Finite Group Databasebeta

← #29695544

Subgroups — #29695544

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840430C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839759C211yesmaximal, characteristic, complemented
5#21448741C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21445833C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445648C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840430—24no—
20#16840430C418yescomplemented
21C2×#14519773—21no—
22C2×#14519773C2211yescharacteristic
23C2×#14519752C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519749—21no—
26C2×#14519742C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519736C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839833—24no—
32C2×#14519706C2211yescharacteristic
33#16839760—24no—
34#16839759—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519687C2211yescharacteristic
48#16839650—21no—
49#16839644—21no—
50#16839638—21no—
51#16839627C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839609—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C414yescomplemented
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—41no—
74C2×#11758224—41no—
75C2×#11758224C2×C414yes—
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61D411yescharacteristic
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519773—28no—
94#14519773—22no—
95#14519773C2×C414yescomplemented
96#14519752—22no—
97#14519752C2×C414yes—
98#14519750—28no—
99#14519749—28no—
100#14519742—22no—
101#14519742C2×C414yescomplemented
102C4×C22⋊D61C2×C414yes—
103C4×C22⋊D61D414yes—
104#14519737—28no—
105#14519736—22no—
106#14519736—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C4⋊C4×D61—22no—
113C4⋊C4×D61—41no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519702—22no—
125#14519702D414yescomplemented
126#14519700—22no—
127#14519700—22no—
128#14519699—22no—
129#14519699—22no—
130#14519698—22no—
131#14519698—41no—
132#14519697—41no—
133#14519697—41no—
134C22⋊#92418—22no—
135#14519689—22no—
136#14519687—22no—
137#14519684—21no—
138#14519684—21no—
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×C414yescomplemented
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×D61C2×D411yescharacteristic
163C2×D4×C61—24no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C2×D4×C61C22×C412yes—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—41no—
188C2×C22⋊D61—41no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61C22⋊C414yes—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—24no—
201C22×Dic61—21no—
202C22×Dic61—42no—
203C22×Dic61—42no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207#11758224—28no—
208#11758224—44no—
209#11758224—44no—
210#11758224—44no—
211#11758222—28no—
212#11758222—44no—
213#11758222—44no—
214#11758222—44no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—24no—
221C2×D244—81no—
222C2×D244—81no—
223C2×D244C22×C412yes—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—81no—
234C2×C4×D61C22×C412yes—
235C2×C4×D61C2×D412yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122#4112yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—44no—
248C2×C8×C61C2×D412yes—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22×C412yes—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—81no—
257C22⋊Dic61—42no—
258C22⋊Dic61C22⋊C414yes—
259#11758198—24no—
260#11758198—42no—
261#11758198C22⋊C414yes—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C2×D412yes—
266#11758196—24no—
267#11758196—42no—
268#11758196C22⋊C414yes—
269C4×Dic61—24no—
270C4×Dic61—42no—
271C4×Dic61—81no—
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—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61C2×C22⋊C412yes—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—84no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—44no—
338C22⋊D61—48no—
339C22⋊D61—48no—
340C22⋊D61—48no—
341C22⋊D61—84no—
342C2×Dic61—22no—
343C2×Dic61—21no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—22no—
352C2×Dic61—48no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61C2×C22⋊C412yes—
359C2×Dic61C2×C22⋊C412yes—
360C2×Dic61C2×C22⋊C412yes—
361D244—22no—
362D244—22no—
363D244—41no—
364D244—41no—
365D244—84no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—48no—
371C4×D61—84no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122C4×D414yes—
376C8×C61—22no—
377C8×C61—41no—
378#92418—41no—
379#92418—41no—
380#22422—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#57511yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C2×D61—81no—
416C4×C61—22no—
417C4×C61—42no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61C2×C4×D411yescharacteristic
421C4×C61#51811yescharacteristic
422C4×C61D4211yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—24no—
425Dic61—22no—
426Dic61—22no—
427Dic61—22no—
428Dic61—42no—
429Dic61—81no—
430C2×#550—611no—
431C2×#435—611no—
432C2×#417—611no—
433C2×#416—611no—
434#2352—611no—
435#1982—611no—
436#1961—611no—
437#1895—611no—
438#1893D6111yescharacteristic, complemented
439#1875—611no—
440#1874—611no—
441#1805—611no—
442#1788—611no—
443#1788—611no—
444#1763—611no—
445C2×C61—42no—
446C2×C61—82no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61#289611yescharacteristic
449C2×C61#289711yescharacteristic
450C2×C61#326811yescharacteristic
451C2×C61#327111yescharacteristic
452C2×C61#330911yescharacteristic
453C2×C61#331711yescharacteristic
454D61—42no—
455D61—82no—
456C22×#41—611no—
457C22×#41—611no—
458C22×M16—611no—
459C23×C8C2×D6111yescharacteristic
460#550—618no—
461#550—1224no—
462C2×#127—611no—
463C2×#127—1221no—
464C2×#121—611no—
465C2×#121—1221no—
466C2×#121—1221no—
467C2×#121C2×D6111yescharacteristic
468C2×C4×Q8—611no—
469C2×C4×D4—611no—
470C2×C4×D4—1221no—
471C2×#117—611no—
472C22×C4⋊C4—611no—
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102C2×D6111yescharacteristic
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382—611no—
496#380—611no—
497#380C2×D6111yescharacteristic
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340C2×D6111yescharacteristic
503#340C2×D6111yescharacteristic
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—614no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4C22×D6111yescharacteristic
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8C22×D6111yescharacteristic
541C22×C8C22×D6111yescharacteristic
542#127—614no—
543#127—1222no—
544#127—1228no—
545#121—22no—
546#121—614no—
547#121—1228no—
548#121—1228no—
549#121—1222no—
550#121C4×D6114yescomplemented
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1228no—
556#117—1222no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—2441no—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C4⋊C8—1222no—
580#103—614no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#102—22no—
585#102—41no—
586#102—1222no—
587#102—1222no—
588#102—1222no—
589#102—2441no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—1222no—
593C22⋊C8—1222no—
594#97—1222no—
595#95—21no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600C24—21no—
601C24—611no—
602C24—1221no—
603C24D4×D6111yescharacteristic
604#41—1228no—
605#41—1228no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—612no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—2441no—
643C2×D4—2441no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1224no—
671C22×C4—1221no—
672C22×C4—4881no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4C2×C4×D6112yes—
680C22×C4D4×D6112yes—
681C22×C4D4×D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683M16—2444no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—44no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8D4×D6112yes—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—614no—
703C4⋊C4—612no—
704C4⋊C4—1224no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—2442no—
709C4⋊C4C2×C4×D6112yes—
710C22⋊C4—24no—
711C22⋊C4—81no—
712C22⋊C4—614no—
713C22⋊C4—614no—
714C22⋊C4—1224no—
715C22⋊C4—2442no—
716C22⋊C4—2442no—
717C42—612no—
718C42—612no—
719C42—1224no—
720C42—4881no—
721C42—2442no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—612no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1222no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23—2441no—
749C23C22⋊C4×D6112yes—
750C23C2×D4×D6111yescharacteristic
751Q8—614no—
752Q8—1222no—
753Q8—1222no—
754Q8—1222no—
755D4—22no—
756D4—22no—
757D4—41no—
758D4—41no—
759D4—84no—
760D4—1222no—
761D4—1222no—
762D4—4884no—
763D4—4884no—
764D4—2444no—
765D4—2448no—
766D4—2448no—
767D4—2448no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—4884no—
803C2×C4—2448no—
804C2×C4—2448no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4C22⋊C4×D6112yes—
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4#41×D6111yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982311yescharacteristic
817C8—22no—
818C8—41no—
819C8—2441no—
820C8—2441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22—2441no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22C2×C22⋊C4×D6111yescharacteristic
850C22#1684039611yescharacteristic
851C22#1684040111yescharacteristic
852C22#1684055911yescharacteristic
853C22#1684055911yescharacteristic
854C22#1684056311yescharacteristic
855C22#1684056811yescharacteristic
856C4—22no—
857C4—42no—
858C4—81no—
859C4—81no—
860C4—1222no—
861C4—1222no—
862C4—1224no—
863C4—1222no—
864C4—4881no—
865C4—2442no—
866C4C4×D4×D6111yescharacteristic
867C4#1684023411yescharacteristic
868C4#1684039411yescharacteristic
869C4#1684040411yescharacteristic
870C2—42no—
871C2—82no—
872C2—4882no—
873C2—2442no—
874C2#2144863711yescharacteristic
875C2#2145433411yescharacteristic
876C2#2145434011yescharacteristic
877C2#2145735611yescharacteristic
878C2#2145740111yescharacteristic
879C2#2145783111yescharacteristic
880C2#2145795111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840430C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22422
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×#16839760C2semidirect
4. C2×#16839759C2semidirect
5. #21448741C2semidirect
6. #21446744C2semidirect
7. #21446641C2semidirect
8. #21446256C2semidirect
9. #21446142C2semidirect
10. #21446135C2semidirect
11. #21445833C2semidirect
12. #21445757C2semidirect
13. #21445756C2semidirect
14. #21445648C2semidirect
15. C61×#1893C2semidirect
20. #16840430C4semidirect
69. C2×#11758222C2×C4semidirect
95. #14519773C2×C4semidirect
101. #14519742C2×C4semidirect
125. #14519702D4semidirect
150. #121×C61C2×C4semidirect
438. #1893D61semidirect
504. C61#22422semidirect
550. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404302
C2×#168398332
C2×#168397602
C2×#168397592
#214487412
#214467442
#214466412
#214462562
#214461422
#214461352
#214458332
#214457572
#214457562
#214456482
C61×#18932
#2242261