Finite Group Databasebeta

← #30575890

Subgroups — #30575890

Order 15616.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic, complemented
2#21459383C211yesmaximal, characteristic, complemented
3#21458779C212yesmaximal, complemented
4#21458648C212yesmaximal, complemented
5#21458381C212yesmaximal, complemented
6#21458336C212yesmaximal, complemented
7#21458321C212yesmaximal, complemented
8#21458022C212yesmaximal, complemented
9#21457977C212yesmaximal, complemented
10#21457797C212yesmaximal, complemented
11#21457207C211yesmaximal, characteristic, complemented
12#21457182C211yesmaximal, characteristic, complemented
13#21457146C211yesmaximal, characteristic, complemented
14#21457042C211yesmaximal, characteristic, complemented
15#21457035C211yesmaximal, characteristic, complemented
16#21457000C211yesmaximal, characteristic, complemented
17#21455971C211yesmaximal, characteristic, complemented
18#21455911C211yesmaximal, characteristic, complemented
19#21455880C211yesmaximal, characteristic, complemented
20#21455635C211yesmaximal, characteristic, complemented
21#21455618C211yesmaximal, characteristic, complemented
22#21455609C211yesmaximal, characteristic, complemented
23C61×#2989C211yesmaximal, characteristic, complemented
24#16840485—21no—
25#16840485C2211yescharacteristic
26#16840477C2212yes—
27#16840477C2211yescharacteristic
28#16840472C2211yescharacteristic
29#16840472C2212yescomplemented
30#16840462—21no—
31#16840458C2212yes—
32#16840458C2212yescomplemented
33#16840453—21no—
34#16840452C2211yescharacteristic
35#16840452C2211yescharacteristic
36#16840441—21no—
37#16840441—21no—
38#16840421—21no—
39#16840421—21no—
40#16840417—21no—
41#16840417C2211yescharacteristic
42#16840408C2211yescharacteristic
43#16840408C2211yescharacteristic
44#16840383—21no—
45#16840383—21no—
46#16840340—21no—
47#16840319C2211yescharacteristic
48#16840319C2211yescharacteristic
49#16840319C2211yescharacteristic, complemented
50#16840312C2211yescharacteristic
51#16840312C2211yescharacteristic, complemented
52#16840312C2211yescharacteristic, complemented
53C2×#14519777C2211yescharacteristic, complemented
54#16840296C2211yescharacteristic
55#16840296C2211yescharacteristic
56#16840290—21no—
57#16840290—21no—
58#16840269—21no—
59#16840242—21no—
60C4×#11758222C2211yescharacteristic
61C4×#11758222C2211yescharacteristic
62C2×C4×D244C2211yescharacteristic
63#117×D61—21no—
64#16840171C2212yescomplemented
65#16840171C2212yescomplemented
66#16840164C2212yescomplemented
67#16840131C2212yescomplemented
68#16840122C2212yes—
69#16840117C2212yes—
70#16840104C2212yes—
71#16840104C2212yes—
72#16840104C2212yescomplemented
73#16840093C2212yescomplemented
74#16840087C2212yes—
75#16840087C2212yescomplemented
76#16840087C2212yescomplemented
77#16840081C2212yes—
78#16840076C2212yes—
79#16840070C2212yescomplemented
80#16840063C2212yes—
81#16840063C2212yes—
82#16840063C2212yes—
83#16840063C2212yescomplemented
84#16840063C2212yescomplemented
85#16840058C2211yescharacteristic, complemented
86#16840058C2211yescharacteristic, complemented
87#16840058C2211yescharacteristic, complemented
88#16840058C2211yescharacteristic, complemented
89#16840053C2211yescharacteristic
90#16840053C2211yescharacteristic
91#16840053C2211yescharacteristic
92#16840053C2211yescharacteristic
93#16840048C2212yescomplemented
94#16840048C2211yescharacteristic, complemented
95#16840048C2211yescharacteristic, complemented
96#16840043C2211yescharacteristic
97#16840043C2211yescharacteristic
98#16840043C2212yes—
99#16840043C2212yescomplemented
100#16840015C2212yes—
101#16840008C2212yes—
102#16840008C2212yes—
103#16840008C2212yescomplemented
104#16839998C2212yes—
105#16839991C2212yescomplemented
106#16839978C2212yes—
107#16839978C2212yes—
108#16839968C2212yescomplemented
109#16839963C2211yescharacteristic, complemented
110#16839963C2211yescharacteristic, complemented
111#16839958C2211yescharacteristic
112#16839958C2211yescharacteristic
113#16839909C2212yes—
114#16839909C2212yes—
115#16839898C2212yes—
116#16839875C2212yes—
117#16839875C2212yes—
118#16839875C2212yes—
119#16839864C2212yescomplemented
120C4×#11758190C2212yescomplemented
121C4×D488C2212yes—
122#16839804C2212yes—
123#16839804C2212yescomplemented
124#16839800C2212yescomplemented
125#16839768C2212yes—
126#16839764C2212yes—
127#16839759C2212yes—
128C4×#41×C61C2211yescharacteristic
129C61×#446C2212yescomplemented
130C61×#436C2212yes—
131C61×#435C2212yes—
132C61×#435C2212yescomplemented
133C61×#432C2211yescharacteristic
134C61×#432C2211yescharacteristic, complemented
135C61×#431C2211yescharacteristic, complemented
136C61×#423C2211yescharacteristic
137C61×#423C2211yescharacteristic, complemented
138C2×C4⋊C8×C61C2211yescharacteristic, complemented
139C2×#11758222—21no—
140C2×#11758222—21no—
141C2×#11758222—21no—
142C2×#11758222C2311yescharacteristic
143C2×#11758222C2311yescharacteristic
144C22×Dic122—21no—
145C22×D244C2311yescharacteristic
146C22×C4×D61—21no—
147C2×#11758190C2312yes—
148C2×#11758190C2312yes—
149C2×D488C2312yes—
150C2×D488C2312yes—
151#14519777—21no—
152#14519777—21no—
153#14519777C2311yescharacteristic
154#14519777C2311yescharacteristic
155#14519777C2312yes—
156#14519777C2311yescharacteristic
157#14519777C2311yescharacteristic
158#14519777C2311yescharacteristic
159#14519774C2311yescharacteristic
160#14519772—22no—
161#14519772—22no—
162#14519772—21no—
163#14519772—21no—
164#14519771—21no—
165#14519771—21no—
166#14519770—21no—
167#14519770—21no—
168#14519769—21no—
169#14519769C2311yescharacteristic
170#14519769C2311yescharacteristic
171#14519769C2312yes—
172#14519769C2312yes—
173#14519767—21no—
174#14519767—21no—
175#14519765—21no—
176#14519765—21no—
177#14519765—21no—
178#14519765C2311yescharacteristic
179#14519765C2311yescharacteristic
180#14519763—21no—
181#14519763—21no—
182#14519763—22no—
183#14519763—22no—
184#14519762—21no—
185#14519762—21no—
186#14519760—21no—
187#14519760—21no—
188#14519759—22no—
189#14519759—22no—
190#14519759—21no—
191#14519759—21no—
192#14519758—21no—
193#14519758—21no—
194#14519756—21no—
195#14519756—21no—
196#14519756—21no—
197#14519756—21no—
198#14519756—21no—
199#14519756C2311yescharacteristic
200#14519756C2311yescharacteristic
201#14519756C2311yescharacteristic
202#14519756C2311yescharacteristic
203#14519755—21no—
204#14519755—21no—
205#14519755—22no—
206#14519755—22no—
207#14519753—21no—
208#14519753—21no—
209#14519753—22no—
210#14519751—21no—
211#14519751—21no—
212#14519751—21no—
213#14519751C2312yes—
214#14519751C2312yes—
215#14519751C2312yes—
216#14519751C2311yescharacteristic
217#14519751C2311yescharacteristic
218#14519750—21no—
219#14519750—21no—
220#14519749—22no—
221#14519749—22no—
222#14519748—21no—
223#14519748—21no—
224#14519748—22no—
225#14519745—21no—
226#14519745—21no—
227C4×Dic122—21no—
228C4×Dic122—21no—
229C4×Dic122—21no—
230C4×Dic122—21no—
231C4×Dic122—21no—
232C4×Dic122C2311yescharacteristic
233C4×Dic122C2311yescharacteristic
234C4×Dic122C2311yescharacteristic
235C4×Dic122C2311yescharacteristic
236C4×D244—21no—
237C4×D244—21no—
238C4×D244—21no—
239C4×D244—21no—
240C4×D244—21no—
241C4×D244C2312yes—
242C4×D244C2312yes—
243C4×D244C2311yescharacteristic
244C4×D244C2311yescharacteristic
245C4×D244C2311yescharacteristic
246C4×D244C2311yescharacteristic
247C4×D244C2311yescharacteristic
248C4×D244C2312yes—
249C4×D244C2311yescharacteristic
250C4×C22⋊D61—21no—
251C4×C22⋊D61—21no—
252C4×C22⋊D61—21no—
253C4×C22⋊D61—21no—
254C4×C22⋊D61—21no—
255C4×C22⋊D61—21no—
256#14519737—22no—
257#14519737—22no—
258#14519736—21no—
259#14519736C2311yescharacteristic
260#14519736C2311yescharacteristic
261#14519736C2312yes—
262#14519736C2312yes—
263#14519735—21no—
264#14519735—21no—
265#14519735—22no—
266#14519734—21no—
267#14519734—21no—
268#14519734—21no—
269#14519734—21no—
270#14519733—21no—
271#14519733—21no—
272C2×C4⋊Dic61—21no—
273C2×C4⋊Dic61C2311yescharacteristic
274C2×C4⋊Dic61C2312yes—
275C4⋊C4×D61—21no—
276C4⋊C4×D61—21no—
277C4⋊C4×D61—22no—
278C2×#11758198—21no—
279C22⋊C4×D61—21no—
280C22⋊C4×D61—21no—
281C42×D61—21no—
282C42×D61—21no—
283#14519711C2312yes—
284#14519711C2312yes—
285#14519711C2312yes—
286#14519711C2312yes—
287#14519711C2312yes—
288#14519711C2312yes—
289#14519709C2312yes—
290#14519709C2312yes—
291#14519709C2312yes—
292#14519709C2312yes—
293#14519709C2312yes—
294#14519709C2312yes—
295#14519702C2312yes—
296#14519702C2312yes—
297#14519702C2312yes—
298#14519702C2312yes—
299#14519702C2312yes—
300#14519702C2312yes—
301#14519699C2312yes—
302#14519699C2312yes—
303#14519699C2312yes—
304#14519699C2312yes—
305#14519699C2312yes—
306#14519699C2312yes—
307#14519699C2312yes—
308#14519699C2312yes—
309#14519699C2312yes—
310#14519699C2312yes—
311C2×#41×C61D411yescharacteristic
312C2×M16×C61C2312yes—
313C2×M16×C61C2312yes—
314C22×C8×C61C2312yes—
315C4×Q8×C61D411yescharacteristic
316C4×Q8×C61C2311yescharacteristic
317C4×D4×C61D411yescharacteristic
318C4×D4×C61D411yescharacteristic
319C4×D4×C61D411yescharacteristic
320C4×D4×C61C2311yescharacteristic
321C4×D4×C61C2311yescharacteristic
322C4×D4×C61C2311yescharacteristic
323#117×C61D411yescharacteristic
324#117×C61D411yescharacteristic
325#117×C61D411yescharacteristic
326C2×C42×C61C2311yescharacteristic
327C2×C42×C61C2311yescharacteristic
328C2×C42×C61C2311yescharacteristic
329C4⋊C8×C61C2311yescharacteristic
330C4⋊C8×C61C2311yescharacteristic
331C4⋊C8×C61C2311yescharacteristic
332C4⋊C8×C61C2311yescharacteristic
333C4⋊C8×C61C2312yes—
334C4⋊C8×C61C2312yes—
335C4⋊C8×C61C2312yes—
336C22⋊C8×C61C2312yes—
337C22⋊C8×C61C2312yes—
338C22⋊C8×C61C2312yes—
339#97×C61C2312yes—
340#97×C61C2312yes—
341C4×C8×C61C2312yes—
342C23×D61—21no—
343#41×C61—42no—
344C2×Q8×C61C2×D411yescharacteristic
345C2×D4×C61C2×D411yescharacteristic
346C2×D4×C61C2×D411yescharacteristic
347C2×D4×C61C2×D411yescharacteristic
348C22×C4×C61C2×D411yescharacteristic
349C22×C4×C61C2×D411yescharacteristic
350C22×C4×C61C2×D411yescharacteristic
351C22×C4×C61C2×D411yescharacteristic
352C22×C4×C61C2×D411yescharacteristic
353C22×C4×C61C2×D411yescharacteristic
354C22×C4×C61C2411yescharacteristic
355C22×C4×C61C2411yescharacteristic
356C22×C4×C61C2411yescharacteristic
357C2×C22⋊D61—22no—
358C2×C22⋊D61—21no—
359C2×C22⋊D61—21no—
360C2×C22⋊D61—22no—
361C2×C22⋊D61—22no—
362C2×C22⋊D61—21no—
363C2×C22⋊D61—21no—
364C22×Dic61—21no—
365C22×Dic61—22no—
366#11758222—22no—
367#11758222—22no—
368#11758222—41no—
369#11758222—41no—
370#11758222—44no—
371#11758222—82no—
372#11758222—82no—
373C2×D244—22no—
374C2×D244—21no—
375C2×D244—21no—
376C2×D244—21no—
377C2×D244—41no—
378C2×D244C2411yescharacteristic
379C2×D244C2412yes—
380C2×D244C2411yescharacteristic
381C2×C4×D61—21no—
382C2×C4×D61—21no—
383C2×C4×D61—21no—
384C2×C4×D61—21no—
385C2×C4×D61—22no—
386C2×C4×D61—21no—
387C2×C4×D61—21no—
388C2×C4×D61—22no—
389C2×C4×D61—22no—
390C2×C4×D61—21no—
391C2×C4×D61—21no—
392C2×C4×D61—44no—
393C2×Dic122—21no—
394C2×Dic122—21no—
395C2×Dic122—21no—
396C2×Dic122—22no—
397C2×Dic122—21no—
398C2×Dic122—82no—
399C2×Dic122C2411yescharacteristic
400C2×Dic122C2411yescharacteristic
401M16×C61—42no—
402M16×C61—42no—
403C2×C8×C61—42no—
404C2×C8×C61C2412yes—
405C2×C8×C61C2412yes—
406C2×C8×C61C2412yes—
407C2×C8×C61C2412yes—
408C4⋊C4×C61C2×D411yescharacteristic
409C4⋊C4×C61C2×D411yescharacteristic
410C4⋊C4×C61C2×D411yescharacteristic
411C4⋊C4×C61C2×D411yescharacteristic
412C4⋊C4×C61C2×D411yescharacteristic
413C4⋊C4×C61C2×D411yescharacteristic
414C22⋊C4×C61C2×D411yescharacteristic
415C22⋊C4×C61C2×D411yescharacteristic
416C22⋊C4×C61C2×D411yescharacteristic
417C22⋊C4×C61C2×D411yescharacteristic
418C22⋊C4×C61C2×D411yescharacteristic
419C22⋊C4×C61C2×D411yescharacteristic
420C42×C61C2×D411yescharacteristic
421C42×C61C2×D411yescharacteristic
422C42×C61C2×D411yescharacteristic
423C42×C61C2×D411yescharacteristic
424C42×C61C2×D411yescharacteristic
425C42×C61C2×D411yescharacteristic
426C42×C61C2411yescharacteristic
427C42×C61C2411yescharacteristic
428C42×C61C2411yescharacteristic
429C42×C61C2411yescharacteristic
430C22⋊Dic61—21no—
431C22⋊Dic61—21no—
432C22⋊Dic61—21no—
433C22⋊Dic61—21no—
434C22⋊Dic61—22no—
435C22⋊Dic61—22no—
436C22⋊Dic61—21no—
437C22⋊Dic61—21no—
438#11758198—21no—
439#11758198—21no—
440#11758198—21no—
441#11758198—21no—
442#11758198—21no—
443#11758198—21no—
444#11758198—21no—
445#11758198—21no—
446#11758198—21no—
447#11758198—21no—
448#11758198—22no—
449#11758198—22no—
450#11758198—21no—
451#11758198—21no—
452#11758198—22no—
453#11758198—22no—
454#11758198—22no—
455#11758198—22no—
456C4⋊Dic61—22no—
457C4⋊Dic61—21no—
458C4⋊Dic61—21no—
459C4⋊Dic61—21no—
460C4⋊Dic61—21no—
461C4⋊Dic61—21no—
462C4⋊Dic61—22no—
463C4⋊Dic61—21no—
464C4⋊Dic61—21no—
465C4⋊Dic61C2412yes—
466C4⋊Dic61C2412yes—
467C4⋊Dic61C2412yes—
468C4⋊Dic61C2411yescharacteristic
469C4⋊Dic61C2411yescharacteristic
470C4⋊Dic61C2411yescharacteristic
471C4⋊Dic61C2411yescharacteristic
472#11758196—21no—
473#11758196—21no—
474#11758196—21no—
475#11758196—21no—
476#11758196—22no—
477#11758196—22no—
478#11758196—21no—
479#11758196—21no—
480#11758196—21no—
481#11758196—21no—
482#11758196—21no—
483#11758196—21no—
484#11758196—22no—
485#11758196—22no—
486#11758196—21no—
487#11758196—21no—
488C4×Dic61—21no—
489C4×Dic61—21no—
490C4×Dic61—21no—
491C4×Dic61—21no—
492C4×Dic61—21no—
493C4×Dic61—21no—
494C4×Dic61—22no—
495C4×Dic61—22no—
496D488—24no—
497D488—42no—
498#11758190—42no—
499#11758190—42no—
500C23×C61C22×D411yescharacteristic
501C23×C61C22×D411yescharacteristic
502C23×C61C22×D411yescharacteristic
503C22×D61—21no—
504C22×D61—21no—
505C22×D61—22no—
506C22×D61—42no—
507C22×D61—42no—
508C22×D61—81no—
509Q8×C61—41no—
510D4×C61—41no—
511D4×C61—41no—
512D4×C61—41no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—21no—
517C2×C4×C61—21no—
518C2×C4×C61—21no—
519C2×C4×C61—21no—
520C2×C4×C61—21no—
521C2×C4×C61—21no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61C22×D411yescharacteristic
526C2×C4×C61C22×D411yescharacteristic
527C2×C4×C61C22×D411yescharacteristic
528C2×C4×C61C22×D411yescharacteristic
529C2×C4×C61C22×D411yescharacteristic
530C2×C4×C61C22×D411yescharacteristic
531C2×C4×C61C22×D411yescharacteristic
532C2×C4×C61C22×D411yescharacteristic
533C2×C4×C61C22×D411yescharacteristic
534C2×C4×C61C22×D411yescharacteristic
535C2×C4×C61C22×D411yescharacteristic
536C2×C4×C61C2511yescharacteristic
537C22⋊D61—42no—
538C22⋊D61—42no—
539C22⋊D61—44no—
540C22⋊D61—82no—
541C22⋊D61—82no—
542C22⋊D61—81no—
543C22⋊D61—81no—
544C2×Dic61—21no—
545C2×Dic61—21no—
546C2×Dic61—21no—
547C2×Dic61—21no—
548C2×Dic61—21no—
549C2×Dic61—22no—
550C2×Dic61—22no—
551C2×Dic61—22no—
552C2×Dic61—21no—
553C2×Dic61—42no—
554C2×Dic61—82no—
555D244—22no—
556D244—21no—
557D244—21no—
558D244—22no—
559D244—21no—
560D244—42no—
561D244—42no—
562D244—42no—
563D2442−1+412yes—
564C4×D61—42no—
565C4×D61—42no—
566C4×D61—42no—
567C4×D61—42no—
568C4×D61—44no—
569C4×D61—42no—
570C4×D61—42no—
571C4×D61—81no—
572C4×D61—81no—
573C4×D61—82no—
574C4×D61—82no—
575Dic122—21no—
576Dic122—21no—
577Dic122—21no—
578Dic122—21no—
579Dic122—42no—
580Dic122—42no—
581Dic122—42no—
582Dic122—81no—
583Dic122—82no—
584C8×C61—22no—
585C8×C61—22no—
586C8×C61—22no—
587C8×C61—22no—
588#62115—611nomaximal, Sylow
589C22×C61—21no—
590C22×C61—21no—
591C22×C61—21no—
592C22×C61—21no—
593C22×C61—21no—
594C22×C61—21no—
595C22×C61—21no—
596C22×C61—21no—
597C22×C61—21no—
598C22×C61C23×D411yescharacteristic
599C2×D61—22no—
600C2×D61—41no—
601C2×D61—41no—
602C2×D61—42no—
603C2×D61—41no—
604C2×D61—41no—
605C2×D61—42no—
606C2×D61—41no—
607C2×D61—42no—
608C2×D61—84no—
609C4×C61—21no—
610C4×C61—21no—
611C4×C61—21no—
612C4×C61—21no—
613C4×C61—21no—
614C4×C61—21no—
615C4×C61—21no—
616C4×C61—21no—
617C4×C61—21no—
618C4×C61—21no—
619C4×C61#57512yes—
620C4×C61C2×2−1+411yescharacteristic
621C4×C61#58511yescharacteristic
622Dic61—42no—
623Dic61—42no—
624Dic61—41no—
625Dic61—41no—
626Dic61—41no—
627Dic61—41no—
628Dic61—42no—
629Dic61—41no—
630Dic61—41no—
631#3511—611no—
632#3475—611no—
633#3389—612no—
634#3376—612no—
635#3351—612no—
636#3348—612no—
637#3347—612no—
638#3322—612no—
639#3319—612no—
640#3307—612no—
641#3254—611no—
642#3251—611no—
643#3247—611no—
644#3238—611no—
645#3237—611no—
646#3233—611no—
647#3115—611no—
648#3109—611no—
649#3106—611no—
650#3079—611no—
651#3077—611no—
652#3076—611no—
653#2989D6111yescharacteristic, complemented
654C2×C61—41no—
655C2×C61—41no—
656C2×C61—41no—
657C2×C61#348911yescharacteristic
658C2×C61C2×#57511yescharacteristic
659C2×C61#358511yescharacteristic
660D61—42no—
661D61—82no—
662D61—81no—
663#556—611no—
664#556—1221no—
665#555—611no—
666#555—612no—
667#554—611no—
668#554—612no—
669#553—612no—
670#553—612no—
671#553—1221no—
672#552—611no—
673#552—611no—
674#552—1221no—
675#551—1221no—
676#551—1221no—
677#548—1221no—
678#548—1221no—
679#547—611no—
680#547—1221no—
681#546—611no—
682#546—611no—
683#542—1221no—
684#542—1221no—
685#537—1221no—
686#533—611no—
687#533—611no—
688#533—611no—
689#532—611no—
690#532—611no—
691#532—611no—
692C2×C4⋊Q8—611no—
693#529—611no—
694#529—611no—
695#529—1221no—
696#529—1221no—
697#525—1221no—
698#520—1221no—
699C4×#41—611no—
700C4×#41—611no—
701C4×#41C2×D6111yescharacteristic
702C2×C4×D4—611no—
703C2×#117—1221no—
704#501—612no—
705#501—612no—
706#499—612no—
707#491—612no—
708#489—612no—
709#488—612no—
710#485—612no—
711#485—612no—
712#485—612no—
713#483—612no—
714#482—612no—
715#482—612no—
716#482—612no—
717#481—612no—
718#480—612no—
719#479—612no—
720#478—612no—
721#478—612no—
722#478—612no—
723#478—612no—
724#478—612no—
725#477—611no—
726#477—611no—
727#477—611no—
728#477—611no—
729#476—611no—
730#476—611no—
731#476—611no—
732#476—611no—
733#475—611no—
734#475—612no—
735#475—611no—
736#474—611no—
737#474—611no—
738#474—612no—
739#474—612no—
740#469—612no—
741#468—612no—
742#468—612no—
743#468—612no—
744#466—612no—
745#465—612no—
746#463—612no—
747#463—612no—
748#461—612no—
749#460—611no—
750#460—611no—
751#459—611no—
752#459—611no—
753#449—612no—
754#449—612no—
755#447—612no—
756#446C2×D6112yescomplemented
757#442—612no—
758#442—612no—
759#442—612no—
760#440—612no—
761C4×SD16—612no—
762C4×D8—612no—
763#436C2×D6112yes—
764#435C2×D6112yes—
765#435C2×D6112yescomplemented
766#432C2×D6111yescharacteristic
767#432C2×D6111yescharacteristic, complemented
768#431C2×D6111yescharacteristic, complemented
769#428—612no—
770#428—612no—
771#427—612no—
772#423C2×D6111yescharacteristic
773#423C2×D6111yescharacteristic, complemented
774C2×C4⋊C8C2×D6111yescharacteristic, complemented
775#418—612no—
776#417—612no—
777#416—612no—
778C61#6211511yescharacteristic, complemented, Sylow
779C2×#41—611no—
780C2×#41—611no—
781C2×#41—1221no—
782C2×#41—1221no—
783C2×#41—1221no—
784C2×#41D24411yescharacteristic
785C22×Q8—1221no—
786C22×D4—611no—
787C23×C4—1221no—
788C2×SD16—612no—
789C2×SD16—612no—
790C2×D8—612no—
791C2×D8—612no—
792C2×M16C22×D6112yes—
793C2×M16C22×D6112yes—
794C22×C8C22×D6112yes—
795C4⋊Q8—611no—
796C4⋊Q8—611no—
797C4⋊Q8—612no—
798C4⋊Q8—611no—
799C4⋊Q8—611no—
800C4⋊Q8—611no—
801C4⋊Q8—1221no—
802C4⋊Q8—1221no—
803#127—611no—
804#126—1221no—
805#126—1221no—
806#126—1222no—
807#126—1222no—
808#126—1221no—
809#126—1221no—
810#126—1221no—
811#126—1221no—
812#125—611no—
813#125—611no—
814#125—612no—
815#125—612no—
816#125—1221no—
817#125—1221no—
818#125—1221no—
819#124—611no—
820#124—611no—
821#124—1221no—
822#124—1221no—
823#124—1222no—
824#124—1222no—
825#124—1221no—
826#124—1221no—
827#124—1221no—
828#123—1221no—
829#123—1221no—
830#123—1221no—
831#123—1221no—
832#123—1221no—
833#123—1221no—
834#123—1221no—
835#123—1221no—
836#123—1222no—
837#123—1222no—
838C22⋊Q8—611no—
839C22⋊Q8—611no—
840C22⋊Q8—611no—
841C22⋊Q8—611no—
842C22⋊Q8—1221no—
843C22⋊Q8—1221no—
844C22⋊Q8—1222no—
845C22⋊Q8—1221no—
846C22⋊Q8—1221no—
847C22⋊Q8—1221no—
848C22⋊Q8—1221no—
849C22⋊Q8—1221no—
850C22⋊Q8—1221no—
851C22⋊Q8—1221no—
852C22⋊Q8—1222no—
853C22⋊Q8—1222no—
854#121—611no—
855#121—611no—
856#121—612no—
857#121—612no—
858#121—612no—
859#121—1221no—
860#121—1221no—
861#121—1222no—
862#121—1222no—
863#121—1222no—
864#121—1221no—
865#121—1221no—
866#121—1221no—
867#121—1221no—
868#121—1221no—
869#120—1221no—
870#120—1221no—
871C4×Q8—611no—
872C4×Q8—611no—
873C4×Q8—611no—
874C4×Q8—611no—
875C4×Q8—1221no—
876C4×Q8—1221no—
877C4×Q8—1221no—
878C4×Q8—1221no—
879C4×Q8—1221no—
880C4×Q8D24411yescharacteristic
881C4×Q8C22×D6111yescharacteristic
882C4×D4—611no—
883C4×D4—611no—
884C4×D4—611no—
885C4×D4—611no—
886C4×D4—611no—
887C4×D4—611no—
888C4×D4—612no—
889C4×D4—612no—
890C4×D4—612no—
891C4×D4—1221no—
892C4×D4—1221no—
893C4×D4—1221no—
894C4×D4—1221no—
895C4×D4—1221no—
896C4×D4—1221no—
897C4×D4—1222no—
898C4×D4—1222no—
899C4×D4—1221no—
900C4×D4—1221no—
901C4×D4—1221no—
902C4×D4—1221no—
903C4×D4—1221no—
904C4×D4D24411yescharacteristic
905C4×D4D24411yescharacteristic
906C4×D4D24411yescharacteristic
907C4×D4C22×D6111yescharacteristic
908C4×D4C22×D6111yescharacteristic
909C4×D4C22×D6111yescharacteristic
910#117—611no—
911#117—611no—
912#117—612no—
913#117—612no—
914#117—1221no—
915#117—1221no—
916#117—1221no—
917#117—1222no—
918#117—1221no—
919#117—1221no—
920#117—1221no—
921#117—1221no—
922#117—1221no—
923#117—1221no—
924#117D24411yescharacteristic
925#117D24411yescharacteristic
926#117D24411yescharacteristic
927C2×C4⋊C4—611no—
928C2×C4⋊C4—612no—
929C2×C4⋊C4—1221no—
930C2×C4⋊C4—1221no—
931C2×C4⋊C4—1221no—
932C2×C4⋊C4—1222no—
933C2×C22⋊C4—1221no—
934C2×C22⋊C4—1221no—
935C2×C22⋊C4—1221no—
936C2×C42—1221no—
937C2×C42—1221no—
938C2×C42C22×D6111yescharacteristic
939C2×C42C22×D6111yescharacteristic
940C2×C42C22×D6111yescharacteristic
941#107—612no—
942#107—612no—
943#107—612no—
944#107—612no—
945#107—612no—
946#107—612no—
947#106—612no—
948#106—612no—
949#106—612no—
950#106—612no—
951#106—612no—
952#106—612no—
953C4⋊C8C22×D6111yescharacteristic
954C4⋊C8C22×D6111yescharacteristic
955C4⋊C8C22×D6112yes—
956C4⋊C8C22×D6111yescharacteristic
957C4⋊C8C22×D6112yes—
958C4⋊C8C22×D6112yes—
959C4⋊C8C22×D6111yescharacteristic
960#103—612no—
961#103—612no—
962#103—612no—
963#103—612no—
964#103—612no—
965#103—612no—
966#102—612no—
967#102—612no—
968#102—612no—
969#102—612no—
970#102—612no—
971#102—612no—
972#102—612no—
973#102—612no—
974#102—612no—
975#102—612no—
976C22⋊C8C22×D6112yes—
977C22⋊C8C22×D6112yes—
978C22⋊C8C22×D6112yes—
979#97C22×D6112yes—
980#97C22×D6112yes—
981C4×C8C22×D6112yes—
982C24—1221no—
983#41—42no—
984#41—1222no—
985#41—1222no—
986#41—4882no—
987#41—4882no—
988#41—2441no—
989#41—2441no—
990#41—2444no—
991C2×Q8—611no—
992C2×Q8—611no—
993C2×Q8—1221no—
994C2×Q8—1222no—
995C2×Q8—1221no—
996C2×Q8—1221no—
997C2×Q8—1221no—
998C2×Q8—4882no—
999C2×Q8C2×D24411yescharacteristic
1000C2×D4—611no—
1001C2×D4—611no—
1002C2×D4—612no—
1003C2×D4—1222no—
1004C2×D4—1221no—
1005C2×D4—1221no—
1006C2×D4—1222no—
1007C2×D4—1222no—
1008C2×D4—1221no—
1009C2×D4—1221no—
1010C2×D4—1222no—
1011C2×D4—1221no—
1012C2×D4—1221no—
1013C2×D4—1221no—
1014C2×D4—2441no—
1015C2×D4C2×D24411yescharacteristic
1016C2×D4C2×D24411yescharacteristic
1017C2×D4C2×D24411yescharacteristic
1018C22×C4—1222no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1222no—
1023C22×C4—1222no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1222no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—2444no—
1032C22×C4C2×D24411yescharacteristic
1033C22×C4C2×D24411yescharacteristic
1034C22×C4C2×D24411yescharacteristic
1035C22×C4C2×D24411yescharacteristic
1036C22×C4C2×D24411yescharacteristic
1037C22×C4C2×D24411yescharacteristic
1038C22×C4C23×D6111yescharacteristic
1039C22×C4C23×D6111yescharacteristic
1040C22×C4C23×D6111yescharacteristic
1041SD16—2442no—
1042SD16—2442no—
1043D8—1224no—
1044D8—2442no—
1045M16—42no—
1046M16—42no—
1047C2×C8—42no—
1048C2×C8C23×D6112yes—
1049C2×C8C23×D6112yes—
1050C2×C8C23×D6112yes—
1051C2×C8C23×D6112yes—
1052C4⋊C4—612no—
1053C4⋊C4—612no—
1054C4⋊C4—612no—
1055C4⋊C4—611no—
1056C4⋊C4—611no—
1057C4⋊C4—611no—
1058C4⋊C4—611no—
1059C4⋊C4—1221no—
1060C4⋊C4—1222no—
1061C4⋊C4—1222no—
1062C4⋊C4—1221no—
1063C4⋊C4—1221no—
1064C4⋊C4—1221no—
1065C4⋊C4—1221no—
1066C4⋊C4—1222no—
1067C4⋊C4—1222no—
1068C4⋊C4—1221no—
1069C4⋊C4—1221no—
1070C4⋊C4—1221no—
1071C4⋊C4—1221no—
1072C4⋊C4—1221no—
1073C4⋊C4—1221no—
1074C4⋊C4—1221no—
1075C4⋊C4—1221no—
1076C4⋊C4—1221no—
1077C4⋊C4—1221no—
1078C4⋊C4—1221no—
1079C4⋊C4—1221no—
1080C4⋊C4—1222no—
1081C4⋊C4—1222no—
1082C4⋊C4—1221no—
1083C4⋊C4—1221no—
1084C4⋊C4C2×D24411yescharacteristic
1085C4⋊C4C2×D24411yescharacteristic
1086C4⋊C4C2×D24411yescharacteristic
1087C4⋊C4C2×D24411yescharacteristic
1088C4⋊C4C2×D24411yescharacteristic
1089C4⋊C4C2×D24411yescharacteristic
1090C22⋊C4—1221no—
1091C22⋊C4—1221no—
1092C22⋊C4—1221no—
1093C22⋊C4—1221no—
1094C22⋊C4—1222no—
1095C22⋊C4—1222no—
1096C22⋊C4—1221no—
1097C22⋊C4—1221no—
1098C22⋊C4—1221no—
1099C22⋊C4—1221no—
1100C22⋊C4—1221no—
1101C22⋊C4—1221no—
1102C22⋊C4—1221no—
1103C22⋊C4—1221no—
1104C22⋊C4—1221no—
1105C22⋊C4—1221no—
1106C22⋊C4—1221no—
1107C22⋊C4—1221no—
1108C22⋊C4—1222no—
1109C22⋊C4—1222no—
1110C22⋊C4—1222no—
1111C22⋊C4—1222no—
1112C22⋊C4—1222no—
1113C22⋊C4—1221no—
1114C22⋊C4—1221no—
1115C22⋊C4—1222no—
1116C22⋊C4C2×D24411yescharacteristic
1117C22⋊C4C2×D24411yescharacteristic
1118C22⋊C4C2×D24411yescharacteristic
1119C22⋊C4C2×D24411yescharacteristic
1120C22⋊C4C2×D24411yescharacteristic
1121C22⋊C4C2×D24411yescharacteristic
1122C42—1221no—
1123C42—1221no—
1124C42—1221no—
1125C42—1221no—
1126C42—1221no—
1127C42—1221no—
1128C42—1222no—
1129C42—1222no—
1130C42C2×D24411yescharacteristic
1131C42C2×D24411yescharacteristic
1132C42C2×D24411yescharacteristic
1133C42C2×D24411yescharacteristic
1134C42C2×D24411yescharacteristic
1135C42C2×D24411yescharacteristic
1136C42C23×D6111yescharacteristic
1137C42C23×D6111yescharacteristic
1138C42C23×D6111yescharacteristic
1139C42C23×D6111yescharacteristic
1140C23—1221no—
1141C23—1221no—
1142C23—1222no—
1143C23—4881no—
1144C23—2442no—
1145C23—2442no—
1146C23C22×D24411yescharacteristic
1147C23C22×D24411yescharacteristic
1148C23C22×D24411yescharacteristic
1149Q8—41no—
1150Q8—1221no—
1151Q8—1221no—
1152Q8—1221no—
1153Q8—1221no—
1154Q8—4881no—
1155Q8—4882no—
1156Q8—2442no—
1157Q8—2442no—
1158Q8—2442no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—612no—
1163D4—1222no—
1164D4—1221no—
1165D4—1221no—
1166D4—1221no—
1167D4—1222no—
1168D4—4881no—
1169D4—4881no—
1170D4—4882no—
1171D4—4882no—
1172D4—2442no—
1173D4—2442no—
1174D4—2442no—
1175D4—2442no—
1176D4—2444no—
1177D4—2442no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—1221no—
1191C2×C4—1222no—
1192C2×C4—1221no—
1193C2×C4—1221no—
1194C2×C4—1221no—
1195C2×C4—1221no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—1221no—
1199C2×C4—4881no—
1200C2×C4—4881no—
1201C2×C4—4882no—
1202C2×C4—4882no—
1203C2×C4—4882no—
1204C2×C4—2442no—
1205C2×C4—2442no—
1206C2×C4—2442no—
1207C2×C4—2442no—
1208C2×C4—2444no—
1209C2×C4—2442no—
1210C2×C4—2442no—
1211C2×C4—2442no—
1212C2×C4C22×D24411yescharacteristic
1213C2×C4C22×D24411yescharacteristic
1214C2×C4C22×D24411yescharacteristic
1215C2×C4C22×D24411yescharacteristic
1216C2×C4C22×D24411yescharacteristic
1217C2×C4C22×D24411yescharacteristic
1218C2×C4C22×D24411yescharacteristic
1219C2×C4C22×D24411yescharacteristic
1220C2×C4C22×D24411yescharacteristic
1221C2×C4C22×D24411yescharacteristic
1222C2×C4C22×D24411yescharacteristic
1223C2×C4C24×D6111yescharacteristic
1224C8—22no—
1225C8—22no—
1226C8—22no—
1227C8—22no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—1222no—
1238C22—4884no—
1239C22—2441no—
1240C22—2442no—
1241C22—2441no—
1242C22—2442no—
1243C22—2442no—
1244C22—2441no—
1245C22—2441no—
1246C22—2441no—
1247C22C23×D24411yescharacteristic
1248C4—21no—
1249C4—21no—
1250C4—21no—
1251C4—21no—
1252C4—21no—
1253C4—21no—
1254C4—21no—
1255C4—21no—
1256C4—21no—
1257C4—21no—
1258C4—2441no—
1259C4—2441no—
1260C4—2441no—
1261C4—2441no—
1262C4—2442no—
1263C4—2442no—
1264C4—2442no—
1265C4—2441no—
1266C4—2441no—
1267C4#1684056212yes—
1268C42−1+4×D6111yescharacteristic
1269C4#1684059711yescharacteristic
1270C2—41no—
1271C2—41no—
1272C2—41no—
1273C2—4881no—
1274C2—4882no—
1275C2—2442no—
1276C2#2145950011yescharacteristic
1277C2C2×#1684056211yescharacteristic
1278C2#2146060011yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2989C2
socleC22×C61C23×D4
hypercenter#2989D61
hypocenterC61#62115
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
1. #21459730C2semidirect
2. #21459383C2semidirect
3. #21458779C2semidirect
4. #21458648C2semidirect
5. #21458381C2semidirect
6. #21458336C2semidirect
7. #21458321C2semidirect
8. #21458022C2semidirect
9. #21457977C2semidirect
10. #21457797C2semidirect
11. #21457207C2semidirect
12. #21457182C2semidirect
13. #21457146C2semidirect
14. #21457042C2semidirect
15. #21457035C2semidirect
16. #21457000C2semidirect
17. #21455971C2semidirect
18. #21455911C2semidirect
19. #21455880C2semidirect
20. #21455635C2semidirect
21. #21455618C2semidirect
22. #21455609C2semidirect
23. C61×#2989C2semidirect
29. #16840472C22semidirect
32. #16840458C22semidirect
49. #16840319C22semidirect
51. #16840312C22semidirect
52. #16840312C22semidirect
53. C2×#14519777C22semidirect
64. #16840171C22semidirect
65. #16840171C22semidirect
66. #16840164C22semidirect
67. #16840131C22semidirect
72. #16840104C22semidirect
73. #16840093C22semidirect
75. #16840087C22semidirect
76. #16840087C22semidirect
79. #16840070C22semidirect
83. #16840063C22semidirect
84. #16840063C22semidirect
85. #16840058C22semidirect
86. #16840058C22semidirect
87. #16840058C22semidirect
88. #16840058C22semidirect
93. #16840048C22semidirect
94. #16840048C22semidirect
95. #16840048C22semidirect
99. #16840043C22semidirect
103. #16840008C22semidirect
105. #16839991C22semidirect
108. #16839968C22semidirect
109. #16839963C22semidirect
110. #16839963C22semidirect
119. #16839864C22semidirect
120. C4×#11758190C22semidirect
123. #16839804C22semidirect
124. #16839800C22semidirect
129. C61×#446C22semidirect
132. C61×#435C22semidirect
134. C61×#432C22semidirect
135. C61×#431C22semidirect
137. C61×#423C22semidirect
138. C2×C4⋊C8×C61C22semidirect
653. #2989D61semidirect
756. #446C2×D61semidirect
765. #435C2×D61semidirect
767. #432C2×D61semidirect
768. #431C2×D61semidirect
773. #423C2×D61semidirect
774. C2×C4⋊C8C2×D61semidirect
778. C61#62115semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214593832
#214587792
#214586482
#214583812
#214583362
#214583212
#214580222
#214579772
#214577972
#214572072
#214571822
#214571462
#214570422
#214570352
#214570002
#214559712
#214559112
#214558802
#214556352
#214556182
#214556092
C61×#29892
#6211561