Finite Group Databasebeta

← C4×#16840573 #30544242

Subgroups — C4×#16840573 #30544242

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840573C211yesmaximal, characteristic
2C4×#14519824C211yesmaximal, characteristic, complemented
3#21454700C213yesmaximal, complemented
4#21454676C213yesmaximal, complemented
5#21454658C213yesmaximal, complemented
6#21454651C213yesmaximal, complemented
7C4×#14519807C213yesmaximal, complemented
8C4×#14519803C213yesmaximal, complemented
9C4×#14519797C213yesmaximal, complemented
10C2×C4×#11758200C213yesmaximal, complemented
11#21454412C211yesmaximal, characteristic, complemented
12#21454349C211yesmaximal, characteristic, complemented
13#21454345C211yesmaximal, characteristic, complemented
14C4×#14519784C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17#16840573C4116yesdirect product factor
18C2×#14519807C2213yes—
19C2×#14519803C2213yes—
20C2×#14519797C2213yes—
21C22×#11758200C2213yes—
22C2×#14519784C2211yescharacteristic
23C2×#14519784C2211yescharacteristic
24#16840245C2211yescharacteristic
25#16840242C2213yescomplemented
26#16840241—23no—
27#16840239C2213yescomplemented
28#16840238—21no—
29C4×#11758222C2213yescomplemented
30C4×#11758224—23no—
31C2×C4×Dic122C2213yescomplemented
32C4×Q8×D61—21no—
33#16839872C2216yescomplemented
34#16839867C2216yescomplemented
35#16839862C2216yescomplemented
36#16839862C2216yescomplemented
37C4×#11758202C2213yescomplemented
38C4×#11758202C2213yescomplemented
39C4×#11758201C2213yescomplemented
40C4×#11758201C2211yescharacteristic, complemented
41C4×#11758200C2216yescomplemented
42C4×#11758200C2216yescomplemented
43C4×#11758200C2213yescomplemented
44C4×#11758200C2216yescomplemented
45C4×#11758200C2213yescomplemented
46C4×#11758199C2213yescomplemented
47C4×#11758199C2213yescomplemented
48#16839805C2213yescomplemented
49#16839802C2213yescomplemented
50#16839798C2213yescomplemented
51C2×#14519708C2213yescomplemented
52#16839770C2213yescomplemented
53#16839767C2213yes—
54#16839763C2213yes—
55#16839761C2213yescomplemented
56#16839758C2213yes—
57#16839756C2213yescomplemented
58C2×#14519700C2213yescomplemented
59C2×#14519698C2213yes—
60#16839718C2213yescomplemented
61#16839718C2213yescomplemented
62C4×#11758194C2213yescomplemented
63C2×C4×#92418C2213yescomplemented
64C2×H(5,𝔽2)×C61C2211yescharacteristic
65C61×#520—21no—
66C61×#520C2213yes—
67C61×#520C2211yescharacteristic
68C61×#518—23no—
69C61×#518C2213yes—
70C4×#41×C61—21no—
71C4×#41×C61C2213yes—
72C4×#41×C61C2211yescharacteristic
73C2×C4×D4×C61—23no—
74C2×C4×D4×C61C2213yes—
75#14519824—24no—
76#14519824C2×C418yescomplemented
77C2×#11758222C2313yes—
78C2×#11758224—23no—
79C22×Dic122C2313yes—
80C2×Q8×D61—21no—
81#14519807C2×C4124yescomplemented
82#14519803C2×C4124yescomplemented
83#14519797C2×C4124yescomplemented
84C2×#11758202C2313yes—
85C2×#11758200C2×C4124yescomplemented
86C2×#11758200C2313yes—
87C2×#11758200C2316yes—
88C2×#11758201C2311yescharacteristic
89C2×#11758199C2313yes—
90#14519784—24no—
91#14519784C2×C418yescomplemented
92C2×#11758194C2313yes—
93C2×#11758194C2313yes—
94C22×#92418C2313yes—
95C22×#92418C2313yes—
96Q8×Dic61—21no—
97C4×Dic122—23no—
98C4×Dic122—23no—
99C4×Dic122C2313yes—
100C4×Dic122C2316yes—
101C4×Dic122C2313yes—
102#14519742—23no—
103#14519742—23no—
104C4×D244C2311yescharacteristic
105C4×D244C2313yes—
106D4×Dic61—23no—
107C4×C22⋊D61—23no—
108C4×C22⋊D61—23no—
109#14519737—26no—
110#14519736C2313yes—
111#14519735—23no—
112#14519734—23no—
113#14519733—26no—
114C2×C4⋊Dic61C2313yes—
115C2×#11758196—23no—
116C4⋊C4×D61—23no—
117C2×C4×Dic61—23no—
118C42×D61—23no—
119#14519710C2313yes—
120#14519710C2313yes—
121#14519708C2313yes—
122#14519708C2316yes—
123#14519708C2311yescharacteristic
124#14519701C2311yescharacteristic
125#14519701C2313yes—
126#14519700C2313yes—
127#14519700C2316yes—
128#14519700C2313yes—
129#14519698C2313yes—
130#14519698C2316yes—
131#14519698C2313yes—
132#14519697C2311yescharacteristic
133#14519697C2313yes—
134#14519688C2316yes—
135C4×#92418C2311yescharacteristic
136C4×#92418C2313yes—
137C4×#92418C2313yes—
138C4×#92418C2313yes—
139H(5,𝔽2)×C61—24no—
140H(5,𝔽2)×C61C2×C418yescomplemented
141C2×#41×C61—21no—
142C2×#41×C61C2313yes—
143C2×#41×C61C2311yescharacteristic
144C22×D4×C61—23no—
145C22×D4×C61C2313yes—
146C23×C4×C61—23no—
147C4×Q8×C61—21no—
148C4×Q8×C61D411yescharacteristic
149C4×Q8×C61D411yescharacteristic
150C4×Q8×C61C2311yescharacteristic
151C4×Q8×C61C2313yes—
152C4×D4×C61—23no—
153C4×D4×C61—23no—
154C4×D4×C61—23no—
155C4×D4×C61—23no—
156C4×D4×C61—23no—
157C4×D4×C61—26no—
158C4×D4×C61—23no—
159C4×D4×C61—23no—
160C4×D4×C61D413yes—
161C4×D4×C61D413yes—
162C4×D4×C61C2313yes—
163C4×D4×C61C2313yes—
164C4×D4×C61C2316yes—
165#117×C61—23no—
166#117×C61—23no—
167#117×C61C2313yes—
168#117×C61C2313yes—
169C2×C4⋊C4×C61—23no—
170C2×C4⋊C4×C61C2313yes—
171C2×C22⋊C4×C61—23no—
172C2×C22⋊C4×C61—26no—
173C2×C42×C61—23no—
174C2×C42×C61C2313yes—
175C24×C61—23no—
176#41×C61—28no—
177#41×C61—26no—
178#41×C61C22×C4112yes—
179#41×C61C22×C414yes—
180#41×C61#4114yes—
181C2×Q8×C61C2×D411yescharacteristic
182C2×Q8×C61C2411yescharacteristic
183C2×D4×C61—23no—
184C2×D4×C61—224no—
185C2×D4×C61—23no—
186C2×D4×C61—26no—
187C2×D4×C61C22×C4112yes—
188C2×D4×C61C2×D413yes—
189C2×D4×C61C2413yes—
190C22×C4×C61—23no—
191C22×C4×C61—23no—
192C22×C4×C61—23no—
193C22×C4×C61—23no—
194C22×C4×C61—26no—
195C22×C4×C61—86no—
196C22×C4×C61C2×D413yes—
197C22×C4×C61C2×D413yes—
198C22×C4×C61C2413yes—
199C2×C22⋊D61—23no—
200C22×Dic61—23no—
201C22×Dic61—23no—
202Q8×D61—28no—
203#11758224—224no—
204#11758222—26no—
205#11758222C22×C4112yescomplemented
206C2×D244C2411yescharacteristic
207C2×C4×D61—23no—
208C2×C4×D61—21no—
209C2×C4×D61—23no—
210C2×Dic122—23no—
211C2×Dic122—26no—
212C2×Dic122C22×C4112yescomplemented
213C2×Dic122C2413yes—
214C4⋊C4×C61—23no—
215C4⋊C4×C61—23no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C2×D413yes—
218C4⋊C4×C61C2×D413yes—
219C4⋊C4×C61C2413yes—
220C4⋊C4×C61C2411yescharacteristic
221C22⋊C4×C61—23no—
222C22⋊C4×C61—23no—
223C22⋊C4×C61—26no—
224C22⋊C4×C61—23no—
225C22⋊C4×C61C2×D416yes—
226C42×C61—21no—
227C42×C61—23no—
228C42×C61—23no—
229C42×C61C2×D413yes—
230C42×C61C2×D413yes—
231C42×C61C2411yescharacteristic
232C42×C61C2413yes—
233C22⋊Dic61—23no—
234#11758202C22×C4112yescomplemented
235#11758201C22×C414yescomplemented
236#11758200C22×C4112yescomplemented
237#11758200C22×C4124yescomplemented
238#11758199C22×C4112yescomplemented
239#11758198—21no—
240#11758198—23no—
241C4⋊Dic61—23no—
242C4⋊Dic61C2413yes—
243C4⋊Dic61C2411yescharacteristic
244#11758196—26no—
245#11758196—23no—
246#11758196—23no—
247C4×Dic61—23no—
248C4×Dic61—23no—
249C4×Dic61—23no—
250C4×Dic61—26no—
251#11758194—26no—
252#11758194C22×C4112yescomplemented
253C2×#92418—26no—
254C2×#92418C22×C4112yescomplemented
255C2×#92418C2411yescharacteristic
256C2×#92418C2413yes—
257C2×#92418C2411yescharacteristic
258C2×#92418C2413yes—
259C23×C61—23no—
260C23×C61—212no—
261C23×C61—83no—
262C23×C61—83no—
263C23×C61C22×D413yes—
264C22×D61—21no—
265Q8×C61—21no—
266Q8×C61C4×D414yes—
267Q8×C61C23×C412yes—
268D4×C61—212no—
269D4×C61—212no—
270D4×C61—23no—
271D4×C61C4×D4112yes—
272D4×C61C23×C416yes—
273C2×C4×C61—21no—
274C2×C4×C61—212no—
275C2×C4×C61—26no—
276C2×C4×C61—21no—
277C2×C4×C61—23no—
278C2×C4×C61—43no—
279C2×C4×C61—46no—
280C2×C4×C61—83no—
281C2×C4×C61—86no—
282C2×C4×C61—83no—
283C2×C4×C61C23×C416yes—
284C2×C4×C61C22×D413yes—
285C2×C4×C61C22×D413yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D413yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C2×#4116yes—
290C2×C4×C61C2511yescharacteristic
291C22⋊D61—212no—
292C2×Dic61—212no—
293C2×Dic61—23no—
294C2×Dic61—21no—
295C2×Dic61—23no—
296C2×Dic61—83no—
297D244—21no—
298D244C23×C412yes—
299C4×D61—212no—
300C4×D61—42no—
301C4×D61—83no—
302Dic122—212no—
303Dic122—23no—
304Dic122C23×C416yes—
305#92418—21no—
306#92418—23no—
307#92418C23×C412yes—
308#92418C23×C416yes—
309C4×#577—611nomaximal, Sylow
310C22×C61—23no—
311C22×C61—23no—
312C22×C61—26no—
313C22×C61—43no—
314C22×C61—43no—
315C22×C61—812no—
316C22×C61C2×C4×D416yes—
317C22×C61C23×D411yescharacteristic
318C2×D61—22no—
319C2×D61—41no—
320C2×D61—41no—
321C4×C61—23no—
322C4×C61—21no—
323C4×C61—22no—
324C4×C61—23no—
325C4×C61—41no—
326C4×C61—43no—
327C4×C61C2×C4×D416yes—
328C4×C61#57712yescomplemented
329C4×C61C24×C411yescharacteristic
330C4×C61C22×#4111yescharacteristic
331Dic61—26no—
332Dic61—43no—
333Dic61—41no—
334C2×#577—611no—
335C4×2−1+4—611no—
336C4×H(5,𝔽2)D6111yescharacteristic, complemented
337#2952—613no—
338#2949—613no—
339#2947—613no—
340#2946—613no—
341C4×#137—613no—
342C4×AGL(1,ℤ/8)—613no—
343C4×#135—613no—
344C2×C4×SD16—613no—
345#2912—611no—
346#2898—611no—
347#2897—611no—
348C4×#131—611no—
349C2×C61—26no—
350C2×C61—46no—
351C2×C61C22×C4×D411yescharacteristic
352C2×C61C2×#57711yescharacteristic
353C2×C61#358411yescharacteristic
354D61—42no—
355C2×2−1+4—611no—
356C2×H(5,𝔽2)C2×D6111yescharacteristic
357#577—6116no—
358C2×#137—613no—
359C2×AGL(1,ℤ/8)—613no—
360C2×#135—613no—
361C22×SD16—613no—
362C2×#131—611no—
363C2×#131—611no—
364#520—21no—
365#520—611no—
366#520—613no—
367#520—1223no—
368#520C2×D6113yes—
369#520C2×D6111yescharacteristic
370#519—613no—
371#519—1221no—
372#518—23no—
373#518C2×D6113yes—
374C4×#41—21no—
375C4×#41—613no—
376C4×#41—1223no—
377C4×#41C2×D6113yes—
378C4×#41C2×D6111yescharacteristic
379C2×C4×Q8—613no—
380C2×C4×Q8—1221no—
381C2×C4×D4—23no—
382C2×C4×D4C2×D6113yes—
383#442—616no—
384#441—616no—
385#440—616no—
386#440—616no—
387C4×Q16—613no—
388C4×Q16—613no—
389C4×SD16—611no—
390C4×SD16—613no—
391C4×SD16—613no—
392C4×SD16—616no—
393C4×SD16—616no—
394C4×SD16—616no—
395C4×SD16—613no—
396C4×D8—613no—
397C4×D8—613no—
398#428—613no—
399#428—613no—
400#427—613no—
401C2×#106—613no—
402#419—613no—
403#418—613no—
404#417—613no—
405#417—613no—
406#416—613no—
407#416—613no—
408C2×#103—613no—
409C2×#102—613no—
410#405—613no—
411#405—613no—
412C4×M16—613no—
413C2×C4×C8—613no—
414C61C4×#57711yescharacteristic, complemented, Sylow
4152−1+4—618no—
4162−1+4—1224no—
417H(5,𝔽2)—24no—
418H(5,𝔽2)C4×D6118yescomplemented
419C2×#41—21no—
420C2×#41—613no—
421C2×#41—1223no—
422C2×#41C22×D6113yes—
423C2×#41C22×D6111yescharacteristic
424C22×Q8—613no—
425C22×Q8—1221no—
426C22×D4—23no—
427C22×D4C22×D6113yes—
428C23×C4—23no—
429#137—6124no—
430AGL(1,ℤ/8)—6124no—
431#135—6124no—
432C2×Q16—613no—
433C2×SD16—611no—
434C2×SD16—6124no—
435C2×SD16—613no—
436C2×SD16—616no—
437C2×D8—613no—
438#131—618no—
439#131—1224no—
440C2×M16—613no—
441C2×M16—613no—
442C22×C8—613no—
443C22×C8—613no—
444C4×Q8—21no—
445C4×Q8—613no—
446C4×Q8—616no—
447C4×Q8—613no—
448C4×Q8—1221no—
449C4×Q8—1223no—
450C4×Q8—1223no—
451C4×Q8—1223no—
452C4×Q8—1223no—
453C4×Q8C22⋊D6111yescharacteristic
454C4×Q8C22⋊D6111yescharacteristic
455C4×Q8C22×D6111yescharacteristic
456C4×Q8C22×D6113yes—
457C4×D4—23no—
458C4×D4—23no—
459C4×D4—23no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—26no—
463C4×D4—23no—
464C4×D4—23no—
465C4×D4—611no—
466C4×D4—613no—
467C4×D4—1223no—
468C4×D4—1223no—
469C4×D4—1223no—
470C4×D4—1226no—
471C4×D4C22⋊D6113yes—
472C4×D4C22⋊D6113yes—
473C4×D4C22×D6113yes—
474C4×D4C22×D6116yes—
475C4×D4C22×D6113yes—
476#117—23no—
477#117—23no—
478#117—613no—
479#117—1223no—
480#117—1226no—
481#117—1223no—
482#117C22×D6113yes—
483#117C22×D6113yes—
484C2×C4⋊C4—23no—
485C2×C4⋊C4—613no—
486C2×C4⋊C4—1223no—
487C2×C4⋊C4—1223no—
488C2×C4⋊C4C22×D6113yes—
489C2×C22⋊C4—23no—
490C2×C22⋊C4—26no—
491C2×C42—23no—
492C2×C42—1223no—
493C2×C42—1223no—
494C2×C42C22×D6113yes—
495#107—613no—
496#107—613no—
497#106—613no—
498#106—616no—
499#106—611no—
500#103—611no—
501#103—613no—
502#103—613no—
503#103—616no—
504#103—613no—
505#102—613no—
506#102—616no—
507#102—613no—
508#102—611no—
509#102—613no—
510#97—616no—
511C4×C8—611no—
512C4×C8—613no—
513C4×C8—613no—
514C4×C8—613no—
515C24—23no—
516#41—28no—
517#41—26no—
518#41—6112no—
519#41—12224no—
520#41—1226no—
521#41C2×C4×D61112yes—
522#41C2×C4×D6114yes—
523#41#1175822214yes—
524C2×Q8—6112no—
525C2×Q8—613no—
526C2×Q8—1228no—
527C2×Q8—1223no—
528C2×Q8—1226no—
529C2×Q8C2×C22⋊D6111yescharacteristic
530C2×Q8C23×D6111yescharacteristic
531C2×D4—23no—
532C2×D4—224no—
533C2×D4—23no—
534C2×D4—26no—
535C2×D4—611no—
536C2×D4—1223no—
537C2×D4C2×C4×D61112yes—
538C2×D4C2×C22⋊D6113yes—
539C2×D4C23×D6113yes—
540C22×C4—23no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—23no—
544C22×C4—26no—
545C22×C4—86no—
546C22×C4—1223no—
547C22×C4—1223no—
548C22×C4—1223no—
549C22×C4—1223no—
550C22×C4—1221no—
551C22×C4C2×C22⋊D6113yes—
552C22×C4C2×C22⋊D6113yes—
553C22×C4C23×D6113yes—
554Q16—6112no—
555SD16—614no—
556SD16—6112no—
557SD16—6124no—
558D8—6112no—
559M16—6112no—
560M16—1226no—
561C2×C8—6112no—
562C2×C8—611no—
563C2×C8—613no—
564C2×C8—611no—
565C2×C8—613no—
566C2×C8—1226no—
567C4⋊C4—23no—
568C4⋊C4—23no—
569C4⋊C4—21no—
570C4⋊C4—613no—
571C4⋊C4—611no—
572C4⋊C4—1223no—
573C4⋊C4—1226no—
574C4⋊C4—1223no—
575C4⋊C4—1223no—
576C4⋊C4C2×C22⋊D6113yes—
577C4⋊C4C2×C22⋊D6113yes—
578C4⋊C4C23×D6113yes—
579C4⋊C4C23×D6111yescharacteristic
580C22⋊C4—23no—
581C22⋊C4—23no—
582C22⋊C4—26no—
583C22⋊C4—23no—
584C22⋊C4—1223no—
585C22⋊C4—1221no—
586C22⋊C4—1223no—
587C22⋊C4C2×C22⋊D6116yes—
588C42—23no—
589C42—23no—
590C42—21no—
591C42—1223no—
592C42—1223no—
593C42—1226no—
594C42—1223no—
595C42C2×C22⋊D6113yes—
596C42C2×C22⋊D6113yes—
597C42C23×D6113yes—
598C42C23×D6111yescharacteristic
599C23—23no—
600C23—212no—
601C23—83no—
602C23—83no—
603C23—1221no—
604C23C22×C22⋊D6113yes—
605Q8—21no—
606Q8—616no—
607Q8—12212no—
608Q8—1223no—
609Q8C4×C22⋊D6114yes—
610Q8C22×C4×D6112yes—
611D4—212no—
612D4—212no—
613D4—23no—
614D4—612no—
615D4—12212no—
616D4—1221no—
617D4C4×C22⋊D61112yes—
618D4C22×C4×D6116yes—
619C2×C4—21no—
620C2×C4—212no—
621C2×C4—26no—
622C2×C4—21no—
623C2×C4—23no—
624C2×C4—43no—
625C2×C4—46no—
626C2×C4—83no—
627C2×C4—86no—
628C2×C4—83no—
629C2×C4—12212no—
630C2×C4—1223no—
631C2×C4—12212no—
632C2×C4—1221no—
633C2×C4—1223no—
634C2×C4—4883no—
635C2×C4—4883no—
636C2×C4—2442no—
637C2×C4C22×C4×D6116yes—
638C2×C4C22×C22⋊D6113yes—
639C2×C4C22×C22⋊D6113yes—
640C2×C4C22×C22⋊D6111yescharacteristic
641C2×C4C22×C22⋊D6113yes—
642C2×C4C22×C22⋊D6111yescharacteristic
643C2×C4C2×#1175822216yes—
644C2×C4C24×D6111yescharacteristic
645C8—612no—
646C8—616no—
647C8—1221no—
648C8—1223no—
649C22—23no—
650C22—23no—
651C22—26no—
652C22—43no—
653C22—43no—
654C22—812no—
655C22—1222no—
656C22—2441no—
657C22—2441no—
658C22C2×C4×C22⋊D6116yes—
659C22C23×C22⋊D6111yescharacteristic
660C4—22no—
661C4—23no—
662C4—21no—
663C4—23no—
664C4—43no—
665C4—41no—
666C4—1226no—
667C4—2441no—
668C4—2443no—
669C4C2×C4×C22⋊D6116yes—
670C4#1684057312yesdirect product factor
671C4C23×C4×D6111yescharacteristic
672C4C22×#1175822211yescharacteristic
673C2—26no—
674C2—46no—
675C2—2442no—
676C2C22×C4×C22⋊D6111yescharacteristic
677C2C2×#1684057311yescharacteristic
678C2#2146059011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C23×D4
prime radicalC2×#16840573C2
cosocleC2×C4×C61C25
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#577
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#14519824C2semidirect
3. #21454700C2semidirect
4. #21454676C2semidirect
5. #21454658C2semidirect
6. #21454651C2semidirect
7. C4×#14519807C2semidirect
8. C4×#14519803C2semidirect
9. C4×#14519797C2semidirect
10. C2×C4×#11758200C2semidirect
11. #21454412C2semidirect
12. #21454349C2semidirect
13. #21454345C2semidirect
14. C4×#14519784C2semidirect
15. C4×H(5,𝔽2)×C61C2semidirect
17. #16840573C4direct (N × H)
25. #16840242C22semidirect
27. #16840239C22semidirect
29. C4×#11758222C22semidirect
31. C2×C4×Dic122C22semidirect
33. #16839872C22semidirect
34. #16839867C22semidirect
35. #16839862C22semidirect
36. #16839862C22semidirect
37. C4×#11758202C22semidirect
38. C4×#11758202C22semidirect
39. C4×#11758201C22semidirect
40. C4×#11758201C22semidirect
41. C4×#11758200C22semidirect
42. C4×#11758200C22semidirect
43. C4×#11758200C22semidirect
44. C4×#11758200C22semidirect
45. C4×#11758200C22semidirect
46. C4×#11758199C22semidirect
47. C4×#11758199C22semidirect
48. #16839805C22semidirect
49. #16839802C22semidirect
50. #16839798C22semidirect
51. C2×#14519708C22semidirect
52. #16839770C22semidirect
55. #16839761C22semidirect
57. #16839756C22semidirect
58. C2×#14519700C22semidirect
60. #16839718C22semidirect
61. #16839718C22semidirect
62. C4×#11758194C22semidirect
63. C2×C4×#92418C22semidirect
76. #14519824C2×C4semidirect
81. #14519807C2×C4semidirect
82. #14519803C2×C4semidirect
83. #14519797C2×C4semidirect
85. C2×#11758200C2×C4semidirect
91. #14519784C2×C4semidirect
140. H(5,𝔽2)×C61C2×C4semidirect
205. #11758222C22×C4semidirect
212. C2×Dic122C22×C4semidirect
234. #11758202C22×C4semidirect
235. #11758201C22×C4semidirect
236. #11758200C22×C4semidirect
237. #11758200C22×C4semidirect
238. #11758199C22×C4semidirect
252. #11758194C22×C4semidirect
254. C2×#92418C22×C4semidirect
328. C4×C61#577semidirect
336. C4×H(5,𝔽2)D61semidirect
414. C61C4×#577semidirect
418. H(5,𝔽2)C4×D61semidirect
670. C4#16840573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405732
C4×#145198242
#214547002
#214546762
#214546582
#214546512
C4×#145198072
C4×#145198032
C4×#145197972
C2×C4×#117582002
#214544122
#214543492
#214543452
C4×#145197842
C4×H(5,𝔽2)×C612
C4×#57761