Finite Group Databasebeta

← #29717768

Subgroups — #29717768

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C2×#16840001C211yesmaximal, characteristic, complemented
3C2×#16839920C211yesmaximal, characteristic, complemented
4C2×#16839919C211yesmaximal, characteristic, complemented
5C22×#14519700C211yesmaximal, characteristic, complemented
6#21449264C211yesmaximal, characteristic
7#21447064C211yesmaximal, characteristic, complemented
8#21447025C211yesmaximal, characteristic, complemented
9#21446920C211yesmaximal, characteristic, complemented
10#21446830C211yesmaximal, characteristic, complemented
11#21446161C211yesmaximal, characteristic, complemented
12#21446109C211yesmaximal, characteristic
13#21446074C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840425—24no—
23#16840425—24no—
24C2×#14519776—21no—
25C2×#14519775C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519757C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519755—21no—
30C2×#14519754—21no—
31C2×#14519742C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×#14519737—21no—
34#16840001—24no—
35#16839920—24no—
36#16839919—24no—
37C2×#14519710C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700—24no—
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49#16839692—21no—
50#16839684—21no—
51#16839667C2211yescharacteristic
52#16839661C2211yescharacteristic
53#16839641—21no—
54#16839622—21no—
55#16839619C2211yescharacteristic
56#16839516C2211yescharacteristic
57#16839516C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—21no—
68C22×Dic122—22no—
69C22×Dic122—21no—
70C22×Dic122—41no—
71C22×Dic122—41no—
72C22×Dic122D414yes—
73C22×Dic122C2311yescharacteristic
74C22×Dic122C2311yescharacteristic
75C22×Dic122C2311yescharacteristic
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61—22no—
80C2×Q8×D61—41no—
81C2×Q8×D61—41no—
82C22×C22⋊D61D411yescharacteristic
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×Dic244—22no—
87C2×Dic244—22no—
88C2×Dic244—22no—
89C2×Dic244—22no—
90C2×Dic244—41no—
91C2×Dic244—41no—
92C2×#11758202—22no—
93C2×#11758202—22no—
94C2×#11758202—41no—
95C22×#92418—22no—
96C22×#92418—22no—
97C22×#92418—41no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519776—28no—
101#14519775—22no—
102#14519775—22no—
103#14519757—22no—
104#14519757—22no—
105#14519757—22no—
106#14519757—41no—
107#14519756—22no—
108#14519756—22no—
109#14519755—28no—
110#14519754—28no—
111#14519742—22no—
112#14519742—22no—
113C4×C22⋊D61—22no—
114C4×C22⋊D61—22no—
115#14519737—28no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×#11758196—21no—
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196D411yescharacteristic
125C2×C22⋊Dic61—21no—
126C2×C22⋊Dic61D411yescharacteristic
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198D411yescharacteristic
131C2×C4×Dic61—21no—
132C2×C4×Dic61C2311yescharacteristic
133#14519710—22no—
134#14519702—22no—
135#14519702—22no—
136#14519701—22no—
137#14519700—22no—
138#14519700—22no—
139#14519700—22no—
140#14519700—22no—
141#14519700D414yescomplemented
142#14519689—22no—
143#14519689—41no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
148C22×Q8×C61C2311yescharacteristic
149C23×C4×C61—21no—
150C23×C4×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153C22⋊Q8×C61—22no—
154C22⋊Q8×C61D414yes—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61—41no—
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C22⋊C4×C61—21no—
163#103×C61—22no—
164#103×C61—41no—
165C22⋊C8×C61—22no—
166C24×C61C2×D411yescharacteristic
167C23×D61C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61C2×D412yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—81no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61Q1614yescomplemented
192C22×Dic61—21no—
193C22×Dic61—24no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202Q8×D61—44no—
203Q8×D61—44no—
204Q8×D61—44no—
205Q8×D61—44no—
206C2×C4×D61—24no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—28no—
223C2×Dic122—24no—
224C2×Dic122—24no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—44no—
233C2×Dic122—44no—
234C2×Dic122—44no—
235C2×Dic122—42no—
236C2×Dic122—42no—
237C2×Dic122—42no—
238C2×Dic122—42no—
239C2×Dic122C2×D412yes—
240C2×Dic122C2×D412yes—
241C2×Dic122C2×D412yes—
242C2×Dic122#4112yes—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61C2×D412yes—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—24no—
258C22⋊Dic61—22no—
259C22⋊Dic61—42no—
260#11758202—44no—
261#11758198—24no—
262#11758198—22no—
263#11758198—42no—
264#11758198—81no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—42no—
269C4⋊Dic61—81no—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—22no—
274#11758196—42no—
275C4×Dic61—24no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—44no—
284C2×#92418C2×D412yes—
285Dic244—44no—
286Dic244—44no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61#12012yes—
292C23×C61C2×Q1612yes—
293C23×C61#13712yes—
294C23×C61C22×D411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61C2×Q1612yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—41no—
305Q8×C61—41no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—84no—
325C2×C4×C61#12012yes—
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C22⋊D61—28no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—22no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—48no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61C2×Q1612yes—
355C4×D61—48no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—22no—
365Dic122—48no—
366Dic122—48no—
367Dic122—41no—
368Dic122—41no—
369Dic122—41no—
370Dic122—41no—
371Dic122—41no—
372Dic122—41no—
373Dic122#12114yes—
374C8×C61—41no—
375C8×C61—41no—
376#92418—22no—
377#92418—41no—
378#24437—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61#45114yescomplemented
386C22×C61C2×#12011yescharacteristic
387C22×C61D4211yescharacteristic
388C22×C61#54611yescharacteristic
389C22×C61C22×Q1611yescharacteristic
390C22×C61C2×#13711yescharacteristic
391C22×C61#57711yescharacteristic
392C22×C61#57811yescharacteristic
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C4×C61—22no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—81no—
405C4×C61C2×#12111yescharacteristic
406C4×C61#53411yescharacteristic
407C4×C61D4211yescharacteristic
408C4×C61#54611yescharacteristic
409Dic61—24no—
410Dic61—22no—
411Dic61—42no—
412Dic61—41no—
413Dic61—41no—
414Dic61—81no—
415Dic61—81no—
416C2×D4×Q8—611no—
417C2×#467—611no—
418C2×#451—611no—
419C2×#451—611no—
420C22×#103—611no—
421#2417—611no—
422#2043—611no—
423#2036—611no—
424#2016—611no—
425#2001—611no—
426#1878—611no—
427#1872D6111yescharacteristic, complemented
428#1869—611no—
429#1863—611no—
430#1787—611no—
431C2×C61—24no—
432C2×C61#241011yescharacteristic
433C2×C61C2×#45111yescharacteristic
434C2×C61#301311yescharacteristic
435C2×C61#326611yescharacteristic
436C2×C61D4×Q1611yescharacteristic
437C2×C61#329911yescharacteristic
438C2×C61#331211yescharacteristic
439D61—42no—
440C23×Q8—611no—
441C23×Q8—611no—
442C22×Q16—611no—
443C22×Q16—611no—
444C22×Q16—611no—
445C23×C8—611no—
446D4×Q8—1224no—
447D4×Q8—1224no—
448C2×C4⋊Q8—611no—
449C2×C4⋊Q8—1221no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—611no—
452C2×C22⋊Q8—611no—
453C2×C22⋊Q8—1221no—
454C2×C22⋊Q8—1221no—
455C2×C22⋊Q8C2×D6111yescharacteristic
456C2×C4×Q8—611no—
457C2×C4×D4—611no—
458C2×C4×D4—1221no—
459C22×C4⋊C4C2×D6111yescharacteristic
460#467—1224no—
461#451—1224no—
462#451—1224no—
463C2×#107—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—1224no—
473C2×#103C2×D6111yescharacteristic
474C2×#103C2×D6111yescharacteristic
475C2×C22⋊C8—611no—
476C2×C22⋊C8—611no—
477C2×C22⋊C8C2×D6111yescharacteristic
478#398—1221no—
479#396—1221no—
480#391—611no—
481#389—611no—
482#386—1221no—
483#380—611no—
484#380—1221no—
485#340C2×D6111yescharacteristic
486#340C2×D6111yescharacteristic
487#336—611no—
488#336—611no—
489C61#2443711yescharacteristic, complemented, Sylow
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—611no—
493C22×Q8—611no—
494C22×Q8—1221no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—1222no—
498C22×Q8—1222no—
499C22×Q8—1222no—
500C22×Q8—1221no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8—2441no—
504C22×Q8—2441no—
505C22×Q8—2441no—
506C22×Q8—2441no—
507C22×Q8C22×D6111yescharacteristic
508C22×D4—611no—
509C23×C4—21no—
510C23×C4—611no—
511C23×C4—1221no—
512C23×C4—1221no—
513C23×C4C22×D6111yescharacteristic
514C2×Q16—1222no—
515C2×Q16—1222no—
516C2×Q16—1222no—
517C2×Q16—1222no—
518C2×Q16—1222no—
519C2×Q16—1222no—
520C2×Q16—2441no—
521C2×Q16—2441no—
522C2×Q16—2441no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—1222no—
526C22×C8—1222no—
527C22×C8—2441no—
528C22×C8C22×D6111yescharacteristic
529C22×C8C22×D6111yescharacteristic
530C4⋊Q8—1228no—
531C4⋊Q8—1222no—
532C4⋊Q8—1222no—
533C22⋊Q8—22no—
534C22⋊Q8—1228no—
535C22⋊Q8—1222no—
536C22⋊Q8—1228no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—2441no—
542C22⋊Q8D24414yes—
543C4×Q8—1222no—
544C4×Q8—1222no—
545C4×D4—1228no—
546C4×D4—1222no—
547C4×D4—1222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C42—611no—
572C2×C42—1221no—
573#107—1222no—
574#103—22no—
575#103—41no—
576#103—614no—
577#103—1222no—
578#103—1222no—
579#103—1222no—
580#103—1222no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584C22⋊C8—22no—
585C22⋊C8—1222no—
586C22⋊C8—2441no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591C24—611no—
592C24D4×D6111yescharacteristic
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—612no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—612no—
602C2×Q8—1224no—
603C2×Q8—1228no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1224no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—2442no—
620C2×Q8—2442no—
621C2×Q8—2444no—
622C2×Q8—2444no—
623C2×Q8—2444no—
624C2×Q8—2442no—
625C2×Q8—2442no—
626C2×Q8—2444no—
627C2×Q8—2444no—
628C2×Q8—2444no—
629C2×Q8—2444no—
630C2×Q8C2×D24412yes—
631C2×D4—614no—
632C2×D4—1222no—
633C2×D4—1222no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—1224no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1224no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4C2×D24412yes—
665C22×C4D4×D6112yes—
666C22×C4D4×D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—2444no—
669Q16—2444no—
670Q16—2444no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—612no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—2444no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—42no—
690C4⋊C4—1224no—
691C4⋊C4—1224no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1222no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—4881no—
698C4⋊C4—2442no—
699C4⋊C4—2442no—
700C4⋊C4C2×D24412yes—
701C4⋊C4D4×D6112yes—
702C22⋊C4—24no—
703C22⋊C4—1224no—
704C22⋊C4—1222no—
705C22⋊C4—1222no—
706C22⋊C4—4881no—
707C22⋊C4—2442no—
708C22⋊C4—2442no—
709C42—1224no—
710C42—1221no—
711C42—1221no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—612no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23#1451974712yes—
724C23Q16×D6112yes—
725C23#1451980612yes—
726C23C2×D4×D6111yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—41no—
730Q8—41no—
731Q8—614no—
732Q8—1222no—
733Q8—1222no—
734Q8—1222no—
735Q8—1222no—
736Q8—1222no—
737Q8—2448no—
738Q8—2448no—
739Q8—2441no—
740Q8—2441no—
741Q8—2441no—
742Q8—2441no—
743Q8—2441no—
744Q8—2441no—
745D4—1228no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—84no—
765C2×C4—612no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—1221no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1222no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—2448no—
779C2×C4—2448no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4#1451974712yes—
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4C22×D24411yescharacteristic
796C2×C4#41×D6111yescharacteristic
797C2×C4#1451982211yescharacteristic
798C2×C4#1451982311yescharacteristic
799C8—41no—
800C8—41no—
801C8—1222no—
802C8—2441no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—1222no—
810C22—1222no—
811C22—1222no—
812C22—2441no—
813C22—2441no—
814C22—2441no—
815C22—2441no—
816C22#1683991914yescomplemented
817C22C2×#1451974711yescharacteristic
818C22#1684039411yescharacteristic
819C22#1684040411yescharacteristic
820C22C2×Q16×D6111yescharacteristic
821C22C2×#1451980611yescharacteristic
822C22#1684057211yescharacteristic
823C22#1684057811yescharacteristic
824C4—22no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—81no—
829C4—1222no—
830C4—1224no—
831C4—4881no—
832C4—4881no—
833C4—2441no—
834C4—2441no—
835C4—2442no—
836C4#121×D6111yescharacteristic
837C4#1684032011yescharacteristic
838C4D4×D24411yescharacteristic
839C4#1684040711yescharacteristic
840C2—24no—
841C2—2442no—
842C2#2144919211yescharacteristic
843C2C2×#1683991911yescharacteristic
844C2#2145513611yescharacteristic
845C2#2145733311yescharacteristic
846C2#2145756411yescharacteristic
847C2#2145769311yescharacteristic
848C2#2145786811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1872D61
hypocenterC61#24437
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#16840001C2semidirect
3. C2×#16839920C2semidirect
4. C2×#16839919C2semidirect
5. C22×#14519700C2semidirect
7. #21447064C2semidirect
8. #21447025C2semidirect
9. #21446920C2semidirect
10. #21446830C2semidirect
11. #21446161C2semidirect
13. #21446074C2semidirect
14. #21445752C2semidirect
15. C61×#1872C2semidirect
141. #14519700D4semidirect
191. C2×C22⋊D61Q16semidirect
385. C22×C61#451semidirect
427. #1872D61semidirect
489. C61#24437semidirect
816. C22#16839919semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168400012
C2×#168399202
C2×#168399192
C22×#145197002
#214492642
#214470642
#214470252
#214469202
#214468302
#214461612
#214461092
#214460742
#214457522
C61×#18722
#2443761