Finite Group Databasebeta

← #30543592

Subgroups — #30543592

Order 15616.

4902 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840597C211yesmaximal, characteristic
2C2×#16840527C211yesmaximal, characteristic, complemented
3#520×D61C211yesmaximal, characteristic, complemented
4#21454353C211yesmaximal, characteristic, complemented
5#21454350C213yesmaximal, complemented
6#21454349C211yesmaximal, characteristic, complemented
7#21454348C213yesmaximal, complemented
8#21454345C211yesmaximal, characteristic, complemented
9#21454344C213yesmaximal, complemented
10#21454340C213yesmaximal, complemented
11#21454334C213yesmaximal, complemented
12#21454333C213yesmaximal, complemented
13C2×#16839760C213yesmaximal, complemented
14#417×D61C213yesmaximal, complemented
15C61×#2897C211yesmaximal, characteristic, complemented
16#16840597—28no—
17#16840597C4116yescomplemented
18C2×#14519824—21no—
19C2×#14519824C2211yescharacteristic
20C2×#14519824C2213yes—
21C2×#14519822—23no—
22C2×#14519822C2213yes—
23C22×#11758224—23no—
24C22×#11758224C2213yes—
25C2×#41×D61—21no—
26C2×#41×D61C2213yes—
27C2×#41×D61C2211yescharacteristic
28#16840527—28no—
29C2×#14519785C2213yescomplemented
30C2×#14519784C2211yescharacteristic, complemented
31C2×#14519783C2213yescomplemented
32C22×#11758189C2213yescomplemented
33C2×M16×D61C2213yescomplemented
34#16840245C2211yescharacteristic, complemented
35#16840244—21no—
36#16840243C2213yescomplemented
37#16840242C2213yescomplemented
38#16840241—23no—
39C4×Q8×D61—21no—
40C4×D4×D61—23no—
41#117×D61C2213yescomplemented
42C2×C4⋊C4×D61C2213yescomplemented
43#16839772C2213yescomplemented
44#16839770C2213yescomplemented
45#16839769C2213yescomplemented
46#16839769C2213yescomplemented
47#16839767C2213yescomplemented
48#16839765C2213yescomplemented
49#16839765C2213yescomplemented
50#16839764C2213yescomplemented
51#16839763C2213yescomplemented
52#16839762C2213yescomplemented
53#16839762C2211yescharacteristic, complemented
54#16839761C2213yescomplemented
55#16839760C2216yescomplemented
56#16839760C2216yescomplemented
57#16839760C2216yescomplemented
58#16839760C2213yescomplemented
59#16839760C2213yescomplemented
60#16839759C2213yescomplemented
61#16839758C2213yescomplemented
62#16839756C2213yescomplemented
63#16839755C2216yescomplemented
64#16839755C2216yescomplemented
65C2×#14519702C2213yescomplemented
66C2×#14519700C2213yescomplemented
67#103×D61C2216yescomplemented
68C2×#14519698C2213yescomplemented
69#102×D61C2216yescomplemented
70C2×H(5,𝔽2)×C61C2211yescharacteristic
71C2×#131×C61C2211yescharacteristic, complemented
72C61×#520C2211yescharacteristic, complemented
73C61×#418C2213yescomplemented
74C61×#417C2213yescomplemented
75C61×#416C2213yescomplemented
76C2×#102×C61C2213yescomplemented
77#14519824—24no—
78#14519824—216no—
79#14519824—212no—
80#14519824C2×C4124yescomplemented
81#14519824C2×C418yescomplemented
82#14519822—248no—
83#14519822—212no—
84#14519822C2×C4124yescomplemented
85C2×#11758226D411yescharacteristic
86C2×#11758226C2311yescharacteristic
87C2×#11758222—23no—
88C2×#11758222—23no—
89C2×#11758222C2313yes—
90C2×#11758222C2313yes—
91C2×#11758224—23no—
92C2×#11758224—26no—
93C2×#11758224—23no—
94C2×#11758224—248no—
95C2×#11758224—23no—
96C2×#11758224—23no—
97C2×#11758224—212no—
98C2×#11758224—23no—
99C2×#11758224C2×C4124yescomplemented
100C2×#11758224D413yes—
101C2×#11758224C2313yes—
102C2×#11758224C2316yes—
103#41×D61—216no—
104#41×D61—212no—
105#41×D61C2×C418yes—
106#41×D61C2×C4124yescomplemented
107#41×D61D418yes—
108C22×Dic122—23no—
109C22×Dic122C2313yes—
110C2×Q8×D61—21no—
111C2×Q8×D61D411yescharacteristic
112C2×Q8×D61C2313yes—
113C22×C22⋊D61—23no—
114C22×C22⋊D61—26no—
115C2×D4×D61—23no—
116C2×D4×D61—23no—
117C2×D4×D61D413yes—
118C2×D4×D61C2313yes—
119C23×Dic61—23no—
120C22×C4×D61—23no—
121C22×C4×D61—23no—
122C22×C4×D61C2313yes—
123#14519785—212no—
124#14519784—24no—
125#14519783—212no—
126C2×#11758194C2313yes—
127C2×#11758189—212no—
128C2×#11758189C2313yes—
129C2×#11758189C2311yescharacteristic
130C2×#11758189C2313yes—
131C2×#11758189C2313yes—
132M16×D61—212no—
133C22×#92418C2313yes—
134C2×C8×D61C2316yes—
135Q8×Dic61—21no—
136C4×Dic122—23no—
137#14519742—23no—
138C4×D244—23no—
139D4×Dic61—23no—
140#14519739—23no—
141C4×C22⋊D61—26no—
142#14519737—26no—
143#14519736C2313yes—
144#14519735C2313yes—
145#14519735C2313yes—
146#14519734—23no—
147#14519733—23no—
148C2×C4⋊Dic61C2313yes—
149C2×#11758196—23no—
150C4⋊C4×D61—23no—
151C4⋊C4×D61—23no—
152C4⋊C4×D61C2313yes—
153C4⋊C4×D61C2316yes—
154C4⋊C4×D61C2311yescharacteristic
155C22⋊C4×D61—23no—
156C42×D61—23no—
157#14519702C2316yes—
158#14519702C2313yes—
159#14519702C2313yes—
160#14519701C2313yes—
161#14519701C2311yescharacteristic
162#14519700C2316yes—
163#14519700C2313yes—
164#14519700C2313yes—
165#14519699C2313yes—
166#14519699C2311yescharacteristic
167#14519698C2316yes—
168#14519698C2313yes—
169#14519698C2313yes—
170#14519697C2313yes—
171#14519697C2311yescharacteristic
172H(5,𝔽2)×C61—24no—
173H(5,𝔽2)×C61C2×C418yescomplemented
174C2×#41×C61—21no—
175C2×#41×C61C2313yes—
176C2×#41×C61C2311yescharacteristic
177C22×D4×C61—23no—
178C22×D4×C61C2313yes—
179#131×C61—24no—
180C2×M16×C61C2313yes—
181C22×C8×C61C2313yes—
182C4×Q8×C61—21no—
183C4×D4×C61—23no—
184#117×C61C2313yes—
185C2×C4⋊C4×C61C2313yes—
186#103×C61C2313yes—
187#103×C61C2311yescharacteristic
188#102×C61C2316yes—
189#102×C61C2313yes—
190#102×C61C2313yes—
191C24×C61—23no—
192C23×D61—23no—
193C23×D61C2×D413yes—
194#41×C61—28no—
195#41×C61—26no—
196#41×C61C22×C414yes—
197#41×C61C22×C4112yescomplemented
198#41×C61C2×D414yes—
199C2×Q8×C61C2×D411yescharacteristic
200C2×Q8×C61C2411yescharacteristic
201C2×D4×C61—23no—
202C2×D4×C61—224no—
203C2×D4×C61—23no—
204C2×D4×C61—26no—
205C2×D4×C61C22×C4112yescomplemented
206C2×D4×C61C2×D413yes—
207C2×D4×C61C2413yes—
208C22×C4×C61—23no—
209C22×C4×C61—23no—
210C22×C4×C61C2413yes—
211C2×C22⋊D61—23no—
212C2×C22⋊D61—224no—
213C2×C22⋊D61—23no—
214C2×C22⋊D61—26no—
215C2×C22⋊D61—248no—
216C2×C22⋊D61—23no—
217C2×C22⋊D61C2×D416yes—
218C22×Dic61—23no—
219C22×Dic61—224no—
220C22×Dic61—23no—
221C22×Dic61—26no—
222C22×Dic61—23no—
223C22×Dic61C2×D413yes—
224#11758226—22no—
225#11758226C22⋊C418yes—
226#11758226C22×C414yes—
227Q8×D61—28no—
228Q8×D61—26no—
229Q8×D61C22⋊C418yes—
230Q8×D61C22×C4112yescomplemented
231#11758224—224no—
232#11758224—248no—
233#11758224—224no—
234#11758224—224no—
235#11758224—224no—
236#11758224—26no—
237#11758224—212no—
238#11758224—224no—
239#11758224C22⋊C4124yes—
240#11758224C22×C4112yes—
241#11758224C22×C4124yescomplemented
242D4×D61—224no—
243D4×D61—224no—
244D4×D61—26no—
245D4×D61C22⋊C4124yes—
246D4×D61C22×C4112yescomplemented
247#11758222—26no—
248#11758222—224no—
249#11758222—224no—
250#11758222C22×C4112yes—
251#11758222C22×C4112yescomplemented
252#11758222C2×D4112yes—
253C2×D244—21no—
254C2×D244C2×D413yes—
255C2×D244C2411yescharacteristic
256C2×C4×D61—23no—
257C2×C4×D61—23no—
258C2×C4×D61—21no—
259C2×C4×D61—224no—
260C2×C4×D61—23no—
261C2×C4×D61—21no—
262C2×C4×D61—26no—
263C2×C4×D61—86no—
264C2×C4×D61C22×C4112yes—
265C2×C4×D61C2×D413yes—
266C2×C4×D61C2×D413yes—
267C2×C4×D61C2×D4112yes—
268C2×C4×D61C2411yescharacteristic
269C2×C4×D61C2413yes—
270C2×Dic122—23no—
271C2×Dic122—26no—
272C2×Dic122—23no—
273C2×Dic122—224no—
274C2×Dic122C22×C4112yescomplemented
275C2×Dic122C2×D413yes—
276C2×Dic122C2413yes—
277M16×C61—26no—
278C2×C8×C61—26no—
279C2×C8×C61C2411yescharacteristic
280C2×C8×C61C2413yes—
281C4⋊C4×C61—23no—
282C4⋊C4×C61C2413yes—
283C4⋊C4×C61C2411yescharacteristic
284C22⋊C4×C61—23no—
285C42×C61—23no—
286C22⋊Dic61—23no—
287#11758198—23no—
288#11758198—23no—
289C4⋊Dic61—23no—
290C4⋊Dic61C2413yes—
291C4⋊Dic61C2411yescharacteristic
292#11758196—23no—
293#11758196—26no—
294#11758196—21no—
295C4×Dic61—23no—
296C4×Dic61—23no—
297C4×Dic61—23no—
298#11758194—26no—
299C2×#92418—26no—
300C2×#92418C2413yes—
301C2×#92418C2411yescharacteristic
302#11758189—26no—
303#11758189—22no—
304#11758189—26no—
305#11758189—26no—
306C8×D61—212no—
307C23×C61—23no—
308C23×C61—212no—
309C23×C61—83no—
310C23×C61—83no—
311C23×C61C22×D413yes—
312C22×D61—21no—
313C22×D61—212no—
314C22×D61—43no—
315C22×D61—43no—
316C22×D61—83no—
317C22×D61—83no—
318C22×D61C2×C22⋊C4112yes—
319C22×D61C22×D413yes—
320C22×D61C22×D411yescharacteristic
321Q8×C61—21no—
322Q8×C61C2×C22⋊C414yes—
323Q8×C61C23×C412yes—
324D4×C61—212no—
325D4×C61—212no—
326D4×C61—23no—
327D4×C61C2×C22⋊C4112yes—
328D4×C61C23×C416yes—
329C2×C4×C61—21no—
330C2×C4×C61—212no—
331C2×C4×C61—21no—
332C2×C4×C61—23no—
333C2×C4×C61—83no—
334C2×C4×C61C23×C416yes—
335C2×C4×C61C22×D413yes—
336C2×C4×C61C22×D416yes—
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—212no—
339C22⋊D61—212no—
340C22⋊D61—224no—
341C22⋊D61—212no—
342C22⋊D61C2×C22⋊C4124yes—
343C2×Dic61—212no—
344C2×Dic61—23no—
345C2×Dic61—224no—
346C2×Dic61—212no—
347C2×Dic61—21no—
348C2×Dic61—23no—
349C2×Dic61—83no—
350C2×Dic61C2×C22⋊C4112yes—
351C2×Dic61C22×D413yes—
352C2×Dic61C22×D411yescharacteristic
353D244—24no—
354D244—21no—
355D244C2×C22⋊C4112yes—
356D244C23×C412yes—
357C4×D61—212no—
358C4×D61—212no—
359C4×D61—24no—
360C4×D61—42no—
361C4×D61—46no—
362C4×D61—86no—
363C4×D61C2×C22⋊C4112yes—
364C4×D61C2×C22⋊C4112yes—
365C4×D61C23×C412yes—
366C4×D61C23×C416yes—
367C4×D61C22×D416yes—
368C4×D61C22×D412yes—
369Dic122—212no—
370Dic122—23no—
371Dic122—212no—
372Dic122C2×C22⋊C4112yes—
373Dic122C23×C416yes—
374C8×C61—23no—
375C8×C61—21no—
376#92418—23no—
377#92418—21no—
378#60089—611nomaximal, Sylow
379C22×C61—23no—
380C22×C61—23no—
381C22×C61—26no—
382C22×C61—43no—
383C22×C61—43no—
384C22×C61—812no—
385C22×C61C22×C22⋊C416yes—
386C22×C61C23×D411yescharacteristic
387C2×D61—21no—
388C2×D61—23no—
389C2×D61—21no—
390C2×D61—23no—
391C2×D61—22no—
392C2×D61—412no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—812no—
396C2×D61C22×C22⋊C416yes—
397C2×D61C22×C22⋊C412yes—
398C4×C61—22no—
399C4×C61—43no—
400C4×C61—41no—
401C4×C61C22×C22⋊C416yes—
402C4×C61C24×C411yescharacteristic
403C4×C61C23×D411yescharacteristic
404Dic61—26no—
405Dic61—43no—
406Dic61—41no—
407Dic61C22×C22⋊C416yes—
408Dic61C22×C22⋊C412yes—
409C2×#585—611no—
410C2×#568—611no—
411C2×#520—611no—
412#2898—613no—
413#2898—613no—
414#2898—611no—
415#2898—611no—
416#2897—613no—
417#2897—613no—
418#2897—611no—
419#2897D6111yescharacteristic, complemented
420#2896—613no—
421#2896—613no—
422C2×#417—613no—
423C2×#417—613no—
424C2×C61—26no—
425C2×C61—46no—
426C2×C61C23×C22⋊C411yescharacteristic
427C2×C61#358511yescharacteristic
428C2×C61#358611yescharacteristic
429D61—22no—
430D61—26no—
431D61—42no—
432#585—6116no—
433#585—1228no—
434C2×2−1+4—613no—
435C2×2−1+4—611no—
436C2×2−1+4—1221no—
437C2×H(5,𝔽2)—613no—
438C2×H(5,𝔽2)—1223no—
439C2×H(5,𝔽2)C2×D6111yescharacteristic
440C22×#41—611no—
441C22×#41—613no—
442C22×#41—613no—
443C22×#41—1223no—
444C22×#41—1221no—
445#568—1228no—
446C2×#131—611no—
447C2×#131—613no—
448C2×#131—613no—
449C2×#131C2×D6111yescharacteristic, complemented
450C22×M16—613no—
451C22×M16—613no—
452#520—611no—
453#520—613no—
454#520—613no—
455#520—1223no—
456#520—1221no—
457#520C2×D6111yescharacteristic, complemented
458C2×C4×Q8—1221no—
459C2×C4×D4—1223no—
460C2×#117—613no—
461C22×C4⋊C4—613no—
462#419—613no—
463#419—613no—
464#419—613no—
465#419—613no—
466#418—613no—
467#418—613no—
468#418—613no—
469#418C2×D6113yescomplemented
470#417—613no—
471#417—613no—
472#417—613no—
473#417—613no—
474#417—611no—
475#417—616no—
476#417—613no—
477#417—616no—
478#417—616no—
479#417—613no—
480#417C2×D6113yescomplemented
481#416—613no—
482#416—613no—
483#416—613no—
484#416—616no—
485#416—616no—
486#416C2×D6113yescomplemented
487C2×#103—613no—
488C2×#103—613no—
489C2×#103—616no—
490C2×#102—613no—
491C2×#102—616no—
492C2×#102C2×D6113yescomplemented
493C61#6008911yescharacteristic, complemented, Sylow
4942−1+4—618no—
4952−1+4—6124no—
4962−1+4—12216no—
4972−1+4—12212no—
4982−1+4—1224no—
499H(5,𝔽2)—24no—
500H(5,𝔽2)—6124no—
501H(5,𝔽2)—12248no—
502H(5,𝔽2)—12212no—
503H(5,𝔽2)C4×D6118yescomplemented
504C2×#41—21no—
505C2×#41—618no—
506C2×#41—618no—
507C2×#41—611no—
508C2×#41—613no—
509C2×#41—613no—
510C2×#41—6124no—
511C2×#41—611no—
512C2×#41—6124no—
513C2×#41—613no—
514C2×#41—616no—
515C2×#41—613no—
516C2×#41—1223no—
517C2×#41—1223no—
518C2×#41—1223no—
519C2×#41—1223no—
520C2×#41—1223no—
521C2×#41—12212no—
522C2×#41—12212no—
523C2×#41—1226no—
524C2×#41—1223no—
525C2×#41—12248no—
526C2×#41—12216no—
527C2×#41—1223no—
528C2×#41C22×D6113yes—
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×Q8—613no—
532C22×Q8—613no—
533C22×Q8—1223no—
534C22×Q8—1221no—
535C22×D4—23no—
536C22×D4—613no—
537C22×D4—613no—
538C22×D4—1223no—
539C22×D4—1223no—
540C22×D4—1226no—
541C22×D4—1223no—
542C22×D4C22×D6113yes—
543C23×C4—613no—
544C23×C4—1223no—
545C23×C4—1223no—
546C23×C4—1223no—
547#131—24no—
548#131—12212no—
549#131—12212no—
550#131—1224no—
551C2×M16—613no—
552C2×M16—613no—
553C2×M16—611no—
554C2×M16—613no—
555C2×M16—613no—
556C2×M16—12212no—
557C2×M16—12212no—
558C2×M16C22×D6113yes—
559C22×C8—613no—
560C22×C8—616no—
561C22×C8C22×D6113yes—
562C4×Q8—21no—
563C4×Q8—1223no—
564C4×Q8—1223no—
565C4×Q8—1221no—
566C4×D4—23no—
567C4×D4—1223no—
568C4×D4—1226no—
569C4×D4—1223no—
570C4×D4—1226no—
571C4×D4—1223no—
572#117—613no—
573#117—613no—
574#117—613no—
575#117—1223no—
576#117—1223no—
577#117C22×D6113yes—
578C2×C4⋊C4—613no—
579C2×C4⋊C4—613no—
580C2×C4⋊C4—616no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—1223no—
583C2×C4⋊C4—1223no—
584C2×C4⋊C4—1223no—
585C2×C4⋊C4C22×D6113yes—
586C2×C22⋊C4—1223no—
587C2×C42—1223no—
588#103—613no—
589#103—611no—
590#103—616no—
591#103—613no—
592#103—613no—
593#103—616no—
594#103—613no—
595#103—613no—
596#103C22×D6113yes—
597#103C22×D6111yescharacteristic
598#102—616no—
599#102—613no—
600#102—613no—
601#102—613no—
602#102—611no—
603#102—613no—
604#102—611no—
605#102C22×D6116yes—
606#102C22×D6113yes—
607#102C22×D6113yes—
608C24—23no—
609C24—613no—
610C24—1223no—
611#41—28no—
612#41—26no—
613#41—618no—
614#41—6124no—
615#41—6112no—
616#41—6112no—
617#41—614no—
618#41—6112no—
619#41—6124no—
620#41—6112no—
621#41—12224no—
622#41—12224no—
623#41—12224no—
624#41—12224no—
625#41—1226no—
626#41—12224no—
627#41—12212no—
628#41—1222no—
629#41—12248no—
630#41—12224no—
631#41—12224no—
632#41—1226no—
633#41C2×C4×D6114yes—
634#41C2×C4×D61112yescomplemented
635#41D4×D6114yes—
636C2×Q8—618no—
637C2×Q8—613no—
638C2×Q8—6112no—
639C2×Q8—6112no—
640C2×Q8—613no—
641C2×Q8—1223no—
642C2×Q8—12224no—
643C2×Q8—1226no—
644C2×Q8—1228no—
645C2×Q8—1223no—
646C2×Q8—1226no—
647C2×Q8D4×D6111yescharacteristic
648C2×Q8C23×D6111yescharacteristic
649C2×D4—23no—
650C2×D4—224no—
651C2×D4—23no—
652C2×D4—26no—
653C2×D4—616no—
654C2×D4—6124no—
655C2×D4—6112no—
656C2×D4—613no—
657C2×D4—611no—
658C2×D4—1221no—
659C2×D4—1226no—
660C2×D4—1223no—
661C2×D4—12224no—
662C2×D4—12224no—
663C2×D4—12248no—
664C2×D4—1226no—
665C2×D4—1223no—
666C2×D4—12224no—
667C2×D4—1223no—
668C2×D4C2×C4×D61112yescomplemented
669C2×D4D4×D6113yes—
670C2×D4C23×D6113yes—
671C22×C4—23no—
672C22×C4—23no—
673C22×C4—613no—
674C22×C4—6112no—
675C22×C4—613no—
676C22×C4—613no—
677C22×C4—6112no—
678C22×C4—611no—
679C22×C4—613no—
680C22×C4—1221no—
681C22×C4—12224no—
682C22×C4—1223no—
683C22×C4—1226no—
684C22×C4—1221no—
685C22×C4—1223no—
686C22×C4—1223no—
687C22×C4—1226no—
688C22×C4—12224no—
689C22×C4—1223no—
690C22×C4—1223no—
691C22×C4—1223no—
692C22×C4—4886no—
693C22×C4C23×D6113yes—
694M16—26no—
695M16—1222no—
696M16—1226no—
697M16—1226no—
698M16—1226no—
699M16—1226no—
700C2×C8—26no—
701C2×C8—611no—
702C2×C8—613no—
703C2×C8—12212no—
704C2×C8—1226no—
705C2×C8C23×D6113yes—
706C2×C8C23×D6111yescharacteristic
707C4⋊C4—23no—
708C4⋊C4—613no—
709C4⋊C4—611no—
710C4⋊C4—1223no—
711C4⋊C4—1226no—
712C4⋊C4—1221no—
713C4⋊C4—1223no—
714C4⋊C4C23×D6113yes—
715C4⋊C4C23×D6111yescharacteristic
716C22⋊C4—23no—
717C22⋊C4—1223no—
718C22⋊C4—1223no—
719C22⋊C4—1223no—
720C42—23no—
721C42—1223no—
722C42—1223no—
723C42—1223no—
724C23—23no—
725C23—212no—
726C23—83no—
727C23—83no—
728C23—613no—
729C23—611no—
730C23—6112no—
731C23—12212no—
732C23—1221no—
733C23—4883no—
734C23—4883no—
735C23—2443no—
736C23—2443no—
737C23C2×D4×D6113yes—
738Q8—21no—
739Q8—6112no—
740Q8—616no—
741Q8—12212no—
742Q8—12212no—
743Q8—1223no—
744Q8C22⋊C4×D6114yes—
745Q8C22×C4×D6112yes—
746D4—212no—
747D4—212no—
748D4—23no—
749D4—6124no—
750D4—6112no—
751D4—612no—
752D4—1224no—
753D4—12212no—
754D4—12212no—
755D4—12224no—
756D4—12212no—
757D4—1221no—
758D4C22⋊C4×D61112yes—
759D4C22×C4×D6116yes—
760C2×C4—21no—
761C2×C4—212no—
762C2×C4—21no—
763C2×C4—23no—
764C2×C4—83no—
765C2×C4—6112no—
766C2×C4—613no—
767C2×C4—611no—
768C2×C4—6112no—
769C2×C4—6112no—
770C2×C4—612no—
771C2×C4—616no—
772C2×C4—616no—
773C2×C4—612no—
774C2×C4—1224no—
775C2×C4—12212no—
776C2×C4—12212no—
777C2×C4—12224no—
778C2×C4—12212no—
779C2×C4—1223no—
780C2×C4—12212no—
781C2×C4—1221no—
782C2×C4—1223no—
783C2×C4—4886no—
784C2×C4—4883no—
785C2×C4—2442no—
786C2×C4—2446no—
787C2×C4C22×C4×D6116yes—
788C2×C4C2×D4×D6113yes—
789C2×C4C2×D4×D6116yes—
790C2×C4C24×D6111yescharacteristic
791C8—21no—
792C8—23no—
793C8—1223no—
794C8—1221no—
795C22—23no—
796C22—23no—
797C22—26no—
798C22—43no—
799C22—43no—
800C22—812no—
801C22—612no—
802C22—616no—
803C22—1223no—
804C22—1221no—
805C22—1221no—
806C22—1223no—
807C22—1222no—
808C22—48812no—
809C22—24412no—
810C22—2441no—
811C22—2441no—
812C22C2×C22⋊C4×D6116yes—
813C22C22×D4×D6111yescharacteristic
814C4—22no—
815C4—43no—
816C4—41no—
817C4—612no—
818C4—616no—
819C4—1226no—
820C4—2443no—
821C4—2441no—
822C4C2×C22⋊C4×D6116yes—
823C4C23×C4×D6111yescharacteristic
824C4C22×D4×D6111yescharacteristic
825C2—26no—
826C2—46no—
827C2—1226no—
828C2—1222no—
829C2—2442no—
830C2C22×C22⋊C4×D6111yescharacteristic
831C2#2146059411yescharacteristic
832C2#2146060111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC61×#2897C2
socleC22×C61C23×D4
prime radicalC2×#16840597C2
cosocleC2×C4×C61C25
hypercenter#2897D61
hypocenterC61#60089
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#16840527C2semidirect
3. #520×D61C2semidirect
4. #21454353C2semidirect
5. #21454350C2semidirect
6. #21454349C2semidirect
7. #21454348C2semidirect
8. #21454345C2semidirect
9. #21454344C2semidirect
10. #21454340C2semidirect
11. #21454334C2semidirect
12. #21454333C2semidirect
13. C2×#16839760C2semidirect
14. #417×D61C2semidirect
15. C61×#2897C2semidirect
17. #16840597C4semidirect
29. C2×#14519785C22semidirect
30. C2×#14519784C22semidirect
31. C2×#14519783C22semidirect
32. C22×#11758189C22semidirect
33. C2×M16×D61C22semidirect
34. #16840245C22semidirect
36. #16840243C22semidirect
37. #16840242C22semidirect
41. #117×D61C22semidirect
42. C2×C4⋊C4×D61C22semidirect
43. #16839772C22semidirect
44. #16839770C22semidirect
45. #16839769C22semidirect
46. #16839769C22semidirect
47. #16839767C22semidirect
48. #16839765C22semidirect
49. #16839765C22semidirect
50. #16839764C22semidirect
51. #16839763C22semidirect
52. #16839762C22semidirect
53. #16839762C22semidirect
54. #16839761C22semidirect
55. #16839760C22semidirect
56. #16839760C22semidirect
57. #16839760C22semidirect
58. #16839760C22semidirect
59. #16839760C22semidirect
60. #16839759C22semidirect
61. #16839758C22semidirect
62. #16839756C22semidirect
63. #16839755C22semidirect
64. #16839755C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519700C22semidirect
67. #103×D61C22semidirect
68. C2×#14519698C22semidirect
69. #102×D61C22semidirect
71. C2×#131×C61C22semidirect
72. C61×#520C22semidirect
73. C61×#418C22semidirect
74. C61×#417C22semidirect
75. C61×#416C22semidirect
76. C2×#102×C61C22semidirect
80. #14519824C2×C4semidirect
81. #14519824C2×C4semidirect
84. #14519822C2×C4semidirect
99. C2×#11758224C2×C4semidirect
106. #41×D61C2×C4semidirect
173. H(5,𝔽2)×C61C2×C4semidirect
197. #41×C61C22×C4semidirect
205. C2×D4×C61C22×C4semidirect
230. Q8×D61C22×C4semidirect
241. #11758224C22×C4semidirect
246. D4×D61C22×C4semidirect
251. #11758222C22×C4semidirect
274. C2×Dic122C22×C4semidirect
419. #2897D61semidirect
449. C2×#131C2×D61semidirect
457. #520C2×D61semidirect
469. #418C2×D61semidirect
480. #417C2×D61semidirect
486. #416C2×D61semidirect
492. C2×#102C2×D61semidirect
493. C61#60089semidirect
503. H(5,𝔽2)C4×D61semidirect
634. #41C2×C4×D61semidirect
668. C2×D4C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405972
C2×#168405272
#520×D612
#214543532
#214543502
#214543492
#214543482
#214543452
#214543442
#214543402
#214543342
#214543332
C2×#168397602
#417×D612
C61×#28972
#6008961