Finite Group Databasebeta

← C2×#21455503 #30547253

Subgroups — C2×#21455503 #30547253

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic, complemented
2C22×#14519783C211yesmaximal, characteristic, complemented
3C2×#16840341C211yesmaximal, characteristic
4C2×#16840335C211yesmaximal, characteristic, complemented
5#21455503C2116yesmaximal, direct product factor
6C2×#16840021C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16840005C211yesmaximal, characteristic, complemented
10C2×#16840003C211yesmaximal, characteristic, complemented
11C2×#16840002C211yesmaximal, characteristic, complemented
12C2×#16839990C211yesmaximal, characteristic, complemented
13C2×#16839801C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519806—28no—
21C2×#14519806C2218yescomplemented
22C22×Dic244C2211yescharacteristic
23C22×#11758202C2211yescharacteristic
24C22×#11758200C2211yescharacteristic
25C2×#14519783—28no—
26C2×#14519783C2218yescomplemented
27C22×#11758194C2211yescharacteristic
28C22×#11758189C2211yescharacteristic
29C22×#11758189C2211yescharacteristic
30C22×C8×D61C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840341—24no—
33#16840341C2218yes—
34#16840335—24no—
35#16840335C2218yescomplemented
36C2×#14519776—21no—
37C2×#14519763—21no—
38C2×#14519762—21no—
39C2×#14519759—21no—
40C2×#14519757C2211yescharacteristic
41C2×#14519757C2211yescharacteristic
42C2×#14519756C2211yescharacteristic
43C2×#14519756C2211yescharacteristic
44C2×#14519754—21no—
45C2×#14519753C2211yescharacteristic
46C2×#14519750—21no—
47C2×#14519749—21no—
48C2×#14519748—21no—
49C2×#14519748C2211yescharacteristic
50C2×#14519735C2211yescharacteristic
51C2×C4⋊C4×D61C2211yescharacteristic
52#16840021C2218yescomplemented
53#16840018C2218yescomplemented
54#16840006C2218yescomplemented
55#16840005C2218yescomplemented
56#16840003C2218yescomplemented
57#16840002C2218yescomplemented
58#16839990C2218yescomplemented
59#16839801C2218yescomplemented
60C2×#14519711C2211yescharacteristic
61C2×#14519710C2211yescharacteristic
62C2×#14519708C2211yescharacteristic
63#16839755C2218yescomplemented
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519700C2211yescharacteristic
69#103×D61C2218yescomplemented
70C2×#14519698C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C23×C8×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×#121×C61C2211yescharacteristic
75C61×#465C2218yescomplemented
76C2×#106×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#102×C61C2211yescharacteristic
79C2×#11758222—24no—
80C2×#11758222—24no—
81C2×#11758222D414yes—
82C2×#11758222C2314yes—
83C2×#11758224—24no—
84C2×#11758224—22no—
85C2×#11758224—24no—
86C2×#11758224C2314yes—
87C22×Dic122—21no—
88C22×Dic122D411yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×Dic122C2311yescharacteristic
91C2×Q8×D61—22no—
92C2×Q8×D61—24no—
93C2×Q8×D61—24no—
94C2×Q8×D61C2314yes—
95C22×D244D411yescharacteristic
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61D411yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C23×Dic61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519806—232no—
106C2×Dic244—24no—
107C2×Dic244C2314yes—
108C2×#11758202—24no—
109C2×#11758202C2314yes—
110C2×#11758200—24no—
111C2×#11758200C2314yes—
112#14519783—232no—
113C2×#11758194—24no—
114C2×#11758194C2314yes—
115C2×#11758189—24no—
116C2×#11758189D418yescomplemented
117C2×#11758189C2314yes—
118C2×#11758189C2314yes—
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C2×C8×D61—24no—
122C2×C8×D61—24no—
123C2×C8×D61C2314yes—
124C2×C8×D61C2314yes—
125#14519776—28no—
126#14519763—28no—
127#14519762—28no—
128#14519759—28no—
129#14519757—22no—
130#14519757—22no—
131#14519757C2314yes—
132#14519757C2314yes—
133#14519756—22no—
134#14519756—22no—
135#14519756C2314yes—
136#14519756C2314yes—
137#14519754—28no—
138#14519753—22no—
139#14519753C2314yes—
140#14519750—28no—
141#14519749—28no—
142#14519748—28no—
143#14519748—22no—
144#14519748C2314yes—
145#14519735—22no—
146#14519735C2314yes—
147C2×C4⋊Dic61—21no—
148C2×C4⋊Dic61—21no—
149C2×C4⋊Dic61C2311yescharacteristic
150C2×C4⋊Dic61C2311yescharacteristic
151C2×#11758196—21no—
152C2×#11758196—21no—
153C2×#11758196—21no—
154C2×#11758196—21no—
155C4⋊C4×D61—22no—
156C4⋊C4×D61C2314yes—
157C2×C22⋊Dic61—21no—
158C2×C22⋊Dic61—21no—
159C2×C22⋊Dic61—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×C4×Dic61—21no—
165#14519711C2314yes—
166#14519710C2314yes—
167#14519708C2314yes—
168#14519702C2314yes—
169#14519702C2314yes—
170#14519701C2314yes—
171#14519700C2314yes—
172#14519700C2314yes—
173#14519698C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C22×D4×C61—21no—
176C22×D4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C2×SD16×C61—24no—
179C2×SD16×C61C2314yes—
180C22×C8×C61—24no—
181C22×C8×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C22⋊Q8×C61—22no—
185C22⋊Q8×C61C2314yes—
186#121×C61—22no—
187#121×C61C2314yes—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193#106×C61C2314yes—
194#103×C61C2314yes—
195#102×C61C2314yes—
196C24×C61—21no—
197C24×C61C2×D411yescharacteristic
198C23×D61C2×D411yescharacteristic
199C23×D61C2×D411yescharacteristic
200C2×Q8×C61—21no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—22no—
206C2×D4×C61—21no—
207C2×D4×C61—22no—
208C2×D4×C61—82no—
209C2×D4×C61C2412yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61C2×D414yes—
226C2×C22⋊D61C2×D414yes—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—44no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235Q8×D61—28no—
236Q8×D61—28no—
237Q8×D61—48no—
238#11758224—28no—
239#11758224—28no—
240#11758224—48no—
241#11758222—216no—
242#11758222—28no—
243#11758222—28no—
244C2×D244—24no—
245C2×D244C2×D414yes—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—44no—
251C2×C4×D61—82no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×C4×D61C2×D414yes—
255C2×C4×D61#4114yes—
256C2×C4×D61C2412yes—
257C2×C4×D61C2412yes—
258C2×Dic122—24no—
259C2×Dic122—22no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122—24no—
266C2×Dic122—44no—
267C2×Dic122C2×D414yes—
268C2×Dic122C2412yes—
269C2×Dic122C2412yes—
270SD16×C61—28no—
271C2×C8×C61—22no—
272C2×C8×C61—28no—
273C2×C8×C61C2×D414yes—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—24no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C4⋊C4×C61C2412yes—
281C22⋊C4×C61—24no—
282C22⋊C4×C61—24no—
283C22⋊Dic61—24no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286#11758202—28no—
287#11758200—28no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—24no—
295C4⋊Dic61—24no—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298#11758196—24no—
299#11758196—24no—
300#11758196—24no—
301#11758196—24no—
302C4×Dic61—24no—
303#11758194—28no—
304C2×#92418—22no—
305C2×#92418C2×D414yes—
306C2×#92418C2412yes—
307C2×#92418C2412yes—
308Dic244—28no—
309#11758189—28no—
310#11758189C2×D4116yescomplemented
311C8×D61—28no—
312C8×D61—28no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61C22×D412yes—
321C23×C61C22×D411yescharacteristic
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61#12114yes—
328C22×D61C22×D412yes—
329C22×D61C22×D412yes—
330Q8×C61—22no—
331Q8×C61—22no—
332Q8×C61—42no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—42no—
336D4×C61—84no—
337C2×C4×C61—22no—
338C2×C4×C61—24no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D412yes—
350C2×C4×C61C2×#4112yes—
351C2×C4×C61C2511yescharacteristic
352C22⋊D61—28no—
353C22⋊D61—28no—
354C22⋊D61—48no—
355C22⋊D61—84no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—48no—
366C2×Dic61#12114yes—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369D244—28no—
370C4×D61—24no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—48no—
374C4×D61—84no—
375C4×D61#12118yes—
376C4×D61C22×D414yes—
377C4×D61C2×#4114yes—
378Dic122—28no—
379Dic122—22no—
380Dic122—22no—
381Dic122—22no—
382Dic122—22no—
383Dic122—42no—
384Dic122—42no—
385Dic122—48no—
386C8×C61—22no—
387C8×C61C22×D414yes—
388#92418—22no—
389#92418C22×D414yes—
390C2×#3063—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—44no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—84no—
399C22×C61C2×#12112yes—
400C22×C61#57712yes—
401C22×C61#57812yes—
402C22×C61C23×D411yescharacteristic
403C2×D61—28no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—44no—
410C2×D61C2×#12114yes—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61C2×#12112yes—
416C4×C61C23×D411yescharacteristic
417C4×C61C22×#4111yescharacteristic
418Dic61—22no—
419Dic61—42no—
420Dic61—42no—
421Dic61—42no—
422Dic61—42no—
423Dic61C2×#12114yes—
424C22×#137—611no—
425C22×#131—611no—
426C2×#537—611no—
427C2×#536—611no—
428#3063—6116no—
429C2×#470—611no—
430C2×#470—611no—
431C2×#468—611no—
432C2×#468—611no—
433C2×#467—611no—
434C2×#467—611no—
435C2×#465—611no—
436C2×#465D6111yescharacteristic, complemented
437C2×#428—611no—
438C2×#416—611no—
439C22×#103—611no—
440C2×C61—42no—
441C2×C61—82no—
442C2×C61#306314yescomplemented
443C2×C61C22×#12111yescharacteristic
444C2×C61C2×#57711yescharacteristic
445C2×C61C2×#57811yescharacteristic
446D61—24no—
447D61—42no—
448C22×#41—611no—
449C22×#41—611no—
450C23×Q8—611no—
451C2×#137—618no—
452C2×#137—1228no—
453C22×Q16—611no—
454C22×Q16—611no—
455C22×SD16—611no—
456C22×SD16C2×D6111yescharacteristic
457C2×#131—618no—
458C2×#131—1228no—
459C22×M16—611no—
460C22×M16—611no—
461C22×M16—611no—
462C23×C8—611no—
463C23×C8—611no—
464C23×C8C2×D6111yescharacteristic
465#537—618no—
466#537—1224no—
467#536—618no—
468#536—1224no—
469C2×C4⋊Q8—1221no—
470C2×#124—1221no—
471C2×#123—1221no—
472C2×#123—1221no—
473C2×C22⋊Q8—611no—
474C2×C22⋊Q8—611no—
475C2×C22⋊Q8—611no—
476C2×C22⋊Q8—611no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8—1221no—
479C2×C22⋊Q8C2×D6111yescharacteristic
480C2×#121—611no—
481C2×#121—1221no—
482C2×#121—1221no—
483C2×#121—1221no—
484C2×#121C2×D6111yescharacteristic
485C2×#117—611no—
486C22×C4⋊C4—611no—
487#470—618no—
488#470—618no—
489#468—618no—
490#468—618no—
491#467—618no—
492#467—618no—
493#465—618no—
494#465C2×D6118yescomplemented
495#428—618no—
496C2×#107—611no—
497C2×#107—611no—
498C2×#106—611no—
499C2×#106C2×D6111yescharacteristic
500#416—618no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#103—618no—
507C2×#103C2×D6111yescharacteristic
508C2×#102—611no—
509C2×#102C2×D6111yescharacteristic
510C61C2×#306311yescharacteristic, complemented, Sylow
511C2×#41—614no—
512C2×#41—614no—
513C2×#41—614no—
514C2×#41—1224no—
515C2×#41—1224no—
516C2×#41—1222no—
517C2×#41—1224no—
518C2×#41—1224no—
519C22×Q8—611no—
520C22×Q8—614no—
521C22×Q8—611no—
522C22×Q8—611no—
523C22×Q8—1221no—
524C22×Q8—1222no—
525C22×Q8—1224no—
526C22×Q8—1224no—
527C22×Q8C22×D6111yescharacteristic
528C22×D4—21no—
529C22×D4—611no—
530C22×D4—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4C22×D6111yescharacteristic
535C23×C4—611no—
536C23×C4—611no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4C22×D6111yescharacteristic
541#137—12232no—
542C2×Q16—614no—
543C2×Q16—614no—
544C2×Q16—1224no—
545C2×Q16—1224no—
546C2×SD16—24no—
547C2×SD16—614no—
548C2×SD16—1224no—
549C2×SD16C22×D6114yes—
550#131—12232no—
551C2×M16—614no—
552C2×M16—618no—
553C2×M16—614no—
554C2×M16—614no—
555C2×M16—1224no—
556C2×M16—1224no—
557C22×C8—24no—
558C22×C8—611no—
559C22×C8—611no—
560C22×C8—614no—
561C22×C8—614no—
562C22×C8—1224no—
563C22×C8—1224no—
564C22×C8C22×D6111yescharacteristic
565C22×C8C22×D6114yes—
566C22×C8C22×D6111yescharacteristic
567C4⋊Q8—1228no—
568#124—1228no—
569#123—1228no—
570#123—1228no—
571C22⋊Q8—22no—
572C22⋊Q8—614no—
573C22⋊Q8—614no—
574C22⋊Q8—614no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580C22⋊Q8—1222no—
581C22⋊Q8—1222no—
582C22⋊Q8—1222no—
583C22⋊Q8C22×D6114yes—
584#121—22no—
585#121—614no—
586#121—1228no—
587#121—1222no—
588#121—1228no—
589#121—1228no—
590#121C22×D6114yes—
591#117—614no—
592#117—1222no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—614no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C42—1221no—
616#107—614no—
617#107—614no—
618#106—614no—
619#106C22×D6114yes—
620#103—614no—
621#103—614no—
622#103—614no—
623#103—614no—
624#103—614no—
625#103C22×D6114yes—
626#102—614no—
627#102C22×D6114yes—
628C24—21no—
629C24—611no—
630C24—611no—
631C24D4×D6111yescharacteristic
632#41—1228no—
633#41—12216no—
634#41—1228no—
635#41—1228no—
636#41—1228no—
637#41—2448no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—614no—
642C2×Q8—612no—
643C2×Q8—612no—
644C2×Q8—1224no—
645C2×Q8—1224no—
646C2×Q8—1228no—
647C2×Q8—1228no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1222no—
651C2×Q8—1222no—
652C2×Q8—1222no—
653C2×Q8—1222no—
654C2×Q8—2444no—
655C2×Q8—2448no—
656C2×Q8C23×D6112yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—82no—
662C2×D4—614no—
663C2×D4—614no—
664C2×D4—614no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—4882no—
671C2×D4—2444no—
672C2×D4C23×D6112yes—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—611no—
679C22×C4—612no—
680C22×C4—614no—
681C22×C4—614no—
682C22×C4—612no—
683C22×C4—611no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—1224no—
687C22×C4—1224no—
688C22×C4—1224no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—4882no—
696C22×C4—2444no—
697C22×C4—2444no—
698C22×C4D4×D6112yes—
699C22×C4D4×D6111yescharacteristic
700C22×C4C23×D6112yes—
701C22×C4C23×D6111yescharacteristic
702Q16—1228no—
703Q16—1228no—
704SD16—28no—
705SD16—1228no—
706M16—6116no—
707M16—1228no—
708M16—1228no—
709C2×C8—22no—
710C2×C8—28no—
711C2×C8—614no—
712C2×C8—612no—
713C2×C8—612no—
714C2×C8—1228no—
715C2×C8—1228no—
716C2×C8—1222no—
717C2×C8D4×D6114yes—
718C2×C8C23×D6112yes—
719C2×C8C23×D6112yes—
720C4⋊C4—24no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—612no—
724C4⋊C4—612no—
725C4⋊C4—1224no—
726C4⋊C4—1224no—
727C4⋊C4—1224no—
728C4⋊C4—1224no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1224no—
732C4⋊C4—1224no—
733C4⋊C4C23×D6112yes—
734C4⋊C4C23×D6112yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—1224no—
738C22⋊C4—1224no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C22⋊C4—1224no—
742C22⋊C4—1224no—
743C22⋊C4—1224no—
744C42—1224no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—614no—
753C23—612no—
754C23—612no—
755C23—1222no—
756C23—1222no—
757C23—1222no—
758C23—1222no—
759C23—1222no—
760C23C2×D4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—42no—
765Q8—1228no—
766Q8—1222no—
767Q8—1222no—
768Q8—1222no—
769Q8—1222no—
770Q8—2448no—
771Q8—2442no—
772Q8—2442no—
773D4—22no—
774D4—22no—
775D4—42no—
776D4—84no—
777D4—1228no—
778D4—1228no—
779D4—1228no—
780D4—4884no—
781D4—2448no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—614no—
793C2×C4—612no—
794C2×C4—618no—
795C2×C4—614no—
796C2×C4—614no—
797C2×C4—612no—
798C2×C4—1222no—
799C2×C4—1224no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4884no—
807C2×C4—2448no—
808C2×C4—2448no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4C2×D4×D6112yes—
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6112yes—
816C2×C4#41×D6112yes—
817C2×C4C24×D6111yescharacteristic
818C8—22no—
819C8—614no—
820C8—1222no—
821C8C2×D4×D6114yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—84no—
830C22—614no—
831C22—1222no—
832C22—1222no—
833C22—1228no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—2444no—
838C22#121×D6112yes—
839C22#1684056812yes—
840C22#1684057612yes—
841C22C22×D4×D6111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—614no—
847C4—1222no—
848C4—2442no—
849C4—2442no—
850C4—2442no—
851C4—2442no—
852C4#121×D6112yes—
853C4C22×D4×D6111yescharacteristic
854C4C2×#41×D6111yescharacteristic
855C2—42no—
856C2—82no—
857C2—1224no—
858C2—2442no—
859C2#2145550314yesdirect product factor
860C2C2×#121×D6111yescharacteristic
861C2C2×#1684056811yescharacteristic
862C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840341C2
hypercenterC2×#465D61
hypocenterC61C2×#3063
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#14519806C2semidirect
2. C22×#14519783C2semidirect
4. C2×#16840335C2semidirect
5. #21455503C2direct (N × H)
6. C2×#16840021C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16840005C2semidirect
10. C2×#16840003C2semidirect
11. C2×#16840002C2semidirect
12. C2×#16839990C2semidirect
13. C2×#16839801C2semidirect
14. C2×#16839755C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#465C2semidirect
21. C2×#14519806C22semidirect
26. C2×#14519783C22semidirect
35. #16840335C22semidirect
52. #16840021C22semidirect
53. #16840018C22semidirect
54. #16840006C22semidirect
55. #16840005C22semidirect
56. #16840003C22semidirect
57. #16840002C22semidirect
58. #16839990C22semidirect
59. #16839801C22semidirect
63. #16839755C22semidirect
69. #103×D61C22semidirect
75. C61×#465C22semidirect
116. C2×#11758189D4semidirect
310. #11758189C2×D4semidirect
436. C2×#465D61semidirect
442. C2×C61#3063semidirect
494. #465C2×D61semidirect
510. C61C2×#3063semidirect
859. C2#21455503direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198062
C22×#145197832
C2×#168403412
C2×#168403352
#214555032
C2×#168400212
C2×#168400182
C2×#168400062
C2×#168400052
C2×#168400032
C2×#168400022
C2×#168399902
C2×#168398012
C2×#168397552
C2×#103×D612
C2×C61×#4652
C2×#306361