Finite Group Databasebeta

← #29695520

Subgroups — #29695520

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840424C211yesmaximal, characteristic
2C2×#16839832C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448719C211yesmaximal, characteristic, complemented
6#21446749C211yesmaximal, characteristic, complemented
7#21446633C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446246C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C61×#1803C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840424—24no—
21#16840424C418yescomplemented
22C2×#14519765—21no—
23C2×#14519765C2211yescharacteristic
24C2×#14519757—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519752—21no—
27C2×#14519752C2211yescharacteristic
28C2×C4×D244—21no—
29C2×C4×D244C2211yescharacteristic
30C2×#14519739—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33#16839832—24no—
34#16839762—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41#103×D61—24no—
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519688C2211yescharacteristic
49#16839658—21no—
50#16839633—21no—
51#16839633—21no—
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4×C4⋊Dic61C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#384C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C22×Dic122—21no—
71C22×Dic122C2311yescharacteristic
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61—22no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61C2×C414yescomplemented
78C22×D244—21no—
79C22×D244—21no—
80C22×D244D411yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—41no—
96#14519765—22no—
97#14519765—28no—
98#14519765C2×C414yescomplemented
99#14519757—22no—
100#14519757—28no—
101#14519757C2×C414yescomplemented
102#14519752—28no—
103#14519752—22no—
104#14519752C2×C414yescomplemented
105C4×D244—28no—
106C4×D244C2×C414yes—
107C4×D244D414yes—
108#14519739—44no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61D411yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C4⋊C4×D61—41no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198D411yescharacteristic
126C2×#11758198D411yescharacteristic
127C2×C4×Dic61—21no—
128#14519702—22no—
129#14519702—41no—
130#14519701—22no—
131#14519701D414yescomplemented
132#14519700—22no—
133#14519700—41no—
134#14519699—22no—
135#14519699—41no—
136#14519697—22no—
137#14519697—41no—
138#14519689—22no—
139#14519689—22no—
140#14519688—22no—
141#14519684—21no—
142#14519684—21no—
143#14519684—21no—
144C22×Q8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C4×Q8×C61—22no—
148C4×Q8×C61C2×C414yescomplemented
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C42×C61—21no—
156C2×C42×C61C2311yescharacteristic
157C4⋊C8×C61—22no—
158#103×C61—22no—
159#103×C61—22no—
160C23×D61—21no—
161C23×D61C2×D411yescharacteristic
162C23×D61C2×D411yescharacteristic
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
167C2×Q8×C61C2×D412yes—
168C2×Q8×C61#4112yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181#11758226—28no—
182#11758226—44no—
183#11758226—44no—
184#11758226—44no—
185Q8×D61—28no—
186Q8×D61—44no—
187Q8×D61—44no—
188Q8×D61—44no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—24no—
196C2×D244—24no—
197C2×D244—21no—
198C2×D244—42no—
199C2×D244—42no—
200C2×D244—42no—
201C2×D244—42no—
202C2×D244C22⋊C414yes—
203C2×D244C22×C412yes—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—81no—
223C2×C4×D61—81no—
224C2×C4×D61C22×C412yes—
225C2×C4×D61C22×C412yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—24no—
234C2×Dic122—42no—
235C2×Dic122—42no—
236C2×Dic122C22×C412yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61—81no—
251C4⋊C4×C61C22×C412yes—
252C42×C61—24no—
253C42×C61C22×C412yes—
254C42×C61C2×D412yes—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—42no—
260#11758198—42no—
261#11758198C22⋊C414yes—
262#11758198C22⋊C414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61C22⋊C414yes—
268C4⋊Dic61C2×D412yes—
269#11758196—42no—
270#11758196—42no—
271C4×Dic61—42no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418C2×D412yes—
278#11758189—44no—
279C8×D61—44no—
280C23×C61C22×D411yescharacteristic
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—22no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61C2×C22⋊C412yes—
299C22×D61C2×C22⋊C412yes—
300C22×D61AGL(1,ℤ/8)12yes—
301C22×D61#13712yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61C4×D414yescomplemented
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×C22⋊C412yes—
323C2×C4×C61C2×C22⋊C412yes—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61C2×C22⋊C412yes—
344C2×Dic61C2×C22⋊C412yes—
345D244—28no—
346D244—22no—
347D244—22no—
348D244—48no—
349D244—48no—
350D244—41no—
351D244—41no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—48no—
361C4×D61—48no—
362C4×D61—84no—
363C4×D61—84no—
364Dic122—22no—
365Dic122—22no—
366Dic122—48no—
367Dic122—41no—
368Dic122—41no—
369C8×C61—41no—
370C8×C61—41no—
371#92418—22no—
372#92418—41no—
373#22421—611nomaximal, Sylow
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61D4211yescharacteristic
376C22×C61#54611yescharacteristic
377C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C61C2×#13711yescharacteristic
379C22×C61#57711yescharacteristic
380C22×C61#57811yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—81no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61#41714yescomplemented
402C4×C61—24no—
403C4×C61—22no—
404C4×C61—22no—
405C4×C61—42no—
406C4×C61—81no—
407C4×C61—81no—
408C4×C61C2×C4×D411yescharacteristic
409C4×C61#51811yescharacteristic
410C4×C61D4211yescharacteristic
411C4×C61#54611yescharacteristic
412Dic61—22no—
413Dic61—22no—
414Dic61—42no—
415Dic61—42no—
416Dic61—81no—
417C2×#548—611no—
418C2×#435—611no—
419C2×#417—611no—
420C22×#103—611no—
421D4×C4⋊C4—611no—
422#1983—611no—
423#1959—611no—
424#1894—611no—
425#1893—611no—
426#1874—611no—
427#1872—611no—
428#1803D6111yescharacteristic, complemented
429#1788—611no—
430#1787—611no—
431#1763—611no—
432C2×C61D4×C22⋊C411yescharacteristic
433C2×C61C2×#41711yescharacteristic
434C2×C61#289811yescharacteristic
435C2×C61#326511yescharacteristic
436C2×C61#327011yescharacteristic
437C2×C61#330811yescharacteristic
438C2×C61#331611yescharacteristic
439D61—24no—
440D61—42no—
441D61—82no—
442C22×#41—611no—
443C23×Q8—611no—
444C22×M16—611no—
445C23×C8—611no—
446#548—618no—
447#548—1224no—
448C2×#124—611no—
449C2×#124—1221no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—1221no—
452C2×#121—611no—
453C2×#121—1221no—
454C2×C4×Q8C2×D6111yescharacteristic
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C22×C4⋊C4—611no—
459C22×C4⋊C4—611no—
460#435—1224no—
461C2×C4⋊C8C2×D6111yescharacteristic
462#417—1224no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—1224no—
470C2×#103C2×D6111yescharacteristic
471C2×#103C2×D6111yescharacteristic
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×C22⋊C8—611no—
477C2×C22⋊C8—611no—
478C2×#97—611no—
479#389—1221no—
480#385—1221no—
481#385—1221no—
482#384C2×D6111yescharacteristic
483#380—611no—
484#380—611no—
485C4×C4⋊C4—611no—
486#340—611no—
487#340—611no—
488#340C2×D6111yescharacteristic
489#340C2×D6111yescharacteristic
490C61#2242111yescharacteristic, complemented, Sylow
491C2×#41—614no—
492C2×#41—1222no—
493C2×#41—1222no—
494C2×#41—1222no—
495C2×#41—2441no—
496C2×#41—2441no—
497C22×Q8—614no—
498C22×Q8—611no—
499C22×Q8—1221no—
500C22×Q8—1222no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8—2441no—
504C22×Q8—2441no—
505C22×Q8C22×D6111yescharacteristic
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1221no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C2×M16—1222no—
517C2×M16—1222no—
518C2×M16—2441no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1222no—
522C22×C8—1222no—
523C22×C8—2441no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526#124—614no—
527#124—1228no—
528#124—1222no—
529C22⋊Q8—614no—
530C22⋊Q8—1228no—
531C22⋊Q8—1222no—
532#121—614no—
533#121—1222no—
534#121—1228no—
535C4×Q8—22no—
536C4×Q8C4×D6114yescomplemented
537C4×D4—614no—
538C4×D4—614no—
539C4×D4—1228no—
540C4×D4—2444no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—2441no—
553C2×C4⋊C4—2441no—
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—21no—
566C2×C42—1221no—
567C2×C42C22×D6111yescharacteristic
568C4⋊C8—22no—
569#103—22no—
570#103—22no—
571#103—614no—
572#103—1222no—
573#103—1222no—
574#103—1222no—
575#103—2441no—
576#103—2441no—
577#102—1222no—
578#102—1222no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583#97—1222no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587C24—611no—
588C24—611no—
589C24—1221no—
590#41—1228no—
591#41—2444no—
592#41—2444no—
593#41—2444no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—612no—
598C2×Q8—1224no—
599C2×Q8—1221no—
600C2×Q8—1228no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—2442no—
606C2×Q8—2442no—
607C2×Q8—2444no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8C2×C4×D6112yes—
611C2×Q8D4×D6112yes—
612C2×Q8#1175822612yes—
613C2×D4—612no—
614C2×D4—614no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—2442no—
625C2×D4—2442no—
626C2×D4—2442no—
627C2×D4—2442no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—1224no—
639C22×C4—1224no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—4881no—
652C22×C4—4881no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4D4×D6111yescharacteristic
662C22×C4D4×D6111yescharacteristic
663C22×C4C23×D6111yescharacteristic
664M16—2444no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—612no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—2444no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—42no—
685C4⋊C4—81no—
686C4⋊C4—614no—
687C4⋊C4—612no—
688C4⋊C4—1224no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—2442no—
693C4⋊C4—2442no—
694C4⋊C4C2×C4×D6112yes—
695C22⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C42—24no—
704C42—2442no—
705C42C2×C4×D6112yes—
706C42D4×D6112yes—
707C23—612no—
708C23—612no—
709C23—612no—
710C23—612no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1222no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23C2×D4×D6111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—1222no—
733Q8—1222no—
734Q8—2448no—
735Q8—2441no—
736Q8—2441no—
737Q8#1451973914yescomplemented
738D4—1228no—
739D4—1222no—
740D4—1222no—
741D4—2448no—
742D4—2448no—
743D4—2441no—
744D4—2441no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—612no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2448no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4C22⋊C4×D6112yes—
789C2×C4C22⋊C4×D6112yes—
790C2×C4C22×C4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×#1175822611yescharacteristic
794C2×C4#1451982311yescharacteristic
795C2×C4#1451982311yescharacteristic
796C8—41no—
797C8—41no—
798C8—1222no—
799C8—2441no—
800C22—614no—
801C22—1222no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—4881no—
811C22—4881no—
812C22—4881no—
813C22—4881no—
814C22—2442no—
815C22—2442no—
816C22—2442no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22C2×C22⋊C4×D6111yescharacteristic
822C22#1684039611yescharacteristic
823C22#1684040311yescharacteristic
824C22AGL(1,ℤ/8)×D6111yescharacteristic
825C22#137×D6111yescharacteristic
826C22#1684056811yescharacteristic
827C22#1684057511yescharacteristic
828C4—22no—
829C4—24no—
830C4—22no—
831C4—42no—
832C4—81no—
833C4—81no—
834C4—1222no—
835C4—1222no—
836C4—4881no—
837C4—2442no—
838C4—2442no—
839C4C2×#1451973911yescharacteristic
840C4#1684023611yescharacteristic
841C4#1684039611yescharacteristic
842C4#1684040311yescharacteristic
843C2—1224no—
844C2—4882no—
845C2—2442no—
846C2#2144863911yescharacteristic
847C2#417×D6111yescharacteristic
848C2#2145434711yescharacteristic
849C2#2145730911yescharacteristic
850C2#2145739511yescharacteristic
851C2#2145780711yescharacteristic
852C2#2145792711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1803C2
socleC23×C61C22×D4
prime radicalC2×#16840424C2
cosocleC22×C4×C61C24
hypercenter#1803D61
hypocenterC61#22421
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#16839832C2semidirect
3. C2×#16839762C2semidirect
4. C2×#103×D61C2semidirect
5. #21448719C2semidirect
6. #21446749C2semidirect
7. #21446633C2semidirect
8. #21446251C2semidirect
9. #21446246C2semidirect
10. #21446135C2semidirect
11. #21446125C2semidirect
12. #21445758C2semidirect
13. #21445752C2semidirect
14. #21445649C2semidirect
15. C61×#1803C2semidirect
21. #16840424C4semidirect
69. C2×#11758226C2×C4semidirect
77. C2×Q8×D61C2×C4semidirect
98. #14519765C2×C4semidirect
101. #14519757C2×C4semidirect
104. #14519752C2×C4semidirect
131. #14519701D4semidirect
148. C4×Q8×C61C2×C4semidirect
305. Q8×C61C4×D4semidirect
401. C2×D61#417semidirect
428. #1803D61semidirect
490. C61#22421semidirect
536. C4×Q8C4×D61semidirect
737. Q8#14519739semidirect

Maximal subgroups

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

subgroupindex
C2×#168404242
C2×#168398322
C2×#168397622
C2×#103×D612
#214487192
#214467492
#214466332
#214462512
#214462462
#214461352
#214461252
#214457582
#214457522
#214456492
C61×#18032
#2242161