Finite Group Databasebeta

← #30550813

Subgroups — #30550813

Order 15616.

2130 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459152C211yesmaximal, characteristic
2C2×#16840335C211yesmaximal, characteristic, complemented
3#21456713C214yesmaximal, complemented
4#21456708C214yesmaximal, complemented
5#21456706C214yesmaximal, complemented
6#21456690C214yesmaximal, complemented
7#21455767C211yesmaximal, characteristic, complemented
8#21455753C212yesmaximal, complemented
9#21455450C212yesmaximal, complemented
10#21455447C212yesmaximal, complemented
11#21455081C211yesmaximal, characteristic, complemented
12#21455077C211yesmaximal, characteristic, complemented
13#21455055C212yesmaximal, complemented
14#21454262C211yesmaximal, characteristic, complemented
15C61×#3095C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic, complemented
19C2×#14519810C2212yes—
20C2×#14519808C2212yes—
21C2×M16×D61C2212yescomplemented
22#16840343C2212yes—
23#16840343C2212yes—
24#16840338—21no—
25#16840338C2212yes—
26#16840335—22no—
27#16840335—22no—
28#16840335C2214yes—
29#16840335C2214yescomplemented
30#16840331—21no—
31#16840331C2212yes—
32#16840324—21no—
33#16840324—21no—
34#16840312—22no—
35C2×#14519776—21no—
36C2×#14519763—21no—
37#16840274—22no—
38#16840274C2212yes—
39#16840274C2212yes—
40C2×#14519762—21no—
41C2×#14519759—21no—
42C2×#14519757C2211yescharacteristic, complemented
43C2×#14519756C2211yescharacteristic
44C2×#14519753C2211yescharacteristic, complemented
45C2×#14519735C2211yescharacteristic, complemented
46#16840106C2214yescomplemented
47#16840105C2214yescomplemented
48#16840103C2214yescomplemented
49#16840097C2212yescomplemented
50#16840092C2212yescomplemented
51#16840089C2214yescomplemented
52#16840088C2214yescomplemented
53#16840021C2214yescomplemented
54#16840019C2214yescomplemented
55#16840011C2214yescomplemented
56#16840009C2214yescomplemented
57#16840004C2214yescomplemented
58#16840002C2214yescomplemented
59#16839994C2214yescomplemented
60#16839992C2214yescomplemented
61#16839926C2214yescomplemented
62#16839922C2214yescomplemented
63#16839920C2212yescomplemented
64#16839919C2214yescomplemented
65#16839919C2214yescomplemented
66#16839917C2212yescomplemented
67#16839915C2212yescomplemented
68#16839912C2212yescomplemented
69#16839902C2214yescomplemented
70#16839902C2214yescomplemented
71#16839805C2212yescomplemented
72#16839770C2212yescomplemented
73#16839764C2212yes—
74#16839761C2212yes—
75#16839727C2214yes—
76#16839727C2214yescomplemented
77#16839726C2211yescharacteristic
78#16839725C2212yescomplemented
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#485C2214yescomplemented
82C61×#484C2212yescomplemented
83C61×#483C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#419C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—44no—
90C2×#11758222—44no—
91C2×#11758222D412yes—
92C2×#11758222D412yes—
93C2×#11758222C2312yes—
94C2×#11758222C2312yes—
95C2×#11758222C2312yes—
96C2×#11758222C2312yes—
97C22×Dic122—21no—
98C22×Dic122D411yescharacteristic
99C22×Dic122C2311yescharacteristic
100C22×Dic122C2311yescharacteristic
101C2×Q8×D61—22no—
102C2×Q8×D61—44no—
103C2×Q8×D61C2314yes—
104C22×D244D411yescharacteristic
105C22×D244C2311yescharacteristic
106C22×C22⋊D61—21no—
107C22×C22⋊D61D411yescharacteristic
108C22×C22⋊D61D411yescharacteristic
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519810—44no—
114#14519808—44no—
115C2×Dic244C2314yes—
116C2×#11758202C2314yes—
117C2×#11758190C2314yes—
118C2×#11758201C2314yes—
119C2×#11758194C2312yes—
120C2×#11758189C2314yes—
121M16×D61—44no—
122C2×C8×D61C2314yes—
123#14519777—22no—
124#14519776—24no—
125#14519776—24no—
126#14519774—22no—
127#14519765—22no—
128#14519765—22no—
129#14519763—24no—
130#14519763—24no—
131#14519762—24no—
132#14519762—24no—
133#14519761—22no—
134#14519761—22no—
135#14519761—22no—
136#14519761—22no—
137#14519759—24no—
138#14519759—24no—
139#14519757—22no—
140#14519757—22no—
141#14519757—22no—
142#14519757C2314yes—
143#14519757C2312yes—
144#14519757C2312yes—
145#14519757C2312yes—
146#14519757C2312yes—
147#14519756—21no—
148#14519756—21no—
149#14519756C2312yes—
150#14519756C2312yes—
151#14519753—22no—
152#14519753C2314yes—
153#14519752—22no—
154#14519752—22no—
155#14519752C2312yes—
156#14519752C2312yes—
157#14519752C2312yes—
158#14519752C2312yes—
159#14519751—22no—
160#14519751—22no—
161#14519751—22no—
162#14519751—22no—
163#14519747—22no—
164#14519747—22no—
165#14519747—22no—
166#14519747—22no—
167C4×D244—22no—
168C4×D244—22no—
169C4×D244—22no—
170C4×D244—22no—
171#14519735—22no—
172#14519735C2314yes—
173C2×C4⋊Dic61—21no—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×C22⋊Dic61—21no—
178C2×#11758198—21no—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×C4×Dic61—21no—
182#14519710C2314yes—
183#14519708C2314yes—
184#14519702C2314yes—
185#14519700C2314yes—
186#14519700C2314yes—
187#14519700C2314yes—
188#14519699C2314yes—
189#14519697C2314yes—
190C22⋊#92418C2312yes—
191C22⋊#92418C2312yes—
192#14519689C2314yes—
193#14519689C2314yes—
194C22×Q8×C61C2311yescharacteristic
195C23×C4×C61C2311yescharacteristic
196C2×M16×C61C2312yes—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61C2312yes—
200C22⋊Q8×C61C2312yes—
201#117×C61—21no—
202#117×C61—21no—
203#117×C61C2312yes—
204#117×C61C2312yes—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C4⋊C4×C61C2311yescharacteristic
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C22⋊C4×C61—21no—
210C2×C22⋊C4×C61—21no—
211C2×C42×C61—21no—
212#107×C61C2314yes—
213#106×C61C2314yes—
214#103×C61C2314yes—
215#103×C61C2314yes—
216C22⋊C8×C61C2312yes—
217C22⋊C8×C61C2312yes—
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61C2×D411yescharacteristic
221C23×D61C2×D411yescharacteristic
222C2×Q8×C61—21no—
223C2×Q8×C61—24no—
224C2×Q8×C61C2412yes—
225C22×C4×C61—24no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—22no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—42no—
239C2×C22⋊D61—42no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61C2×D412yes—
242C2×C22⋊D61C2×D412yes—
243C2×C22⋊D61C2×D412yes—
244C2×C22⋊D61C2×D412yes—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250Q8×D61—44no—
251Q8×D61—44no—
252Q8×D61—48no—
253#11758222—24no—
254#11758222—24no—
255#11758222—42no—
256#11758222—42no—
257#11758222—44no—
258#11758222—44no—
259#11758222—42no—
260#11758222—42no—
261#11758222—42no—
262#11758222—42no—
263#11758222—44no—
264#11758222—44no—
265C2×D244—21no—
266C2×D244—22no—
267C2×D244—22no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—42no—
271C2×D244—42no—
272C2×D244C2×D412yes—
273C2×D244C2×D412yes—
274C2×D244C2412yes—
275C2×C4×D61—24no—
276C2×C4×D61—24no—
277C2×C4×D61—24no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C2×C4×D61C2×D412yes—
283C2×C4×D61C2×D412yes—
284C2×C4×D61C2412yes—
285C2×C4×D61C2412yes—
286C2×Dic122—24no—
287C2×Dic122—21no—
288C2×Dic122—21no—
289C2×Dic122—24no—
290C2×Dic122—42no—
291C2×Dic122—42no—
292C2×Dic122—44no—
293C2×Dic122C2×D412yes—
294C2×Dic122C2×D412yes—
295C2×Dic122C2412yes—
296C2×Dic122C2412yes—
297M16×C61—24no—
298C2×C8×C61C2414yes—
299C4⋊C4×C61—22no—
300C4⋊C4×C61—22no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61C2412yes—
305C4⋊C4×C61C2412yes—
306C4⋊C4×C61C2412yes—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—22no—
310C22⋊C4×C61—22no—
311C42×C61—22no—
312C42×C61—22no—
313C22⋊Dic61—22no—
314C22⋊Dic61—22no—
315#11758202—44no—
316#11758201—44no—
317#11758198—24no—
318#11758198—24no—
319#11758198—24no—
320#11758198—22no—
321#11758198—22no—
322#11758198—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198—22no—
326#11758198—22no—
327#11758198—22no—
328C4⋊Dic61—21no—
329C4⋊Dic61—24no—
330C4⋊Dic61—22no—
331C4⋊Dic61—22no—
332C4⋊Dic61—22no—
333C4⋊Dic61—22no—
334C4⋊Dic61C2412yes—
335#11758196—22no—
336#11758196—22no—
337#11758196—24no—
338C4×Dic61—24no—
339#11758194—24no—
340C2×#92418C2414yes—
341Dic244—44no—
342#11758190—44no—
343#11758189—44no—
344C8×D61—44no—
345C23×C61—22no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C22×D411yescharacteristic
349C23×C61C22×D411yescharacteristic
350C23×C61C22×D411yescharacteristic
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—42no—
359C22×D61—81no—
360C22×D61—81no—
361C22×D61C22×D412yes—
362C22×D61C22×D412yes—
363Q8×C61—24no—
364Q8×C61—42no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—81no—
377C2×C4×C61—81no—
378C2×C4×C61C22×D411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C2×C4×C61H(5,𝔽2)14yes—
382C2×C4×C61C2511yescharacteristic
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C22⋊D61—44no—
388C22⋊D61—44no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—42no—
395C2×Dic61—42no—
396C2×Dic61—42no—
397C2×Dic61C22×D412yes—
398C2×Dic61C22×D412yes—
399D244—22no—
400D244—22no—
401D244—42no—
402D244—42no—
403D244—42no—
404D244—82no—
405D244—82no—
406D244—82no—
407D244—82no—
408C4×D61—24no—
409C4×D61—24no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—44no—
415C4×D61—48no—
416C4×D61—44no—
417Dic122—24no—
418Dic122—22no—
419Dic122—22no—
420Dic122—42no—
421Dic122—42no—
422Dic122—48no—
423Dic122—42no—
424Dic122—42no—
425C8×C61—24no—
426#92418—24no—
427#60754—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—82no—
437C22×C61#53412yes—
438C22×C61C23×D411yescharacteristic
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—44no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—82no—
450C2×D61—84no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61#53412yes—
458C4×C61C2×H(5,𝔽2)12yes—
459Dic61—22no—
460Dic61—22no—
461Dic61—42no—
462Dic61—42no—
463Dic61—42no—
464#3449—611no—
465C2×#536—611no—
466#3202—614no—
467#3201—614no—
468#3201—614no—
469#3200—614no—
470#3095—611no—
471#3095D6111yescharacteristic, complemented
472#3093—612no—
473#3056—612no—
474#3056—612no—
475#3007—611no—
476#3007—611no—
477#3004—612no—
478#2879—611no—
479C2×C61—22no—
480C2×C61—41no—
481C2×C61—41no—
482C2×C61C2×#53411yescharacteristic
483C2×C61#358611yescharacteristic
484C2×C61#358611yescharacteristic
485D61—42no—
486D61—42no—
487D61—82no—
488C22×#41—611no—
489C22×#41—611no—
490C23×Q8—611no—
491C2×#137—612no—
492C2×#137—612no—
493C22×M16—612no—
494#537—612no—
495#537—612no—
496#536—614no—
497#536—614no—
498#536—612no—
499#536—1221no—
500#536—1222no—
501#536—1222no—
502#535—612no—
503#535—1221no—
504#534—1221no—
505#534—1221no—
506#532—1222no—
507C2×C4⋊Q8—1221no—
508C2×#124—1221no—
509#525—612no—
510#525—612no—
511#525—1222no—
512C2×#123—1221no—
513C2×#123—1221no—
514C2×C22⋊Q8—611no—
515C2×C22⋊Q8—611no—
516C2×C22⋊Q8—611no—
517C2×C22⋊Q8C2×D6111yescharacteristic
518C2×#117—611no—
519C2×#117C2×D6111yescharacteristic
520#485—614no—
521#485—614no—
522#485—614no—
523#485C2×D6114yescomplemented
524#484—612no—
525#484C2×D6112yescomplemented
526#483—612no—
527#483C2×D6112yescomplemented
528#482—614no—
529#482—614no—
530#470—614no—
531#470—614no—
532#468—614no—
533#468—614no—
534#467—614no—
535#467—614no—
536#465—614no—
537#465—614no—
538#452—614no—
539#452—614no—
540#451—612no—
541#451—614no—
542#451—614no—
543#451—612no—
544#450—612no—
545#450—612no—
546#448—614no—
547#448—614no—
548#428—612no—
549#428C2×D6112yescomplemented
550#419—612no—
551#419C2×D6112yescomplemented
552#417—612no—
553#417—612no—
554#408—614no—
555#408—614no—
556#407—611no—
557#407—612no—
558#407C2×D6111yescharacteristic
559C61#6075411yescharacteristic, complemented, Sylow
560C2×#41—612no—
561C2×#41—612no—
562C2×#41—612no—
563C2×#41—612no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41—2444no—
569C2×#41—2444no—
570C22×Q8—611no—
571C22×Q8—614no—
572C22×Q8—611no—
573C22×Q8—611no—
574C22×Q8—1221no—
575C22×Q8—1222no—
576C22×Q8—2444no—
577C22×Q8C22×D6111yescharacteristic
578C22×D4—611no—
579C22×D4—611no—
580C22×D4—611no—
581C22×D4—611no—
582C22×D4—1221no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4C22×D6111yescharacteristic
588#137—2444no—
589#137—2444no—
590C2×Q16—614no—
591C2×Q16—614no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×M16—612no—
595C2×M16—614no—
596C2×M16—2444no—
597C2×M16C22×D6112yes—
598C22×C8—614no—
599C4⋊Q8—1222no—
600C4⋊Q8—1224no—
601C4⋊Q8—1224no—
602#127—1222no—
603#124—1222no—
604#124—1222no—
605#124—1224no—
606#124—1224no—
607#123—1222no—
608#123—1222no—
609#123—1224no—
610#123—1224no—
611#123—1222no—
612#123—1222no—
613#123—1224no—
614#123—1224no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—614no—
618C22⋊Q8—612no—
619C22⋊Q8—612no—
620C22⋊Q8—614no—
621C22⋊Q8—612no—
622C22⋊Q8—612no—
623C22⋊Q8—612no—
624C22⋊Q8—612no—
625C22⋊Q8—1222no—
626C22⋊Q8—1222no—
627C22⋊Q8—1222no—
628C22⋊Q8—1222no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8C22×D6112yes—
632C22⋊Q8C22×D6112yes—
633#121—612no—
634#121—612no—
635#121—612no—
636#121—612no—
637#121—1222no—
638#121—1222no—
639#121—1222no—
640#121—1222no—
641#121—1222no—
642#121—1222no—
643#120—1222no—
644#120—1222no—
645#120—1222no—
646#120—1222no—
647C4×D4—1222no—
648C4×D4—1222no—
649C4×D4—1222no—
650C4×D4—1222no—
651#117—21no—
652#117—21no—
653#117—614no—
654#117—1222no—
655#117C22×D6112yes—
656#117C22×D6112yes—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4—1221no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4C22×D6111yescharacteristic
663C2×C4⋊C4C22×D6111yescharacteristic
664C2×C4⋊C4C22×D6111yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1221no—
671C2×C42—21no—
672C2×C42—1221no—
673#107—614no—
674#107C22×D6114yes—
675#106—614no—
676#106C22×D6114yes—
677#103—614no—
678#103—614no—
679#103—614no—
680#103—614no—
681#103C22×D6114yes—
682#103C22×D6114yes—
683#102—614no—
684#102—614no—
685C22⋊C8—612no—
686C22⋊C8—612no—
687C22⋊C8—614no—
688C22⋊C8—614no—
689C22⋊C8C22×D6112yes—
690C22⋊C8C22×D6112yes—
691C24—611no—
692C24—611no—
693C24—1221no—
694C24D4×D6111yescharacteristic
695#41—1224no—
696#41—1224no—
697#41—2444no—
698#41—2444no—
699#41—2442no—
700#41—2442no—
701#41—2442no—
702#41—2442no—
703#41—2442no—
704#41—2442no—
705#41—2444no—
706#41—2444no—
707C2×Q8—21no—
708C2×Q8—24no—
709C2×Q8—612no—
710C2×Q8—612no—
711C2×Q8—612no—
712C2×Q8—612no—
713C2×Q8—1224no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—1224no—
717C2×Q8—2442no—
718C2×Q8—2442no—
719C2×Q8—2444no—
720C2×Q8—2444no—
721C2×Q8—2444no—
722C2×Q8—2448no—
723C2×Q8C23×D6112yes—
724C2×D4—612no—
725C2×D4—612no—
726C2×D4—612no—
727C2×D4—612no—
728C2×D4—612no—
729C2×D4—612no—
730C2×D4—612no—
731C2×D4—1222no—
732C2×D4—1222no—
733C2×D4—1222no—
734C2×D4—1222no—
735C2×D4—1222no—
736C2×D4—1222no—
737C2×D4—1221no—
738C2×D4—2442no—
739C2×D4—2442no—
740C2×D4—2442no—
741C2×D4—2442no—
742C2×D4—2444no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—612no—
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—612no—
754C22×C4—1224no—
755C22×C4—1224no—
756C22×C4—1224no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1222no—
761C22×C4—1222no—
762C22×C4—2444no—
763C22×C4—2444no—
764C22×C4D4×D6111yescharacteristic
765C22×C4D4×D6111yescharacteristic
766C22×C4D4×D6111yescharacteristic
767C22×C4C23×D6111yescharacteristic
768C22×C4C23×D6111yescharacteristic
769C22×C4C23×D6111yescharacteristic
770Q16—2444no—
771Q16—2444no—
772SD16—2444no—
773SD16—2444no—
774M16—24no—
775M16—1224no—
776M16—2444no—
777C2×C8—614no—
778C2×C8—2444no—
779C2×C8C23×D6114yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—612no—
786C4⋊C4—1224no—
787C4⋊C4—1224no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1221no—
793C4⋊C4—1222no—
794C4⋊C4—1222no—
795C4⋊C4C23×D6112yes—
796C4⋊C4C23×D6112yes—
797C4⋊C4C23×D6112yes—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—1222no—
803C22⋊C4—1222no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1224no—
807C22⋊C4—1224no—
808C22⋊C4—1224no—
809C22⋊C4—1222no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C22⋊C4—1222no—
813C22⋊C4—1222no—
814C22⋊C4—1222no—
815C42—22no—
816C42—22no—
817C42—1224no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—612no—
822C23—612no—
823C23—1222no—
824C23—1222no—
825C23—1222no—
826C23—4881no—
827C23—4881no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2442no—
833C23C2×D4×D6111yescharacteristic
834C23C2×D4×D6111yescharacteristic
835C23C2×D4×D6111yescharacteristic
836Q8—24no—
837Q8—42no—
838Q8—1224no—
839Q8—1222no—
840Q8—1222no—
841Q8—2442no—
842Q8—2442no—
843Q8—2442no—
844Q8—2448no—
845Q8—2442no—
846D4—1222no—
847D4—1222no—
848D4—4882no—
849D4—4882no—
850D4—4882no—
851D4—4882no—
852D4—2442no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857D4—2442no—
858D4—2442no—
859D4—2444no—
860D4—2444no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—612no—
875C2×C4—612no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1224no—
879C2×C4—1224no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—2444no—
888C2×C4—2448no—
889C2×C4—2442no—
890C2×C4—2442no—
891C2×C4—2442no—
892C2×C4—2444no—
893C2×C4C2×D4×D6111yescharacteristic
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4C2×D4×D6111yescharacteristic
896C2×C4#1451982314yes—
897C2×C4C24×D6111yescharacteristic
898C8—24no—
899C8—1224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—82no—
909C22—1222no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—1222no—
914C22—1222no—
915C22—4882no—
916C22—4884no—
917C22—2444no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22#1684032312yes—
922C22C22×D4×D6111yescharacteristic
923C4—21no—
924C4—21no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—1222no—
930C4—1222no—
931C4—2442no—
932C4—2442no—
933C4—2442no—
934C4#1684032312yes—
935C4C2×#1451982312yes—
936C2—22no—
937C2—41no—
938C2—41no—
939C2—4882no—
940C2—2442no—
941C2—2442no—
942C2C2×#1684032311yescharacteristic
943C2#2146060211yescharacteristic
944C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radical#21459152C2
hypercenter#3095D61
hypocenterC61#60754
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
2. C2×#16840335C2semidirect
3. #21456713C2semidirect
4. #21456708C2semidirect
5. #21456706C2semidirect
6. #21456690C2semidirect
7. #21455767C2semidirect
8. #21455753C2semidirect
9. #21455450C2semidirect
10. #21455447C2semidirect
11. #21455081C2semidirect
12. #21455077C2semidirect
13. #21455055C2semidirect
14. #21454262C2semidirect
15. C61×#3095C2semidirect
18. C22×Q8×D61C22semidirect
21. C2×M16×D61C22semidirect
29. #16840335C22semidirect
42. C2×#14519757C22semidirect
44. C2×#14519753C22semidirect
45. C2×#14519735C22semidirect
46. #16840106C22semidirect
47. #16840105C22semidirect
48. #16840103C22semidirect
49. #16840097C22semidirect
50. #16840092C22semidirect
51. #16840089C22semidirect
52. #16840088C22semidirect
53. #16840021C22semidirect
54. #16840019C22semidirect
55. #16840011C22semidirect
56. #16840009C22semidirect
57. #16840004C22semidirect
58. #16840002C22semidirect
59. #16839994C22semidirect
60. #16839992C22semidirect
61. #16839926C22semidirect
62. #16839922C22semidirect
63. #16839920C22semidirect
64. #16839919C22semidirect
65. #16839919C22semidirect
66. #16839917C22semidirect
67. #16839915C22semidirect
68. #16839912C22semidirect
69. #16839902C22semidirect
70. #16839902C22semidirect
71. #16839805C22semidirect
72. #16839770C22semidirect
76. #16839727C22semidirect
78. #16839725C22semidirect
81. C61×#485C22semidirect
82. C61×#484C22semidirect
83. C61×#483C22semidirect
84. C61×#428C22semidirect
85. C61×#419C22semidirect
471. #3095D61semidirect
523. #485C2×D61semidirect
525. #484C2×D61semidirect
527. #483C2×D61semidirect
549. #428C2×D61semidirect
551. #419C2×D61semidirect
559. C61#60754semidirect

Maximal subgroups

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

subgroupindex
#214591522
C2×#168403352
#214567132
#214567082
#214567062
#214566902
#214557672
#214557532
#214554502
#214554472
#214550812
#214550772
#214550552
#214542622
C61×#30952
#6075461