Finite Group Databasebeta

← #29685880

Subgroups — #29685880

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic, complemented
2#21455039C211yesmaximal, characteristic
3C2×#16839882C211yesmaximal, characteristic, complemented
4C2×#16839880C211yesmaximal, characteristic, complemented
5#21454524C211yesmaximal, characteristic, complemented
6#21446147C211yesmaximal, characteristic, complemented
7#21446144C211yesmaximal, characteristic, complemented
8#21446120C211yesmaximal, characteristic, complemented
9#21446096C211yesmaximal, characteristic, complemented
10#21446095C211yesmaximal, characteristic, complemented
11#21446025C211yesmaximal, characteristic, complemented
12#21445761C211yesmaximal, characteristic, complemented
13#21445665C211yesmaximal, characteristic, complemented
14#21445602C211yesmaximal, characteristic, complemented
15C61×#1764C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19#16840527—24no—
20#16840527—24no—
21C2×#14519785—21no—
22C2×#14519785C2211yescharacteristic
23C2×#14519784C2211yescharacteristic
24C2×#14519783—21no—
25C2×#14519783C2211yescharacteristic
26C2×#14519783C2211yescharacteristic, complemented
27C22×#11758189—21no—
28C22×#11758189C2211yescharacteristic
29C2×M16×D61—21no—
30C2×M16×D61C2211yescharacteristic
31#16840274C2211yescharacteristic
32#16839927C411yescharacteristic, complemented
33#16839925C411yescharacteristic, complemented
34#16839919C411yescharacteristic, complemented
35#16839914C411yescharacteristic, complemented
36#16839910C411yescharacteristic, complemented
37#16839908C411yescharacteristic, complemented
38#16839902C411yescharacteristic, complemented
39#16839897C411yescharacteristic, complemented
40#16839882—24no—
41#16839880—24no—
42#16839841—21no—
43#16839841—21no—
44#16839835—21no—
45#16839835—21no—
46C2×#14519713C2211yescharacteristic, complemented
47C2×#14519712C2211yescharacteristic, complemented
48#16839789C2211yescharacteristic, complemented
49C2×#14519705C2211yescharacteristic
50C2×#14519705C2211yescharacteristic, complemented
51C2×#14519704C2211yescharacteristic
52C2×#14519703C2211yescharacteristic
53C2×#14519703C2211yescharacteristic, complemented
54#16839756C2211yescharacteristic
55#16839730C2211yescharacteristic, complemented
56#16839725C2211yescharacteristic
57C2×#14519689C2211yescharacteristic
58C2×#14519687C2211yescharacteristic, complemented
59C4×#11758198C2211yescharacteristic
60#16839526C2211yescharacteristic, complemented
61#16839521C2211yescharacteristic, complemented
62#16839517C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C2×#131×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic
66C61×#416C2211yescharacteristic
67C61×#405C2211yescharacteristic, complemented
68C2×C4×C8×C61C2211yescharacteristic, complemented
69C61×#341C2211yescharacteristic, complemented
70C61×#339C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758222C2311yescharacteristic
75C2×#11758224—21no—
76C2×#11758224C2×C411yescharacteristic
77#41×D61—22no—
78#41×D61—22no—
79#41×D61—22no—
80#41×D61—22no—
81C2×Q8×D61C2×C411yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61C2×C411yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519799—22no—
87#14519799—22no—
88#14519797—22no—
89#14519797—22no—
90C2×Dic244C2×C411yescharacteristic
91C2×#11758202C2×C411yescharacteristic
92C2×#11758190C2×C411yescharacteristic
93C2×#11758190C2×C411yescharacteristic
94C2×#11758200C2×C411yescharacteristic
95C2×#11758201C2×C411yescharacteristic
96C2×D488C2×C411yescharacteristic
97C2×#11758199C2×C411yescharacteristic
98#14519785—28no—
99#14519785—22no—
100#14519785—22no—
101#14519784—22no—
102#14519784—22no—
103#14519783—28no—
104#14519783—22no—
105#14519783—22no—
106#14519783—22no—
107#14519783D414yescomplemented
108C2×#11758194—21no—
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758189—28no—
112C2×#11758189—21no—
113C2×#11758189—21no—
114C2×#11758189—22no—
115C2×#11758189—22no—
116C2×#11758189—21no—
117C2×#11758189—21no—
118C2×#11758189D411yescharacteristic
119C2×#11758189D411yescharacteristic
120C2×#11758189D411yescharacteristic
121C2×#11758189D411yescharacteristic
122M16×D61—28no—
123M16×D61—22no—
124M16×D61—22no—
125C22×#92418—21no—
126C22×#92418C2311yescharacteristic
127C22×#92418C2311yescharacteristic
128C2×C8×D61—21no—
129C2×C8×D61—21no—
130C2×C8×D61—21no—
131C2×C8×D61—21no—
132#14519761—21no—
133#14519757C2×C411yescharacteristic
134#14519757C2×C411yescharacteristic
135#14519752C2×C411yescharacteristic
136#14519752C2×C411yescharacteristic
137#14519747—21no—
138C4×D244—21no—
139C4×D244—21no—
140C2×#11758198—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519713—22no—
143#14519712—22no—
144C4⋊#92418—21no—
145C4⋊#92418—21no—
146#14519705—22no—
147#14519705—22no—
148#14519704—22no—
149#14519703—22no—
150#14519703—22no—
151#14519700C2×C411yescharacteristic
152#14519700C2×C411yescharacteristic
153#14519697C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155#14519689—21no—
156#14519689—21no—
157#14519689—21no—
158#14519689—21no—
159#14519689C2×C411yescharacteristic
160#14519689C2×C411yescharacteristic
161#14519689C2×C411yescharacteristic
162#14519689C2×C411yescharacteristic
163#14519687—22no—
164#14519684—21no—
165C2×#41×C61C2311yescharacteristic
166#131×C61—22no—
167#131×C61D414yescomplemented
168C2×M16×C61—21no—
169C2×M16×C61C2311yescharacteristic
170C2×M16×C61C2311yescharacteristic
171C22×C8×C61—21no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#117×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176#104×C61—22no—
177#103×C61C2×C411yescharacteristic
178#103×C61C2×C411yescharacteristic
179#102×C61C2×C411yescharacteristic
180#102×C61C2×C411yescharacteristic
181#97×C61—21no—
182C4×C8×C61—22no—
183C4×C8×C61—21no—
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61C2×D412yes—
189#41×C61#4112yes—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61#4111yescharacteristic
203#11758226—22no—
204#11758226—22no—
205Q8×D61—22no—
206Q8×D61—22no—
207#11758224—24no—
208#11758224—24no—
209#11758224—22no—
210#11758224—22no—
211D4×D61—24no—
212D4×D61—24no—
213D4×D61—22no—
214D4×D61—22no—
215#11758222—24no—
216#11758222—24no—
217#11758222—21no—
218#11758222—21no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—21no—
223#11758222C2×D412yes—
224#11758222#4112yes—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×Dic122—21no—
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—21no—
248M16×C61—24no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61C2×D412yes—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—24no—
256C2×C8×C61—21no—
257C2×C8×C61C22×C411yescharacteristic
258C2×C8×C61C22×C411yescharacteristic
259C2×C8×C61C2×D412yes—
260C2×C8×C61C2×D411yescharacteristic
261C2×C8×C61C2×D412yes—
262C2×C8×C61C2×D411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C22⋊C4×C61—21no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269#11758202—22no—
270#11758201—22no—
271#11758200—22no—
272#11758199—22no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—42no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282#11758194—24no—
283#11758194—21no—
284#11758194—21no—
285#11758194—21no—
286#11758194C2×D412yes—
287C2×#92418—24no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418C22×C411yescharacteristic
295C2×#92418C22×C411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297C2×#92418C2×D411yescharacteristic
298Dic244—22no—
299D488—22no—
300#11758190—22no—
301#11758190—22no—
302#11758189—24no—
303#11758189—24no—
304#11758189—22no—
305#11758189—22no—
306#11758189—24no—
307#11758189—22no—
308#11758189—22no—
309#11758189—42no—
310C8×D61—24no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—42no—
314C23×C61—21no—
315C23×C61C2×#4111yescharacteristic
316C22×D61—21no—
317C22×D61—24no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—81no—
324C22×D61—81no—
325C22×D61C4×D411yescharacteristic
326C22×D61C4×D411yescharacteristic
327Q8×C61—21no—
328Q8×C61C4×D412yes—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—21no—
332D4×C61C4×D412yes—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C22⋊D61—24no—
348C22⋊D61—24no—
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C2×Dic61—24no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61C4×D411yescharacteristic
362C2×Dic61C4×D411yescharacteristic
363D244—24no—
364D244—21no—
365D244—21no—
366D244—21no—
367D244—81no—
368D244—81no—
369D244C4×D412yes—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—22no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—41no—
383C4×D61—41no—
384Dic122—24no—
385Dic122—21no—
386Dic122—21no—
387Dic122—21no—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—22no—
392C8×C61—41no—
393C8×C61#12012yes—
394C8×C61#12012yes—
395#92418—21no—
396#92418—21no—
397#92418—22no—
398#92418—21no—
399#92418—21no—
400#92418—41no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61C2×C4×D411yescharacteristic
408C22×C61#52511yescharacteristic
409C22×C61#52511yescharacteristic
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—22no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×C4×D411yescharacteristic
431C4×C61C2×#12011yescharacteristic
432C4×C61#52511yescharacteristic
433Dic61—21no—
434Dic61—22no—
435Dic61—21no—
436Dic61—41no—
437Dic61—81no—
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764D6111yescharacteristic, complemented
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—42no—
456C2×C61C4×#12011yescharacteristic
457C2×C61#295611yescharacteristic
458C2×C61#295711yescharacteristic
459D61—41no—
460D61—41no—
461D61—42no—
462D61—81no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—611no—
472C2×#131—1221no—
473C2×#131—1221no—
474C2×#131C2×D6111yescharacteristic
475C22×M16—611no—
476C22×M16—611no—
477C22×M16—1221no—
478C22×M16—1221no—
479#525—611no—
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447—611no—
488#444—1224no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108—611no—
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104C2×D6111yescharacteristic
503#416—611no—
504#416C2×D6111yescharacteristic
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405C2×D6111yescharacteristic, complemented
509C2×#97—611no—
510C2×C4×C8C2×D6111yescharacteristic, complemented
511C4×C22⋊C4—611no—
512#341—611no—
513#341C2×D6111yescharacteristic, complemented
514#339—611no—
515#339C2×D6111yescharacteristic, complemented
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—1221no—
524C2×#41—1221no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16—611no—
545C2×D8—611no—
546C2×D8—611no—
547#131—22no—
548#131—614no—
549#131—1228no—
550#131—1222no—
551#131—1228no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1222no—
558#131D24414yescomplemented
559C2×M16—21no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—1221no—
567C2×M16—1221no—
568C2×M16—1228no—
569C2×M16—1221no—
570C2×M16—1222no—
571C2×M16—1228no—
572C2×M16—1222no—
573C2×M16—1222no—
574C2×M16—1222no—
575C2×M16—1221no—
576C2×M16—1221no—
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1221no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6111yescharacteristic
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121—611no—
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117C22×D6111yescharacteristic
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42C22×D6111yescharacteristic
601#108—1222no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—22no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103C4×D6111yescharacteristic
614#103C4×D6111yescharacteristic
615#102—611no—
616#102—611no—
617#102C4×D6111yescharacteristic
618#102C4×D6111yescharacteristic
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—21no—
628#97—1222no—
629C4×C8—22no—
630C4×C8—21no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—21no—
635#41—21no—
636#41—612no—
637#41—612no—
638#41—1224no—
639#41—1224no—
640#41—1222no—
641#41—1224no—
642#41—1224no—
643#41—1222no—
644#41—1222no—
645#41—1222no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41C2×D24412yes—
653#41#1175822212yes—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1222no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1222no—
673C2×D4—1221no—
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1224no—
685C22×C4—1224no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C23×D6111yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—21no—
704M16—24no—
705M16—21no—
706M16—21no—
707M16—612no—
708M16—1224no—
709M16—1224no—
710M16—1224no—
711M16—1221no—
712M16—1222no—
713M16—1222no—
714M16—1222no—
715M16—1222no—
716M16—1224no—
717M16—1221no—
718M16—1221no—
719M16—2442no—
720M16C2×D24412yes—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—24no—
725C2×C8—21no—
726C2×C8—611no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—611no—
730C2×C8—1224no—
731C2×C8—1224no—
732C2×C8—1224no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1224no—
739C2×C8—1221no—
740C2×C8—2442no—
741C2×C8C2×C4×D6111yescharacteristic
742C2×C8C2×C4×D6111yescharacteristic
743C2×C8C2×D24412yes—
744C2×C8D4×D6112yes—
745C2×C8D4×D6111yescharacteristic
746C2×C8D4×D6111yescharacteristic
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4C2×C4×D6111yescharacteristic
750C4⋊C4C2×C4×D6111yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—611no—
764C23—611no—
765C23—1224no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23—2441no—
773C23—2441no—
774C23#41×D6111yescharacteristic
775Q8—21no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8—1221no—
780Q8—1221no—
781Q8C4×D24412yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—612no—
786D4—1224no—
787D4—1224no—
788D4—1224no—
789D4—1222no—
790D4—1222no—
791D4—1221no—
792D4—1221no—
793D4—1221no—
794D4—4881no—
795D4—4881no—
796D4—2441no—
797D4—2441no—
798D4C4×D24412yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—1224no—
810C2×C4—1224no—
811C2×C4—1224no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1222no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1221no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×D24411yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4C2×#1175822211yescharacteristic
837C8—21no—
838C8—21no—
839C8—22no—
840C8—41no—
841C8—1221no—
842C8—1221no—
843C8—1221no—
844C8—1221no—
845C8—1222no—
846C8—2441no—
847C8#1451974712yes—
848C8#1451974712yes—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—1221no—
855C22—1222no—
856C22—1221no—
857C22—1221no—
858C22—1221no—
859C22—1221no—
860C22—1221no—
861C22—4881no—
862C22—4881no—
863C22—4884no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C4×D4×D6111yescharacteristic
870C22#1684027111yescharacteristic
871C22#1684027411yescharacteristic
872C4—22no—
873C4—42no—
874C4—41no—
875C4—41no—
876C4—1221no—
877C4—1221no—
878C4—1222no—
879C4—4881no—
880C4—2441no—
881C4C4×D4×D6111yescharacteristic
882C4C2×C4×D24411yescharacteristic
883C4C2×#1451974711yescharacteristic
884C4#1684027111yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—4881no—
889C2—2441no—
890C2—2441no—
891C2—2442no—
892C2C4×#1451974711yescharacteristic
893C2#2145472411yescharacteristic
894C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1764C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1764D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
1. C2×#16840527C2semidirect
3. C2×#16839882C2semidirect
4. C2×#16839880C2semidirect
5. #21454524C2semidirect
6. #21446147C2semidirect
7. #21446144C2semidirect
8. #21446120C2semidirect
9. #21446096C2semidirect
10. #21446095C2semidirect
11. #21446025C2semidirect
12. #21445761C2semidirect
13. #21445665C2semidirect
14. #21445602C2semidirect
15. C61×#1764C2semidirect
26. C2×#14519783C22semidirect
32. #16839927C4semidirect
33. #16839925C4semidirect
34. #16839919C4semidirect
35. #16839914C4semidirect
36. #16839910C4semidirect
37. #16839908C4semidirect
38. #16839902C4semidirect
39. #16839897C4semidirect
46. C2×#14519713C22semidirect
47. C2×#14519712C22semidirect
48. #16839789C22semidirect
50. C2×#14519705C22semidirect
53. C2×#14519703C22semidirect
55. #16839730C22semidirect
58. C2×#14519687C22semidirect
60. #16839526C22semidirect
61. #16839521C22semidirect
62. #16839517C22semidirect
63. #16839516C22semidirect
67. C61×#405C22semidirect
68. C2×C4×C8×C61C22semidirect
69. C61×#341C22semidirect
70. C61×#339C22semidirect
107. #14519783D4semidirect
167. #131×C61D4semidirect
451. #1764D61semidirect
508. #405C2×D61semidirect
510. C2×C4×C8C2×D61semidirect
513. #341C2×D61semidirect
515. #339C2×D61semidirect
518. C61#21468semidirect
558. #131D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#214550392
C2×#168398822
C2×#168398802
#214545242
#214461472
#214461442
#214461202
#214460962
#214460952
#214460252
#214457612
#214456652
#214456022
C61×#17642
#2146861