Finite Group Databasebeta

← #29696363

Subgroups — #29696363

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic
2#21448748C211yesmaximal, characteristic, complemented
3#21446792C211yesmaximal, characteristic, complemented
4#21446766C211yesmaximal, characteristic, complemented
5#21446257C211yesmaximal, characteristic, complemented
6#21446247C211yesmaximal, characteristic, complemented
7#21446139C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21445910C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445830C211yesmaximal, characteristic, complemented
12#21445645C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14C2×#16839525C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758224—21no—
17#16840416—24no—
18#16840416C418yescomplemented
19C2×#14519777C2211yescharacteristic
20C2×#14519761—21no—
21C2×#14519761—21no—
22C2×#14519757—21no—
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34#16839655—21no—
35#16839648—21no—
36#16839642—21no—
37#16839628C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C22⋊C4×Dic61—21no—
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#435—24no—
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C2×#11758224—28no—
63C2×#11758224—44no—
64C2×#11758224—44no—
65C22×Dic122—21no—
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C23×Dic61—21no—
70C23×Dic61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73#14519777—22no—
74#14519777C2×C414yescomplemented
75#14519761—28no—
76#14519761—28no—
77#14519757—28no—
78#14519751—22no—
79#14519751—22no—
80#14519751C2×C414yes—
81#14519751C2×C414yescomplemented
82C4×D244—22no—
83C4×D244C2×C414yescomplemented
84#14519736—22no—
85#14519736—41no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61C2×C414yes—
95C2×C4⋊Dic61C2×C414yescomplemented
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111#14519699—22no—
112#14519699—22no—
113#14519699—41no—
114#14519699—41no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C22×D4×C61D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C2×M16×C61—22no—
124C2×M16×C61—22no—
125C2×M16×C61—41no—
126C22×C8×C61—22no—
127C22×C8×C61—22no—
128C22×C8×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C4×D4×C61C2×C414yes—
134C4×D4×C61D414yes—
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C4⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141C22⋊C8×C61—22no—
142#97×C61—22no—
143C24×C61C2×D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61C22⋊C414yes—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—24no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—24no—
173C22×Dic61—24no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61—81no—
188#11758224—432no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244C22×C412yes—
195C2×C4×D61—24no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×Dic122—24no—
199C2×Dic122—42no—
200C2×Dic122—42no—
201M16×C61—44no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—44no—
214C2×C8×C61#4112yescomplemented
215C4⋊C4×C61C22⋊C414yes—
216C22⋊C4×C61C22⋊C414yes—
217C22⋊C4×C61C22⋊C414yes—
218C42×C61C22×C412yes—
219C42×C61C2×D412yes—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—81no—
223#11758198—24no—
224#11758198—24no—
225#11758198—24no—
226C4⋊Dic61—24no—
227C4⋊Dic61—24no—
228C4⋊Dic61—24no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—42no—
240C4⋊Dic61C22×C412yes—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C22×C412yes—
243C4⋊Dic61#4112yescomplemented
244C4×Dic61—42no—
245C4×Dic61—81no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61C2×C22⋊C412yes—
257C23×C61C2×C22⋊C412yes—
258C23×C61AGL(1,ℤ/8)12yes—
259C23×C61AGL(1,ℤ/8)12yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268D4×C61—28no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C2×C22⋊C412yes—
287C2×C4×C61C2×C22⋊C412yes—
288C2×C4×C61C2×C22⋊C412yes—
289C2×C4×C61C23×C411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C612−1+411yescharacteristic
295C22⋊D61—48no—
296C22⋊D61—48no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—48no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—48no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—84no—
321D244—22no—
322D244—22no—
323D244—41no—
324D244—41no—
325C4×D61—48no—
326Dic122—48no—
327C8×C61—22no—
328C8×C61—41no—
329C8×C61—41no—
330C8×C61—41no—
331#22495—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61#41814yes—
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61#54611yescharacteristic
348C22×C61#54711yescharacteristic
349C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61C4×#4111yescharacteristic
365C4×C61#52011yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#54711yescharacteristic
368Dic61—42no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375C2×#547—611no—
376C2×#435D6111yescharacteristic, complemented
377#2352—611no—
378#1993—611no—
379#1987—611no—
380#1895—611no—
381#1893—611no—
382#1875—611no—
383#1874—611no—
384#1824—611no—
385#1823—611no—
386#1804—611no—
387#1762—611no—
388#1736—611no—
389C2×#340—611no—
390C2×C61—24no—
391C2×C61—42no—
392C2×C61#233911yescharacteristic
393C2×C61C2×#41811yescharacteristic
394C2×C61#289811yescharacteristic
395C2×C61#330611yescharacteristic
396C2×C61#330811yescharacteristic
397C2×C61#334311yescharacteristic
398C2×C61#334511yescharacteristic
399D61—82no—
400C22×#41—1221no—
401C22×M16C2×D6111yescharacteristic
402C23×C8C2×D6111yescharacteristic
403#547—618no—
404#547—1224no—
405C2×C4⋊Q8—611no—
406C2×#123—1221no—
407C2×#123—1221no—
408C2×C22⋊Q8—1221no—
409C2×#121—611no—
410C2×#121—611no—
411C2×C4×D4—611no—
412C2×C4×D4C2×D6111yescharacteristic
413C2×#117—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417#435—24no—
418C2×C4⋊C8C2×D6111yescharacteristic
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×C22⋊C8C2×D6111yescharacteristic
424C2×C22⋊C8C2×D6111yescharacteristic
425C2×#97C2×D6111yescharacteristic
426#388—1221no—
427#387—1221no—
428#386—1221no—
429#382—611no—
430#380—611no—
431#380—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—1221no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446C61#2249511yescharacteristic, complemented, Sylow
447C2×#41—1228no—
448C2×#41—2444no—
449C2×#41—2444no—
450C22×Q8—1221no—
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4—1221no—
454C22×D4D24411yescharacteristic
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8—41no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C4⋊Q8—614no—
472C4⋊Q8—1222no—
473#123—1228no—
474#123—1228no—
475C22⋊Q8—1228no—
476#121—614no—
477#121—614no—
478#121—1222no—
479#121—1222no—
480C4×D4—614no—
481C4×D4—1222no—
482C4×D4C4×D6114yes—
483C4×D4C22⋊D6114yes—
484#117—1222no—
485#117—2441no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—2441no—
503C2×C4⋊C4D24411yescharacteristic
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4D24411yescharacteristic
511C2×C22⋊C4D24411yescharacteristic
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42C22×D6111yescharacteristic
515C4⋊C8—22no—
516#102—1222no—
517#102—1222no—
518#102—2441no—
519#102—2441no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522#97—22no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—1221no—
529C24C2×D24411yescharacteristic
530C24C2×D24411yescharacteristic
531#41—24432no—
532C2×Q8—1224no—
533C2×Q8—2442no—
534C2×Q8—2442no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—612no—
538C2×D4—1224no—
539C2×D4—1224no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—2442no—
546C2×D4—2442no—
547C2×D4—2442no—
548C2×D4—2442no—
549C2×D4#1175819814yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1224no—
563C22×C4—1224no—
564C22×C4—1224no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4C2×C4×D6112yes—
578C22×C4C2×C4×D6112yes—
579C22×C4C2×D24411yescharacteristic
580C22×C4C2×D24411yescharacteristic
581C22×C4C2×D24411yescharacteristic
582C22×C4C2×D24411yescharacteristic
583C22×C4C2×C22⋊D6112yes—
584C22×C4C2×C22⋊D6112yes—
585C22×C4C23×D6111yescharacteristic
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8#1175822412yescomplemented
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—612no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—2442no—
618C4⋊C4#1175819814yes—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C22⋊C4—4881no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4#1175819814yes—
626C22⋊C4#1175819814yes—
627C42—4881no—
628C42—2442no—
629C42C2×C4×D6112yes—
630C42C2×C22⋊D6112yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—1222no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23C2×#1175819812yes—
649C23C2×#1175819812yes—
650C23#1451980512yes—
651C23#1451980512yes—
652C23C22×D24411yescharacteristic
653Q8—2448no—
654D4—28no—
655D4—1222no—
656D4—1222no—
657D4—2448no—
658D4—2448no—
659D4—2441no—
660D4—2441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—4884no—
682C2×C4—2448no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2448no—
693C2×C4—2448no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4C2×#1175819812yes—
703C2×C4C2×#1175819812yes—
704C2×C4C2×#1175819812yes—
705C2×C4C2×#1175819812yes—
706C2×C4C22×C4×D6111yescharacteristic
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4#41×D6111yescharacteristic
709C2×C4C2×#1175822411yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982411yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22#1683976814yes—
737C22C22×#1175819811yescharacteristic
738C22#1684040711yescharacteristic
739C22#1684041611yescharacteristic
740C22C2×#1451980511yescharacteristic
741C22C2×#1451980511yescharacteristic
742C22#1684057411yescharacteristic
743C22#1684057911yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—4881no—
749C4—4881no—
750C4—4881no—
751C4—2442no—
752C4—2442no—
753C4—2442no—
754C4—2442no—
755C4C4×#1175822411yescharacteristic
756C4#1684024111yescharacteristic
757C4#1684040611yescharacteristic
758C4#1684041111yescharacteristic
759C2—24no—
760C2—42no—
761C2—4882no—
762C2#2144864411yescharacteristic
763C2C2×#1683976811yescharacteristic
764C2#2145435311yescharacteristic
765C2#2145778211yescharacteristic
766C2#2145781211yescharacteristic
767C2#2145826111yescharacteristic
768C2#2145829111yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840416C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #21448748C2semidirect
3. #21446792C2semidirect
4. #21446766C2semidirect
5. #21446257C2semidirect
6. #21446247C2semidirect
7. #21446139C2semidirect
8. #21446134C2semidirect
9. #21445910C2semidirect
10. #21445906C2semidirect
11. #21445830C2semidirect
12. #21445645C2semidirect
13. #21445539C2semidirect
14. C2×#16839525C2semidirect
15. C2×C61×#435C2semidirect
18. #16840416C4semidirect
74. #14519777C2×C4semidirect
81. #14519751C2×C4semidirect
83. C4×D244C2×C4semidirect
95. C2×C4⋊Dic61C2×C4semidirect
214. C2×C8×C61#41semidirect
243. C4⋊Dic61#41semidirect
376. C2×#435D61semidirect
446. C61#22495semidirect
599. C2×C8#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168404162
#214487482
#214467922
#214467662
#214462572
#214462472
#214461392
#214461342
#214459102
#214459062
#214458302
#214456452
#214455392
C2×#168395252
C2×C61×#4352
#2249561