Finite Group Databasebeta

← #29685871

Subgroups — #29685871

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×#16840528C211yesmaximal, characteristic, complemented
2#21455041C211yesmaximal, characteristic
3C2×#16839883C211yesmaximal, characteristic, complemented
4C2×#16839878C211yesmaximal, characteristic, complemented
5#21454518C211yesmaximal, characteristic, complemented
6#21446147C211yesmaximal, characteristic, complemented
7#21446147C211yesmaximal, characteristic, complemented
8#21446121C211yesmaximal, characteristic, complemented
9#21446091C211yesmaximal, characteristic, complemented
10#21446091C211yesmaximal, characteristic, complemented
11#21445762C211yesmaximal, characteristic, complemented
12#21445662C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519799C2211yescharacteristic
19#16840528—24no—
20#16840528—24no—
21C2×#14519785C2211yescharacteristic
22C2×#14519785C2211yescharacteristic
23C2×#14519785C2211yescharacteristic
24C2×#14519785C2211yescharacteristic
25C2×#14519785C2211yescharacteristic, complemented
26C2×#14519783—21no—
27C2×#14519783—21no—
28C22×#11758194C2211yescharacteristic
29C2×M16×D61—21no—
30C2×M16×D61—21no—
31#16840273C2211yescharacteristic
32#16839926C411yescharacteristic, complemented
33#16839926C411yescharacteristic, complemented
34#16839920C411yescharacteristic, complemented
35#16839915C411yescharacteristic, complemented
36#16839909C411yescharacteristic, complemented
37#16839909C411yescharacteristic, complemented
38#16839903C411yescharacteristic, complemented
39#16839898C411yescharacteristic, complemented
40#16839883—24no—
41#16839878—24no—
42#16839837—21no—
43#16839837—21no—
44#16839836—21no—
45#16839836—21no—
46#16839790C2211yescharacteristic, complemented
47C2×#14519703C2211yescharacteristic
48C2×#14519703C2211yescharacteristic
49C2×#14519703C2211yescharacteristic
50C2×#14519703C2211yescharacteristic
51C2×#14519703C2211yescharacteristic, complemented
52C2×#14519703C2211yescharacteristic, complemented
53#16839759C2211yescharacteristic
54#16839759C2211yescharacteristic
55#16839730C2211yescharacteristic, complemented
56#16839720C2211yescharacteristic, complemented
57C2×#14519687C2211yescharacteristic, complemented
58C2×C8×Dic61C2211yescharacteristic, complemented
59C4×C22⋊Dic61C2211yescharacteristic
60#16839523C2211yescharacteristic, complemented
61#16839523C2211yescharacteristic, complemented
62#16839516C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C22×M16×C61C2211yescharacteristic
65C2×#108×C61C2211yescharacteristic, complemented
66C2×#108×C61C2211yescharacteristic, complemented
67C61×#407C2211yescharacteristic
68C2×C22⋊C8×C61C2211yescharacteristic
69C61×#341C2211yescharacteristic, complemented
70C61×#341C2211yescharacteristic, complemented
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—22no—
74C2×#11758222—22no—
75C2×#11758222—22no—
76C2×#11758222—22no—
77C2×#11758222C2×C411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2311yescharacteristic
80C2×#11758222C2311yescharacteristic
81C2×#11758222C2311yescharacteristic
82C22×Dic122C2×C411yescharacteristic
83C22×D244C2×C411yescharacteristic
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86#14519799—22no—
87#14519799—22no—
88#14519799—22no—
89#14519799—22no—
90C2×Dic244C2×C411yescharacteristic
91C2×Dic244C2×C411yescharacteristic
92C2×#11758190C2×C411yescharacteristic
93C2×#11758190C2×C411yescharacteristic
94C2×#11758190C2×C411yescharacteristic
95C2×#11758190C2×C411yescharacteristic
96C2×D488C2×C411yescharacteristic
97C2×D488C2×C411yescharacteristic
98#14519785—22no—
99#14519785—22no—
100#14519785—22no—
101#14519785—22no—
102#14519785—22no—
103#14519785—22no—
104#14519785—22no—
105#14519785—22no—
106#14519785D414yescomplemented
107#14519785D414yescomplemented
108#14519783—28no—
109#14519783—28no—
110C2×#11758194—22no—
111C2×#11758194—22no—
112C2×#11758194D411yescharacteristic
113C2×#11758194D411yescharacteristic
114C2×#11758194D411yescharacteristic
115C2×#11758194D411yescharacteristic
116C2×#11758189—21no—
117C2×#11758189—21no—
118C2×#11758189—21no—
119C2×#11758189—21no—
120C2×#11758189—21no—
121M16×D61—28no—
122M16×D61—28no—
123C22×#92418C2311yescharacteristic
124C22×#92418C2311yescharacteristic
125C2×C8×D61—21no—
126C2×C8×D61—21no—
127C2×C8×D61—21no—
128C2×C8×D61—21no—
129C2×C8×D61—21no—
130#14519760—21no—
131#14519756C2×C411yescharacteristic
132#14519756C2×C411yescharacteristic
133#14519751C2×C411yescharacteristic
134#14519751C2×C411yescharacteristic
135#14519746—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138#14519736C2311yescharacteristic
139C2×C22⋊Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142#14519706—21no—
143#14519706—21no—
144#14519703—22no—
145#14519703—22no—
146#14519703—22no—
147#14519703—22no—
148#14519703—22no—
149#14519703—22no—
150#14519702C2×C411yescharacteristic
151#14519702C2×C411yescharacteristic
152#14519702C2×C411yescharacteristic
153#14519702C2×C411yescharacteristic
154#14519699C2×C411yescharacteristic
155#14519699C2×C411yescharacteristic
156#14519699C2×C411yescharacteristic
157#14519699C2×C411yescharacteristic
158#14519689—21no—
159#14519689—21no—
160#14519687—22no—
161#14519687—21no—
162C8×Dic61—22no—
163C8×Dic61—21no—
164#14519684—21no—
165C23×C4×C61C2311yescharacteristic
166C2×M16×C61—21no—
167C2×M16×C61—22no—
168C2×M16×C61—22no—
169C2×M16×C61C2311yescharacteristic
170C2×M16×C61C2311yescharacteristic
171C2×M16×C61C2311yescharacteristic
172C2×M16×C61C2311yescharacteristic
173C22×C8×C61—21no—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176#108×C61—22no—
177#108×C61—22no—
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2×C411yescharacteristic
181C22⋊C8×C61C2×C411yescharacteristic
182C22⋊C8×C61C2×C411yescharacteristic
183C22⋊C8×C61C2×C411yescharacteristic
184C24×C61#4111yescharacteristic
185C23×D61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208#11758222—24no—
209#11758222—24no—
210#11758222—24no—
211#11758222—24no—
212#11758222—21no—
213#11758222—21no—
214#11758222—21no—
215#11758222—21no—
216#11758222—22no—
217#11758222—22no—
218#11758222—21no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—22no—
223#11758222—22no—
224#11758222C2×D412yes—
225#11758222C2×D412yes—
226#11758222#4112yes—
227#11758222#4112yes—
228C2×D244—21no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244C22×C411yescharacteristic
232C2×D244C22×C411yescharacteristic
233C2×D244C22×C411yescharacteristic
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×Dic122—21no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122C22×C411yescharacteristic
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—24no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61C2×D412yes—
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×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61C22×C411yescharacteristic
266C2×C8×C61C22×C411yescharacteristic
267C2×C8×C61C22×C411yescharacteristic
268C2×C8×C61C22×C411yescharacteristic
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—42no—
273#11758198—21no—
274#11758198—21no—
275C4⋊Dic61C22×C411yescharacteristic
276C4⋊Dic61C22×C411yescharacteristic
277#11758196—21no—
278#11758196—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284#11758194—22no—
285#11758194—22no—
286#11758194—22no—
287#11758194—22no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418C2×D411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293C2×#92418C2×D412yes—
294C2×#92418C2×D411yescharacteristic
295C2×#92418C2×D412yes—
296Dic244—22no—
297Dic244—22no—
298D488—22no—
299D488—22no—
300#11758190—22no—
301#11758190—22no—
302#11758190—22no—
303#11758190—22no—
304#11758189—24no—
305#11758189—24no—
306#11758189—24no—
307#11758189—24no—
308#11758189—42no—
309C8×D61—24no—
310C8×D61—24no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—42no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61C4×D411yescharacteristic
319C23×C61C4×D411yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—24no—
324C22×D61—21no—
325C22×D61—81no—
326C22×D61—81no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61C4×D411yescharacteristic
338C2×C4×C61C4×D411yescharacteristic
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C22⋊D61—24no—
346C22⋊D61—24no—
347C22⋊D61—22no—
348C22⋊D61—22no—
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C22⋊D61—81no—
354C22⋊D61—81no—
355C2×Dic61—24no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367D244—24no—
368D244—21no—
369D244—21no—
370D244—21no—
371D244—21no—
372D244C4×D412yes—
373D244C4×D412yes—
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—41no—
381C4×D61—41no—
382Dic122—24no—
383Dic122—21no—
384Dic122—21no—
385Dic122—21no—
386Dic122—21no—
387Dic122C4×D412yes—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—21no—
392C8×C61—21no—
393C8×C61—22no—
394C8×C61—22no—
395C8×C61—41no—
396C8×C61—41no—
397#92418—21no—
398#92418—21no—
399#92418#12012yes—
400#92418#12012yes—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61C2×C4×D411yescharacteristic
413C22×C61#52511yescharacteristic
414C22×C61#52511yescharacteristic
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—84no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61C2×C4×D411yescharacteristic
428C4×C61C2×C4×D411yescharacteristic
429C4×C61C2×#12011yescharacteristic
430C4×C61#52511yescharacteristic
431Dic61—22no—
432Dic61—22no—
433Dic61—42no—
434Dic61—41no—
435Dic61—41no—
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#1855D6111yescharacteristic, complemented
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—41no—
456C2×C61—41no—
457C2×C61C4×#12011yescharacteristic
458C2×C61#295611yescharacteristic
459C2×C61#295711yescharacteristic
460D61—42no—
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—611no—
473C2×#131—1221no—
474C2×#131—1221no—
475C22×M16—611no—
476C22×M16—1221no—
477C22×M16—1221no—
478C22×M16C2×D6111yescharacteristic
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×#108C2×D6111yescharacteristic, complemented
495C2×#108C2×D6111yescharacteristic, complemented
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408—611no—
506#407C2×D6111yescharacteristic
507C2×C22⋊C8C2×D6111yescharacteristic
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341C2×D6111yescharacteristic, complemented
513#341C2×D6111yescharacteristic, complemented
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—611no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1221no—
529C2×#41—1221no—
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
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—614no—
548#131—614no—
549#131—1228no—
550#131—1228no—
551#131—1222no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1222no—
558#131—1222no—
559C2×M16—21no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—1221no—
567C2×M16—1221no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1221no—
571C2×M16—1222no—
572C2×M16—1222no—
573C2×M16—1228no—
574C2×M16—1228no—
575C2×M16C22×D6111yescharacteristic
576C2×M16C22×D6111yescharacteristic
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×C42—611no—
601#108—22no—
602#108—22no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—1222no—
606#104—1222no—
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—1221no—
622C22⋊C8—1221no—
623C22⋊C8C4×D6111yescharacteristic
624C22⋊C8C4×D6111yescharacteristic
625C22⋊C8C4×D6111yescharacteristic
626C22⋊C8C4×D6111yescharacteristic
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—1221no—
633C24#1175822611yescharacteristic
634#41—612no—
635#41—612no—
636#41—612no—
637#41—612no—
638#41—1222no—
639#41—1222no—
640#41—1222no—
641#41—1222no—
642#41—1224no—
643#41—1224no—
644#41—1224no—
645#41—1224no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41—1221no—
653#41—1221no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—611no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8—1221no—
660C2×D4—611no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—1222no—
664C2×D4—1222no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—1224no—
680C22×C4—1224no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4C2×C4×D6111yescharacteristic
690C22×C4C2×C4×D6111yescharacteristic
691C22×C4D4×D6111yescharacteristic
692C22×C4D4×D6111yescharacteristic
693C22×C4#1175822611yescharacteristic
694C22×C4C23×D6111yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—1224no—
711M16—1224no—
712M16—1224no—
713M16—1224no—
714M16—1222no—
715M16—1222no—
716M16—1222no—
717M16—1222no—
718M16—2442no—
719M16D4×D6112yes—
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—21no—
729C2×C8—21no—
730C2×C8—612no—
731C2×C8—612no—
732C2×C8—611no—
733C2×C8—611no—
734C2×C8—611no—
735C2×C8—611no—
736C2×C8—1224no—
737C2×C8—1224no—
738C2×C8—1224no—
739C2×C8—1224no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—2442no—
743C2×C8C2×C4×D6111yescharacteristic
744C2×C8C2×C4×D6111yescharacteristic
745C2×C8C2×C4×D6111yescharacteristic
746C2×C8C2×C4×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—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—1224no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23#1451973911yescharacteristic
773C23#1451973911yescharacteristic
774C23C2×#1175822611yescharacteristic
775Q8—612no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8—1221no—
780Q8—1221no—
781Q8—1221no—
782D4—612no—
783D4—612no—
784D4—1224no—
785D4—1224no—
786D4—1224no—
787D4—1222no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1221no—
792D4—1221no—
793D4—1221no—
794D4—1221no—
795D4—4881no—
796D4—4881no—
797D4—2441no—
798D4—2441no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—1224no—
810C2×C4—1224no—
811C2×C4—1224no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4#1451973911yescharacteristic
830C2×C4#1451973911yescharacteristic
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#41×D6111yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—22no—
842C8—22no—
843C8—41no—
844C8—41no—
845C8—612no—
846C8—612no—
847C8—1221no—
848C8—1221no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—81no—
858C22—81no—
859C22—1222no—
860C22—1222no—
861C22—4884no—
862C22—2441no—
863C22—2441no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C2×#1451973911yescharacteristic
870C22#1684027511yescharacteristic
871C22#1684027511yescharacteristic
872C4—21no—
873C4—21no—
874C4—1222no—
875C4—1222no—
876C4—4881no—
877C4—2442no—
878C4—2441no—
879C4—2441no—
880C4—2441no—
881C4C4×D4×D6111yescharacteristic
882C4C4×D4×D6111yescharacteristic
883C4#120×D6111yescharacteristic
884C4#1684027011yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—4881no—
890C2—2442no—
891C2—2442no—
892C2#2144832011yescharacteristic
893C2#2145472811yescharacteristic
894C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1855C2
socleC22×C61C2×C4×D4
prime radical#21455041C2
cosocleC22×C4×C61C24
hypercenter#1855D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839883C2semidirect
4. C2×#16839878C2semidirect
5. #21454518C2semidirect
6. #21446147C2semidirect
7. #21446147C2semidirect
8. #21446121C2semidirect
9. #21446091C2semidirect
10. #21446091C2semidirect
11. #21445762C2semidirect
12. #21445662C2semidirect
13. #21445655C2semidirect
14. #21445605C2semidirect
15. C61×#1855C2semidirect
25. C2×#14519785C22semidirect
32. #16839926C4semidirect
33. #16839926C4semidirect
34. #16839920C4semidirect
35. #16839915C4semidirect
36. #16839909C4semidirect
37. #16839909C4semidirect
38. #16839903C4semidirect
39. #16839898C4semidirect
46. #16839790C22semidirect
51. C2×#14519703C22semidirect
52. C2×#14519703C22semidirect
55. #16839730C22semidirect
56. #16839720C22semidirect
57. C2×#14519687C22semidirect
58. C2×C8×Dic61C22semidirect
60. #16839523C22semidirect
61. #16839523C22semidirect
62. #16839516C22semidirect
63. #16839516C22semidirect
65. C2×#108×C61C22semidirect
66. C2×#108×C61C22semidirect
69. C61×#341C22semidirect
70. C61×#341C22semidirect
106. #14519785D4semidirect
107. #14519785D4semidirect
448. #1855D61semidirect
494. C2×#108C2×D61semidirect
495. C2×#108C2×D61semidirect
512. #341C2×D61semidirect
513. #341C2×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×#168405282
#214550412
C2×#168398832
C2×#168398782
#214545182
#214461472
#214461212
#214460912
#214457622
#214456622
#214456552
#214456052
C61×#18552
#2146861