Finite Group Databasebeta

← C2×#21457406 #30555076

Subgroups — C2×#21457406 #30555076

Order 15616.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C22×#14519800C211yesmaximal, characteristic, complemented
3C2×#16840434C211yesmaximal, characteristic, complemented
4C2×#16840424C211yesmaximal, characteristic, complemented
5#21457406C2116yesmaximal, direct product factor
6C2×#16840151C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16839992C211yesmaximal, characteristic, complemented
9C2×#16839984C211yesmaximal, characteristic, complemented
10C2×#16839962C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839910C211yesmaximal, characteristic, complemented
13C2×#16839910C211yesmaximal, characteristic, complemented
14C2×#16839902C211yesmaximal, characteristic, complemented
15C2×#16839835C211yesmaximal, characteristic, complemented
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic
19C22×#11758226C2211yescharacteristic
20C22×Q8×D61C2211yescharacteristic
21C2×#14519809—28no—
22C2×#14519809C2218yescomplemented
23C2×#14519800—28no—
24C2×#14519800C2218yescomplemented
25C22×#11758202C2211yescharacteristic
26C22×#11758190C2211yescharacteristic
27C22×#11758190C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758201C2211yescharacteristic
31C22×D488C2211yescharacteristic
32C22×D488C2211yescharacteristic
33C22×#11758189C2211yescharacteristic
34C22×C8×D61C2211yescharacteristic
35#16840434—24no—
36#16840434C2218yescomplemented
37#16840424—24no—
38#16840424C2218yescomplemented
39C2×#14519774—21no—
40C2×#14519774C2211yescharacteristic
41C2×#14519765—21no—
42C2×#14519765C2211yescharacteristic
43C2×#14519757—21no—
44C2×#14519757C2211yescharacteristic
45C2×#14519752—21no—
46C2×#14519752—21no—
47C2×#14519752—21no—
48C2×#14519752C2211yescharacteristic
49C2×#14519752C2211yescharacteristic
50C2×#14519752C2211yescharacteristic
51C2×C4×D244—21no—
52C2×C4×D244—21no—
53C2×C4×D244C2211yescharacteristic
54#16840151C2218yescomplemented
55#16840016C2218yescomplemented
56#16839992C2218yescomplemented
57#16839984C2218yescomplemented
58#16839962C2218yescomplemented
59#16839927C2218yescomplemented
60#16839910C2218yescomplemented
61#16839910C2218yescomplemented
62#16839902C2218yescomplemented
63#16839835C2218yescomplemented
64C2×C4⋊#92418C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C61×#441C2218yescomplemented
75C2×#106×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—22no—
81C2×#11758226—22no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226—24no—
85C2×#11758226—42no—
86C2×#11758226—42no—
87C2×#11758226—42no—
88C2×#11758226C2314yes—
89C2×#11758226C2314yes—
90C2×#11758226C2314yes—
91C22×Dic122—21no—
92C22×Dic122C2311yescharacteristic
93C2×Q8×D61—22no—
94C2×Q8×D61—24no—
95C2×Q8×D61—42no—
96C2×Q8×D61C2314yes—
97C22×D244—21no—
98C22×D244—21no—
99C22×D244—21no—
100C22×D244—21no—
101C22×D244—21no—
102C22×D244—21no—
103C22×D244—21no—
104C22×D244—21no—
105C22×D244D411yescharacteristic
106C22×D244C2311yescharacteristic
107C22×D244C2311yescharacteristic
108C22×D244C2311yescharacteristic
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61—21no—
112C22×C4×D61—21no—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519809—232no—
116#14519800—232no—
117C2×#11758202—24no—
118C2×#11758202C2314yes—
119C2×#11758190—24no—
120C2×#11758190—42no—
121C2×#11758190C2314yes—
122C2×#11758190C2314yes—
123C2×#11758201—24no—
124C2×#11758201—24no—
125C2×#11758201—24no—
126C2×#11758201C2314yes—
127C2×#11758201C2314yes—
128C2×#11758201C2314yes—
129C2×D488—24no—
130C2×D488—42no—
131C2×D488C2314yes—
132C2×D488C2314yes—
133C2×#11758189—24no—
134C2×#11758189C2314yes—
135C22×#92418C2311yescharacteristic
136C22×#92418C2311yescharacteristic
137C2×C8×D61—24no—
138C2×C8×D61C2314yes—
139#14519774—28no—
140#14519774—22no—
141#14519774C2314yes—
142#14519765—22no—
143#14519765—28no—
144#14519765C2314yes—
145#14519757—22no—
146#14519757—28no—
147#14519757C2314yes—
148#14519752—28no—
149#14519752—22no—
150#14519752—22no—
151#14519752—22no—
152#14519752—28no—
153#14519752—28no—
154#14519752C2314yes—
155#14519752C2314yes—
156#14519752C2314yes—
157C4×D244—28no—
158C4×D244—28no—
159C4×D244D414yes—
160C4×D244C2314yes—
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C4⋊#92418C2314yes—
172#14519700C2314yes—
173#14519697C2314yes—
174#14519697C2314yes—
175#14519697C2314yes—
176#14519689C2314yes—
177#14519689C2314yes—
178C22×Q8×C61C2311yescharacteristic
179C22×Q8×C61C2311yescharacteristic
180C2×Q16×C61D418yescomplemented
181C2×Q16×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C4×Q8×C61—22no—
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yes—
187C4×Q8×C61C2314yes—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C42×C61—21no—
193C2×C42×C61—21no—
194C2×C42×C61C2311yescharacteristic
195#106×C61C2314yes—
196#103×C61C2314yes—
197#103×C61C2314yes—
198#97×C61C2314yes—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203C23×D61C2×D411yescharacteristic
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—22no—
207C2×Q8×C61—22no—
208C2×Q8×C61C2×D414yes—
209C2×Q8×C61C2×D414yes—
210C2×Q8×C61C2412yes—
211C2×Q8×C61C2412yes—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C22×Dic61—21no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222#11758226—28no—
223#11758226—28no—
224#11758226—28no—
225#11758226—44no—
226#11758226—44no—
227#11758226—44no—
228#11758226—48no—
229#11758226—48no—
230#11758226—48no—
231Q8×D61—28no—
232Q8×D61—44no—
233Q8×D61—48no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—24no—
243C2×D244—24no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—24no—
249C2×D244—24no—
250C2×D244—24no—
251C2×D244—42no—
252C2×D244—44no—
253C2×D244—44no—
254C2×D244—44no—
255C2×D244—44no—
256C2×D244—44no—
257C2×D244—82no—
258C2×D244—82no—
259C2×D244—82no—
260C2×D244C2×D414yes—
261C2×D244C2412yes—
262C2×D244C2412yes—
263C2×D244C2412yes—
264C2×C4×D61—22no—
265C2×C4×D61—22no—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—24no—
269C2×C4×D61—24no—
270C2×C4×D61—24no—
271C2×C4×D61—24no—
272C2×C4×D61—44no—
273C2×C4×D61—44no—
274C2×C4×D61—44no—
275C2×C4×D61—44no—
276C2×C4×D61C2×D412yes—
277C2×C4×D61C2×D412yes—
278C2×C4×D61C2412yes—
279C2×C4×D61C2412yes—
280C2×Dic122—22no—
281C2×Dic122—22no—
282C2×Dic122—21no—
283C2×Dic122—24no—
284C2×Dic122—44no—
285C2×Dic122C2412yes—
286Q16×C61C2×D4116yescomplemented
287C2×C8×C61—22no—
288C2×C8×C61C2×D414yes—
289C2×C8×C61C2412yes—
290C2×C8×C61C2412yes—
291C4⋊C4×C61—24no—
292C4⋊C4×C61—24no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C2412yes—
296C4⋊C4×C61C2412yes—
297C42×C61—24no—
298C42×C61—24no—
299C42×C61C2×D412yes—
300C42×C61C2412yes—
301#11758202—28no—
302#11758201—28no—
303#11758201—28no—
304#11758201—28no—
305#11758198—24no—
306#11758198—24no—
307#11758198—24no—
308#11758198—24no—
309#11758198—24no—
310#11758198—24no—
311#11758198C2×D414yes—
312#11758198C2×D414yes—
313C4⋊Dic61—24no—
314C4⋊Dic61C2×D414yes—
315C2×#92418—22no—
316C2×#92418—22no—
317C2×#92418C2412yes—
318C2×#92418C2412yes—
319D488—28no—
320D488—44no—
321#11758190—28no—
322#11758190—44no—
323#11758189—28no—
324C8×D61—28no—
325C23×C61C22×D411yescharacteristic
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61C22×D412yes—
345C22×D61C22×D412yes—
346Q8×C61—24no—
347Q8×C61—24no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61C22×D414yes—
351Q8×C61C22×D414yes—
352C2×C4×C61—24no—
353C2×C4×C61—24no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61C22×D412yes—
363C2×C4×C61C22×D412yes—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D412yes—
366C2×C4×C61H(5,𝔽2)12yes—
367C2×C4×C61C2511yescharacteristic
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61C22×D412yes—
373C2×Dic61C22×D412yes—
374D244—22no—
375D244—22no—
376D244—22no—
377D244—22no—
378D244—22no—
379D244—22no—
380D244—44no—
381D244—48no—
382D244—48no—
383D244—48no—
384D244—48no—
385D244—48no—
386D244—42no—
387D244—42no—
388D244—42no—
389D244—84no—
390D244—84no—
391D244—84no—
392C4×D61—24no—
393C4×D61—24no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—48no—
399C4×D61—48no—
400C4×D61—48no—
401C4×D61—48no—
402Dic122—22no—
403Dic122—22no—
404Dic122—48no—
405Dic122—42no—
406C8×C61—22no—
407C8×C61C22×D414yes—
408#92418—22no—
409#92418—22no—
410C2×#3271—611nomaximal, Sylow
411C22×C61D4212yes—
412C22×C61#57512yes—
413C22×C61#57712yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—44no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—84no—
433C2×D61—84no—
434C2×D61—84no—
435C4×C61—24no—
436C4×C61—24no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—42no—
440C4×C61—42no—
441C4×C61D4212yes—
442C4×C61C23×D411yescharacteristic
443C4×C61C2×H(5,𝔽2)11yescharacteristic
444Dic61—22no—
445Dic61—22no—
446Dic61—42no—
447C22×#137—611no—
448C22×#135—611no—
449C2×#550—611no—
450C2×#548—611no—
451#3271—6116no—
452C2×#496—611no—
453C2×#469—611no—
454C2×#465—611no—
455C2×#464—611no—
456C2×#460—611no—
457C2×#452—611no—
458C2×#449—611no—
459C2×#449—611no—
460C2×#448—611no—
461C2×#441D6111yescharacteristic, complemented
462C2×#435—611no—
463C2×C61#327114yescomplemented
464C2×C61C2×D4211yescharacteristic
465C2×C61C2×#57511yescharacteristic
466C2×C61C2×#57711yescharacteristic
467D61—42no—
468D61—42no—
469D61—82no—
470D61—82no—
471D61—82no—
472C22×#41—611no—
473C22×#41—611no—
474C22×#41—611no—
475C23×Q8—611no—
476C2×#137—618no—
477C2×#137—1228no—
478C2×#135—618no—
479C2×#135—1228no—
480C22×Q16—611no—
481C22×Q16C2×D6111yescharacteristic
482C22×SD16—611no—
483C22×SD16—611no—
484C22×SD16—611no—
485C22×SD16—611no—
486C22×SD16—611no—
487C22×D8—611no—
488C22×D8—611no—
489C22×M16—611no—
490C23×C8—611no—
491#550—618no—
492#550—1224no—
493#548—618no—
494#548—1224no—
495C2×#127—611no—
496C2×#127—1221no—
497C2×#124—611no—
498C2×#124—1221no—
499C2×C22⋊Q8—611no—
500C2×C22⋊Q8—1221no—
501C2×#121—611no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121—1221no—
505C2×#121—1221no—
506C2×#121—1221no—
507C2×C4×Q8C2×D6111yescharacteristic
508C2×C4×Q8C2×D6111yescharacteristic
509C2×C4×D4—611no—
510C2×C4×D4—1221no—
511C2×C4×D4—1221no—
512#496—618no—
513#469—618no—
514#465—618no—
515#464—618no—
516#460—618no—
517#452—618no—
518#449—618no—
519#449—618no—
520#448—618no—
521#441C2×D6118yescomplemented
522#435—618no—
523C2×#106C2×D6111yescharacteristic
524C2×C4⋊C8—611no—
525C2×#103—611no—
526C2×#103C2×D6111yescharacteristic
527C2×#103C2×D6111yescharacteristic
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×#97C2×D6111yescharacteristic
534C61C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—614no—
536C2×#41—614no—
537C2×#41—614no—
538C2×#41—1222no—
539C2×#41—1222no—
540C2×#41—1222no—
541C2×#41—1224no—
542C2×#41—1224no—
543C2×#41—1224no—
544C2×#41—2442no—
545C2×#41—2442no—
546C2×#41—2442no—
547C22×Q8—614no—
548C22×Q8—611no—
549C22×Q8—1221no—
550C22×Q8—1222no—
551C22×Q8—1224no—
552C22×Q8—2442no—
553C22×Q8C22×D6111yescharacteristic
554C22×Q8C22×D6111yescharacteristic
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—611no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4—1221no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4—1221no—
572C23×C4—1221no—
573#137—12232no—
574#135—12232no—
575C2×Q16—614no—
576C2×Q16—1224no—
577C2×Q16D24418yescomplemented
578C2×Q16C22×D6114yes—
579C2×SD16—614no—
580C2×SD16—614no—
581C2×SD16—614no—
582C2×SD16—614no—
583C2×SD16—614no—
584C2×SD16—1224no—
585C2×SD16—1224no—
586C2×SD16—1224no—
587C2×SD16—1224no—
588C2×SD16—2442no—
589C2×D8—614no—
590C2×D8—614no—
591C2×D8—1224no—
592C2×D8—2442no—
593C2×M16—614no—
594C2×M16—1224no—
595C22×C8—611no—
596C22×C8—611no—
597C22×C8—614no—
598C22×C8—1224no—
599C22×C8C22×D6111yescharacteristic
600C22×C8C22×D6111yescharacteristic
601#127—614no—
602#127—1228no—
603#127—1222no—
604#124—614no—
605#124—1228no—
606#124—1222no—
607C22⋊Q8—614no—
608C22⋊Q8—1228no—
609C22⋊Q8—1222no—
610#121—614no—
611#121—614no—
612#121—614no—
613#121—1228no—
614#121—1228no—
615#121—1222no—
616#121—1222no—
617#121—1222no—
618#121—1228no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8C22×D6114yes—
622C4×Q8C22×D6114yes—
623C4×D4—614no—
624C4×D4—614no—
625C4×D4—1228no—
626C4×D4—1228no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C4⋊C4C22×D6111yescharacteristic
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42C22×D6111yescharacteristic
644#106C22×D6114yes—
645C4⋊C8—614no—
646#103—614no—
647#103C22×D6114yes—
648#103C22×D6114yes—
649#102—614no—
650#102—614no—
651#102—614no—
652C22⋊C8—614no—
653C22⋊C8—614no—
654#97C22×D6114yes—
655C24—611no—
656C24—611no—
657C24—1221no—
658C24—1221no—
659C24—1221no—
660#41—1228no—
661#41—1228no—
662#41—1228no—
663#41—2444no—
664#41—2444no—
665#41—2444no—
666#41—2448no—
667#41—2448no—
668#41—2448no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—612no—
674C2×Q8—1224no—
675C2×Q8—1221no—
676C2×Q8—1228no—
677C2×Q8—1222no—
678C2×Q8—1222no—
679C2×Q8—2444no—
680C2×Q8—2444no—
681C2×Q8—2448no—
682C2×Q8C2×D24414yes—
683C2×Q8C2×D24414yes—
684C2×Q8C23×D6112yes—
685C2×Q8C23×D6112yes—
686C2×D4—614no—
687C2×D4—612no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1224no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1224no—
697C2×D4—1224no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1222no—
702C2×D4—1222no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—4882no—
708C2×D4—4882no—
709C2×D4—4882no—
710C2×D4—2442no—
711C2×D4—2444no—
712C2×D4—2444no—
713C2×D4—2444no—
714C2×D4—2444no—
715C2×D4—2444no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—612no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—1224no—
727C22×C4—1224no—
728C22×C4—1224no—
729C22×C4—1224no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1222no—
733C22×C4—1222no—
734C22×C4—1221no—
735C22×C4—2444no—
736C22×C4—2444no—
737C22×C4—2444no—
738C22×C4—2444no—
739C22×C4D4×D6111yescharacteristic
740C22×C4D4×D6111yescharacteristic
741C22×C4C23×D6111yescharacteristic
742Q16—1228no—
743Q16C2×D244116yescomplemented
744SD16—1228no—
745SD16—1228no—
746SD16—1228no—
747SD16—1228no—
748SD16—2444no—
749D8—1228no—
750D8—2444no—
751M16—1228no—
752C2×C8—22no—
753C2×C8—612no—
754C2×C8—612no—
755C2×C8—1222no—
756C2×C8—1222no—
757C2×C8—1228no—
758C2×C8C2×D24414yes—
759C2×C8C23×D6112yes—
760C2×C8C23×D6112yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—614no—
766C4⋊C4—1224no—
767C4⋊C4C23×D6112yes—
768C4⋊C4C23×D6112yes—
769C22⋊C4—614no—
770C22⋊C4—614no—
771C22⋊C4—1224no—
772C22⋊C4—1224no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C42—24no—
778C42—24no—
779C42D4×D6112yes—
780C42C23×D6112yes—
781C23—612no—
782C23—612no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1222no—
790C23—1222no—
791C23—1222no—
792C23—2442no—
793C23—2442no—
794C23—2442no—
795C23—2442no—
796C23—2442no—
797C23—2442no—
798C23—2442no—
799C23—2442no—
800C23—2442no—
801C23C2×D4×D6111yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—24no—
805Q8—24no—
806Q8—1222no—
807Q8—1222no—
808Q8—2448no—
809Q8—2442no—
810Q8C22×D24414yes—
811Q8C22×D24414yes—
812D4—1222no—
813D4—1222no—
814D4—1222no—
815D4—1222no—
816D4—1222no—
817D4—1222no—
818D4—4884no—
819D4—4884no—
820D4—4884no—
821D4—2444no—
822D4—2448no—
823D4—2448no—
824D4—2448no—
825D4—2448no—
826D4—2448no—
827D4—2442no—
828D4—2442no—
829D4—2442no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—612no—
841C2×C4—612no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1224no—
849C2×C4—1224no—
850C2×C4—1222no—
851C2×C4—2448no—
852C2×C4—2448no—
853C2×C4—2448no—
854C2×C4—2448no—
855C2×C4—2442no—
856C2×C4C2×D4×D6112yes—
857C2×C4C2×D4×D6112yes—
858C2×C4C2×D4×D6111yescharacteristic
859C2×C4C22×D24412yes—
860C2×C4#1451982312yes—
861C2×C4C24×D6111yescharacteristic
862C8—22no—
863C8—1222no—
864C8—1222no—
865C8C22×D24414yes—
866C22—1222no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—1222no—
871C22—1222no—
872C22—4884no—
873C22—4884no—
874C22—4884no—
875C22—2442no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—2444no—
885C22—2444no—
886C22D4×D24412yes—
887C22#1684056112yes—
888C22#1684057112yes—
889C22C22×D4×D6111yescharacteristic
890C4—24no—
891C4—24no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—1222no—
897C4—1222no—
898C4—2442no—
899C4D4×D24412yes—
900C4C23×D24411yescharacteristic
901C4C2×#1451982311yescharacteristic
902C2—4882no—
903C2—4882no—
904C2—4882no—
905C2—2442no—
906C2—2442no—
907C2#2145740614yesdirect product factor
908C2C2×D4×D24411yescharacteristic
909C2C2×#1684056111yescharacteristic
910C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
hypercenterC2×#441D61
hypocenterC61C2×#3271
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
2. C22×#14519800C2semidirect
3. C2×#16840434C2semidirect
4. C2×#16840424C2semidirect
5. #21457406C2direct (N × H)
6. C2×#16840151C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16839992C2semidirect
9. C2×#16839984C2semidirect
10. C2×#16839962C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839910C2semidirect
13. C2×#16839910C2semidirect
14. C2×#16839902C2semidirect
15. C2×#16839835C2semidirect
16. C2×C61×#441C2semidirect
22. C2×#14519809C22semidirect
24. C2×#14519800C22semidirect
36. #16840434C22semidirect
38. #16840424C22semidirect
54. #16840151C22semidirect
55. #16840016C22semidirect
56. #16839992C22semidirect
57. #16839984C22semidirect
58. #16839962C22semidirect
59. #16839927C22semidirect
60. #16839910C22semidirect
61. #16839910C22semidirect
62. #16839902C22semidirect
63. #16839835C22semidirect
74. C61×#441C22semidirect
180. C2×Q16×C61D4semidirect
286. Q16×C61C2×D4semidirect
461. C2×#441D61semidirect
463. C2×C61#3271semidirect
521. #441C2×D61semidirect
534. C61C2×#3271semidirect
577. C2×Q16D244semidirect
743. Q16C2×D244semidirect
907. C2#21457406direct (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×#168404342
C2×#168404242
#214574062
C2×#168401512
C2×#168400162
C2×#168399922
C2×#168399842
C2×#168399622
C2×#168399272
C2×#168399102
C2×#168399022
C2×#168398352
C2×C61×#4412
C2×#327161