacteristic
35C2×#16838747C2211yescharacteristic
36C2×#16838747C2211yescharacteristic
37C2×#16838747C2211yescharacteristic
38C2×#16838747C2211yescharacteristic
39C2×C4×Dic241C2211yescharacteristic
40C2×C4×Dic241C2211yescharacteristic
41C2×C4×Dic241C2211yescharacteristic
42C2×C4×Dic241C2211yescharacteristic
43C2×C4×Dic241C2211yescharacteristic
44C42×D241—24no—
45#21440549C2211yescharacteristic
46#21440549C2211yescharacteristic
47#21440549C2211yescharacteristic
48#21440549C2211yescharacteristic
49C2×C4⋊C4×C241C2211yescharacteristic
50C2×C22⋊C4×C241C2211yescharacteristic
51C2×C22⋊C4×C241C2211yescharacteristic
52C2×C22⋊C4×C241C2211yescharacteristic
53C2×C42×C241C2211yescharacteristic
54#95×C241C2211yescharacteristic
55#95×C241C2211yescharacteristic
56C23×D241C2311yescharacteristic
57C23×D241C2311yescharacteristic
58C2×D964—22no—
59C2×D964—22no—
60C2×D964C2×C414yescomplemented
61C2×C22⋊D241—22no—
62C2×C22⋊D241—22no—
63C2×C22⋊D241—22no—
64C2×C22⋊D241—22no—
65C2×C22⋊D241C2×C414yescomplemented
66C2×C22⋊D241C2×C414yescomplemented
67C22×Dic241—22no—
68C22×Dic241—22no—
69C22×Dic241—22no—
70C22×Dic241C2311yescharacteristic
71C22×Dic241C2311yescharacteristic
72C22×Dic241C2311yescharacteristic
73C22×Dic241C2311yescharacteristic
74C22×Dic241C2311yescharacteristic
75C22×Dic241C2311yescharacteristic
76C2×C4×D241—22no—
77C2×C4×D241—22no—
78C2×C4×D241—22no—
79C2×C4×D241—22no—
80C2×C4×D241—22no—
81C2×C4×D241—22no—
82C2×C4×D241—22no—
83C2×C4×D241—22no—
84C2×C4×D241—22no—
85C2×C4×D241—22no—
86C2×C4×D241C2×C414yescomplemented
87C2×C4×D241D414yescomplemented
88#16838749—22no—
89#16838749—22no—
90#16838749—22no—
91#16838749C2×C414yescomplemented
92C22⋊Dic241—22no—
93#16838747—22no—
94#16838747—22no—
95#16838747—22no—
96#16838747—22no—
97#16838747—22no—
98#16838747C2×C414yescomplemented
99C4×Dic241—22no—
100C4×Dic241—22no—
101C4×Dic241—22no—
102C4×Dic241—22no—
103C4×Dic241D414yescomplemented
104C24×C241C2311yescharacteristic
105C22×C4×C241C2311yescharacteristic
106C22×C4×C241C2311yescharacteristic
107C22×C4×C241C2311yescharacteristic
108C22×C4×C241C2311yescharacteristic
109C22×C4×C241C2311yescharacteristic
110C22×C4×C241C2311yescharacteristic
111C4⋊C4×C241—22no—
112C22⋊C4×C241—22no—
113C22⋊C4×C241—22no—
114C22⋊C4×C241C2×C414yescomplemented
115C42×C241—22no—
116C22×D241—21no—
117C22×D241—21no—
118C22×D241—21no—
119C22×D241—21no—
120C22×D241—21no—
121C22×D241—21no—
122C22×D241—21no—
123C22×D241—21no—
124C22×D241—21no—
125C22×D241—21no—
126C22×D241C22×C412yes—
127C22×D241C22×C412yes—
128C22×D241C2×D412yes—
129C22×D241#4112yes—
130D964—28no—
131C22⋊D241—28no—
132C22⋊D241—28no—
133C2×Dic241—21no—
134C2×Dic241—21no—
135C2×Dic241—21no—
136C2×Dic241—21no—
137C2×Dic241—21no—
138C2×Dic241—21no—
139C2×Dic241—21no—
140C2×Dic241—21no—
141C2×Dic241—21no—
142C2×Dic241—21no—
143C2×Dic241—44no—
144C2×Dic241C22×C412yes—
145C2×Dic241C22×C412yes—
146C2×Dic241C2×D412yes—
147C2×Dic241C2×D412yes—
148C2×Dic241C2×D412yes—
149C2×Dic241#4112yes—
150C2×Dic241#4112yes—
151C2×Dic241#4112yes—
152C4×D241—28no—
153C4×D241—28no—
154C4×D241—28no—
155C4×D241—44no—
156C23×C241—21no—
157C23×C241—21no—
158C23×C241—21no—
159C23×C241—21no—
160C23×C241—21no—
161C23×C241—21no—
162C23×C241C22×C412yes—
163C23×C241C2411yescharacteristic
164C2×C4×C241—21no—
165C2×C4×C241—21no—
166C2×C4×C241—21no—
167C2×C4×C241—21no—
168C2×C4×C241—21no—
169C2×C4×C241—21no—
170C2×C4×C241—21no—
171C2×C4×C241—21no—
172C2×C4×C241—21no—
173C2×C4×C241—21no—
174C2×C4×C241—21no—
175C2×C4×C241—21no—
176C2×C4×C241—21no—
177C2×C4×C241—21no—
178C2×C4×C241C22×C412yes—
179C2×C4×C241C22×C412yes—
180C2×C4×C241C2×D412yes—
181C2×C4×C241C2×D412yes—
182C22×C241—22no—
183C22×C241—22no—
184C22×C241—22no—
185C22×C241—41no—
186C22×C241—41no—
187C22×C241—41no—
188C22×C241—41no—
189C22×C241C23×C411yescharacteristic
190C22×C241C22×D411yescharacteristic
191C22×C241C22×D411yescharacteristic
192C22×C241C2×#4111yescharacteristic
193C22×C241C2×#4111yescharacteristic
194C22×C241C2×#4111yescharacteristic
195C22×C241C2×#4111yescharacteristic
196C2×D241—22no—
197C2×D241—22no—
198C2×D241—22no—
199C2×D241—22no—
200C2×D241—22no—
201C2×D241—22no—
202C2×D241—22no—
203C2×D241—22no—
204C2×D241—22no—
205C2×D241—41no—
206C2×D241—41no—
207C2×D241—41no—
208C2×D241—41no—
209C2×D241C4×D414yescomplemented
210C4×C241—22no—
211C4×C241—22no—
212C4×C241—22no—
213C4×C241—22no—
214C4×C241—41no—
215C4×C241—41no—
216Dic241—22no—
217Dic241—22no—
218Dic241—41no—
219Dic241—41no—
220Dic241C4×D414yescomplemented
221Dic241#12114yescomplemented
222C2×C241—42no—
223C2×C241C2×C4×D411yescharacteristic
224C2×C241C2×C4×D411yescharacteristic
225C2×C241C4×#4111yescharacteristic
226C2×C241C2×#12111yescharacteristic
227C2×C241#52511yescharacteristic
228C2×C241#52911yescharacteristic
229C2×C241#53211yescharacteristic
230D241—24no—
231D241—42no—
232C241C4×#12111yescharacteristic, complemented, Sylow
233C4×#121—2411nomaximal, Sylow
234C2×#121—2411no—
235C2×C4×D4—2411no—
236C2×C4×D4—2411no—
237C2×C4×D4—2411no—
238C22×C42—2411no—
239#390—2411no—
240#389—2411no—
241#388—2411no—
242#388D24111yescharacteristic, complemented
243#386—2411no—
244#386—2411no—
245#380—2411no—
246C4×C4⋊C4—2411no—
247C4×C22⋊C4—2411no—
248C4×C22⋊C4—2411no—
249C22×D4—2411no—
250C22×D4—2411no—
251C22×D4—2411no—
252C23×C4—2411no—
253C23×C4—2411no—
254C23×C4—2411no—
255C23×C4—2411no—
256C23×C4—2411no—
257#121—2418no—
258C4×D4—4824no—
259C4×D4—4824no—
260C4×D4—4824no—
261C2×C4⋊C4—2411no—
262C2×C4⋊C4—2411no—
263C2×C4⋊C4—2411no—
264C2×C4⋊C4—2411no—
265C2×C4⋊C4C2×D24111yescharacteristic
266C2×C22⋊C4—2411no—
267C2×C22⋊C4—2411no—
268C2×C22⋊C4—2411no—
269C2×C22⋊C4—2411no—
270C2×C22⋊C4—2411no—
271C2×C22⋊C4—2411no—
272C2×C22⋊C4—2411no—
273C2×C22⋊C4C2×D24111yescharacteristic
274C2×C22⋊C4C2×D24111yescharacteristic
275C2×C22⋊C4C2×D24111yescharacteristic
276C2×C42—4824no—
277C2×C42—2411no—
278C2×C42—2411no—
279C2×C42—2411no—
280C2×C42—2411no—
281C2×C42—2411no—
282C2×C42C2×D24111yescharacteristic
283#95—2411no—
284#95—2411no—
285#95—2411no—
286#95—2411no—
287#95C2×D24111yescharacteristic
288#95C2×D24111yescharacteristic
289C24—2411no—
290C24—2411no—
291C24C22×D24111yescharacteristic
292C2×D4—4822no—
293C2×D4—4822no—
294C2×D4—4822no—
295C2×D4—4822no—
296C2×D4—4822no—
297C2×D4—4822no—
298C2×D4—2414no—
299C2×D4—2414no—
300C2×D4—2414no—
301C22×C4—4822no—
302C22×C4—4822no—
303C22×C4—4822no—
304C22×C4—4822no—
305C22×C4—4822no—
306C22×C4—4822no—
307C22×C4—4822no—
308C22×C4—4822no—
309C22×C4—4822no—
310C22×C4—4822no—
311C22×C4—4822no—
312C22×C4—4822no—
313C22×C4—4822no—
314C22×C4—2411no—
315C22×C4—2411no—
316C22×C4—2411no—
317C22×C4—2411no—
318C22×C4—2414no—
319C22×C4—2414no—
320C22×C4—2411no—
321C22×C4—2411no—
322C22×C4C22×D24111yescharacteristic
323C22×C4C22×D24111yescharacteristic
324C22×C4C22×D24111yescharacteristic
325C22×C4C22×D24111yescharacteristic
326C22×C4C22×D24111yescharacteristic
327C22×C4C22×D24111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—4822no—
330C4⋊C4—4822no—
331C4⋊C4—4822no—
332C4⋊C4—2414no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—4822no—
336C22⋊C4—4822no—
337C22⋊C4—4822no—
338C22⋊C4—4822no—
339C22⋊C4—4822no—
340C22⋊C4—4822no—
341C22⋊C4—2414no—
342C22⋊C4C4×D24114yescomplemented
343C42—22no—
344C42—4822no—
345C42—4822no—
346C42—4822no—
347C42—4822no—
348C42—2414no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—4821no—
356C23—4821no—
357C23—4821no—
358C23—4821no—
359C23—4821no—
360C23—4821no—
361C23—4821no—
362C23—4821no—
363C23—4821no—
364C23—4821no—
365C23—2412no—
366C23—2412no—
367C23—2412no—
368C23—2412no—
369C23C2×C4×D24112yes—
370C23C23×D24111yescharacteristic
371D4—4828no—
372D4—4828no—
373D4—4828no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—9644no—
389C2×C4—9644no—
390C2×C4—4828no—
391C2×C4—4828no—
392C2×C4—4828no—
393C2×C4—4821no—
394C2×C4—4821no—
395C2×C4—4821no—
396C2×C4—4821no—
397C2×C4—4821no—
398C2×C4—4821no—
399C2×C4—4821no—
400C2×C4—4821no—
401C2×C4—4821no—
402C2×C4—4821no—
403C2×C4—2412no—
404C2×C4—2412no—
405C2×C4—2412no—
406C2×C4—2412no—
407C2×C4—2412no—
408C2×C4—2412no—
409C2×C4—2412no—
410C2×C4—2412no—
411C2×C4C2×C4×D24112yes—
412C2×C4C2×C4×D24112yes—
413C2×C4D4×D24112yes—
414C2×C4D4×D24112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—9641no—
423C22—9641no—
424C22—9641no—
425C22—9641no—
426C22—4822no—
427C22—4822no—
428C22—4822no—
429C22—4822no—
430C22—4822no—
431C22—4822no—
432C22—4822no—
433C22—4822no—
434C22—4822no—
435C22—2414no—
436C22C22×C4×D24111yescharacteristic
437C22C2×D4×D24111yescharacteristic
438C22C2×D4×D24111yescharacteristic
439C22#41×D24111yescharacteristic
440C22#41×D24111yescharacteristic
441C22#41×D24111yescharacteristic
442C22#41×D24111yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—9641no—
450C4—9641no—
451C4—4822no—
452C4—4822no—
453C4—2414no—
454C4—2414no—
455C2—42no—
456C2—9642no—
457C2—4824no—
458C2C4×D4×D24111yescharacteristic
459C2C4×D4×D24111yescharacteristic
460C2#2950818511yescharacteristic
461C2#121×D24111yescharacteristic
462C2#2950822511yescharacteristic
463C2#2950825011yescharacteristic
464C2#2950826611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC2×#21440615C2
hypercenter#388D241
hypocenterC241C4×#121
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#21440604C2semidirect
3. C2×#21440602C2semidirect
4. C2×#21440602C2semidirect
5. C2×C42×D241C2semidirect
6. #29507617C2semidirect
7. #29507612C2semidirect
8. #29507608C2semidirect
9. #29507595C2semidirect
10. #29507593C2semidirect
11. #29507576C2semidirect
12. #29507568C2semidirect
13. C22⋊C4×Dic241C2semidirect
14. #29507564C2semidirect
15. #388×C241C2semidirect
24. #21440615C4semidirect
60. C2×D964C2×C4semidirect
65. C2×C22⋊D241C2×C4semidirect
66. C2×C22⋊D241C2×C4semidirect
86. C2×C4×D241C2×C4semidirect
87. C2×C4×D241D4semidirect
91. #16838749C2×C4semidirect
98. #16838747C2×C4semidirect
103. C4×Dic241D4semidirect
114. C22⋊C4×C241C2×C4semidirect
209. C2×D241C4×D4semidirect
220. Dic241C4×D4semidirect
221. Dic241#121semidirect
232. C241C4×#121semidirect
242. #388D241semidirect
342. C22⋊C4C4×D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406152
C2×#214406042
C2×#214406022
C2×C42×D2412
#295076172
#295076122
#295076082
#295075952
#295075932
#295075762
#295075682
C22⋊C4×Dic2412
#295075642
#388×C2412
C4×#121241