Finite Group Databasebeta

← #29695574

Subgroups — #29695574

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840409C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839759C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446634C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840409—24no—
20#16840409C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519745—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic, complemented
29C2×#14519735C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31#16839833—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839765—24no—
34#16839759—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic, complemented
46C2×#14519689C2211yescharacteristic
47C2×#14519687C2211yescharacteristic, complemented
48#16839662—21no—
49#16839656—21no—
50#16839651—21no—
51#16839631C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54#16839613—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61D411yescharacteristic
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yes—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519764—22no—
91#14519764C2×C414yes—
92#14519759—28no—
93#14519757—22no—
94#14519757C2×C414yes—
95#14519748—28no—
96#14519745—28no—
97#14519739—22no—
98#14519739C2×C414yes—
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519736—22no—
102#14519736—41no—
103#14519735—22no—
104#14519735—41no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196D411yescharacteristic
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C22⋊C4×D61—28no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519702—22no—
127#14519702—22no—
128#14519700—41no—
129#14519700—41no—
130#14519699—22no—
131#14519699D414yescomplemented
132#14519698—22no—
133#14519698—41no—
134#14519697—22no—
135#14519697—22no—
136C22⋊#92418—22no—
137#14519689—22no—
138#14519687—22no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#121×C61—22no—
150#121×C61C2×C414yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61C22×C412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61C22⋊C414yes—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205D4×D61—28no—
206D4×D61—44no—
207D4×D61—44no—
208D4×D61—44no—
209#11758222—28no—
210#11758222—44no—
211#11758222—44no—
212#11758222—44no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244C22×C412yes—
217C2×D244C2×D412yes—
218C2×D244#4112yes—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—81no—
228C2×C4×D61—81no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C2×D412yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—44no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C22×C412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—81no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—42no—
255C22⋊Dic61C22⋊C414yes—
256#11758198—24no—
257#11758198—24no—
258#11758198—42no—
259#11758198—81no—
260#11758198C22⋊C414yes—
261C4⋊Dic61—21no—
262C4⋊Dic61—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C2×D412yes—
266#11758196—42no—
267#11758196—81no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—42no—
271C4×Dic61—42no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280#11758189—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—48no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—84no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61C2×C22⋊C412yes—
338C2×C4×C61C23×C411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—44no—
345C22⋊D61—48no—
346C22⋊D61—48no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365D244—22no—
366D244—22no—
367D244—22no—
368D244C4×D414yes—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—48no—
374C4×D61—84no—
375Dic122—22no—
376Dic122—22no—
377Dic122—41no—
378Dic122—41no—
379C8×C61—22no—
380C8×C61—41no—
381#92418—41no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C22×C22⋊C411yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61#54611yescharacteristic
401C22×C61#57511yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C2×D61—22no—
406C2×D61—24no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—41no—
414C2×D61—42no—
415C2×D61—41no—
416C2×D61—42no—
417C2×D61—41no—
418C2×D61—42no—
419C2×D61—816no—
420C4×C61—22no—
421C4×C61—42no—
422C4×C61—81no—
423C4×C61—81no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#51811yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
432Dic61—42no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
437C2×#416—611no—
438#2354—611no—
439#1983—611no—
440#1959—611no—
441#1894—611no—
442#1893D6111yescharacteristic, complemented
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—42no—
450C2×C61—82no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#289611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#326711yescharacteristic
455C2×C61#326811yescharacteristic
456C2×C61#331111yescharacteristic
457C2×C61#331911yescharacteristic
458D61—42no—
459D61—44no—
460C22×#41—611no—
461C23×D4—611no—
462C22×M16—611no—
463C23×C8C2×D6111yescharacteristic, complemented
464#546—618no—
465#546—1224no—
466C2×#124—611no—
467C2×#123—1221no—
468C2×C22⋊Q8—611no—
469C2×#121—1221no—
470C2×#121C2×D6111yescharacteristic
471C2×#120—1221no—
472C2×C4×D4—611no—
473C2×C4×D4—611no—
474C2×#117—611no—
475C2×#117—611no—
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380C2×D6111yescharacteristic, complemented
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340C2×D6111yescharacteristic, complemented
507#340C2×D6111yescharacteristic, complemented
508C61#2242411yescharacteristic, complemented, Sylow
509C25—1221no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8—611no—
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—614no—
520C22×D4—611no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1221no—
526C22×D4—2441no—
527C22×D4—2441no—
528C22×D4C22×D6111yescharacteristic
529C23×C4—611no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4C22×D6111yescharacteristic
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543#124—614no—
544#124—1222no—
545#123—1228no—
546C22⋊Q8—614no—
547C22⋊Q8—1222no—
548#121—22no—
549#121—1228no—
550#121C4×D6114yes—
551#120—1228no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1222no—
556#117—1222no—
557#117—1222no—
558#117—2441no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42—1221no—
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—22no—
591#102—41no—
592#102—614no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—1222no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—21no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—611no—
606C24—1224no—
607C24—1221no—
608C24—4881no—
609C24—4881no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24D4×D6111yescharacteristic
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—614no—
634C2×D4—612no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—1224no—
638C2×D4—1228no—
639C2×D4—1224no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2441no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4C2×C4×D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1224no—
673C22×C4—1221no—
674C22×C4—4881no—
675C22×C4—4881no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4C2×C4×D6112yes—
679C22×C4D4×D6112yes—
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—44no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8D4×D6112yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—614no—
702C4⋊C4—612no—
703C4⋊C4—1224no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—4881no—
708C4⋊C4—2442no—
709C4⋊C4C2×C4×D6112yes—
710C22⋊C4—24no—
711C22⋊C4—81no—
712C22⋊C4—614no—
713C22⋊C4—614no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C42—612no—
722C42—612no—
723C42—2442no—
724C42—2442no—
725C42—2442no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—612no—
740C23—1222no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1222no—
747C23—1221no—
748C23—1222no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—2448no—
755C23—2448no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—1222no—
763Q8—1222no—
764Q8—2441no—
765Q8—2441no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—84no—
771D4—614no—
772D4—1222no—
773D4—1222no—
774D4—1222no—
775D4—2444no—
776D4—2448no—
777D4—2448no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—612no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
809C2×C4—2448no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4C22⋊C4×D6112yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4#41×D6111yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982311yescharacteristic
824C8—22no—
825C8—41no—
826C8—2441no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—1222no—
843C22—1222no—
844C22—1224no—
845C22—1222no—
846C22—48816no—
847C22—2442no—
848C22—2441no—
849C22—2442no—
850C22—2441no—
851C22—2442no—
852C22—2441no—
853C22—2442no—
854C22—2441no—
855C22—2442no—
856C22—2442no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22#1684039611yescharacteristic
859C22#1684040111yescharacteristic
860C22#1684055911yescharacteristic
861C22#1684055911yescharacteristic
862C22#1684056311yescharacteristic
863C22#1684056811yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4—1222no—
869C4—1222no—
870C4—1222no—
871C4—4881no—
872C4—2442no—
873C4—2442no—
874C4C4×D4×D6111yescharacteristic
875C4#1684023411yescharacteristic
876C4#1684039411yescharacteristic
877C4#1684040411yescharacteristic
878C2—42no—
879C2—82no—
880C2—2442no—
881C2—2444no—
882C2#2144863711yescharacteristic
883C2#2145433411yescharacteristic
884C2#2145434011yescharacteristic
885C2#2145734111yescharacteristic
886C2#2145735611yescharacteristic
887C2#2145786111yescharacteristic
888C2#2145798111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839759C2semidirect
5. #21448763C2semidirect
6. #21446750C2semidirect
7. #21446634C2semidirect
8. #21446251C2semidirect
9. #21446142C2semidirect
10. #21446130C2semidirect
11. #21445818C2semidirect
12. #21445757C2semidirect
13. #21445748C2semidirect
14. #21445643C2semidirect
15. C61×#1893C2semidirect
20. #16840409C4semidirect
28. C2×#14519736C22semidirect
32. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
45. C2×C22⋊#92418C22semidirect
47. C2×#14519687C22semidirect
51. #16839631C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. C23×C8×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
131. #14519699D4semidirect
442. #1893D61semidirect
463. C23×C8C2×D61semidirect
501. #380C2×D61semidirect
506. #340C2×D61semidirect
507. #340C2×D61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168404092
C2×#168398332
C2×#168397652
C2×#168397592
#214487632
#214467502
#214466342
#214462512
#214461422
#214461302
#214458182
#214457572
#214457482
#214456432
C61×#18932
#2242461