Finite Group Databasebeta

← #29685356

Subgroups — #29685356

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2#21448202C211yesmaximal, characteristic, complemented
3#21446804C212yesmaximal, complemented
4#21446655C212yesmaximal, complemented
5#21446272C214yesmaximal, complemented
6C4×#14519691C214yesmaximal, complemented
7C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
8C22×#11758222C411yescharacteristic, complemented
9#16840273—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273—21no—
14#16840273—21no—
15#16840273—21no—
16#16840273—21no—
17C2×#14519760C412yescomplemented
18C2×#14519756C411yescharacteristic, complemented
19C2×#14519756C2211yescharacteristic
20C2×#14519751C411yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519746C2212yes—
23C2×C4×C22⋊D61C412yescomplemented
24C2×C4×C22⋊D61C2212yes—
25C2×#14519736—21no—
26C2×#14519736C411yescharacteristic, complemented
27C2×#14519691C2218yes—
28#16839625—21no—
29#16839622—21no—
30#16839622C2212yes—
31#16839618C2212yes—
32C4×C22⋊Dic61—21no—
33C4×C22⋊Dic61C2212yes—
34#16839528C2218yes—
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C22×C42×C61—21no—
38C4×C22⋊C4×C61—21no—
39C4×C22⋊C4×C61—21no—
40C4×C22⋊C4×C61C2212yes—
41C4×C22⋊C4×C61C2212yes—
42C2×#95×C61—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—44no—
48C22×Dic122C2×C411yescharacteristic, complemented
49C22×D244C2×C411yescharacteristic, complemented
50C22×C22⋊D61C2×C412yes—
51C22×C22⋊D61C2×C412yes—
52C22×C22⋊D61C2312yes—
53C22×C4×D61C2×C412yescomplemented
54#14519760—22no—
55#14519760—22no—
56#14519760—22no—
57#14519760—22no—
58#14519756—21no—
59#14519756—21no—
60#14519756—21no—
61#14519756—21no—
62#14519756—21no—
63#14519756—21no—
64#14519756—21no—
65#14519756—21no—
66#14519751—21no—
67#14519751—21no—
68#14519751—21no—
69#14519751—21no—
70#14519751—21no—
71#14519751—21no—
72#14519751—21no—
73#14519751—21no—
74#14519746—22no—
75#14519746—22no—
76#14519746—22no—
77#14519746—22no—
78C4×C22⋊D61—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—
86#14519736—21no—
87#14519736—21no—
88#14519736—21no—
89#14519736—21no—
90#14519736—44no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×C4⋊Dic61C2×C411yescharacteristic, complemented
94C2×#11758196C2×C412yescomplemented
95C2×#11758196C2×C412yescomplemented
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61C2×C412yes—
99C2×C22⋊Dic61C2×C412yes—
100C2×C22⋊Dic61C2314yes—
101C2×C22⋊Dic61C2312yes—
102C2×#11758198C2×C412yescomplemented
103C2×#11758198C2×C412yescomplemented
104C2×C4×Dic61—22no—
105C2×C4×Dic61C2×C412yescomplemented
106#14519691—216no—
107#14519684—22no—
108#14519684—22no—
109C25×C61C2311yescharacteristic
110C23×C4×C61—22no—
111C23×C4×C61—44no—
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61C2×C411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D411yescharacteristic
122C23×C4×C61D411yescharacteristic
123C23×C4×C61D411yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—28no—
128C2×C22⋊C4×C61C2314yes—
129C2×C42×C61—22no—
130C2×C42×C61—22no—
131C2×C42×C61—44no—
132#95×C61—22no—
133#95×C61—22no—
134C24×C61—24no—
135C24×C61—42no—
136C24×C61—42no—
137C24×C61C22×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C24×C61C2411yescharacteristic
144C23×D61C22×C412yes—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—24no—
148C22×C4×C61—28no—
149C22×C4×C61—24no—
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×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—44no—
162C22×C4×C61—44no—
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×C61C22⋊C411yescharacteristic
177C22×C4×C61C22⋊C411yescharacteristic
178C22×C4×C61C22⋊C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—28no—
198C2×C22⋊D61—44no—
199C2×C22⋊D61—44no—
200C22×Dic61—24no—
201C22×Dic61C22×C412yes—
202C22×Dic61C22×C412yes—
203C22×Dic61C22×C412yes—
204#11758222—44no—
205#11758222—44no—
206#11758222—44no—
207#11758222—44no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—42no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—44no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—42no—
217C22⋊C4×C61—28no—
218C22⋊C4×C61—24no—
219C22⋊C4×C61#4118yescomplemented
220C42×C61—44no—
221C42×C61—44no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—28no—
229C22⋊Dic61—44no—
230C22⋊Dic61—44no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—44no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—22no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61—44no—
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—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—416no—
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C23×C411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C2×#4114yes—
276C22×D61—22no—
277C22×D61—24no—
278C22×D61—42no—
279C22×D61—42no—
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—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—28no—
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—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—44no—
309C2×C4×C61—416no—
310C2×C4×C61—44no—
311C2×C4×C61#9914yescomplemented
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C22⋊D61—44no—
321C22⋊D61—44no—
322C22⋊D61—44no—
323C22⋊D61—44no—
324C22⋊D61—44no—
325C22⋊D61—44no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—44no—
333C2×Dic61—44no—
334C2×Dic61—44no—
335D244—42no—
336D244—42no—
337C4×D61—44no—
338C4×D61—44no—
339Dic122—42no—
340Dic122—42no—
341#21420—611nomaximal, Sylow
342C22×C61—28no—
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—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—44no—
360C22×C61—44no—
361C22×C61—44no—
362C22×C61—44no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61C2×#9912yes—
366C22×C61#41012yes—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C4×#4112yes—
369C22×C61#52512yes—
370C22×C61#53212yes—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—84no—
375C4×C61—21no—
376C4×C61—21no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—48no—
382C4×C61C2×#9912yes—
383C4×C61C2×#9912yes—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—84no—
388C2×#525—611no—
389#2280—611no—
390C2×C4×C22⋊C4D6111yescharacteristic, complemented
391#1996—612no—
392#1964—612no—
393#1898—614no—
394C4×#99—614no—
395C2×C61—22no—
396C2×C61—22no—
397C2×C61—22no—
398C2×C61—22no—
399C2×C61—22no—
400C2×C61—41no—
401C2×C61—41no—
402C2×C61#229711yescharacteristic
403C2×C61C22×#9911yescharacteristic
404C2×C61C2×#41011yescharacteristic
405D61—82no—
406C22×#41—611no—
407C24×C4C2×D6111yescharacteristic
408#525—1221no—
409#525—1221no—
410#525—1221no—
411#525—1221no—
412#525—1221no—
413#525—1221no—
414#525—1221no—
415#525—1221no—
416C2×#123—612no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—612no—
422C2×C4×D4—612no—
423C2×C4×D4—612no—
424C2×#117—611no—
425C2×#117—1221no—
426C22×C22⋊C4C2×D6112yes—
427C22×C42—21no—
428C2×#99—618no—
429#381—1221no—
430#380—612no—
431#380—1221no—
432#379—612no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—612no—
436C4×C22⋊C4—1221no—
437C4×C22⋊C4C2×D6112yes—
438C4×C22⋊C4C2×D6112yes—
439C2×#95—21no—
440#342—618no—
441C61#2142011yescharacteristic, complemented, Sylow
442C25C22×D6111yescharacteristic
443C2×#41—1221no—
444C2×#41—1221no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—2444no—
448C22×Q8—611no—
449C22×D4—612no—
450C22×D4—612no—
451C22×D4—612no—
452C22×D4—611no—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4—612no—
456C23×C4C4×D6111yescharacteristic
457C23×C4C4×D6111yescharacteristic
458C23×C4C4×D6111yescharacteristic
459C23×C4C4×D6111yescharacteristic
460C23×C4D24411yescharacteristic
461C23×C4D24411yescharacteristic
462C23×C4D24411yescharacteristic
463C23×C4D24411yescharacteristic
464C23×C4C22⋊D6111yescharacteristic
465C23×C4C22⋊D6111yescharacteristic
466C23×C4C22⋊D6111yescharacteristic
467C23×C4C22⋊D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470#123—1222no—
471#123—1222no—
472#123—1222no—
473#123—1222no—
474C22⋊Q8—1221no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479C22⋊Q8—1221no—
480C22⋊Q8—1221no—
481C22⋊Q8—1221no—
482#121—1221no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#121—1221no—
488#121—1221no—
489#121—1221no—
490#120—1222no—
491#120—1222no—
492#120—1222no—
493#120—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—1221no—
503#117—1221no—
504#117—1221no—
505#117—1221no—
506#117—2444no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1222no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—612no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4C22×D6114yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—44no—
526C2×C42—612no—
527C2×C42—1222no—
528#99—12216no—
529#95—22no—
530#95—22no—
531#95—1222no—
532#95—1222no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—612no—
537C24C2×C4×D6111yescharacteristic
538C24C2×C4×D6111yescharacteristic
539C24C2×D24411yescharacteristic
540C24C2×D24411yescharacteristic
541C24C2×C22⋊D6111yescharacteristic
542C24C2×C22⋊D6111yescharacteristic
543C24C23×D6111yescharacteristic
544#41—2444no—
545#41—2444no—
546#41—2444no—
547#41—2444no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—2442no—
551C2×D4—1222no—
552C2×D4—1222no—
553C2×D4—1228no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—2442no—
561C2×D4—2444no—
562C2×D4—2444no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1224no—
587C22×C4—2444no—
588C22×C4#1175819811yescharacteristic
589C22×C4#1175819811yescharacteristic
590C22×C4#1175819811yescharacteristic
591C22×C4#1175819811yescharacteristic
592C22×C4#1175819811yescharacteristic
593C22×C4#1175819811yescharacteristic
594C22×C4#1175819811yescharacteristic
595C22×C4#1175819811yescharacteristic
596C22×C4#1175819811yescharacteristic
597C22×C4#1175819811yescharacteristic
598C22×C4#1175819811yescharacteristic
599C22×C4#1175819811yescharacteristic
600C22×C4#1175819811yescharacteristic
601C22×C4#1175819811yescharacteristic
602C22×C4#1175819811yescharacteristic
603C22×C4#1175819811yescharacteristic
604C22×C4C2×C4×D6111yescharacteristic
605C22×C4C2×C4×D6111yescharacteristic
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×D24411yescharacteristic
609C22×C4C2×D24411yescharacteristic
610C22×C4C2×D24411yescharacteristic
611C22×C4C2×D24411yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—2444no—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1228no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C22⋊C4#1175822218yescomplemented
641C42—44no—
642C42—44no—
643C42—1222no—
644C42—1222no—
645C42—2444no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—1224no—
668C23—1222no—
669C23—2442no—
670C23—2442no—
671C23C2×#1175819811yescharacteristic
672C23C2×#1175819811yescharacteristic
673C23C2×#1175819811yescharacteristic
674C23C2×#1175819811yescharacteristic
675C23C22×C4×D6111yescharacteristic
676C23C22×C22⋊D6111yescharacteristic
677C23C22×D24411yescharacteristic
678C23C2×#1175822214yes—
679Q8—2442no—
680Q8—2442no—
681D4—2442no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
685D4—2444no—
686D4—2444no—
687D4—2444no—
688D4—2442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1224no—
724C2×C4—2444no—
725C2×C4—2444no—
726C2×C4—2444no—
727C2×C4—2444no—
728C2×C4—2444no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4#1451969114yescomplemented
732C2×C4C2×#1175819811yescharacteristic
733C2×C4C2×#1175819811yescharacteristic
734C2×C4C2×#1175819811yescharacteristic
735C2×C4C2×#1175819811yescharacteristic
736C2×C4C2×#1175819811yescharacteristic
737C2×C4C2×#1175819811yescharacteristic
738C2×C4C2×#1175819811yescharacteristic
739C2×C4C2×#1175819811yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—4884no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22C2×#1451969112yes—
768C22#1683973512yes—
769C22C22×#1175819811yescharacteristic
770C22C4×#1175822212yes—
771C22#1684027312yes—
772C22#1684031212yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—4884no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4C2×#1451969112yes—
785C4C2×#1451969112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—4882no—
794C2#2144830911yescharacteristic
795C2C22×#1451969111yescharacteristic
796C2C2×#1683973511yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C4×C22⋊C4×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC24×C61C24
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21448202C2semidirect
3. #21446804C2semidirect
4. #21446655C2semidirect
5. #21446272C2semidirect
6. C4×#14519691C2semidirect
7. C2×C4×C22⋊C4×C61C2semidirect
8. C22×#11758222C4semidirect
17. C2×#14519760C4semidirect
18. C2×#14519756C4semidirect
20. C2×#14519751C4semidirect
23. C2×C4×C22⋊D61C4semidirect
26. C2×#14519736C4semidirect
48. C22×Dic122C2×C4semidirect
49. C22×D244C2×C4semidirect
53. C22×C4×D61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
93. C2×C4⋊Dic61C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
102. C2×#11758198C2×C4semidirect
103. C2×#11758198C2×C4semidirect
105. C2×C4×Dic61C2×C4semidirect
219. C22⋊C4×C61#41semidirect
311. C2×C4×C61#99semidirect
390. C2×C4×C22⋊C4D61semidirect
441. C61#21420semidirect
640. C22⋊C4#11758222semidirect
731. C2×C4#14519691semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
#214482022
#214468042
#214466552
#214462722
C4×#145196912
C2×C4×C22⋊C4×C612
#2142061