Finite Group Databasebeta

← #29685879

Subgroups — #29685879

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#21455035C211yesmaximal, characteristic
3C2×#16839881C211yesmaximal, characteristic, complemented
4C2×#16839876C211yesmaximal, characteristic, complemented
5#21454523C211yesmaximal, characteristic, complemented
6#21446143C211yesmaximal, characteristic, complemented
7#21446143C211yesmaximal, characteristic, complemented
8#21446095C211yesmaximal, characteristic, complemented
9#21446095C211yesmaximal, characteristic, complemented
10#21446024C211yesmaximal, characteristic, complemented
11#21445764C211yesmaximal, characteristic, complemented
12#21445660C211yesmaximal, characteristic, complemented
13#21445653C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#1871C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19#16840528—24no—
20#16840528—24no—
21C2×#14519785C2211yescharacteristic
22C2×#14519785C2211yescharacteristic
23C2×#14519785C2211yescharacteristic
24C2×#14519785C2211yescharacteristic
25C2×#14519784C2211yescharacteristic, complemented
26C2×#14519783—21no—
27C2×#14519783—21no—
28C22×#11758194C2211yescharacteristic
29C2×M16×D61—21no—
30C2×M16×D61—21no—
31#16839922C411yescharacteristic, complemented
32#16839922C411yescharacteristic, complemented
33#16839917C411yescharacteristic, complemented
34#16839912C411yescharacteristic, complemented
35#16839905C411yescharacteristic, complemented
36#16839905C411yescharacteristic, complemented
37#16839900C411yescharacteristic, complemented
38#16839895C411yescharacteristic, complemented
39#16839881—24no—
40#16839876—24no—
41#16839840—21no—
42#16839840—21no—
43#16839834—21no—
44#16839834—21no—
45C2×#14519712C2211yescharacteristic, complemented
46C2×#14519712C2211yescharacteristic, complemented
47#16839789C2211yescharacteristic, complemented
48C2×#14519705C2211yescharacteristic
49C2×#14519705C2211yescharacteristic
50C2×#14519705C2211yescharacteristic
51C2×#14519705C2211yescharacteristic
52#16839756C2211yescharacteristic
53#16839756C2211yescharacteristic
54#16839729C2211yescharacteristic, complemented
55#16839726C2211yescharacteristic
56C2×C22⋊#92418C2211yescharacteristic
57#16839718C2211yescharacteristic, complemented
58C2×#14519688C2211yescharacteristic, complemented
59C2×C4×#92418C2211yescharacteristic, complemented
60#16839526C2211yescharacteristic, complemented
61#16839526C2211yescharacteristic, complemented
62#16839517C2211yescharacteristic, complemented
63#16839517C2211yescharacteristic, complemented
64C22×M16×C61C2211yescharacteristic
65C61×#525C2211yescharacteristic
66C2×#104×C61C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic, complemented
68C4×C22⋊C4×C61C2211yescharacteristic
69C61×#339C2211yescharacteristic, complemented
70C61×#339C2211yescharacteristic, 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
81C22×Dic122C2×C411yescharacteristic
82C22×D244C2×C411yescharacteristic
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85#14519797—22no—
86#14519797—22no—
87#14519797—22no—
88#14519797—22no—
89C2×#11758202C2×C411yescharacteristic
90C2×#11758202C2×C411yescharacteristic
91C2×#11758200C2×C411yescharacteristic
92C2×#11758200C2×C411yescharacteristic
93C2×#11758201C2×C411yescharacteristic
94C2×#11758201C2×C411yescharacteristic
95C2×#11758199C2×C411yescharacteristic
96C2×#11758199C2×C411yescharacteristic
97#14519785—22no—
98#14519785—22no—
99#14519785—22no—
100#14519785—22no—
101#14519785—22no—
102#14519785—22no—
103#14519785D414yescomplemented
104#14519785D414yescomplemented
105#14519784—22no—
106#14519784—22no—
107#14519783—28no—
108#14519783—28no—
109C2×#11758194—22no—
110C2×#11758194—22no—
111C2×#11758194—21no—
112C2×#11758194D411yescharacteristic
113C2×#11758194D411yescharacteristic
114C2×#11758194D411yescharacteristic
115C2×#11758194D411yescharacteristic
116C2×#11758194C2311yescharacteristic
117C2×#11758194C2311yescharacteristic
118C2×#11758189—21no—
119C2×#11758189—21no—
120C2×#11758189—21no—
121C2×#11758189—21no—
122M16×D61—28no—
123M16×D61—28no—
124C22×#92418—21no—
125C22×#92418C2311yescharacteristic
126C22×#92418C2311yescharacteristic
127C22×#92418C2311yescharacteristic
128C22×#92418C2311yescharacteristic
129C2×C8×D61—21no—
130C2×C8×D61—21no—
131C2×C8×D61—21no—
132C2×C8×D61—21no—
133#14519712—22no—
134#14519712—22no—
135C4⋊#92418—21no—
136C4⋊#92418—21no—
137#14519705—22no—
138#14519705—22no—
139#14519705—22no—
140#14519705—22no—
141#14519700C2×C411yescharacteristic
142#14519700C2×C411yescharacteristic
143#14519700C2×C411yescharacteristic
144#14519700C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519697C2×C411yescharacteristic
148#14519697C2×C411yescharacteristic
149C22⋊#92418—21no—
150C22⋊#92418—21no—
151C22⋊#92418—21no—
152C22⋊#92418—21no—
153C22⋊#92418C2×C411yescharacteristic
154C22⋊#92418C2×C411yescharacteristic
155C22⋊#92418C2×C411yescharacteristic
156C22⋊#92418C2×C411yescharacteristic
157#14519688—22no—
158#14519688—21no—
159C4×#92418—22no—
160C4×#92418—21no—
161C2×#41×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C2×M16×C61—21no—
164C2×M16×C61—22no—
165C2×M16×C61—22no—
166C2×M16×C61C2311yescharacteristic
167C2×M16×C61C2311yescharacteristic
168C22×C8×C61—21no—
169#123×C61—21no—
170C22⋊Q8×C61C2×C411yescharacteristic
171C22⋊Q8×C61C2×C411yescharacteristic
172#121×C61C2×C411yescharacteristic
173#121×C61C2×C411yescharacteristic
174#120×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177#117×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C42×C61C2311yescharacteristic
180C2×C42×C61C2311yescharacteristic
181#104×C61—22no—
182#104×C61—22no—
183#95×C61—21no—
184C24×C61#4111yescharacteristic
185C23×D61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61#4111yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C22×Dic61—21no—
215#11758222—24no—
216#11758222—24no—
217#11758222—24no—
218#11758222—24no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—21no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222C2×D412yes—
228#11758222C2×D412yes—
229#11758222#4112yes—
230#11758222#4112yes—
231C2×D244—21no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244C22×C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×Dic122—21no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—24no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61C2×D412yes—
251M16×C61C2×D412yes—
252C2×C8×C61—24no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—42no—
265C42×C61—21no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269C42×C61—21no—
270#11758202—22no—
271#11758202—22no—
272#11758201—22no—
273#11758201—22no—
274#11758200—22no—
275#11758200—22no—
276#11758199—22no—
277#11758199—22no—
278#11758194—22no—
279#11758194—22no—
280#11758194—22no—
281#11758194—22no—
282#11758194—21no—
283#11758194—21no—
284#11758194—21no—
285#11758194—21no—
286#11758194—42no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—42no—
296C2×#92418C22×C411yescharacteristic
297C2×#92418C22×C411yescharacteristic
298C2×#92418C22×C411yescharacteristic
299C2×#92418C22×C411yescharacteristic
300C2×#92418C2×D411yescharacteristic
301C2×#92418C2×D411yescharacteristic
302C2×#92418C2×D411yescharacteristic
303C2×#92418C2×D412yes—
304C2×#92418C2×D411yescharacteristic
305C2×#92418C2×D412yes—
306#11758189—24no—
307#11758189—24no—
308#11758189—24no—
309#11758189—24no—
310C8×D61—24no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—24no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61C4×D411yescharacteristic
320C23×C61C4×D411yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—24no—
325C22×D61—81no—
326C22×D61—81no—
327Q8×C61—21no—
328Q8×C61—21no—
329D4×C61—21no—
330D4×C61—21no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—81no—
334D4×C61—81no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—22no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61C4×D411yescharacteristic
357C2×C4×C61C4×D411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C2×#4111yescharacteristic
363C2×C4×C61C2×#4111yescharacteristic
364C22⋊D61—24no—
365C22⋊D61—24no—
366C22⋊D61—22no—
367C22⋊D61—22no—
368C22⋊D61—22no—
369C22⋊D61—22no—
370C2×Dic61—24no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373D244—24no—
374D244—21no—
375D244—21no—
376D244C4×D412yes—
377D244C4×D412yes—
378C4×D61—24no—
379C4×D61—24no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384Dic122—24no—
385Dic122—21no—
386Dic122—21no—
387Dic122C4×D412yes—
388Dic122C4×D412yes—
389C8×C61—22no—
390C8×C61—22no—
391#92418—21no—
392#92418—21no—
393#92418—21no—
394#92418—21no—
395#92418—21no—
396#92418—21no—
397#92418—41no—
398#92418—41no—
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—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61C2×C4×D411yescharacteristic
416C22×C61#52511yescharacteristic
417C22×C61#52511yescharacteristic
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—84no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—42no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—81no—
432C4×C61C2×C4×D411yescharacteristic
433C4×C61C2×C4×D411yescharacteristic
434C4×C61C2×#12011yescharacteristic
435C4×C61#52511yescharacteristic
436Dic61—22no—
437Dic61—22no—
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871D6111yescharacteristic, complemented
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—41no—
456C2×C61—41no—
457C2×C61—81no—
458C2×C61C4×#12011yescharacteristic
459C2×C61#295611yescharacteristic
460C2×C61#295711yescharacteristic
461D61—42no—
462D61—42no—
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#525C2×D6111yescharacteristic
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, complemented
502C2×#104C2×D6111yescharacteristic, complemented
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4C2×D6111yescharacteristic
512#341—611no—
513#341—611no—
514#339C2×D6111yescharacteristic, complemented
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—1222no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1221no—
528C2×#41—1221no—
529C2×#41C22×D6111yescharacteristic
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—611no—
567C2×M16—611no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1221no—
571C2×M16—1221no—
572C2×M16—1222no—
573C2×M16—1222no—
574C2×M16—1221no—
575C2×M16—1228no—
576C2×M16—1228no—
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—611no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8—1221no—
588C22×C8—1221no—
589#123—21no—
590C22⋊Q8C4×D6111yescharacteristic
591C22⋊Q8C4×D6111yescharacteristic
592#121C4×D6111yescharacteristic
593#121C4×D6111yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C22×D6111yescharacteristic
598C2×C22⋊C4—21no—
599C2×C42C22×D6111yescharacteristic
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—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—21no—
632C24—1221no—
633C24#1175822411yescharacteristic
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—612no—
639#41—612no—
640#41—612no—
641#41—612no—
642#41—1222no—
643#41—1222no—
644#41—1222no—
645#41—1222no—
646#41—1224no—
647#41—1224no—
648#41—1224no—
649#41—1224no—
650#41—1221no—
651#41—1221no—
652#41—1221no—
653#41—1221no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8—1221no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—1224no—
683C22×C4—1224no—
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#1175822411yescharacteristic
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—1224no—
707M16—1224no—
708M16—1224no—
709M16—1224no—
710M16—1222no—
711M16—1222no—
712M16—1222no—
713M16—1222no—
714M16—1221no—
715M16—1221no—
716M16—1221no—
717M16—1221no—
718M16—2442no—
719M16D4×D6112yes—
720M16D4×D6112yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—612no—
725C2×C8—612no—
726C2×C8—611no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—611no—
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—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—2442no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C2×C4×D6111yescharacteristic
750C4⋊C4C2×C4×D6111yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—1224no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23#1451973711yescharacteristic
773C23#1451973711yescharacteristic
774C23C2×#1175822411yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—612no—
778Q8—612no—
779Q8—1224no—
780Q8—1221no—
781Q8—1221no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—41no—
786D4—81no—
787D4—81no—
788D4—612no—
789D4—612no—
790D4—1224no—
791D4—1224no—
792D4—1224no—
793D4—1222no—
794D4—1222no—
795D4—1222no—
796D4—1222no—
797D4—1221no—
798D4—1221no—
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—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—1224no—
821C2×C4—1224no—
822C2×C4—1224no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4#1451973711yescharacteristic
830C2×C4#1451973711yescharacteristic
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—22no—
838C8—22no—
839C8—612no—
840C8—612no—
841C8—1221no—
842C8—1221no—
843C8—1221no—
844C8—1221no—
845C8—1221no—
846C8—1221no—
847C8—2441no—
848C8—2441no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—1222no—
863C22—1222no—
864C22—4884no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C2×#1451973711yescharacteristic
870C22#1684027211yescharacteristic
871C22#1684027211yescharacteristic
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—81no—
879C4—1222no—
880C4—1222no—
881C4C4×D4×D6111yescharacteristic
882C4C4×D4×D6111yescharacteristic
883C4#120×D6111yescharacteristic
884C4#1684027011yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—2442no—
891C2—2442no—
892C2#2144832411yescharacteristic
893C2#2145472511yescharacteristic
894C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839881C2semidirect
4. C2×#16839876C2semidirect
5. #21454523C2semidirect
6. #21446143C2semidirect
7. #21446143C2semidirect
8. #21446095C2semidirect
9. #21446095C2semidirect
10. #21446024C2semidirect
11. #21445764C2semidirect
12. #21445660C2semidirect
13. #21445653C2semidirect
14. #21445603C2semidirect
15. C61×#1871C2semidirect
25. C2×#14519784C22semidirect
31. #16839922C4semidirect
32. #16839922C4semidirect
33. #16839917C4semidirect
34. #16839912C4semidirect
35. #16839905C4semidirect
36. #16839905C4semidirect
37. #16839900C4semidirect
38. #16839895C4semidirect
45. C2×#14519712C22semidirect
46. C2×#14519712C22semidirect
47. #16839789C22semidirect
54. #16839729C22semidirect
57. #16839718C22semidirect
58. C2×#14519688C22semidirect
59. C2×C4×#92418C22semidirect
60. #16839526C22semidirect
61. #16839526C22semidirect
62. #16839517C22semidirect
63. #16839517C22semidirect
66. C2×#104×C61C22semidirect
67. C2×#104×C61C22semidirect
69. C61×#339C22semidirect
70. C61×#339C22semidirect
103. #14519785D4semidirect
104. #14519785D4semidirect
445. #1871D61semidirect
501. C2×#104C2×D61semidirect
502. C2×#104C2×D61semidirect
514. #339C2×D61semidirect
515. #339C2×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
#214550352
C2×#168398812
C2×#168398762
#214545232
#214461432
#214460952
#214460242
#214457642
#214456602
#214456532
#214456032
C61×#18712
#2146861