Finite Group Databasebeta

← C4×#16840565 #30544230

Subgroups — C4×#16840565 #30544230

Order 15616.

2826 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840565C211yesmaximal, characteristic
2C4×#14519823C211yesmaximal, characteristic, complemented
3#21454692C213yesmaximal, complemented
4#21454669C213yesmaximal, complemented
5#21454651C213yesmaximal, complemented
6#21454647C213yesmaximal, complemented
7C4×#14519803C213yesmaximal, complemented
8C4×#14519802C213yesmaximal, complemented
9C4×#14519797C213yesmaximal, complemented
10C2×C4×#11758199C213yesmaximal, complemented
11#21454417C211yesmaximal, characteristic, complemented
12#21454345C211yesmaximal, characteristic, complemented
13#21454342C211yesmaximal, characteristic, complemented
14C4×#14519784C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17#16840565C4116yesdirect product factor
18C2×#14519803C2213yes—
19C2×#14519802C2213yes—
20C2×#14519797C2213yes—
21C22×#11758199C2213yes—
22C2×#14519784C2211yescharacteristic
23C2×#14519784C2211yescharacteristic
24#16840245C2211yescharacteristic
25#16840244—21no—
26#16840242C2213yescomplemented
27#16840236C2213yescomplemented
28#16840234—23no—
29C4×#11758226—21no—
30C4×#11758222C2213yescomplemented
31C2×C4×D244C2213yescomplemented
32C4×D4×D61—23no—
33#16839872C2216yescomplemented
34#16839872C2216yescomplemented
35#16839862C2216yescomplemented
36#16839860C2216yescomplemented
37C4×#11758202C2213yescomplemented
38C4×#11758202C2211yescharacteristic, complemented
39C4×#11758201C2213yescomplemented
40C4×#11758201C2213yescomplemented
41C4×#11758200C2213yescomplemented
42C4×#11758200C2213yescomplemented
43C4×#11758199C2216yescomplemented
44C4×#11758199C2216yescomplemented
45C4×#11758199C2213yescomplemented
46C4×#11758199C2216yescomplemented
47C4×#11758199C2213yescomplemented
48#16839805C2213yescomplemented
49#16839802C2213yescomplemented
50#16839798C2213yescomplemented
51C2×#14519710C2213yescomplemented
52#16839767C2213yescomplemented
53#16839766C2213yescomplemented
54#16839763C2213yescomplemented
55#16839761C2213yescomplemented
56#16839758C2213yescomplemented
57#16839756C2213yescomplemented
58C2×#14519698C2213yescomplemented
59C2×#14519697C2213yescomplemented
60#16839718C2213yescomplemented
61#16839718C2213yescomplemented
62C4×#11758194C2213yescomplemented
63C2×C4×#92418C2213yescomplemented
64C2×H(5,𝔽2)×C61C2211yescharacteristic
65C61×#520—21no—
66C61×#520C2211yescharacteristic
67C61×#520C2213yescomplemented
68C61×#518—23no—
69C61×#518C2213yescomplemented
70C4×#41×C61—21no—
71C4×#41×C61C2211yescharacteristic
72C4×#41×C61C2213yescomplemented
73C2×C4×D4×C61—23no—
74C2×C4×D4×C61C2213yescomplemented
75#14519823—24no—
76#14519823C2×C418yescomplemented
77C2×#11758226—21no—
78C2×#11758222C2313yes—
79C22×D244C2313yes—
80C2×D4×D61—23no—
81C22×C4×D61—23no—
82#14519803C2×C4124yescomplemented
83#14519802C2×C4124yescomplemented
84#14519797C2×C4124yescomplemented
85C2×#11758202C2311yescharacteristic
86C2×#11758200C2313yes—
87C2×#11758201C2313yes—
88C2×#11758199C2×C4124yescomplemented
89C2×#11758199C2313yes—
90C2×#11758199C2316yes—
91#14519784—24no—
92#14519784C2×C418yescomplemented
93C2×#11758194C2313yes—
94C2×#11758194C2313yes—
95C22×#92418C2313yes—
96C22×#92418C2313yes—
97Q8×Dic61—21no—
98C4×Dic122C2311yescharacteristic
99C4×Dic122C2313yes—
100C4×D244—23no—
101C4×D244—23no—
102C4×D244C2313yes—
103C4×D244C2316yes—
104C4×D244C2313yes—
105D4×Dic61—23no—
106#14519739—23no—
107#14519739—23no—
108C4×C22⋊D61—23no—
109C4×C22⋊D61—23no—
110#14519737—26no—
111#14519736C2313yes—
112#14519735—23no—
113#14519734—23no—
114C2×C4⋊Dic61C2313yes—
115C4⋊C4×D61—23no—
116C2×#11758198—23no—
117C22⋊C4×D61—26no—
118C42×D61—23no—
119#14519710C2313yes—
120#14519710C2316yes—
121#14519710C2311yescharacteristic
122#14519708C2313yes—
123#14519708C2313yes—
124#14519701C2311yescharacteristic
125#14519701C2313yes—
126#14519700C2311yescharacteristic
127#14519700C2313yes—
128#14519698C2313yes—
129#14519698C2316yes—
130#14519698C2313yes—
131#14519697C2313yes—
132#14519697C2316yes—
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×C61C2316yes—
164C4×D4×C61C2313yes—
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—
176C23×D61—23no—
177#41×C61—28no—
178#41×C61—26no—
179#41×C61C22×C414yes—
180#41×C61C22×C4112yescomplemented
181#41×C61#4114yes—
182C2×Q8×C61C2×D411yescharacteristic
183C2×Q8×C61C2411yescharacteristic
184C2×D4×C61—23no—
185C2×D4×C61—224no—
186C2×D4×C61—23no—
187C2×D4×C61—26no—
188C2×D4×C61C22×C4112yescomplemented
189C2×D4×C61C2×D413yes—
190C2×D4×C61C2413yes—
191C22×C4×C61—23no—
192C22×C4×C61—23no—
193C22×C4×C61—23no—
194C22×C4×C61—23no—
195C22×C4×C61—26no—
196C22×C4×C61—86no—
197C22×C4×C61C2×D413yes—
198C22×C4×C61C2×D413yes—
199C22×C4×C61C2413yes—
200C2×C22⋊D61—23no—
201C22×Dic61—23no—
202#11758226—28no—
203D4×D61—224no—
204#11758222—26no—
205#11758222C22×C4112yescomplemented
206C2×D244—23no—
207C2×D244—26no—
208C2×D244C22×C4112yescomplemented
209C2×D244C2413yes—
210C2×C4×D61—23no—
211C2×C4×D61—23no—
212C2×C4×D61—26no—
213C2×C4×D61—23no—
214C2×C4×D61—86no—
215C2×Dic122C2411yescharacteristic
216C4⋊C4×C61—23no—
217C4⋊C4×C61—23no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61C2×D413yes—
220C4⋊C4×C61C2×D413yes—
221C4⋊C4×C61C2413yes—
222C4⋊C4×C61C2411yescharacteristic
223C22⋊C4×C61—23no—
224C22⋊C4×C61—23no—
225C22⋊C4×C61—26no—
226C22⋊C4×C61—23no—
227C22⋊C4×C61C2×D416yes—
228C42×C61—21no—
229C42×C61—23no—
230C42×C61—23no—
231C42×C61C2×D413yes—
232C42×C61C2×D413yes—
233C42×C61C2411yescharacteristic
234C42×C61C2413yes—
235C22⋊Dic61—23no—
236#11758202C22×C414yescomplemented
237#11758201C22×C4112yescomplemented
238#11758200C22×C4112yescomplemented
239#11758199C22×C4112yescomplemented
240#11758199C22×C4124yescomplemented
241#11758198—23no—
242#11758198—26no—
243#11758198—23no—
244C4⋊Dic61—23no—
245C4⋊Dic61C2411yescharacteristic
246C4⋊Dic61C2413yes—
247#11758196—23no—
248#11758196—21no—
249C4×Dic61—21no—
250C4×Dic61—23no—
251C4×Dic61—23no—
252#11758194—26no—
253#11758194C22×C4112yescomplemented
254C2×#92418—26no—
255C2×#92418C22×C4112yescomplemented
256C2×#92418C2411yescharacteristic
257C2×#92418C2413yes—
258C2×#92418C2411yescharacteristic
259C2×#92418C2413yes—
260C23×C61—23no—
261C23×C61—212no—
262C23×C61—83no—
263C23×C61—83no—
264C23×C61C22×D413yes—
265C22×D61—23no—
266C22×D61—212no—
267C22×D61—83no—
268C22×D61—83no—
269Q8×C61—21no—
270Q8×C61C4×D414yes—
271Q8×C61C23×C412yes—
272D4×C61—212no—
273D4×C61—212no—
274D4×C61—23no—
275D4×C61C4×D4112yes—
276D4×C61C23×C416yes—
277C2×C4×C61—21no—
278C2×C4×C61—212no—
279C2×C4×C61—26no—
280C2×C4×C61—21no—
281C2×C4×C61—23no—
282C2×C4×C61—43no—
283C2×C4×C61—46no—
284C2×C4×C61—83no—
285C2×C4×C61—86no—
286C2×C4×C61—83no—
287C2×C4×C61C23×C416yes—
288C2×C4×C61C22×D413yes—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D413yes—
291C2×C4×C61C22×D413yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4116yes—
294C2×C4×C61C2511yescharacteristic
295C22⋊D61—212no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—23no—
299C2×Dic61—83no—
300D244—212no—
301D244—23no—
302D244C23×C416yes—
303C4×D61—212no—
304C4×D61—46no—
305C4×D61—83no—
306C4×D61—86no—
307Dic122—21no—
308Dic122C23×C412yes—
309#92418—21no—
310#92418—23no—
311#92418C23×C412yes—
312#92418C23×C416yes—
313C4×#576—611nomaximal, Sylow
314C22×C61—23no—
315C22×C61—23no—
316C22×C61—26no—
317C22×C61—43no—
318C22×C61—43no—
319C22×C61—812no—
320C22×C61C2×C4×D416yes—
321C22×C61C23×D411yescharacteristic
322C2×D61—26no—
323C2×D61—43no—
324C2×D61—43no—
325C2×D61—812no—
326C4×C61—23no—
327C4×C61—21no—
328C4×C61—22no—
329C4×C61—23no—
330C4×C61—41no—
331C4×C61—43no—
332C4×C61C2×C4×D416yes—
333C4×C61#57612yescomplemented
334C4×C61C24×C411yescharacteristic
335C4×C61C22×#4111yescharacteristic
336Dic61—22no—
337Dic61—41no—
338Dic61—43no—
339C2×#576—611no—
340C4×H(5,𝔽2)—611no—
341C4×H(5,𝔽2)D6111yescharacteristic, complemented
342#2951—613no—
343#2948—613no—
344#2946—613no—
345#2946—613no—
346C4×AGL(1,ℤ/8)—613no—
347C4×AGL(1,ℤ/8)—613no—
348C4×#135—613no—
349C2×C4×D8—613no—
350#2913—611no—
351#2897—611no—
352#2897—611no—
353C4×#131—611no—
354C2×C61—26no—
355C2×C61—46no—
356C2×C61C22×C4×D411yescharacteristic
357C2×C61C2×#57611yescharacteristic
358C2×C61#358411yescharacteristic
359D61—46no—
360C2×H(5,𝔽2)—611no—
361C2×H(5,𝔽2)C2×D6111yescharacteristic
362#576—6116no—
363C2×AGL(1,ℤ/8)—613no—
364C2×AGL(1,ℤ/8)—613no—
365C2×#135—613no—
366C22×D8—613no—
367C2×#131—611no—
368C2×#131—611no—
369#520—21no—
370#520—611no—
371#520—613no—
372#520—1221no—
373#520C2×D6111yescharacteristic
374#520C2×D6113yescomplemented
375#518—23no—
376#518—613no—
377#518—1223no—
378#518C2×D6113yescomplemented
379C4×#41—21no—
380C4×#41—613no—
381C4×#41—1221no—
382C4×#41C2×D6111yescharacteristic
383C4×#41C2×D6113yescomplemented
384C2×C4×D4—23no—
385C2×C4×D4—613no—
386C2×C4×D4—1223no—
387C2×C4×D4C2×D6113yescomplemented
388#442—616no—
389#442—616no—
390#440—616no—
391#440—616no—
392C4×Q16—611no—
393C4×Q16—613no—
394C4×SD16—613no—
395C4×SD16—613no—
396C4×SD16—613no—
397C4×SD16—613no—
398C4×D8—613no—
399C4×D8—616no—
400C4×D8—616no—
401C4×D8—616no—
402C4×D8—613no—
403#428—613no—
404#428—613no—
405#427—613no—
406C2×#107—613no—
407#418—613no—
408#418—613no—
409#417—613no—
410#417—613no—
411#416—613no—
412#416—613no—
413C2×#102—613no—
414C2×#102—613no—
415#405—613no—
416#405—613no—
417C4×M16—613no—
418C2×C4×C8—613no—
419C61C4×#57611yescharacteristic, complemented, Sylow
420H(5,𝔽2)—24no—
421H(5,𝔽2)—618no—
422H(5,𝔽2)—1224no—
423H(5,𝔽2)C4×D6118yescomplemented
424C2×#41—21no—
425C2×#41—613no—
426C2×#41—1221no—
427C2×#41C22×D6113yes—
428C2×#41C22×D6111yescharacteristic
429C22×D4—23no—
430C22×D4—613no—
431C22×D4—1223no—
432C22×D4C22×D6113yes—
433C23×C4—23no—
434C23×C4—1223no—
435AGL(1,ℤ/8)—6124no—
436AGL(1,ℤ/8)—6124no—
437#135—6124no—
438C2×Q16—611no—
439C2×SD16—613no—
440C2×SD16—613no—
441C2×D8—6124no—
442C2×D8—613no—
443C2×D8—616no—
444#131—618no—
445#131—1224no—
446C2×M16—613no—
447C2×M16—613no—
448C22×C8—613no—
449C22×C8—613no—
450C4×Q8—21no—
451C4×Q8—611no—
452C4×Q8—613no—
453C4×Q8—1221no—
454C4×Q8C22⋊D6111yescharacteristic
455C4×Q8C22⋊D6111yescharacteristic
456C4×Q8C22×D6111yescharacteristic
457C4×Q8C22×D6113yes—
458C4×D4—23no—
459C4×D4—23no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—23no—
463C4×D4—26no—
464C4×D4—23no—
465C4×D4—23no—
466C4×D4—613no—
467C4×D4—616no—
468C4×D4—613no—
469C4×D4—1223no—
470C4×D4—1223no—
471C4×D4—1223no—
472C4×D4—1223no—
473C4×D4—1223no—
474C4×D4—1226no—
475C4×D4—1223no—
476C4×D4—1223no—
477C4×D4C22⋊D6113yes—
478C4×D4C22⋊D6113yes—
479C4×D4C22×D6113yes—
480C4×D4C22×D6116yes—
481C4×D4C22×D6113yes—
482#117—23no—
483#117—23no—
484#117—613no—
485#117—1223no—
486#117—1223no—
487#117C22×D6113yes—
488#117C22×D6113yes—
489C2×C4⋊C4—23no—
490C2×C4⋊C4—613no—
491C2×C4⋊C4—1223no—
492C2×C4⋊C4C22×D6113yes—
493C2×C22⋊C4—23no—
494C2×C22⋊C4—26no—
495C2×C22⋊C4—1223no—
496C2×C22⋊C4—1226no—
497C2×C42—23no—
498C2×C42—1223no—
499C2×C42C22×D6113yes—
500#107—613no—
501#107—616no—
502#107—611no—
503#106—613no—
504#106—613no—
505#103—611no—
506#103—613no—
507#103—611no—
508#103—613no—
509#102—613no—
510#102—616no—
511#102—613no—
512#102—613no—
513#102—616no—
514#102—613no—
515#97—616no—
516C4×C8—611no—
517C4×C8—613no—
518C4×C8—613no—
519C4×C8—613no—
520C24—23no—
521C24—1223no—
522#41—28no—
523#41—26no—
524#41—6112no—
525#41—1228no—
526#41—1226no—
527#41C2×C4×D6114yes—
528#41C2×C4×D61112yescomplemented
529#41#1175822214yes—
530C2×Q8—611no—
531C2×Q8C2×C22⋊D6111yescharacteristic
532C2×Q8C23×D6111yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—23no—
536C2×D4—26no—
537C2×D4—6112no—
538C2×D4—613no—
539C2×D4—1223no—
540C2×D4—12224no—
541C2×D4—1223no—
542C2×D4—1226no—
543C2×D4C2×C4×D61112yescomplemented
544C2×D4C2×C22⋊D6113yes—
545C2×D4C23×D6113yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—26no—
551C22×C4—86no—
552C22×C4—1223no—
553C22×C4—1223no—
554C22×C4—1223no—
555C22×C4—1226no—
556C22×C4—1223no—
557C22×C4—4886no—
558C22×C4C2×C22⋊D6113yes—
559C22×C4C2×C22⋊D6113yes—
560C22×C4C23×D6113yes—
561Q16—614no—
562SD16—6112no—
563SD16—6112no—
564D8—6112no—
565D8—6124no—
566M16—6112no—
567M16—1226no—
568C2×C8—6112no—
569C2×C8—611no—
570C2×C8—613no—
571C2×C8—611no—
572C2×C8—613no—
573C2×C8—1226no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—21no—
577C4⋊C4—611no—
578C4⋊C4—613no—
579C4⋊C4—1223no—
580C4⋊C4—1223no—
581C4⋊C4—1221no—
582C4⋊C4C2×C22⋊D6113yes—
583C4⋊C4C2×C22⋊D6113yes—
584C4⋊C4C23×D6111yescharacteristic
585C4⋊C4C23×D6113yes—
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—23no—
590C22⋊C4—1223no—
591C22⋊C4—1223no—
592C22⋊C4—1226no—
593C22⋊C4—1223no—
594C22⋊C4C2×C22⋊D6116yes—
595C42—23no—
596C42—23no—
597C42—21no—
598C42—1223no—
599C42—1223no—
600C42—1221no—
601C42C2×C22⋊D6113yes—
602C42C2×C22⋊D6113yes—
603C42C23×D6113yes—
604C42C23×D6111yescharacteristic
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—12212no—
610C23—1223no—
611C23—4883no—
612C23—4883no—
613C23C22×C22⋊D6113yes—
614Q8—21no—
615Q8—612no—
616Q8—1221no—
617Q8C4×C22⋊D6114yes—
618Q8C22×C4×D6112yes—
619D4—212no—
620D4—212no—
621D4—23no—
622D4—616no—
623D4—12212no—
624D4—12212no—
625D4—1223no—
626D4C4×C22⋊D61112yes—
627D4C22×C4×D6116yes—
628C2×C4—21no—
629C2×C4—212no—
630C2×C4—26no—
631C2×C4—21no—
632C2×C4—23no—
633C2×C4—43no—
634C2×C4—46no—
635C2×C4—83no—
636C2×C4—86no—
637C2×C4—83no—
638C2×C4—1221no—
639C2×C4—12212no—
640C2×C4—1221no—
641C2×C4—1223no—
642C2×C4—4883no—
643C2×C4—4886no—
644C2×C4—4883no—
645C2×C4—2446no—
646C2×C4C22×C4×D6116yes—
647C2×C4C22×C22⋊D6113yes—
648C2×C4C22×C22⋊D6111yescharacteristic
649C2×C4C22×C22⋊D6113yes—
650C2×C4C22×C22⋊D6113yes—
651C2×C4C22×C22⋊D6111yescharacteristic
652C2×C4C2×#1175822216yes—
653C2×C4C24×D6111yescharacteristic
654C8—612no—
655C8—616no—
656C8—1221no—
657C8—1223no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—1226no—
665C22—48812no—
666C22—2443no—
667C22—2443no—
668C22C2×C4×C22⋊D6116yes—
669C22C23×C22⋊D6111yescharacteristic
670C4—22no—
671C4—23no—
672C4—21no—
673C4—23no—
674C4—43no—
675C4—41no—
676C4—1222no—
677C4—2443no—
678C4—2441no—
679C4C2×C4×C22⋊D6116yes—
680C4#1684056512yesdirect product factor
681C4C23×C4×D6111yescharacteristic
682C4C22×#1175822211yescharacteristic
683C2—26no—
684C2—46no—
685C2—2446no—
686C2C22×C4×C22⋊D6111yescharacteristic
687C2C2×#1684056511yescharacteristic
688C2#2146059011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C23×D4
prime radicalC2×#16840565C2
cosocleC2×C4×C61C25
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#576
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×#14519823C2semidirect
3. #21454692C2semidirect
4. #21454669C2semidirect
5. #21454651C2semidirect
6. #21454647C2semidirect
7. C4×#14519803C2semidirect
8. C4×#14519802C2semidirect
9. C4×#14519797C2semidirect
10. C2×C4×#11758199C2semidirect
11. #21454417C2semidirect
12. #21454345C2semidirect
13. #21454342C2semidirect
14. C4×#14519784C2semidirect
15. C4×H(5,𝔽2)×C61C2semidirect
17. #16840565C4direct (N × H)
26. #16840242C22semidirect
27. #16840236C22semidirect
30. C4×#11758222C22semidirect
31. C2×C4×D244C22semidirect
33. #16839872C22semidirect
34. #16839872C22semidirect
35. #16839862C22semidirect
36. #16839860C22semidirect
37. C4×#11758202C22semidirect
38. C4×#11758202C22semidirect
39. C4×#11758201C22semidirect
40. C4×#11758201C22semidirect
41. C4×#11758200C22semidirect
42. C4×#11758200C22semidirect
43. C4×#11758199C22semidirect
44. C4×#11758199C22semidirect
45. C4×#11758199C22semidirect
46. C4×#11758199C22semidirect
47. C4×#11758199C22semidirect
48. #16839805C22semidirect
49. #16839802C22semidirect
50. #16839798C22semidirect
51. C2×#14519710C22semidirect
52. #16839767C22semidirect
53. #16839766C22semidirect
54. #16839763C22semidirect
55. #16839761C22semidirect
56. #16839758C22semidirect
57. #16839756C22semidirect
58. C2×#14519698C22semidirect
59. C2×#14519697C22semidirect
60. #16839718C22semidirect
61. #16839718C22semidirect
62. C4×#11758194C22semidirect
63. C2×C4×#92418C22semidirect
67. C61×#520C22semidirect
69. C61×#518C22semidirect
72. C4×#41×C61C22semidirect
74. C2×C4×D4×C61C22semidirect
76. #14519823C2×C4semidirect
82. #14519803C2×C4semidirect
83. #14519802C2×C4semidirect
84. #14519797C2×C4semidirect
88. C2×#11758199C2×C4semidirect
92. #14519784C2×C4semidirect
140. H(5,𝔽2)×C61C2×C4semidirect
180. #41×C61C22×C4semidirect
188. C2×D4×C61C22×C4semidirect
205. #11758222C22×C4semidirect
208. C2×D244C22×C4semidirect
236. #11758202C22×C4semidirect
237. #11758201C22×C4semidirect
238. #11758200C22×C4semidirect
239. #11758199C22×C4semidirect
240. #11758199C22×C4semidirect
253. #11758194C22×C4semidirect
255. C2×#92418C22×C4semidirect
333. C4×C61#576semidirect
341. C4×H(5,𝔽2)D61semidirect
374. #520C2×D61semidirect
378. #518C2×D61semidirect
383. C4×#41C2×D61semidirect
387. C2×C4×D4C2×D61semidirect
419. C61C4×#576semidirect
423. H(5,𝔽2)C4×D61semidirect
528. #41C2×C4×D61semidirect
543. C2×D4C2×C4×D61semidirect
680. C4#16840565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405652
C4×#145198232
#214546922
#214546692
#214546512
#214546472
C4×#145198032
C4×#145198022
C4×#145197972
C2×C4×#117581992
#214544172
#214543452
#214543422
C4×#145197842
C4×H(5,𝔽2)×C612
C4×#57661