Finite Group Databasebeta

← #30551335

Subgroups — #30551335

Order 15616.

2188 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459115C211yesmaximal, characteristic, complemented
2C2×#16840312C211yesmaximal, characteristic, complemented
3#21456858C214yesmaximal, complemented
4#21456848C212yesmaximal, complemented
5#21456839C212yesmaximal, complemented
6#21456832C212yesmaximal, complemented
7#21456824C212yesmaximal, complemented
8#21456816C212yesmaximal, complemented
9#21456808C212yesmaximal, complemented
10#21456265C212yesmaximal, complemented
11#21456165C212yesmaximal, complemented
12#21455276C214yesmaximal, complemented
13#21455041C214yesmaximal, complemented
14C2×C61×#432C211yesmaximal, characteristic, complemented
15C22×#11758222C2212yes—
16C2×#14519799C2218yescomplemented
17#16840319C2211yescharacteristic
18#16840319C2211yescharacteristic, complemented
19#16840319C2211yescharacteristic, complemented
20#16840312—21no—
21#16840312—21no—
22#16840312—21no—
23#16840312—21no—
24#16840312C2211yescharacteristic
25#16840312C2212yes—
26#16840312C2212yes—
27#16840312C2212yes—
28#16840312C2212yes—
29#16840312C2211yescharacteristic, complemented
30#16840312C2211yescharacteristic, complemented
31C2×#14519777C2211yescharacteristic
32C2×#14519774C2211yescharacteristic
33#16840296—21no—
34#16840296—21no—
35#16840296—21no—
36#16840296—21no—
37#16840296C2212yes—
38#16840296C2212yescomplemented
39C2×#14519765C2212yes—
40#16840273—21no—
41#16840273—21no—
42#16840273C2212yes—
43C2×#14519751—21no—
44C2×#14519751—21no—
45C4×#11758222—21no—
46C4×#11758222—21no—
47C4×#11758222C2212yescomplemented
48C2×C4×D244—21no—
49C2×C4×D244—21no—
50#16840156C2214yescomplemented
51#16840156C2214yescomplemented
52#16840151C2214yescomplemented
53#16840151C2214yescomplemented
54#16840131C2214yescomplemented
55#16840127C2214yescomplemented
56#16840122C2214yescomplemented
57#16840122C2214yescomplemented
58#16839985C2218yescomplemented
59#16839978C2218yescomplemented
60#16839973C2214yescomplemented
61#16839968C2214yescomplemented
62#16839963C2214yescomplemented
63#16839958C2214yescomplemented
64#16839926C2218yescomplemented
65#16839920C2214yes—
66#16839915C2214yes—
67#16839909C2218yescomplemented
68#16839903C2214yes—
69#16839898C2214yes—
70#16839759C2218yescomplemented
71C22×C42×C61C2211yescharacteristic
72C61×#432C2212yes—
73C61×#432C2212yes—
74C61×#432C2212yescomplemented
75C61×#432C2212yescomplemented
76C2×C4⋊C8×C61C2212yescomplemented
77C2×C22⋊C8×C61C2212yes—
78C2×#97×C61C2212yescomplemented
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—48no—
84C2×#11758222C2312yes—
85C2×#11758222C2314yes—
86C2×#11758222C2314yes—
87C22×Dic122C2312yes—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244C2312yes—
91C22×C22⋊D61—22no—
92C22×C4×D61—22no—
93#14519799—416no—
94C2×Dic244C2318yes—
95C2×#11758190C2318yes—
96C2×#11758190C2318yes—
97C2×D488C2318yes—
98#14519777—21no—
99#14519777—21no—
100#14519777C2312yes—
101#14519777C2312yes—
102#14519777C2311yescharacteristic
103#14519777C2311yescharacteristic
104#14519777C2311yescharacteristic
105#14519774—21no—
106#14519774—21no—
107#14519774C2312yes—
108#14519774C2312yes—
109#14519774C2311yescharacteristic
110#14519771—22no—
111#14519771—22no—
112#14519769—21no—
113#14519769—21no—
114#14519769C2312yes—
115#14519765—22no—
116#14519765—22no—
117#14519765—21no—
118#14519765—21no—
119#14519765C2314yes—
120#14519765C2314yes—
121#14519765C2312yes—
122#14519760—22no—
123#14519760—22no—
124#14519760—22no—
125#14519756—21no—
126#14519756—21no—
127#14519756—21no—
128#14519756—21no—
129#14519756C2312yes—
130#14519756C2312yes—
131#14519751—22no—
132#14519751—22no—
133#14519751—22no—
134#14519751—22no—
135#14519751—22no—
136#14519751—22no—
137#14519751—22no—
138#14519751—22no—
139#14519751—21no—
140#14519751—21no—
141#14519751—21no—
142#14519751—21no—
143#14519751C2312yes—
144#14519751C2312yes—
145#14519746—22no—
146C4×Dic122—21no—
147C4×Dic122—21no—
148C4×Dic122—21no—
149C4×Dic122—21no—
150C4×Dic122C2312yes—
151C4×Dic122C2312yes—
152C4×D244—22no—
153C4×D244—22no—
154C4×D244—22no—
155C4×D244—22no—
156C4×D244—22no—
157C4×D244—22no—
158C4×D244—22no—
159C4×D244—22no—
160C4×D244—21no—
161C4×D244—21no—
162C4×D244—21no—
163C4×D244—21no—
164C4×D244C2312yes—
165C4×D244C2312yes—
166C4×C22⋊D61—22no—
167C4×C22⋊D61—22no—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—22no—
170C4×C22⋊D61—22no—
171C4×C22⋊D61—22no—
172#14519736—21no—
173#14519736—21no—
174#14519736C2312yes—
175#14519734—22no—
176#14519734—22no—
177#14519734—22no—
178C2×C4⋊Dic61—21no—
179C2×C4⋊Dic61—21no—
180C2×#11758198—22no—
181C2×#11758198—22no—
182C42×D61—22no—
183#14519702C2318yes—
184#14519702C2318yes—
185#14519699C2318yes—
186#14519699C2318yes—
187C23×C4×C61D411yescharacteristic
188C23×C4×C61D411yescharacteristic
189C23×C4×C61C2311yescharacteristic
190C22×C8×C61C2314yes—
191C2×C42×C61D411yescharacteristic
192C2×C42×C61D411yescharacteristic
193C2×C42×C61D411yescharacteristic
194C2×C42×C61D411yescharacteristic
195C2×C42×C61D411yescharacteristic
196C2×C42×C61D411yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C2×C42×C61C2311yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C4⋊C8×C61C2314yes—
204C4⋊C8×C61C2314yes—
205C22⋊C8×C61C2314yes—
206C22⋊C8×C61C2314yes—
207#97×C61C2314yes—
208#97×C61C2314yes—
209C24×C61C2×D411yescharacteristic
210C23×D61—22no—
211C22×C4×C61—24no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—24no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—48no—
238C22×Dic61—22no—
239#11758222—216no—
240#11758222—28no—
241#11758222—48no—
242#11758222—44no—
243#11758222—44no—
244#11758222—48no—
245#11758222—48no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—44no—
254C2×D244—44no—
255C2×D244—44no—
256C2×D244C2414yes—
257C2×D244C2412yes—
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—48no—
264C2×Dic122—22no—
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122—44no—
268C2×Dic122C2414yes—
269C2×Dic122C2412yes—
270C2×C8×C61—28no—
271C2×C8×C61C2418yes—
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2411yescharacteristic
285C42×C61C2411yescharacteristic
286C42×C61C2411yescharacteristic
287C42×C61C2411yescharacteristic
288C22⋊Dic61—22no—
289C22⋊Dic61—22no—
290C22⋊Dic61—22no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295#11758198—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301C4⋊Dic61—22no—
302C4⋊Dic61—22no—
303C4⋊Dic61—22no—
304C4⋊Dic61—22no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61C2412yes—
310C4⋊Dic61C2412yes—
311#11758196—22no—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—22no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320Dic244—48no—
321D488—48no—
322#11758190—48no—
323#11758190—48no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—41no—
327C23×C61C22×D411yescharacteristic
328C23×C61C22×D411yescharacteristic
329C23×C61C22×D411yescharacteristic
330C22×D61—22no—
331C22×D61—24no—
332C22×D61—44no—
333C22×D61—44no—
334C22×D61—44no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61H(5,𝔽2)14yes—
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—48no—
366C22⋊D61—44no—
367C22⋊D61—48no—
368C22⋊D61—44no—
369C22⋊D61—44no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—24no—
374C2×Dic61—44no—
375D244—24no—
376D244—28no—
377D244—44no—
378D244—44no—
379D244—44no—
380D244—44no—
381D244—42no—
382D244—42no—
383D244—44no—
384C4×D61—48no—
385C4×D61—44no—
386C4×D61—48no—
387C4×D61—44no—
388C4×D61—44no—
389Dic122—24no—
390Dic122—28no—
391Dic122—44no—
392Dic122—42no—
393Dic122—42no—
394C8×C61—28no—
395#60790—611nomaximal, Sylow
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—44no—
404C22×C61#53512yes—
405C22×C61#57512yes—
406C22×C61C23×D411yescharacteristic
407C2×D61—44no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—44no—
412C2×D61—44no—
413C2×D61—88no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61#53512yes—
424C4×C61#57512yes—
425C4×C61C2×H(5,𝔽2)12yes—
426Dic61—44no—
427Dic61—42no—
428Dic61—42no—
429Dic61—42no—
430#3444—611no—
431C2×#532—611no—
432#3219—614no—
433#3218—612no—
434#3217—612no—
435#3216—612no—
436#3215—612no—
437#3214—612no—
438#3213—612no—
439#3150—612no—
440#3135—612no—
441#3035—614no—
442#3002—614no—
443C2×#432D6111yescharacteristic, complemented
444C2×C61—22no—
445C2×C61—22no—
446C2×C61—41no—
447C2×C61C2×#53511yescharacteristic
448C2×C61C2×#57511yescharacteristic
449C2×C61C2×#57511yescharacteristic
450D61—82no—
451D61—84no—
452C22×#41—612no—
453C2×#135—618no—
454#533—611no—
455#533—611no—
456#533—611no—
457#532—611no—
458#532—611no—
459#532—612no—
460#532—611no—
461#532—612no—
462#532—612no—
463#532—612no—
464#532—1221no—
465#532—1221no—
466#532—1221no—
467#532—1221no—
468C2×C4⋊Q8—611no—
469C2×#127—611no—
470#529—612no—
471#529—612no—
472#529—1221no—
473#529—1221no—
474#529—1221no—
475#529—1221no—
476C2×#124—612no—
477#525—612no—
478#525—1221no—
479#525—1221no—
480C2×#121—1221no—
481C2×#121—1221no—
482C4×#41—612no—
483C4×#41—1221no—
484C4×#41—1221no—
485C2×C4×D4—1221no—
486C2×C4×D4—1221no—
487C22×C42C2×D6111yescharacteristic
488#497—614no—
489#497—614no—
490#496—614no—
491#496—614no—
492#491—614no—
493#490—614no—
494#489—614no—
495#489—614no—
496#464—618no—
497#463—618no—
498#462—614no—
499#461—614no—
500#460—614no—
501#459—614no—
502#452—618no—
503#451—614no—
504#450—614no—
505#449—618no—
506#448—614no—
507#447—614no—
508#432C2×D6112yes—
509#432C2×D6112yes—
510#432C2×D6112yescomplemented
511#432C2×D6112yescomplemented
512C2×C4⋊C8C2×D6112yescomplemented
513#416—618no—
514C2×C22⋊C8C2×D6112yes—
515C2×#97C2×D6112yescomplemented
516C61#6079011yescharacteristic, complemented, Sylow
517C2×#41—612no—
518C2×#41—614no—
519C2×#41—614no—
520C2×#41—1221no—
521C2×#41—1221no—
522C2×#41—1222no—
523C2×#41—1222no—
524C2×#41—2448no—
525C22×Q8—612no—
526C22×D4—612no—
527C22×D4—1222no—
528C22×D4—1221no—
529C22×D4—1221no—
530C23×C4—1222no—
531C23×C4D24411yescharacteristic
532C23×C4D24411yescharacteristic
533C23×C4C22×D6111yescharacteristic
534#135—24416no—
535C2×Q16—618no—
536C2×SD16—618no—
537C2×SD16—618no—
538C2×D8—618no—
539C22×C8C22×D6114yes—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—612no—
543C4⋊Q8—612no—
544C4⋊Q8—611no—
545C4⋊Q8—1221no—
546C4⋊Q8—1221no—
547#127—612no—
548#127—612no—
549#127—611no—
550#127—1221no—
551#127—1221no—
552#126—1222no—
553#126—1222no—
554#125—612no—
555#125—1221no—
556#125—1221no—
557#124—614no—
558#124—614no—
559#124—612no—
560#124—1222no—
561#124—1222no—
562#124—1221no—
563#124—1221no—
564#123—1222no—
565#123—1222no—
566#123—1222no—
567C22⋊Q8—612no—
568C22⋊Q8—612no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573#121—612no—
574#121—612no—
575#121—1222no—
576#121—1222no—
577#121—1222no—
578#121—1222no—
579#121—1222no—
580#121—1222no—
581#121—1222no—
582#121—1222no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#120—1222no—
588C4×Q8—612no—
589C4×Q8—612no—
590C4×Q8—1221no—
591C4×Q8—1221no—
592C4×Q8—1221no—
593C4×Q8—1221no—
594C4×D4—612no—
595C4×D4—612no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1222no—
603C4×D4—1222no—
604C4×D4—1222no—
605C4×D4—1222no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—1222no—
609C4×D4—1222no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614#117—612no—
615#117—1221no—
616#117—1221no—
617#117—1222no—
618#117—1222no—
619#117—1222no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1222no—
624C2×C42—1222no—
625C2×C42D24411yescharacteristic
626C2×C42D24411yescharacteristic
627C2×C42D24411yescharacteristic
628C2×C42D24411yescharacteristic
629C2×C42D24411yescharacteristic
630C2×C42D24411yescharacteristic
631C2×C42C22×D6111yescharacteristic
632C2×C42C22×D6111yescharacteristic
633C2×C42C22×D6111yescharacteristic
634C2×C42C22×D6111yescharacteristic
635C2×C42C22×D6111yescharacteristic
636C2×C42C22×D6111yescharacteristic
637C4⋊C8C22×D6114yes—
638C4⋊C8C22×D6114yes—
639#103—618no—
640#103—618no—
641#102—618no—
642#102—618no—
643C22⋊C8C22×D6114yes—
644C22⋊C8C22×D6114yes—
645#97C22×D6114yes—
646#97C22×D6114yes—
647C24—1222no—
648C24C2×D24411yescharacteristic
649#41—1228no—
650#41—12216no—
651#41—2448no—
652#41—2448no—
653#41—2448no—
654#41—2444no—
655#41—2444no—
656C2×Q8—614no—
657C2×Q8—612no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8—1222no—
661C2×Q8—2444no—
662C2×D4—614no—
663C2×D4—612no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1222no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2448no—
680C22×C4—24no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1224no—
687C22×C4—1222no—
688C22×C4—1224no—
689C22×C4—2448no—
690C22×C4C2×D24411yescharacteristic
691C22×C4C2×D24411yescharacteristic
692C22×C4C2×D24411yescharacteristic
693C22×C4C2×D24411yescharacteristic
694C22×C4C2×D24411yescharacteristic
695C22×C4C2×D24411yescharacteristic
696C22×C4C2×D24411yescharacteristic
697C22×C4C2×D24411yescharacteristic
698C22×C4C2×D24411yescharacteristic
699C22×C4C2×D24411yescharacteristic
700C22×C4C2×D24411yescharacteristic
701C22×C4C2×D24411yescharacteristic
702C22×C4C2×D24411yescharacteristic
703C22×C4C2×D24411yescharacteristic
704C22×C4C2×D24411yescharacteristic
705C22×C4C23×D6111yescharacteristic
706C22×C4C23×D6111yescharacteristic
707C22×C4C23×D6111yescharacteristic
708Q16—2448no—
709SD16—2448no—
710SD16—2448no—
711D8—2448no—
712C2×C8—28no—
713C2×C8C23×D6118yes—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1222no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4—1222no—
743C42—1222no—
744C42—1222no—
745C42—1222no—
746C42C2×D24411yescharacteristic
747C42C2×D24411yescharacteristic
748C42C2×D24411yescharacteristic
749C42C2×D24411yescharacteristic
750C42C2×D24411yescharacteristic
751C42C2×D24411yescharacteristic
752C42C2×D24411yescharacteristic
753C42C2×D24411yescharacteristic
754C42C2×D24411yescharacteristic
755C42C2×D24411yescharacteristic
756C42C2×D24411yescharacteristic
757C42C2×D24411yescharacteristic
758C42C23×D6111yescharacteristic
759C42C23×D6111yescharacteristic
760C42C23×D6111yescharacteristic
761C42C23×D6111yescharacteristic
762C23—22no—
763C23—22no—
764C23—41no—
765C23—1222no—
766C23—1224no—
767C23—2444no—
768C23—2444no—
769C23—2444no—
770C23C22×D24411yescharacteristic
771C23C22×D24411yescharacteristic
772C23C22×D24411yescharacteristic
773Q8—1224no—
774Q8—1228no—
775Q8—2444no—
776Q8—2442no—
777Q8—2442no—
778D4—1224no—
779D4—1228no—
780D4—2444no—
781D4—2444no—
782D4—2444no—
783D4—2444no—
784D4—2442no—
785D4—2442no—
786D4—2448no—
787D4—2444no—
788D4—2444no—
789D4—2448no—
790D4—2444no—
791D4—2444no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—2448no—
814C2×C4—2444no—
815C2×C4—2444no—
816C2×C4—2444no—
817C2×C4—2448no—
818C2×C4—2444no—
819C2×C4C22×D24411yescharacteristic
820C2×C4C22×D24411yescharacteristic
821C2×C4C22×D24411yescharacteristic
822C2×C4C22×D24411yescharacteristic
823C2×C4C22×D24411yescharacteristic
824C2×C4C22×D24411yescharacteristic
825C2×C4C22×D24411yescharacteristic
826C2×C4C22×D24411yescharacteristic
827C2×C4C22×D24411yescharacteristic
828C2×C4C22×D24411yescharacteristic
829C2×C4C22×D24411yescharacteristic
830C2×C4#1451982314yes—
831C2×C4C24×D6111yescharacteristic
832C8—28no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—44no—
841C22—4888no—
842C22—2442no—
843C22—2442no—
844C22—2444no—
845C22—2444no—
846C22—2444no—
847C22—2442no—
848C22#1684033112yes—
849C22#1684056212yes—
850C22C23×D24411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—2442no—
861C4—2442no—
862C4—2444no—
863C4—2442no—
864C4#1684033112yes—
865C4#1684056212yes—
866C4C2×#1451982312yes—
867C2—22no—
868C2—22no—
869C2—41no—
870C2—4884no—
871C2—4882no—
872C2C2×#1684033111yescharacteristic
873C2C2×#1684056211yescharacteristic
874C2C2×#1684056211yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#432C2
socleC22×C61C23×D4
hypercenterC2×#432D61
hypocenterC61#60790
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. #21459115C2semidirect
2. C2×#16840312C2semidirect
3. #21456858C2semidirect
4. #21456848C2semidirect
5. #21456839C2semidirect
6. #21456832C2semidirect
7. #21456824C2semidirect
8. #21456816C2semidirect
9. #21456808C2semidirect
10. #21456265C2semidirect
11. #21456165C2semidirect
12. #21455276C2semidirect
13. #21455041C2semidirect
14. C2×C61×#432C2semidirect
16. C2×#14519799C22semidirect
18. #16840319C22semidirect
19. #16840319C22semidirect
29. #16840312C22semidirect
30. #16840312C22semidirect
38. #16840296C22semidirect
47. C4×#11758222C22semidirect
50. #16840156C22semidirect
51. #16840156C22semidirect
52. #16840151C22semidirect
53. #16840151C22semidirect
54. #16840131C22semidirect
55. #16840127C22semidirect
56. #16840122C22semidirect
57. #16840122C22semidirect
58. #16839985C22semidirect
59. #16839978C22semidirect
60. #16839973C22semidirect
61. #16839968C22semidirect
62. #16839963C22semidirect
63. #16839958C22semidirect
64. #16839926C22semidirect
67. #16839909C22semidirect
70. #16839759C22semidirect
74. C61×#432C22semidirect
75. C61×#432C22semidirect
76. C2×C4⋊C8×C61C22semidirect
78. C2×#97×C61C22semidirect
443. C2×#432D61semidirect
510. #432C2×D61semidirect
511. #432C2×D61semidirect
512. C2×C4⋊C8C2×D61semidirect
515. C2×#97C2×D61semidirect
516. C61#60790semidirect

Maximal subgroups

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

subgroupindex
#214591152
C2×#168403122
#214568582
#214568482
#214568392
#214568322
#214568242
#214568162
#214568082
#214562652
#214561652
#214552762
#214550412
C2×C61×#4322
#6079061