Finite Group Databasebeta

← #44487366

Subgroups — #44487366

Order 30592.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D239C211yesmaximal, characteristic
2C2×C4×C22⋊D239C211yesmaximal, characteristic, complemented
3C2×(C22⋊D239)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
6#29504672C211yesmaximal, characteristic, complemented
7#29504672C211yesmaximal, characteristic, complemented
8#29504652C211yesmaximal, characteristic, complemented
9#29504650C211yesmaximal, characteristic, complemented
10#29504650C211yesmaximal, characteristic, complemented
11#29504631C211yesmaximal, characteristic, complemented
12#29504627C211yesmaximal, characteristic, complemented
13#29504627C211yesmaximal, characteristic, complemented
14#29504619C211yesmaximal, characteristic, complemented
15#386×C239C211yesmaximal, characteristic, complemented
16C24×D239C2211yescharacteristic
17C24×D239C2211yescharacteristic
18C22×D956C2211yescharacteristic
19C22×C22⋊D239C2211yescharacteristic
20C22×C22⋊D239C2211yescharacteristic
21C2×D4×D239—24no—
22C2×D4×D239—24no—
23C2×D4×D239C418yescomplemented
24C23×Dic239C2211yescharacteristic, complemented
25C22×C4×D239C2211yescharacteristic
26C22×C4×D239C2211yescharacteristic, complemented
27C22×C4×D239C2211yescharacteristic, complemented
28C4×C22⋊D239—24no—
29(C22⋊D239)⋊C4—24no—
30C2×Dic239⋊C4C2211yescharacteristic, complemented
31C2×Dic239⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic239C2211yescharacteristic, complemented
33C2×C22⋊Dic239C2211yescharacteristic, complemented
34C2×C22⋊Dic239C2211yescharacteristic, complemented
35C2×(C2×D239)⋊C4—24no—
36C2×(C2×D239)⋊C4C2211yescharacteristic
37C2×(C2×D239)⋊C4C2211yescharacteristic
38C2×(C2×D239)⋊C4C2211yescharacteristic
39C2×(C2×D239)⋊C4C2211yescharacteristic
40C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D239—24no—
47C2×C4×Dic239C2211yescharacteristic, complemented
48C2×C4×Dic239C2211yescharacteristic, complemented
49C239⋊#95C2211yescharacteristic, complemented
50C239⋊#95C2211yescharacteristic, complemented
51C22×D4×C239C2211yescharacteristic
52C23×C4×C239C2211yescharacteristic, complemented
53C2×C22⋊C4×C239C2211yescharacteristic, complemented
54C2×C22⋊C4×C239C2211yescharacteristic, complemented
55C2×C22⋊C4×C239C2211yescharacteristic, complemented
56#95×C239C2211yescharacteristic, complemented
57#95×C239C2211yescharacteristic, complemented
58C23×D239—22no—
59C23×D239—22no—
60C23×D239—22no—
61C23×D239—22no—
62C23×D239—22no—
63C23×D239—22no—
64C23×D239—22no—
65C23×D239—22no—
66C23×D239—41no—
67C23×D239—41no—
68C23×D239—41no—
69C23×D239—41no—
70C23×D239C2×C414yescomplemented
71C23×D239C2×C414yescomplemented
72C23×D239C2311yescharacteristic
73C23×D239C2311yescharacteristic
74C23×D239C2311yescharacteristic
75C2×D956—22no—
76C2×D956—22no—
77C2×D956C2×C414yescomplemented
78C2×C22⋊D239—22no—
79C2×C22⋊D239—22no—
80C2×C22⋊D239C2×C414yes—
81C2×C22⋊D239C2×C414yescomplemented
82C2×C22⋊D239D414yes—
83C2×C22⋊D239D414yes—
84D4×D239—232no—
85C22×Dic239—22no—
86C22×Dic239—22no—
87C22×Dic239—41no—
88C22×Dic239C2311yescharacteristic
89C22×Dic239C2311yescharacteristic
90C22×Dic239C2311yescharacteristic
91C22×Dic239C2311yescharacteristic
92C22×Dic239C2311yescharacteristic
93C2×C4×D239—22no—
94C2×C4×D239—22no—
95C2×C4×D239—22no—
96C2×C4×D239—22no—
97C2×C4×D239—22no—
98C2×C4×D239—22no—
99C2×C4×D239—41no—
100C2×C4×D239—41no—
101C2×C4×D239C2×C414yescomplemented
102Dic239⋊C4—22no—
103Dic239⋊C4—22no—
104C22⋊Dic239—22no—
105C22⋊Dic239—22no—
106C22⋊Dic239—41no—
107(C2×D239)⋊C4—22no—
108(C2×D239)⋊C4—22no—
109(C2×D239)⋊C4—22no—
110(C2×D239)⋊C4—22no—
111(C2×D239)⋊C4—22no—
112(C2×D239)⋊C4—22no—
113(C2×D239)⋊C4—22no—
114(C2×D239)⋊C4—41no—
115(C2×D239)⋊C4—41no—
116(C2×D239)⋊C4D414yescomplemented
117C4×Dic239—22no—
118C4×Dic239—22no—
119C24×C239C2311yescharacteristic
120C24×C239C2311yescharacteristic
121C2×D4×C239—22no—
122C2×D4×C239—22no—
123C2×D4×C239C2×C414yescomplemented
124C22×C4×C239—22no—
125C22×C4×C239—22no—
126C22×C4×C239—41no—
127C22×C4×C239C2311yescharacteristic
128C22×C4×C239C2311yescharacteristic
129C22×C4×C239C2311yescharacteristic
130C22×C4×C239C2311yescharacteristic
131C22×C4×C239C2311yescharacteristic
132C22⋊C4×C239—22no—
133C22⋊C4×C239—22no—
134C22⋊C4×C239—41no—
135C22×D239—21no—
136C22×D239—21no—
137C22×D239—21no—
138C22×D239—21no—
139C22×D239—21no—
140C22×D239—21no—
141C22×D239—21no—
142C22×D239—21no—
143C22×D239—28no—
144C22×D239—21no—
145C22×D239—21no—
146C22×D239—21no—
147C22×D239—21no—
148C22×D239—21no—
149C22×D239—21no—
150C22×D239—28no—
151C22×D239—28no—
152C22×D239—28no—
153C22×D239—44no—
154C22×D239—44no—
155C22×D239—44no—
156C22×D239—44no—
157C22×D239—44no—
158C22×D239—44no—
159C22×D239—44no—
160C22×D239—44no—
161C22×D239—44no—
162C22×D239—44no—
163C22×D239C22×C412yes—
164C22×D239C22×C412yes—
165C22×D239C22×C412yes—
166C22×D239C2×D412yes—
167C22×D239C2×D412yes—
168C22×D239C2×D412yes—
169C22×D239#4112yes—
170D956—28no—
171C22⋊D239—28no—
172C22⋊D239C22⋊C4116yescomplemented
173C2×Dic239—21no—
174C2×Dic239—21no—
175C2×Dic239—21no—
176C2×Dic239—21no—
177C2×Dic239—21no—
178C2×Dic239—21no—
179C2×Dic239—21no—
180C2×Dic239—21no—
181C2×Dic239—21no—
182C2×Dic239—21no—
183C2×Dic239—21no—
184C2×Dic239—44no—
185C2×Dic239C22×C412yes—
186C2×Dic239C2×D412yes—
187C2×Dic239C2×D412yes—
188C2×Dic239C2×D412yescomplemented
189C4×D239—28no—
190C4×D239—44no—
191C4×D239—44no—
192C23×C239—21no—
193C23×C239—21no—
194C23×C239—21no—
195C23×C239—21no—
196C23×C239—21no—
197C23×C239—21no—
198C23×C239—21no—
199C23×C239—21no—
200C23×C239—21no—
201C23×C239—21no—
202C23×C239C22×C412yes—
203C23×C239C22×C412yes—
204C23×C239C2×D412yes—
205C23×C239C2×D412yes—
206C23×C239C2411yescharacteristic
207D4×C239—28no—
208C2×C4×C239—21no—
209C2×C4×C239—21no—
210C2×C4×C239—21no—
211C2×C4×C239—21no—
212C2×C4×C239—21no—
213C2×C4×C239—21no—
214C2×C4×C239—21no—
215C2×C4×C239—21no—
216C2×C4×C239—21no—
217C2×C4×C239—21no—
218C2×C4×C239—21no—
219C2×C4×C239—21no—
220C2×C4×C239—21no—
221C2×C4×C239—44no—
222C2×C4×C239C22×C412yes—
223C2×C4×C239C2×D412yescomplemented
224C22×C239—22no—
225C22×C239—22no—
226C22×C239—22no—
227C22×C239—22no—
228C22×C239—22no—
229C22×C239—22no—
230C22×C239—22no—
231C22×C239—22no—
232C22×C239—22no—
233C22×C239—41no—
234C22×C239—41no—
235C22×C239—41no—
236C22×C239—41no—
237C22×C239C2×C22⋊C414yescomplemented
238C22×C239C23×C411yescharacteristic
239C22×C239C22×D411yescharacteristic
240C22×C239C22×D411yescharacteristic
241C22×C239C22×D411yescharacteristic
242C22×C239C2×#4111yescharacteristic
243C22×C239H(5,𝔽2)11yescharacteristic
244C22×C239H(5,𝔽2)11yescharacteristic
245C2×D239—22no—
246C2×D239—22no—
247C2×D239—22no—
248C2×D239—22no—
249C2×D239—22no—
250C2×D239—22no—
251C2×D239—22no—
252C2×D239—22no—
253C2×D239—22no—
254C2×D239—22no—
255C2×D239—22no—
256C2×D239—22no—
257C2×D239—22no—
258C2×D239—22no—
259C2×D239—22no—
260C2×D239—416no—
261C2×D239—416no—
262C2×D239—41no—
263C2×D239—41no—
264C2×D239—41no—
265C2×D239—41no—
266C2×D239C2×C22⋊C414yescomplemented
267C2×D239C4×D414yescomplemented
268C4×C239—22no—
269C4×C239—22no—
270C4×C239—41no—
271C4×C239—41no—
272C4×C239—41no—
273Dic239—22no—
274Dic239—41no—
275Dic239—41no—
276Dic239—41no—
277Dic239C2×C22⋊C414yescomplemented
278C2×C239—24no—
279C2×C239—42no—
280C2×C239C22×C22⋊C411yescharacteristic
281C2×C239C2×C4×D411yescharacteristic
282C2×C239#51811yescharacteristic
283C2×C239D4211yescharacteristic
284C2×C239D4211yescharacteristic
285C2×C239#54611yescharacteristic
286C2×C239#54611yescharacteristic
287D239—24no—
288D239—24no—
289D239—42no—
290C239D4×C22⋊C411yescharacteristic, complemented, Sylow
291D4×C22⋊C4—2391nomaximal, Sylow
292C23×D4—2391no—
293C2×C4×D4—2391no—
294C2×C4×D4—2391no—
295C22×C22⋊C4—2391no—
296C22×C22⋊C4—2391no—
297#390—2391no—
298#390—2391no—
299#386—2391no—
300#386—2391no—
301#386—2391no—
302#386D23911yescharacteristic, complemented
303#380—2391no—
304#379—2391no—
305#379—2391no—
306C4×C22⋊C4—2391no—
307C25—2391no—
308C25—2391no—
309C22×D4—4784no—
310C22×D4—4784no—
311C22×D4—2391no—
312C22×D4—2398no—
313C22×D4—2391no—
314C22×D4—2391no—
315C22×D4C2×D23911yescharacteristic
316C23×C4—2391no—
317C23×C4—2391no—
318C23×C4—2391no—
319C23×C4—2391no—
320C23×C4C2×D23911yescharacteristic, complemented
321C4×D4—4784no—
322C4×D4—4784no—
323C2×C4⋊C4—2391no—
324C2×C4⋊C4—2391no—
325C2×C22⋊C4—4784no—
326C2×C22⋊C4—4784no—
327C2×C22⋊C4—2391no—
328C2×C22⋊C4—2391no—
329C2×C22⋊C4—2391no—
330C2×C22⋊C4—2391no—
331C2×C22⋊C4—2391no—
332C2×C22⋊C4—2391no—
333C2×C22⋊C4—2391no—
334C2×C22⋊C4—2391no—
335C2×C22⋊C4—2391no—
336C2×C22⋊C4—2391no—
337C2×C22⋊C4—2391no—
338C2×C22⋊C4—2391no—
339C2×C22⋊C4—2391no—
340C2×C22⋊C4C2×D23911yescharacteristic, complemented
341C2×C22⋊C4C2×D23911yescharacteristic, complemented
342C2×C22⋊C4C2×D23911yescharacteristic, complemented
343C2×C42—2391no—
344C2×C42—2391no—
345#95—2391no—
346#95—2391no—
347#95C2×D23911yescharacteristic, complemented
348#95C2×D23911yescharacteristic, complemented
349C24—9561no—
350C24—9561no—
351C24—9561no—
352C24—9561no—
353C24—4782no—
354C24—4782no—
355C24—4782no—
356C24—4782no—
357C24—4782no—
358C24—4782no—
359C24—4782no—
360C24—4782no—
361C24—2394no—
362C24—2394no—
363C24—2391no—
364C24—2391no—
365C24—2391no—
366C24C22×D23911yescharacteristic
367C24C22×D23911yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—4782no—
371C2×D4—4782no—
372C2×D4—47832no—
373C2×D4—4782no—
374C2×D4—4782no—
375C2×D4—2394no—
376C2×D4—2394no—
377C2×D4—2394no—
378C2×D4—2394no—
379C2×D4—2394no—
380C2×D4C4×D23914yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—9561no—
385C22×C4—9561no—
386C22×C4—9561no—
387C22×C4—4782no—
388C22×C4—4782no—
389C22×C4—4782no—
390C22×C4—4782no—
391C22×C4—4782no—
392C22×C4—4782no—
393C22×C4—4782no—
394C22×C4—4782no—
395C22×C4—2391no—
396C22×C4—2391no—
397C22×C4—2391no—
398C22×C4—2391no—
399C22×C4—2394no—
400C22×C4—2391no—
401C22×C4C22×D23911yescharacteristic
402C22×C4C22×D23911yescharacteristic
403C22×C4C22×D23911yescharacteristic
404C22×C4C22×D23911yescharacteristic
405C22×C4C22×D23911yescharacteristic
406C4⋊C4—4782no—
407C4⋊C4—4782no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—9561no—
412C22⋊C4—9561no—
413C22⋊C4—9561no—
414C22⋊C4—4782no—
415C22⋊C4—4782no—
416C22⋊C4—4782no—
417C22⋊C4—4782no—
418C22⋊C4—4782no—
419C22⋊C4—4782no—
420C22⋊C4—4782no—
421C22⋊C4—4782no—
422C22⋊C4—4782no—
423C22⋊C4—2394no—
424C42—4782no—
425C42—4782no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—9564no—
437C23—9564no—
438C23—9564no—
439C23—9564no—
440C23—9564no—
441C23—9564no—
442C23—9564no—
443C23—9564no—
444C23—9564no—
445C23—9564no—
446C23—4788no—
447C23—4788no—
448C23—4788no—
449C23—4781no—
450C23—4781no—
451C23—4781no—
452C23—4788no—
453C23—4781no—
454C23—4781no—
455C23—4781no—
456C23—4781no—
457C23—4781no—
458C23—4781no—
459C23—4781no—
460C23—4781no—
461C23—4781no—
462C23—4781no—
463C23—4781no—
464C23—2392no—
465C23—2392no—
466C23—2392no—
467C23—2392no—
468C23—2392no—
469C23—2392no—
470C23—2392no—
471C23C2×C4×D23912yes—
472C23C2×C4×D23912yes—
473C23D4×D23912yes—
474C23D4×D23912yes—
475C23C23×D23911yescharacteristic
476D4—28no—
477D4—4788no—
478D4—4788no—
479D4—23916no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—9564no—
495C2×C4—9564no—
496C2×C4—9564no—
497C2×C4—4788no—
498C2×C4—4781no—
499C2×C4—4781no—
500C2×C4—4781no—
501C2×C4—4781no—
502C2×C4—4781no—
503C2×C4—4781no—
504C2×C4—4781no—
505C2×C4—4781no—
506C2×C4—4781no—
507C2×C4—4781no—
508C2×C4—4781no—
509C2×C4—2392no—
510C2×C4—2392no—
511C2×C4—2392no—
512C2×C4—2392no—
513C2×C4C2×C4×D23912yes—
514C2×C4D4×D23912yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—95616no—
529C22—95616no—
530C22—9561no—
531C22—9561no—
532C22—9561no—
533C22—9561no—
534C22—4782no—
535C22—4782no—
536C22—4782no—
537C22—4782no—
538C22—4782no—
539C22—4782no—
540C22—4782no—
541C22—4782no—
542C22—4782no—
543C22—4782no—
544C22—4782no—
545C22—4782no—
546C22—4782no—
547C22—4782no—
548C22—4782no—
549C22—2394no—
550C22—2394no—
551C22C22⋊C4×D23914yescomplemented
552C22C22×C4×D23911yescharacteristic
553C22C2×D4×D23911yescharacteristic
554C22C2×D4×D23911yescharacteristic
555C22C2×D4×D23911yescharacteristic
556C22#41×D23911yescharacteristic
557C22#2144000511yescharacteristic
558C22#2144000611yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—9561no—
565C4—9561no—
566C4—9561no—
567C4—4782no—
568C4—2394no—
569C2—24no—
570C2—42no—
571C2—9562no—
572C2—4784no—
573C2—4784no—
574C2C2×C22⋊C4×D23911yescharacteristic
575C2C4×D4×D23911yescharacteristic
576C2#2950524411yescharacteristic
577C2#2950540411yescharacteristic
578C2#2950540611yescharacteristic
579C2#2950541111yescharacteristic
580C2#2950541411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#386×C239C2
socle, cosocleC23×C239C24
prime radicalC22×D4×D239C2
hypercenter#386D239
hypocenterC239D4×C22⋊C4
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D239C2semidirect
3. C2×(C22⋊D239)⋊C4C2semidirect
4. C22×(C2×D239)⋊C4C2semidirect
5. C2×C22⋊C4×D239C2semidirect
6. #29504672C2semidirect
7. #29504672C2semidirect
8. #29504652C2semidirect
9. #29504650C2semidirect
10. #29504650C2semidirect
11. #29504631C2semidirect
12. #29504627C2semidirect
13. #29504627C2semidirect
14. #29504619C2semidirect
15. #386×C239C2semidirect
23. C2×D4×D239C4semidirect
24. C23×Dic239C22semidirect
26. C22×C4×D239C22semidirect
27. C22×C4×D239C22semidirect
30. C2×Dic239⋊C4C22semidirect
31. C2×Dic239⋊C4C22semidirect
32. C2×C22⋊Dic239C22semidirect
33. C2×C22⋊Dic239C22semidirect
34. C2×C22⋊Dic239C22semidirect
40. C2×(C2×D239)⋊C4C22semidirect
41. C2×(C2×D239)⋊C4C22semidirect
42. C2×(C2×D239)⋊C4C22semidirect
43. C2×(C2×D239)⋊C4C22semidirect
44. C2×(C2×D239)⋊C4C22semidirect
45. C2×(C2×D239)⋊C4C22semidirect
47. C2×C4×Dic239C22semidirect
48. C2×C4×Dic239C22semidirect
49. C239⋊#95C22semidirect
50. C239⋊#95C22semidirect
52. C23×C4×C239C22semidirect
53. C2×C22⋊C4×C239C22semidirect
54. C2×C22⋊C4×C239C22semidirect
55. C2×C22⋊C4×C239C22semidirect
56. #95×C239C22semidirect
57. #95×C239C22semidirect
70. C23×D239C2×C4semidirect
71. C23×D239C2×C4semidirect
77. C2×D956C2×C4semidirect
81. C2×C22⋊D239C2×C4semidirect
101. C2×C4×D239C2×C4semidirect
116. (C2×D239)⋊C4D4semidirect
123. C2×D4×C239C2×C4semidirect
172. C22⋊D239C22⋊C4semidirect
188. C2×Dic239C2×D4semidirect
223. C2×C4×C239C2×D4semidirect
237. C22×C239C2×C22⋊C4semidirect
266. C2×D239C2×C22⋊C4semidirect
267. C2×D239C4×D4semidirect
277. Dic239C2×C22⋊C4semidirect
290. C239D4×C22⋊C4semidirect
302. #386D239semidirect
320. C23×C4C2×D239semidirect
340. C2×C22⋊C4C2×D239semidirect
341. C2×C22⋊C4C2×D239semidirect
342. C2×C22⋊C4C2×D239semidirect
347. #95C2×D239semidirect
348. #95C2×D239semidirect
380. C2×D4C4×D239semidirect
514. C2×C4D4×D239semidirect
551. C22C22⋊C4×D239semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2392
C2×C4×C22⋊D2392
C2×(C22⋊D239)⋊C42
C22×(C2×D239)⋊C42
C2×C22⋊C4×D2392
#295046722
#295046522
#295046502
#295046312
#295046272
#295046192
#386×C2392
D4×C22⋊C4239