Finite Group Databasebeta

← #29689385

Subgroups — #29689385

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840326C211yesmaximal, characteristic
2C2×#16839820C211yesmaximal, characteristic, complemented
3#21448426C211yesmaximal, characteristic, complemented
4#21446748C211yesmaximal, characteristic, complemented
5#21446748C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446744C211yesmaximal, characteristic, complemented
8#21446641C211yesmaximal, characteristic, complemented
9#21446632C211yesmaximal, characteristic, complemented
10#21446627C211yesmaximal, characteristic, complemented
11#21446623C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17#16840326—24no—
18#16840326C418yescomplemented
19C2×#14519773C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21C2×#14519766C2211yescharacteristic
22C2×#14519766C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751—21no—
25C2×#14519745—21no—
26C2×#14519745—21no—
27C2×#14519736C2211yescharacteristic
28#16839820—24no—
29C2×#14519706C2211yescharacteristic, complemented
30C2×#14519706C2211yescharacteristic, complemented
31C2×#14519701C2211yescharacteristic, complemented
32C2×#14519701C2211yescharacteristic, complemented
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×#14519687C2211yescharacteristic, complemented
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839656—21no—
47#16839650—21no—
48#16839647—21no—
49#16839645—21no—
50#16839631C2211yescharacteristic, complemented
51#16839627C2211yescharacteristic, complemented
52#16839622C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C4⋊C4×Dic61C2211yescharacteristic, complemented
55C22×#41×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic, complemented
57C2×#103×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic, complemented
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C24×D61—21no—
63C22×D244—21no—
64C22×D244—22no—
65C22×D244—41no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2×C414yes—
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519773—22no—
79#14519773—22no—
80#14519773C2×C414yes—
81#14519773C2×C414yes—
82#14519766—22no—
83#14519766—22no—
84#14519766C2×C414yes—
85#14519766C2×C414yes—
86#14519751—28no—
87#14519751—28no—
88#14519745—28no—
89#14519745—28no—
90#14519736C2×C414yes—
91#14519736D414yes—
92C2×C4⋊Dic61D411yescharacteristic
93C2×C4⋊Dic61D411yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61D411yescharacteristic
100C2×C22⋊Dic61D411yescharacteristic
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519706—22no—
110#14519706—22no—
111#14519701—41no—
112#14519701—41no—
113#14519699—41no—
114#14519699—41no—
115#14519699—41no—
116#14519699—41no—
117#14519698—41no—
118#14519698—41no—
119#14519697—41no—
120#14519697—41no—
121#14519697—41no—
122#14519697—41no—
123C22⋊#92418—22no—
124#14519687—22no—
125C8×Dic61—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C2×#41×C61—22no—
132C2×#41×C61—41no—
133C2×#41×C61—41no—
134C2×#41×C61—41no—
135C2×#41×C61—41no—
136C2×#41×C61C2×C414yes—
137C22×Q8×C61C2311yescharacteristic
138C22×D4×C61—21no—
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#103×C61—41no—
148#103×C61—41no—
149#102×C61—41no—
150#102×C61—41no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—24no—
158C23×D61—42no—
159C23×D61—42no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C23×D61—81no—
164#41×C61—44no—
165#41×C61—44no—
166#41×C61—44no—
167#41×C61—44no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61C22×C412yes—
174C2×D4×C61—24no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61C22×C412yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—81no—
202C2×C22⋊D61—81no—
203C2×C22⋊D61—81no—
204C2×C22⋊D61—81no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—24no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—44no—
227C2×D244—44no—
228C2×D244—42no—
229C2×D244—42no—
230C2×D244—44no—
231C2×D244—44no—
232C2×D244C22×C412yes—
233C2×D244C22×C412yes—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C22⋊C4×C61—81no—
245C22⋊Dic61—81no—
246C22⋊Dic61C22⋊C414yes—
247C22⋊Dic61C22⋊C414yes—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61C22⋊C414yes—
257C4⋊Dic61C22⋊C414yes—
258#11758196—81no—
259#11758196—81no—
260C4×Dic61—81no—
261C4×Dic61—81no—
262C4×Dic61C22×C412yes—
263C4×Dic61C22×C412yes—
264C4×Dic61C2×D412yes—
265C4×Dic61C2×D412yes—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61C2×C22⋊C412yes—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—48no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61—84no—
305C22×D61—84no—
306C22×D61—84no—
307C22×D61—84no—
308Q8×C61—22no—
309Q8×C61—22no—
310Q8×C61—41no—
311Q8×C61—41no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—48no—
315D4×C61—41no—
316D4×C61—41no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—48no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C2×C22⋊C412yes—
334C2×C4×C61C23×C411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C2×C4×C61H(5,𝔽2)11yescharacteristic
340C22⋊D61—84no—
341C22⋊D61—84no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—41no—
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—
361C2×Dic61C2×C22⋊C412yes—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—48no—
367D244—41no—
368D244—41no—
369D244—41no—
370D244—41no—
371C8×C61—41no—
372C8×C61—41no—
373#92418—41no—
374#92418—41no—
375#21813—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C22×C22⋊C411yescharacteristic
391C22×C61#53511yescharacteristic
392C22×C61#53511yescharacteristic
393C22×C61#57611yescharacteristic
394C22×C61#57611yescharacteristic
395C22×C61#57711yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—816no—
404C2×D61—81no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C4×C61—22no—
413C4×C61—42no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61#51811yescharacteristic
417C4×C61#51811yescharacteristic
418C4×C61#53511yescharacteristic
419C4×C61#53511yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—22no—
423Dic61—22no—
424Dic61—81no—
425Dic61—81no—
426C2×#535—611no—
427C2×#433—611no—
428#2314—611no—
429#1983—611no—
430#1983—611no—
431#1982—611no—
432#1982—611no—
433#1961—611no—
434#1959—611no—
435#1958—611no—
436#1957—611no—
437#1788—611no—
438#1788D6111yescharacteristic, complemented
439#1786—611no—
440#1786—611no—
441C2×C61—42no—
442C2×C61—82no—
443C2×C61#230911yescharacteristic
444C2×C61#289711yescharacteristic
445C2×C61#289711yescharacteristic
446C2×C61#322011yescharacteristic
447C2×C61#322211yescharacteristic
448C2×C61#322411yescharacteristic
449C2×C61#322411yescharacteristic
450D61—82no—
451D61—82no—
452C22×#41C2×D6111yescharacteristic
453C23×D4—611no—
454#535—618no—
455#535—1224no—
456C2×#127—611no—
457C2×#127—611no—
458C2×#124—611no—
459C2×#124—611no—
460C2×#121—1221no—
461C2×#121—1221no—
462C2×#120—1221no—
463C2×#120—1221no—
464C2×#117—611no—
465#433—1224no—
466C2×C4⋊C8—611no—
467C2×C4⋊C8—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103C2×D6111yescharacteristic, complemented
471C2×#103C2×D6111yescharacteristic, complemented
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102C2×D6111yescharacteristic, complemented
483C2×#102C2×D6111yescharacteristic, complemented
484C2×C22⋊C8—611no—
485C2×C22⋊C8C2×D6111yescharacteristic
486C2×#97—611no—
487C2×C4×C8—611no—
488#388—1221no—
489#388—1221no—
490#387—1221no—
491#387—1221no—
492#384—611no—
493#382—611no—
494#380—611no—
495#380C2×D6111yescharacteristic
496C4×C4⋊C4—611no—
497C4×C4⋊C4—611no—
498C61#2181311yescharacteristic, complemented, Sylow
499C25—1221no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41C4×D6114yes—
506C22×Q8C22×D6111yescharacteristic
507C22×D4—21no—
508C22×D4—614no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4—1221no—
516C22×D4—1222no—
517C22×D4—2441no—
518C22×D4—2441no—
519C22×D4—2441no—
520C22×D4—2441no—
521C22×D4C22×D6111yescharacteristic
522C23×C4—21no—
523C23×C4C22×D6111yescharacteristic
524C22×C8—611no—
525C22×C8—611no—
526C22×C8C22×D6111yescharacteristic
527C22×C8C22×D6111yescharacteristic
528#127—614no—
529#127—614no—
530#127—1222no—
531#127—1222no—
532#124—614no—
533#124—614no—
534#124—1222no—
535#124—1222no—
536#121—1228no—
537#121—1228no—
538#120—1228no—
539#120—1228no—
540#117—614no—
541#117—614no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C4⋊C4C22×D6111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42—1221no—
562C4⋊C8—1222no—
563C4⋊C8—1222no—
564#103—41no—
565#103—41no—
566#103—2441no—
567#103—2441no—
568#102—41no—
569#102—41no—
570#102—2441no—
571#102—2441no—
572#102—2441no—
573#102—2441no—
574#102—2441no—
575#102—2441no—
576#102—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580C22⋊C8—22no—
581C22⋊C8—1222no—
582#97—1222no—
583C4×C8—1222no—
584#95—21no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590C24—21no—
591C24—1224no—
592C24—1221no—
593C24—1221no—
594C24—4881no—
595C24—4881no—
596C24—4881no—
597C24—4881no—
598C24—2442no—
599C24—2442no—
600C24D4×D6111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×C4×D6112yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—612no—
620C2×D4—612no—
621C2×D4—1224no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1224no—
636C2×D4—4881no—
637C2×D4—4881no—
638C2×D4—4881no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4C2×C4×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4C2×C4×D6112yes—
668C22×C4D4×D6112yes—
669C22×C4D4×D6111yescharacteristic
670C22×C4C23×D6111yescharacteristic
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—614no—
688C4⋊C4—614no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—4881no—
694C4⋊C4—4881no—
695C22⋊C4—81no—
696C22⋊C4—614no—
697C22⋊C4—614no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—4881no—
703C42—612no—
704C42—612no—
705C42—612no—
706C42—612no—
707C42—4881no—
708C42—4881no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—1222no—
723C23—1222no—
724C23—4884no—
725C23—4884no—
726C23—4884no—
727C23—4884no—
728C23—4884no—
729C23—4884no—
730C23—2448no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23C22⋊C4×D6112yes—
744C23C2×D4×D6111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—41no—
748Q8—41no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—1222no—
755D4—1222no—
756D4—1222no—
757D4—1222no—
758D4—4884no—
759D4—4884no—
760D4—4884no—
761D4—4884no—
762D4—2448no—
763D4—2441no—
764D4—2441no—
765D4—2441no—
766D4—2441no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C22⋊C4×D6112yes—
802C2×C4C22×C4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982211yescharacteristic
807C2×C4#1451982211yescharacteristic
808C8—41no—
809C8—41no—
810C8—2441no—
811C8—2441no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—48816no—
827C22—4881no—
828C22—4881no—
829C22—4881no—
830C22—4881no—
831C22—4881no—
832C22—4881no—
833C22—4881no—
834C22—4881no—
835C22—2442no—
836C22—2442no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22C2×C22⋊C4×D6111yescharacteristic
842C22#1684032711yescharacteristic
843C22#1684032711yescharacteristic
844C22#1684056411yescharacteristic
845C22#1684056611yescharacteristic
846C22#1684056911yescharacteristic
847C22#1684057111yescharacteristic
848C4—22no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—1222no—
853C4—1222no—
854C4—1222no—
855C4—1222no—
856C4—4881no—
857C4—4881no—
858C4#1684023511yescharacteristic
859C4#1684023511yescharacteristic
860C4#1684032711yescharacteristic
861C4#1684032711yescharacteristic
862C2—42no—
863C2—82no—
864C2—4882no—
865C2—4882no—
866C2#2144840011yescharacteristic
867C2#2145434111yescharacteristic
868C2#2145434311yescharacteristic
869C2#2145686711yescharacteristic
870C2#2145688911yescharacteristic
871C2#2145691111yescharacteristic
872C2#2145691911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840326C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#21813
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839820C2semidirect
3. #21448426C2semidirect
4. #21446748C2semidirect
5. #21446748C2semidirect
6. #21446744C2semidirect
7. #21446744C2semidirect
8. #21446641C2semidirect
9. #21446632C2semidirect
10. #21446627C2semidirect
11. #21446623C2semidirect
12. #21445759C2semidirect
13. #21445751C2semidirect
14. #21445749C2semidirect
15. C61×#1788C2semidirect
18. #16840326C4semidirect
29. C2×#14519706C22semidirect
30. C2×#14519706C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519701C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
44. C2×#14519687C22semidirect
45. C2×C8×Dic61C22semidirect
50. #16839631C22semidirect
51. #16839627C22semidirect
53. C4⋊C4×Dic61C22semidirect
54. C4⋊C4×Dic61C22semidirect
56. C2×#103×C61C22semidirect
57. C2×#103×C61C22semidirect
58. C2×#102×C61C22semidirect
59. C2×#102×C61C22semidirect
438. #1788D61semidirect
470. C2×#103C2×D61semidirect
471. C2×#103C2×D61semidirect
482. C2×#102C2×D61semidirect
483. C2×#102C2×D61semidirect
498. C61#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#168403262
C2×#168398202
#214484262
#214467482
#214467442
#214466412
#214466322
#214466272
#214466232
#214457592
#214457512
#214457492
C61×#17882
#2181361