Finite Group Databasebeta

← #29647178

Subgroups — #29647178

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
3#21444340C212yesmaximal, complemented
4#21444336C212yesmaximal, complemented
5#21444324C214yesmaximal, complemented
6#21444311C214yesmaximal, complemented
7C2×C61×#407C211yesmaximal, characteristic, complemented
8C22×#11758222C411yescharacteristic, complemented
9#16840273—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273C412yescomplemented
14#16840273C412yescomplemented
15#16840273C2212yes—
16#16840273C2212yes—
17C2×#14519760—21no—
18C2×#14519756C411yescharacteristic, complemented
19C2×#14519756C2211yescharacteristic
20C2×#14519751C411yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519746—21no—
23C2×C4×C22⋊D61—21no—
24C2×C4×C22⋊D61—21no—
25C2×#14519736C411yescharacteristic, complemented
26C22×C22⋊Dic61—21no—
27C22×C4×Dic61—21no—
28C4×C22⋊Dic61—21no—
29C4×C22⋊Dic61—21no—
30C4×C22⋊Dic61C2212yes—
31C4×C22⋊Dic61C2212yescomplemented
32C2×#14519684C2212yescomplemented
33#16839500C2218yescomplemented
34#16839497C2218yescomplemented
35C24×C4×C61C2211yescharacteristic
36C22×M16×C61—21no—
37C61×#407—21no—
38C61×#407—21no—
39C61×#407C2212yes—
40C61×#407C2212yescomplemented
41C2×C22⋊C8×C61—21no—
42C2×C22⋊C8×C61C2212yescomplemented
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—44no—
46C2×#11758222C2×C412yes—
47C2×#11758222C2×C412yescomplemented
48C22×Dic122C2×C411yescharacteristic, complemented
49C22×D244C2×C411yescharacteristic, complemented
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C23×Dic61—22no—
54C22×C4×D61—21no—
55#14519760—22no—
56#14519760—22no—
57#14519760—22no—
58#14519760—22no—
59#14519756—21no—
60#14519756—21no—
61#14519756—21no—
62#14519756—21no—
63#14519756C2×C412yes—
64#14519756C2×C412yescomplemented
65#14519756C2×C412yescomplemented
66#14519756C2312yes—
67#14519751—21no—
68#14519751—21no—
69#14519751—21no—
70#14519751—21no—
71#14519751C2×C412yes—
72#14519751C2×C412yescomplemented
73#14519751C2×C412yescomplemented
74#14519751C2312yes—
75#14519746—22no—
76#14519746—22no—
77#14519746—22no—
78#14519746—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519736—21no—
88#14519736—21no—
89#14519736C2×C412yes—
90#14519736C2×C412yescomplemented
91C2×C4⋊Dic61C2×C411yescharacteristic, complemented
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×C22⋊Dic61—28no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—44no—
107#14519684—22no—
108#14519684C2314yes—
109C25×C61D411yescharacteristic
110C23×C4×C61—44no—
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61D411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—44no—
128C22×C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61—22no—
131C22⋊C8×C61—22no—
132C22⋊C8×C61C2314yes—
133C24×C61—24no—
134C24×C61—42no—
135C24×C61—42no—
136C24×C61C22⋊C411yescharacteristic
137C24×C61C22⋊C411yescharacteristic
138C24×C61C22⋊C411yescharacteristic
139C24×C61C22⋊C411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22⋊C411yescharacteristic
164C22×C4×C61C22⋊C411yescharacteristic
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—44no—
194C2×C22⋊D61—44no—
195C22×Dic61—28no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—24no—
200C22×Dic61—44no—
201C22×Dic61—44no—
202#11758222—44no—
203#11758222—44no—
204#11758222—44no—
205#11758222—44no—
206C2×D244—21no—
207C2×D244—42no—
208C2×D244C22×C412yes—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61—44no—
212C2×Dic122—21no—
213C2×Dic122—42no—
214C2×Dic122C22×C412yes—
215M16×C61—44no—
216M16×C61—44no—
217C2×C8×C61—24no—
218C2×C8×C61—44no—
219C22⋊Dic61—28no—
220C22⋊Dic61—28no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C412yes—
234C4⋊Dic61C22×C412yes—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—44no—
242C4×Dic61—44no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—416no—
264C23×C61#10414yes—
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C22×D411yescharacteristic
272C22×D61—22no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C2×C4×C61—22no—
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×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61#9914yes—
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C22⋊D61—44no—
317C22⋊D61—44no—
318C2×Dic61—28no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—44no—
323C2×Dic61—42no—
324C2×Dic61—416no—
325C2×Dic61—42no—
326C2×Dic61—44no—
327C2×Dic61—42no—
328D244—42no—
329D244—42no—
330C4×D61—44no—
331C4×D61—44no—
332Dic122—42no—
333Dic122—42no—
334C8×C61—44no—
335#17542—611nomaximal, Sylow
336C22×C61—28no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61—44no—
356C22×C61—44no—
357C22×C61—44no—
358C22×C61—44no—
359C22×C61C2×#9912yes—
360C22×C61C2×#10412yes—
361C22×C61C2×#10412yes—
362C22×C61C2×#10412yes—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61#57512yes—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—84no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—21no—
375C4×C61C2×#9912yes—
376C4×C61C2×#9912yes—
377Dic61—48no—
378Dic61—42no—
379Dic61—42no—
380Dic61—42no—
381C2×#525—611no—
382C2×#407D6111yescharacteristic, complemented
383C2×C4×C22⋊C4—611no—
384#1508—612no—
385#1507—612no—
386#1504—614no—
387#1501—614no—
388C2×C61—22no—
389C2×C61—22no—
390C2×C61—22no—
391C2×C61—22no—
392C2×C61—22no—
393C2×C61—41no—
394C2×C61—41no—
395C2×C61C22×#9911yescharacteristic
396C2×C61#289611yescharacteristic
397C2×C61C22×#10411yescharacteristic
398D61—82no—
399C22×#41—611no—
400C24×C4C2×D6111yescharacteristic
401C22×M16—21no—
402#525—612no—
403#525—612no—
404#525—612no—
405#525—612no—
406#525—1221no—
407#525—1221no—
408#525—1221no—
409#525—1221no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8—611no—
413C2×#121—611no—
414C2×#121—611no—
415C2×#120—1221no—
416C2×C4×D4—1221no—
417C2×C4×D4—1221no—
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420C22×C42—1221no—
421#407—21no—
422#407—21no—
423#407C2×D6112yes—
424#407C2×D6112yescomplemented
425C2×C22⋊C8—21no—
426C2×C22⋊C8C2×D6112yescomplemented
427C4×C22⋊C4—612no—
428C4×C22⋊C4—612no—
429C4×C22⋊C4—1221no—
430C4×C22⋊C4—1221no—
431C2×#95—612no—
432#328—618no—
433#327—618no—
434C61#1754211yescharacteristic, complemented, Sylow
435C25D24411yescharacteristic
436C2×#41—612no—
437C2×#41—612no—
438C2×#41—1221no—
439C2×#41—1221no—
440C2×#41—2444no—
441C22×Q8—611no—
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4—1221no—
446C23×C4—44no—
447C23×C4—1222no—
448C23×C4—1221no—
449C23×C4C4×D6111yescharacteristic
450C23×C4C4×D6111yescharacteristic
451C23×C4C4×D6111yescharacteristic
452C23×C4C4×D6111yescharacteristic
453C23×C4D24411yescharacteristic
454C23×C4D24411yescharacteristic
455C23×C4D24411yescharacteristic
456C23×C4C22⋊D6111yescharacteristic
457C23×C4C22⋊D6111yescharacteristic
458C23×C4C22⋊D6111yescharacteristic
459C23×C4C22⋊D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—44no—
466C22×C8—22no—
467#123—1222no—
468#123—1222no—
469#123—1222no—
470#123—1222no—
471C22⋊Q8—612no—
472C22⋊Q8—612no—
473C22⋊Q8—612no—
474C22⋊Q8—612no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479#121—612no—
480#121—612no—
481#121—612no—
482#121—612no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#120—1222no—
488#120—1222no—
489#120—1222no—
490#120—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499#117—612no—
500#117—612no—
501#117—1221no—
502#117—1221no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C22⋊C4—1228no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C42—1221no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—2444no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8C22×D6114yes—
523#95—614no—
524#95—1222no—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—1221no—
529C24#1175819811yescharacteristic
530C24#1175819811yescharacteristic
531C24#1175819811yescharacteristic
532C24#1175819811yescharacteristic
533C24C2×D24411yescharacteristic
534C24C2×D24411yescharacteristic
535C24C2×D24411yescharacteristic
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540C2×Q8—612no—
541C2×Q8—1221no—
542C2×Q8—2442no—
543C2×D4—612no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1221no—
551C2×D4—2442no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2444no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—1228no—
570C22×C4—1224no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—2444no—
577C22×C4—2444no—
578C22×C4—2444no—
579C22×C4#1175819811yescharacteristic
580C22×C4#1175819811yescharacteristic
581C22×C4#1175819811yescharacteristic
582C22×C4#1175819811yescharacteristic
583C22×C4#1175819811yescharacteristic
584C22×C4#1175819811yescharacteristic
585C22×C4#1175819811yescharacteristic
586C22×C4#1175819811yescharacteristic
587C22×C4#1175819811yescharacteristic
588C22×C4#1175819811yescharacteristic
589C22×C4#1175819811yescharacteristic
590C22×C4#1175819811yescharacteristic
591C22×C4C2×C4×D6111yescharacteristic
592C22×C4C2×C4×D6111yescharacteristic
593C22×C4C2×C4×D6111yescharacteristic
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4C2×D24411yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C23×D6111yescharacteristic
607M16—44no—
608M16—44no—
609C2×C8—24no—
610C2×C8—44no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—1222no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C22⋊C4—1228no—
620C22⋊C4—1228no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C42—1222no—
632C42—1222no—
633C42—2444no—
634C42—2444no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—1222no—
657C23—2442no—
658C23—2442no—
659C23—2442no—
660C23#1451970314yes—
661C23C2×#1175819811yescharacteristic
662C23C2×#1175819811yescharacteristic
663C23C2×#1175819811yescharacteristic
664C23C2×#1175819811yescharacteristic
665C23C2×#1175819811yescharacteristic
666C23C2×#1175819811yescharacteristic
667C23C22×D24411yescharacteristic
668Q8—2442no—
669Q8—2442no—
670D4—2442no—
671D4—2444no—
672D4—2444no—
673D4—2444no—
674D4—2444no—
675D4—2444no—
676D4—2444no—
677D4—2442no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—1228no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4—24416no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2444no—
716C2×C4—2444no—
717C2×C4#1451969114yes—
718C2×C4C2×#1175819811yescharacteristic
719C2×C4C2×#1175819811yescharacteristic
720C2×C4C2×#1175819811yescharacteristic
721C2×C4C2×#1175819811yescharacteristic
722C2×C4C2×#1175819811yescharacteristic
723C2×C4C2×#1175819811yescharacteristic
724C2×C4C22×C4×D6111yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C8—44no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—4884no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22C2×#1451969112yes—
755C22C2×#1451970312yes—
756C22C2×#1451970312yes—
757C22C2×#1451970312yes—
758C22C22×#1175819811yescharacteristic
759C22#1684056212yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—2448no—
767C4—2442no—
768C4—2442no—
769C4—2442no—
770C4C2×#1451969112yes—
771C4C2×#1451969112yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—4882no—
780C2C22×#1451969111yescharacteristic
781C2#2145433911yescharacteristic
782C2C22×#1451970311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenterC2×#407D61
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic61C2semidirect
3. #21444340C2semidirect
4. #21444336C2semidirect
5. #21444324C2semidirect
6. #21444311C2semidirect
7. C2×C61×#407C2semidirect
8. C22×#11758222C4semidirect
13. #16840273C4semidirect
14. #16840273C4semidirect
18. C2×#14519756C4semidirect
20. C2×#14519751C4semidirect
25. C2×#14519736C4semidirect
31. C4×C22⋊Dic61C22semidirect
32. C2×#14519684C22semidirect
33. #16839500C22semidirect
34. #16839497C22semidirect
40. C61×#407C22semidirect
42. C2×C22⋊C8×C61C22semidirect
47. C2×#11758222C2×C4semidirect
48. C22×Dic122C2×C4semidirect
49. C22×D244C2×C4semidirect
64. #14519756C2×C4semidirect
65. #14519756C2×C4semidirect
72. #14519751C2×C4semidirect
73. #14519751C2×C4semidirect
90. #14519736C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
382. C2×#407D61semidirect
424. #407C2×D61semidirect
426. C2×C22⋊C8C2×D61semidirect
434. C61#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×C4×C22⋊Dic612
#214443402
#214443362
#214443242
#214443112
C2×C61×#4072
#1754261