Finite Group Databasebeta

← C2×#21455366 #30546947

Subgroups — C2×#21455366 #30546947

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C22×#14519800C211yesmaximal, characteristic
3C2×#16840337C211yesmaximal, characteristic, complemented
4C2×#16840244C211yesmaximal, characteristic, complemented
5#21455366C2116yesmaximal, direct product factor
6C2×#16839986C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839980C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839966C211yesmaximal, characteristic, complemented
12C2×#16839964C211yesmaximal, characteristic, complemented
13C2×#16839787C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#462C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519809—28no—
21C2×#14519809C2218yescomplemented
22C2×#14519800—28no—
23C2×#14519800C2218yes—
24C22×#11758202C2211yescharacteristic
25C22×#11758190C2211yescharacteristic
26C22×#11758201C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×D488C2211yescharacteristic
30C22×#11758189C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840337—24no—
33#16840337C2218yescomplemented
34C2×#14519775C2211yescharacteristic
35C2×#14519766C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519762—21no—
38C2×#14519762—21no—
39C2×#14519755—21no—
40C2×#14519755—21no—
41#16840244—24no—
42#16840244C2218yescomplemented
43C2×Q8×Dic61C2211yescharacteristic
44C2×C4×D244—21no—
45C2×C4×D244C2211yescharacteristic
46C2×#14519739—21no—
47C2×#14519739C2211yescharacteristic
48C2×#14519734—21no—
49C2×#14519734C2211yescharacteristic
50C2×C4⋊C4×D61—21no—
51C2×C4⋊C4×D61C2211yescharacteristic
52#16839986C2218yescomplemented
53#16839984C2218yescomplemented
54#16839980C2218yescomplemented
55#16839978C2218yescomplemented
56#16839970C2218yescomplemented
57#16839966C2218yescomplemented
58#16839964C2218yescomplemented
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63#16839762C2218yescomplemented
64C2×#14519702C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68#103×D61C2218yescomplemented
69C2×#14519699C2211yescharacteristic
70C2×#14519697C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C22×Q16×C61C2211yescharacteristic
73C2×C4⋊Q8×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C61×#462C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#103×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—22no—
81C2×#11758226—24no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226D418yes—
85C2×#11758226C2314yes—
86C2×#11758226C2314yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—24no—
91C2×Q8×D61—24no—
92C2×Q8×D61C2314yes—
93C22×D244—21no—
94C22×D244—21no—
95C22×D244C2311yescharacteristic
96C22×D244C2311yescharacteristic
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104#14519809—232no—
105#14519800—232no—
106C2×#11758202—24no—
107C2×#11758202C2314yes—
108C2×#11758190—24no—
109C2×#11758190C2314yes—
110C2×#11758201—24no—
111C2×#11758201—24no—
112C2×#11758201—24no—
113C2×#11758201C2314yes—
114C2×#11758201C2314yes—
115C2×#11758201C2314yes—
116C2×D488—24no—
117C2×D488C2314yes—
118C2×#11758189—24no—
119C2×#11758189C2314yes—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—24no—
123C2×C8×D61C2314yes—
124#14519775—22no—
125#14519775C2314yes—
126#14519766—22no—
127#14519766C2314yes—
128#14519765—22no—
129#14519765C2314yes—
130#14519762—28no—
131#14519762—28no—
132#14519755—28no—
133#14519755—28no—
134Q8×Dic61—22no—
135Q8×Dic61C2314yes—
136C4×D244—22no—
137C4×D244—28no—
138C4×D244C2314yes—
139#14519739—28no—
140#14519739—22no—
141#14519739C2314yes—
142#14519734—28no—
143#14519734D414yes—
144#14519734C2314yes—
145C2×C4⋊Dic61—21no—
146C2×C4⋊Dic61C2311yescharacteristic
147C2×#11758196—21no—
148C2×#11758196—21no—
149C2×#11758196—21no—
150C2×#11758196D411yescharacteristic
151C2×#11758196D411yescharacteristic
152C4⋊C4×D61—22no—
153C4⋊C4×D61—28no—
154C4⋊C4×D61C2314yes—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198D411yescharacteristic
162C2×#11758198D411yescharacteristic
163C2×C4×Dic61—21no—
164C2×C4×Dic61C2311yescharacteristic
165C4⋊#92418C2314yes—
166#14519706C2314yes—
167#14519706C2314yes—
168#14519702C2314yes—
169#14519701C2314yes—
170#14519701C2314yes—
171#14519700C2314yes—
172#14519699C2314yes—
173#14519697C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C22×Q8×C61C2311yescharacteristic
176C22×Q8×C61C2311yescharacteristic
177C2×Q16×C61—24no—
178C2×Q16×C61—24no—
179C2×Q16×C61C2314yes—
180C2×Q16×C61C2314yes—
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183C4⋊Q8×C61—22no—
184C4⋊Q8×C61C2314yes—
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C42×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yes—
194#103×C61C2314yes—
195#103×C61C2314yes—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61C2×D411yescharacteristic
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61—22no—
207C2×Q8×C61C2×D414yes—
208C2×Q8×C61C2412yes—
209C2×Q8×C61C2412yes—
210C2×Q8×C61C2412yes—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758226—216no—
224#11758226—28no—
225#11758226—28no—
226#11758226—28no—
227#11758226—48no—
228#11758226C2×D4116yes—
229Q8×D61—28no—
230Q8×D61—28no—
231Q8×D61—48no—
232C2×D244—28no—
233C2×D244—24no—
234C2×D244—21no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—24no—
239C2×D244—21no—
240C2×D244—44no—
241C2×D244C2×D414yes—
242C2×D244C2412yes—
243C2×D244C2412yes—
244C2×C4×D61—28no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—44no—
252C2×C4×D61—44no—
253C2×C4×D61—82no—
254C2×C4×D61—82no—
255C2×C4×D61—82no—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2×D414yes—
258C2×C4×D61#4114yes—
259C2×C4×D61C2412yes—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—21no—
263C2×Dic122—24no—
264C2×Dic122—44no—
265C2×Dic122C2412yes—
266Q16×C61—28no—
267Q16×C61—28no—
268C2×C8×C61—22no—
269C2×C8×C61—22no—
270C2×C8×C61C2412yes—
271C2×C8×C61C2412yes—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—24no—
274C4⋊C4×C61—24no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61C2412yes—
277C42×C61—24no—
278C42×C61C2×D412yes—
279C42×C61C2412yes—
280#11758202—28no—
281#11758201—28no—
282#11758201—28no—
283#11758201—28no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289#11758198—24no—
290#11758198C2×D414yes—
291#11758198C2×D414yes—
292C4⋊Dic61—21no—
293C4⋊Dic61—24no—
294C4⋊Dic61C2412yes—
295#11758196—24no—
296#11758196—24no—
297#11758196—24no—
298#11758196C2×D414yes—
299#11758196C2×D414yes—
300C4×Dic61—24no—
301C4×Dic61C2×D412yes—
302C4×Dic61C2412yes—
303C2×#92418—22no—
304C2×#92418—22no—
305C2×#92418C2412yes—
306C2×#92418C2412yes—
307D488—28no—
308#11758190—28no—
309#11758189—28no—
310C8×D61—28no—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—24no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61#12114yes—
323C22×D61C22×D412yes—
324Q8×C61—24no—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—22no—
330Q8×C61—42no—
331Q8×C61—42no—
332Q8×C61C22×D414yes—
333C2×C4×C61—24no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D412yes—
347C2×C4×C61C2×#4112yes—
348C2×C4×C61C2511yescharacteristic
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61#12114yes—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359D244—216no—
360D244—24no—
361D244—22no—
362D244—22no—
363D244—22no—
364D244—48no—
365D244—42no—
366D244C22×D414yes—
367C4×D61—216no—
368C4×D61—48no—
369C4×D61—48no—
370C4×D61—84no—
371C4×D61—84no—
372C4×D61—84no—
373C4×D61#12118yes—
374C4×D61C22×D414yes—
375C4×D61C2×#4114yes—
376Dic122—22no—
377Dic122—22no—
378Dic122—42no—
379Dic122—48no—
380C8×C61—22no—
381C8×C61—22no—
382#92418—22no—
383#92418—22no—
384C2×#3046—611nomaximal, Sylow
385C22×C61C2×#12112yes—
386C22×C61#57712yes—
387C22×C61#57812yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—28no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—24no—
393C2×D61—48no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—84no—
400C2×D61C2×#12114yes—
401C4×C61—24no—
402C4×C61—22no—
403C4×C61—22no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61C2×#12112yes—
408C4×C61C23×D411yescharacteristic
409C4×C61C22×#4111yescharacteristic
410Dic61—22no—
411Dic61—22no—
412Dic61—42no—
413Dic61—42no—
414Dic61C2×#12114yes—
415C22×#137—611no—
416C22×#135—611no—
417C2×#536—611no—
418C2×#520—611no—
419#3046—6116no—
420C2×#464—611no—
421C2×#464—611no—
422C2×#462—611no—
423C2×#462D6111yescharacteristic, complemented
424C2×#463—611no—
425C2×#463—611no—
426C2×#461—611no—
427C2×#461—611no—
428C2×#424—611no—
429C2×#417—611no—
430C22×#103—611no—
431C2×C61#304614yescomplemented
432C2×C61C22×#12111yescharacteristic
433C2×C61C2×#57711yescharacteristic
434C2×C61C2×#57811yescharacteristic
435D61—24no—
436D61—44no—
437D61—82no—
438C22×#41—611no—
439C22×#41—611no—
440C23×Q8—611no—
441C2×#137—618no—
442C2×#137—1228no—
443C2×#135—618no—
444C2×#135—1228no—
445C22×Q16—611no—
446C22×Q16C2×D6111yescharacteristic
447C22×Q16C2×D6111yescharacteristic
448C22×SD16—611no—
449C22×SD16—611no—
450C22×SD16—611no—
451C22×SD16—611no—
452C22×D8—611no—
453C22×M16—611no—
454C23×C8—611no—
455#536—618no—
456#536—1224no—
457C2×C4⋊Q8—611no—
458C2×C4⋊Q8C2×D6111yescharacteristic
459C2×#124—611no—
460C2×#124—611no—
461C2×#123—1221no—
462C2×#123—1221no—
463C2×C22⋊Q8—1221no—
464C2×C22⋊Q8—1221no—
465#520—618no—
466#520—1224no—
467C2×C4×Q8—611no—
468C2×C4×Q8C2×D6111yescharacteristic
469C2×C4×D4—611no—
470C2×C4×D4—611no—
471C2×C4×D4—1221no—
472C2×C4×D4—1221no—
473C2×#117—611no—
474C2×#117—1221no—
475C22×C4⋊C4—611no—
476C22×C4⋊C4—1221no—
477#464—618no—
478#464—618no—
479#463—618no—
480#463—618no—
481#462—618no—
482#462C2×D6118yescomplemented
483#461—618no—
484#461—618no—
485#424—618no—
486C2×C4⋊C8—611no—
487C2×C4⋊C8—611no—
488C2×C4⋊C8—611no—
489C2×C4⋊C8C2×D6111yescharacteristic
490#417—618no—
491C2×#103—611no—
492C2×#103—611no—
493C2×#103—611no—
494C2×#103—611no—
495C2×#103—618no—
496C2×#103C2×D6111yescharacteristic
497C2×#103C2×D6111yescharacteristic
498C2×#102—611no—
499C2×#102—611no—
500C61C2×#304611yescharacteristic, complemented, Sylow
501C2×#41—618no—
502C2×#41—614no—
503C2×#41—614no—
504C2×#41—1222no—
505C2×#41—1224no—
506C2×#41—1222no—
507C2×#41—1224no—
508C2×#41—1224no—
509C22×Q8—614no—
510C22×Q8—611no—
511C22×Q8—1221no—
512C22×Q8—1222no—
513C22×Q8—1224no—
514C22×Q8—1224no—
515C22×Q8C22×D6111yescharacteristic
516C22×Q8C22×D6111yescharacteristic
517C22×Q8C22×D6111yescharacteristic
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C23×C4—611no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1221no—
526C23×C4—1221no—
527C23×C4—1221no—
528C23×C4—1221no—
529#137—12232no—
530#135—12232no—
531C2×Q16—24no—
532C2×Q16—24no—
533C2×Q16—614no—
534C2×Q16—1224no—
535C2×Q16C22×D6114yes—
536C2×Q16C22×D6114yes—
537C2×SD16—614no—
538C2×SD16—614no—
539C2×SD16—614no—
540C2×SD16—614no—
541C2×SD16—1224no—
542C2×SD16—1224no—
543C2×SD16—1224no—
544C2×SD16—1224no—
545C2×D8—614no—
546C2×D8—1224no—
547C2×M16—614no—
548C2×M16—1224no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8—614no—
552C22×C8—1224no—
553C22×C8C22×D6111yescharacteristic
554C22×C8C22×D6111yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—614no—
557C4⋊Q8—1222no—
558C4⋊Q8C22×D6114yes—
559#124—614no—
560#124—614no—
561#124—1222no—
562#124—1222no—
563#123—1228no—
564#123—1228no—
565C22⋊Q8—1228no—
566C22⋊Q8—1228no—
567C4×Q8—22no—
568C4×Q8—614no—
569C4×Q8—1222no—
570C4×Q8C22×D6114yes—
571C4×D4—614no—
572C4×D4—614no—
573C4×D4—1228no—
574C4×D4—1222no—
575C4×D4—1228no—
576C4×D4—1222no—
577#117—614no—
578#117—614no—
579#117—1228no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—614no—
587C2×C4⋊C4—1228no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C22⋊C4—611no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C42—21no—
603C2×C42—611no—
604C2×C42—1221no—
605C2×C42C22×D6111yescharacteristic
606C4⋊C8—614no—
607C4⋊C8—614no—
608C4⋊C8—614no—
609C4⋊C8C22×D6114yes—
610#103—614no—
611#103—614no—
612#103—614no—
613#103—614no—
614#103C22×D6114yes—
615#103C22×D6114yes—
616#102—614no—
617#102—614no—
618C24—611no—
619C24—1221no—
620C24—1221no—
621#41—6116no—
622#41—12216no—
623#41—1228no—
624#41—1228no—
625#41—1228no—
626#41—2448no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—612no—
636C2×Q8—1224no—
637C2×Q8—1228no—
638C2×Q8—1228no—
639C2×Q8—1221no—
640C2×Q8—1222no—
641C2×Q8—1222no—
642C2×Q8—2444no—
643C2×Q8—2448no—
644C2×Q8D4×D6114yes—
645C2×Q8C23×D6112yes—
646C2×Q8C23×D6112yes—
647C2×Q8C23×D6112yes—
648C2×D4—614no—
649C2×D4—612no—
650C2×D4—612no—
651C2×D4—1224no—
652C2×D4—1228no—
653C2×D4—1224no—
654C2×D4—1221no—
655C2×D4—1222no—
656C2×D4—1221no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—2444no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—614no—
667C22×C4—614no—
668C22×C4—612no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—1224no—
672C22×C4—1228no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—1224no—
676C22×C4—1224no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1224no—
680C22×C4—4882no—
681C22×C4—4882no—
682C22×C4—4882no—
683C22×C4—2444no—
684C22×C4—2444no—
685C22×C4D4×D6111yescharacteristic
686C22×C4D4×D6111yescharacteristic
687C22×C4C23×D6111yescharacteristic
688Q16—28no—
689Q16—28no—
690Q16—1228no—
691SD16—1228no—
692SD16—1228no—
693SD16—1228no—
694SD16—1228no—
695D8—1228no—
696M16—1228no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—612no—
700C2×C8—612no—
701C2×C8—1228no—
702C2×C8—1222no—
703C2×C8—1222no—
704C2×C8C23×D6112yes—
705C2×C8C23×D6112yes—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—21no—
710C4⋊C4—614no—
711C4⋊C4—614no—
712C4⋊C4—612no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4—1224no—
716C4⋊C4—1224no—
717C4⋊C4—1221no—
718C4⋊C4C23×D6112yes—
719C22⋊C4—614no—
720C22⋊C4—614no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4—1224no—
727C42—24no—
728C42—612no—
729C42—612no—
730C42—1224no—
731C42D4×D6112yes—
732C42C23×D6112yes—
733C23—614no—
734C23—612no—
735C23—1222no—
736C23—1222no—
737C23—1224no—
738C23—1222no—
739C23—1222no—
740C23—2442no—
741C23—2442no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23C2×D4×D6111yescharacteristic
746Q8—24no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—42no—
753Q8—42no—
754Q8—1222no—
755Q8—1222no—
756Q8—2448no—
757Q8—2442no—
758Q8C2×D4×D6114yes—
759D4—614no—
760D4—12216no—
761D4—1224no—
762D4—1222no—
763D4—1222no—
764D4—1222no—
765D4—2448no—
766D4—2442no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—614no—
778C2×C4—612no—
779C2×C4—618no—
780C2×C4—614no—
781C2×C4—614no—
782C2×C4—612no—
783C2×C4—612no—
784C2×C4—12216no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—4884no—
790C2×C4—4884no—
791C2×C4—4884no—
792C2×C4—2448no—
793C2×C4—2448no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4C2×D4×D6112yes—
797C2×C4C2×D4×D6112yes—
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6112yes—
800C2×C4#41×D6112yes—
801C2×C4C24×D6111yescharacteristic
802C8—22no—
803C8—22no—
804C8—1222no—
805C8—1222no—
806C22—614no—
807C22—1228no—
808C22—1222no—
809C22—1222no—
810C22—1224no—
811C22—4884no—
812C22—2442no—
813C22—2442no—
814C22—2442no—
815C22—2448no—
816C22—2442no—
817C22—2442no—
818C22#121×D6112yes—
819C22#1684057112yes—
820C22#1684057512yes—
821C22C22×D4×D6111yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—614no—
829C4—1222no—
830C4—1222no—
831C4—2442no—
832C4—2442no—
833C4#121×D6112yes—
834C4C22×D4×D6111yescharacteristic
835C4C2×#41×D6111yescharacteristic
836C2—1224no—
837C2—4882no—
838C2—2444no—
839C2#2145536614yesdirect product factor
840C2C2×#121×D6111yescharacteristic
841C2C2×#1684057111yescharacteristic
842C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC22×#14519800C2
hypercenterC2×#462D61
hypocenterC61C2×#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
3. C2×#16840337C2semidirect
4. C2×#16840244C2semidirect
5. #21455366C2direct (N × H)
6. C2×#16839986C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839966C2semidirect
12. C2×#16839964C2semidirect
13. C2×#16839787C2semidirect
14. C2×#16839762C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#462C2semidirect
21. C2×#14519809C22semidirect
33. #16840337C22semidirect
42. #16840244C22semidirect
52. #16839986C22semidirect
53. #16839984C22semidirect
54. #16839980C22semidirect
55. #16839978C22semidirect
56. #16839970C22semidirect
57. #16839966C22semidirect
58. #16839964C22semidirect
59. #16839787C22semidirect
63. #16839762C22semidirect
68. #103×D61C22semidirect
75. C61×#462C22semidirect
423. C2×#462D61semidirect
431. C2×C61#3046semidirect
482. #462C2×D61semidirect
500. C61C2×#3046semidirect
839. C2#21455366direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C22×#145198002
C2×#168403372
C2×#168402442
#214553662
C2×#168399862
C2×#168399842
C2×#168399702
C2×#168399802
C2×#168399782
C2×#168399662
C2×#168399642
C2×#168397872
C2×#168397622
C2×#103×D612
C2×C61×#4622
C2×#304661