Finite Group Databasebeta

← #29685877

Subgroups — #29685877

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#21455033C211yesmaximal, characteristic
3C2×#16839881C211yesmaximal, characteristic, complemented
4C2×#16839879C211yesmaximal, characteristic, complemented
5#21454525C211yesmaximal, characteristic, complemented
6#21446149C211yesmaximal, characteristic, complemented
7#21446118C211yesmaximal, characteristic, complemented
8#21446097C211yesmaximal, characteristic, complemented
9#21446094C211yesmaximal, characteristic, complemented
10#21446025C211yesmaximal, characteristic, complemented
11#21445761C211yesmaximal, characteristic, complemented
12#21445664C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14#21445601C211yesmaximal, characteristic, complemented
15C61×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18#16840527—24no—
19#16840527—24no—
20C2×#14519785—21no—
21C2×#14519785C2211yescharacteristic
22C2×#14519784C2211yescharacteristic
23C2×#14519784C2211yescharacteristic, complemented
24C2×#14519783—21no—
25C2×#14519783C2211yescharacteristic
26C22×#11758189—21no—
27C22×#11758189C2211yescharacteristic
28C2×M16×D61—21no—
29C2×M16×D61C2211yescharacteristic
30#16840269C2211yescharacteristic
31#16839923C411yescharacteristic, complemented
32#16839921C411yescharacteristic, complemented
33#16839916C411yescharacteristic, complemented
34#16839911C411yescharacteristic, complemented
35#16839906C411yescharacteristic, complemented
36#16839904C411yescharacteristic, complemented
37#16839899C411yescharacteristic, complemented
38#16839894C411yescharacteristic, complemented
39#16839881—24no—
40#16839879—24no—
41#16839837—21no—
42#16839837—21no—
43#16839830—21no—
44#16839830—21no—
45C2×#14519713C2211yescharacteristic, complemented
46C2×#14519712C2211yescharacteristic, complemented
47#16839788C2211yescharacteristic, complemented
48C2×#14519705C2211yescharacteristic
49C2×#14519704C2211yescharacteristic
50C2×#14519704C2211yescharacteristic, complemented
51C2×#14519703C2211yescharacteristic
52#16839759C2211yescharacteristic
53#16839758C2211yescharacteristic
54#16839725C2211yescharacteristic
55C2×#14519689C2211yescharacteristic
56#16839720C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58C2×C8×Dic61C2211yescharacteristic, complemented
59C4×#11758198C2211yescharacteristic
60#16839526C2211yescharacteristic, complemented
61#16839523C2211yescharacteristic, complemented
62#16839522C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C2×#135×C61C2211yescharacteristic
65C2×#131×C61C2211yescharacteristic
66C2×#104×C61C2211yescharacteristic
67C2×#104×C61C2211yescharacteristic, complemented
68C61×#408C2211yescharacteristic, complemented
69C61×#341C2211yescharacteristic, complemented
70C61×#336C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758224—21no—
75C2×#11758224C2×C411yescharacteristic
76#41×D61—22no—
77#41×D61—22no—
78#41×D61—22no—
79#41×D61—22no—
80C2×Q8×D61C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519797—22no—
86#14519797—22no—
87C2×#11758202C2×C411yescharacteristic
88C2×#11758200C2×C411yescharacteristic
89C2×#11758201C2×C411yescharacteristic
90C2×#11758199C2×C411yescharacteristic
91#14519785—28no—
92#14519785—22no—
93#14519785D414yescomplemented
94#14519784—22no—
95#14519784—22no—
96#14519784—22no—
97#14519784D414yescomplemented
98#14519783—28no—
99#14519783—22no—
100#14519783—22no—
101C2×#11758194—21no—
102C2×#11758194—21no—
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105C2×#11758189—28no—
106C2×#11758189—21no—
107C2×#11758189—21no—
108C2×#11758189—21no—
109C2×#11758189—22no—
110C2×#11758189—22no—
111C2×#11758189D411yescharacteristic
112C2×#11758189D411yescharacteristic
113C2×#11758189D411yescharacteristic
114C2×#11758189D411yescharacteristic
115M16×D61—28no—
116M16×D61—22no—
117M16×D61—22no—
118C22×#92418—21no—
119C22×#92418—21no—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—21no—
123C2×C8×D61—21no—
124C2×C8×D61—21no—
125#14519758—21no—
126#14519753C2×C411yescharacteristic
127#14519753C2×C411yescharacteristic
128#14519748C2×C411yescharacteristic
129#14519748C2×C411yescharacteristic
130#14519745—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133#14519736C2311yescharacteristic
134C2×#11758198—21no—
135C2×C4×Dic61C2311yescharacteristic
136#14519713—22no—
137#14519712—22no—
138#14519706—21no—
139#14519706—21no—
140#14519705—22no—
141#14519704—22no—
142#14519704—22no—
143#14519703—22no—
144#14519702C2×C411yescharacteristic
145#14519702C2×C411yescharacteristic
146#14519701C2×C411yescharacteristic
147#14519701C2×C411yescharacteristic
148#14519699C2×C411yescharacteristic
149#14519699C2×C411yescharacteristic
150#14519698C2×C411yescharacteristic
151#14519698C2×C411yescharacteristic
152#14519689—21no—
153#14519689—21no—
154#14519689C2×C411yescharacteristic
155#14519689C2×C411yescharacteristic
156#14519689C2×C411yescharacteristic
157#14519689C2×C411yescharacteristic
158#14519688—22no—
159#14519687—21no—
160C8×Dic61—22no—
161C8×Dic61—21no—
162#14519684—21no—
163C2×#41×C61C2311yescharacteristic
164C2×#41×C61C2311yescharacteristic
165#135×C61—22no—
166#135×C61—22no—
167C2×Q16×C61C2×C411yescharacteristic
168C2×SD16×C61C2×C411yescharacteristic
169C2×SD16×C61C2×C411yescharacteristic
170C2×D8×C61C2×C411yescharacteristic
171#131×C61—22no—
172#131×C61—22no—
173C2×M16×C61—21no—
174C2×M16×C61C2311yescharacteristic
175C2×M16×C61C2311yescharacteristic
176C22×C8×C61—21no—
177C22×C8×C61C2311yescharacteristic
178C22×C8×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180#104×C61—22no—
181#104×C61—22no—
182C22⋊C8×C61—21no—
183C22⋊C8×C61—21no—
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190#41×C61—21no—
191#41×C61—21no—
192#41×C61C2×D412yes—
193#41×C61#4112yes—
194C2×Q8×C61C22×C411yescharacteristic
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C2×D4×C61C22×C411yescharacteristic
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61#4111yescharacteristic
212#11758226—22no—
213#11758226—22no—
214Q8×D61—22no—
215Q8×D61—22no—
216#11758224—24no—
217#11758224—24no—
218#11758224—22no—
219#11758224—22no—
220D4×D61—24no—
221D4×D61—24no—
222D4×D61—22no—
223D4×D61—22no—
224#11758222—24no—
225#11758222—24no—
226#11758222—21no—
227#11758222—21no—
228#11758222C2×D412yes—
229#11758222#4112yes—
230C2×D244—21no—
231C2×D244C22×C411yescharacteristic
232C2×C4×D61—24no—
233C2×C4×D61—24no—
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×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247Q16×C61—22no—
248SD16×C61—22no—
249SD16×C61—22no—
250D8×C61—22no—
251M16×C61—24no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61C2×D412yes—
256C2×C8×C61—24no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61C22×C411yescharacteristic
264C2×C8×C61C22×C411yescharacteristic
265C2×C8×C61C2×D411yescharacteristic
266C2×C8×C61C2×D411yescharacteristic
267C42×C61—21no—
268C42×C61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272#11758202—22no—
273#11758201—22no—
274#11758200—22no—
275#11758199—22no—
276#11758198—21no—
277#11758198—21no—
278#11758198—42no—
279C4⋊Dic61C22×C411yescharacteristic
280C4⋊Dic61C22×C411yescharacteristic
281#11758196—21no—
282#11758196—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286#11758194—21no—
287#11758194—24no—
288#11758194—21no—
289#11758194—21no—
290#11758194—42no—
291#11758194C2×D412yes—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—24no—
296C2×#92418—21no—
297C2×#92418—42no—
298C2×#92418C22×C411yescharacteristic
299C2×#92418C22×C411yescharacteristic
300C2×#92418C2×D411yescharacteristic
301C2×#92418C2×D412yes—
302C2×#92418C2×D411yescharacteristic
303C2×#92418C2×D412yes—
304#11758189—24no—
305#11758189—24no—
306#11758189—22no—
307#11758189—22no—
308#11758189—24no—
309#11758189—22no—
310#11758189—22no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—24no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61C2×#4111yescharacteristic
317C22×D61—21no—
318C22×D61—24no—
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×C61—21no—
329Q8×C61—21no—
330Q8×C61C4×D412yes—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—21no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61C4×D412yes—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C22⋊D61—24no—
355C22⋊D61—24no—
356C22⋊D61—22no—
357C22⋊D61—22no—
358C22⋊D61—81no—
359C22⋊D61—81no—
360C2×Dic61—24no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61C4×D411yescharacteristic
370C2×Dic61C4×D411yescharacteristic
371D244—24no—
372D244—21no—
373D244C4×D412yes—
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—22no—
385C4×D61—21no—
386Dic122—24no—
387Dic122—21no—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—22no—
392C8×C61—21no—
393C8×C61—21no—
394C8×C61—41no—
395#92418—21no—
396#92418—21no—
397#92418—22no—
398#92418—41no—
399#92418#12012yes—
400#92418#12012yes—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61C2×C4×D411yescharacteristic
411C22×C61#52511yescharacteristic
412C22×C61#52511yescharacteristic
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—22no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—41no—
427C4×C61—81no—
428C4×C61C2×C4×D411yescharacteristic
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×#12011yescharacteristic
431C4×C61#52511yescharacteristic
432Dic61—21no—
433Dic61—22no—
434Dic61—21no—
435Dic61—42no—
436Dic61—41no—
437Dic61—41no—
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876D6111yescharacteristic, complemented
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—42no—
456C2×C61—81no—
457C2×C61C4×#12011yescharacteristic
458C2×C61#295611yescharacteristic
459C2×C61#295711yescharacteristic
460D61—41no—
461D61—41no—
462D61—42no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135C2×D6111yescharacteristic
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×#104C2×D6111yescharacteristic
502C2×#104C2×D6111yescharacteristic, complemented
503#416—611no—
504#416—611no—
505#408C2×D6111yescharacteristic, complemented
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341C2×D6111yescharacteristic, complemented
514#339—611no—
515#339—611no—
516#336—611no—
517#336C2×D6111yescharacteristic, complemented
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—1221no—
523C2×#41—1221no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41C22×D6111yescharacteristic
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—22no—
536#135—22no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16C4×D6111yescharacteristic
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16C4×D6111yescharacteristic
544C2×SD16C4×D6111yescharacteristic
545C2×D8—611no—
546C2×D8C4×D6111yescharacteristic
547#131—22no—
548#131—22no—
549#131—614no—
550#131—614no—
551#131—1222no—
552#131—1222no—
553#131—1228no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1222no—
558#131—1228no—
559C2×M16—21no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—1222no—
567C2×M16—1222no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1228no—
571C2×M16—1221no—
572C2×M16—1221no—
573C2×M16—1222no—
574C2×M16—1228no—
575C2×M16—1222no—
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#117—611no—
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—22no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—611no—
624C22⋊C8—611no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—612no—
641#41—612no—
642#41—1224no—
643#41—1224no—
644#41—1222no—
645#41—1224no—
646#41—1224no—
647#41—1222no—
648#41—1222no—
649#41—1222no—
650#41—1221no—
651#41—1221no—
652#41D4×D6112yes—
653#41#1175822412yes—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8C2×C4×D6111yescharacteristic
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—611no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1222no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1222no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4C2×C4×D6111yescharacteristic
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1224no—
686C22×C4—1224no—
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—22no—
696Q16—1222no—
697SD16—22no—
698SD16—22no—
699SD16—1222no—
700SD16—1222no—
701D8—22no—
702D8—1222no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—612no—
708M16—1222no—
709M16—1222no—
710M16—1222no—
711M16—1222no—
712M16—1224no—
713M16—1224no—
714M16—1224no—
715M16—1224no—
716M16—1221no—
717M16—1221no—
718M16—1221no—
719M16—2442no—
720M16D4×D6112yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—612no—
729C2×C8—612no—
730C2×C8—611no—
731C2×C8—611no—
732C2×C8—611no—
733C2×C8—611no—
734C2×C8—1224no—
735C2×C8—1224no—
736C2×C8—1224no—
737C2×C8—1224no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—2442no—
743C2×C8C2×C4×D6111yescharacteristic
744C2×C8C2×C4×D6111yescharacteristic
745C2×C8D4×D6111yescharacteristic
746C2×C8D4×D6111yescharacteristic
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—21no—
758C42—21no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—21no—
764C23—611no—
765C23—611no—
766C23—1224no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23—2441no—
773C23—2441no—
774C23#41×D6111yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—612no—
779Q8—1224no—
780Q8—1221no—
781Q8#1451973712yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—41no—
788D4—41no—
789D4—612no—
790D4—1224no—
791D4—1224no—
792D4—1224no—
793D4—1222no—
794D4—1222no—
795D4—1221no—
796D4—4881no—
797D4—4881no—
798D4#1451973712yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—1224no—
811C2×C4—1224no—
812C2×C4—1224no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1222no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4C2×#1175822411yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—22no—
841C8—21no—
842C8—41no—
843C8—612no—
844C8—612no—
845C8—1221no—
846C8—1221no—
847C8—1222no—
848C8—2441no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—1221no—
858C22—1222no—
859C22—1221no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—1221no—
864C22—4881no—
865C22—4881no—
866C22—4884no—
867C22—2441no—
868C22—2441no—
869C22C4×D4×D6111yescharacteristic
870C22#1684027011yescharacteristic
871C22#1684027211yescharacteristic
872C4—22no—
873C4—41no—
874C4—81no—
875C4—1221no—
876C4—1221no—
877C4—1222no—
878C4—2442no—
879C4—2441no—
880C4—2441no—
881C4C4×D4×D6111yescharacteristic
882C4C2×#1451973711yescharacteristic
883C4#120×D6111yescharacteristic
884C4#1684027211yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—81no—
889C2—2441no—
890C2—2441no—
891C2—2442no—
892C2#2144832411yescharacteristic
893C2#2145472711yescharacteristic
894C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1876C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenter#1876D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
1. C2×#16840527C2semidirect
3. C2×#16839881C2semidirect
4. C2×#16839879C2semidirect
5. #21454525C2semidirect
6. #21446149C2semidirect
7. #21446118C2semidirect
8. #21446097C2semidirect
9. #21446094C2semidirect
10. #21446025C2semidirect
11. #21445761C2semidirect
12. #21445664C2semidirect
13. #21445655C2semidirect
14. #21445601C2semidirect
15. C61×#1876C2semidirect
23. C2×#14519784C22semidirect
31. #16839923C4semidirect
32. #16839921C4semidirect
33. #16839916C4semidirect
34. #16839911C4semidirect
35. #16839906C4semidirect
36. #16839904C4semidirect
37. #16839899C4semidirect
38. #16839894C4semidirect
45. C2×#14519713C22semidirect
46. C2×#14519712C22semidirect
47. #16839788C22semidirect
50. C2×#14519704C22semidirect
56. #16839720C22semidirect
57. C2×#14519688C22semidirect
58. C2×C8×Dic61C22semidirect
60. #16839526C22semidirect
61. #16839523C22semidirect
62. #16839522C22semidirect
63. #16839516C22semidirect
67. C2×#104×C61C22semidirect
68. C61×#408C22semidirect
69. C61×#341C22semidirect
70. C61×#336C22semidirect
93. #14519785D4semidirect
97. #14519784D4semidirect
444. #1876D61semidirect
502. C2×#104C2×D61semidirect
505. #408C2×D61semidirect
513. #341C2×D61semidirect
517. #336C2×D61semidirect
518. C61#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#214550332
C2×#168398812
C2×#168398792
#214545252
#214461492
#214461182
#214460972
#214460942
#214460252
#214457612
#214456642
#214456552
#214456012
C61×#18762
#2146861