Finite Group Databasebeta

← #29679409

Subgroups — #29679409

Order 15616.

1522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2C2×#16839734C212yesmaximal
3#21448221C212yesmaximal, complemented
4#21445807C211yesmaximal, characteristic, complemented
5#21445806C212yesmaximal, complemented
6#21445805C212yesmaximal, complemented
7#21445804C212yesmaximal, complemented
8#21445550C212yesmaximal, complemented
9C61×#1799C211yesmaximal, characteristic, complemented
10C22×#11758224C2211yescharacteristic
11C4×#11758224—22no—
12C4×#11758224—22no—
13C4×#11758224—22no—
14C4×#11758224—22no—
15C2×C4×Dic122C411yescharacteristic, complemented
16C2×#14519742C411yescharacteristic, complemented
17C2×D4×Dic61C2211yescharacteristic
18C2×C4×C22⋊D61C411yescharacteristic, complemented
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519737C411yescharacteristic, complemented
21C2×#14519737C2211yescharacteristic
22C2×#14519735C411yescharacteristic, complemented
23C2×#14519733C411yescharacteristic, complemented
24C2×#14519733C2214yes—
25C2×#14519733C2211yescharacteristic
26C22×C4×Dic61C411yescharacteristic, complemented
27C22×C4×Dic61C2211yescharacteristic
28C2×C42×D61C411yescharacteristic, complemented
29#16839734—28no—
30C2×#14519692C2212yes—
31C2×#14519691C2214yes—
32#16839631—22no—
33#16839626—22no—
34#16839622C2212yes—
35#16839620C2214yes—
36C4⋊C4×Dic61—22no—
37#16839613—22no—
38#16839529C2212yes—
39#16839528C2214yes—
40C2×C4×D4×C61C2211yescharacteristic
41C2×#99×C61C2212yes—
42C61×#380C2212yes—
43C61×#342C2212yes—
44C2×#11758224—22no—
45C2×#11758224—22no—
46C2×#11758224—24no—
47C2×#11758224D414yes—
48C2×#11758224Q814yes—
49C22×Dic122C2×C411yescharacteristic
50C22×C22⋊D61C2×C411yescharacteristic
51C22×C22⋊D61C2311yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C4×Dic122—22no—
60C4×Dic122—22no—
61#14519742—22no—
62#14519742—22no—
63D4×Dic61—22no—
64D4×Dic61—22no—
65C4×C22⋊D61—22no—
66C4×C22⋊D61—22no—
67C4×C22⋊D61—22no—
68C4×C22⋊D61—22no—
69#14519737—22no—
70#14519737—22no—
71#14519737—22no—
72#14519737—22no—
73#14519735—22no—
74#14519735—22no—
75#14519733—22no—
76#14519733—22no—
77#14519733—22no—
78#14519733—22no—
79#14519733—28no—
80#14519733—28no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×#11758196—24no—
84C2×#11758196—24no—
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2314yes—
91C2×C22⋊Dic61C2311yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—24no—
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D412yes—
109C2×C4×Dic61D412yes—
110C2×C4×Dic61D412yes—
111C2×C4×Dic61D412yes—
112C42×D61—21no—
113C42×D61—21no—
114C42×D61—21no—
115C42×D61—21no—
116#14519692—24no—
117#14519691—28no—
118#14519684—22no—
119#14519684—24no—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2×C411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2314yes—
129C2×C22⋊C4×C61C2311yescharacteristic
130C2×C42×C61C2×C411yescharacteristic
131#99×C61—24no—
132#95×C61—22no—
133C24×C61C22×C411yescharacteristic
134C24×C61C2411yescharacteristic
135C23×D61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61C2×D412yes—
139C2×D4×C61C2×Q812yes—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—24no—
143C22×C4×C61—42no—
144C22×C4×C61—42no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61C4⋊C414yescomplemented
157C2×C22⋊D61C2×D412yes—
158C2×C22⋊D61C2×Q812yes—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—24no—
165C22×Dic61—42no—
166C22×Dic61—42no—
167C22×Dic61C4⋊C414yescomplemented
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C2×D412yes—
176C22×Dic61C2×D412yes—
177C22×Dic61C2×D412yes—
178C22×Dic61C2×D412yes—
179C22×Dic61C2×D412yes—
180C22×Dic61C2×Q812yes—
181C22×Dic61#4114yes—
182#11758224—28no—
183#11758224—28no—
184#11758224—28no—
185#11758224—28no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61C4⋊C414yescomplemented
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122C4⋊C414yescomplemented
199C4⋊C4×C61—22no—
200C4⋊C4×C61—44no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—24no—
205C42×C61—21no—
206C42×C61—21no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—24no—
210C22⋊Dic61—24no—
211#11758198—22no—
212#11758198—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—44no—
215#11758196—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—48no—
220#11758196—48no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—48no—
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22⋊C411yescharacteristic
236C4×Dic61C22⋊C412yes—
237C4×Dic61C22⋊C412yes—
238C4×Dic61C22⋊C412yes—
239C4×Dic61C22⋊C412yes—
240C4×Dic61C22⋊C412yes—
241C4×Dic61C22⋊C412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61C2×C4⋊C412yes—
249C23×C61C23×C411yescharacteristic
250C23×C61C22×D412yes—
251C23×C61C22×D411yescharacteristic
252C23×C61C22×Q811yescharacteristic
253C23×C61C2×#4112yes—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61C2×C4⋊C412yes—
259D4×C61—24no—
260D4×C61—24no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—24no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—41no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—44no—
274C2×C4×C61—44no—
275C2×C4×C61—44no—
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C2×C4⋊C412yes—
280C22⋊D61—24no—
281C22⋊D61—24no—
282C22⋊D61—28no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—24no—
286C2×Dic61—24no—
287C2×Dic61—24no—
288C2×Dic61—22no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—41no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—44no—
298C2×Dic61—44no—
299C2×Dic61—44no—
300C2×Dic61C2×C22⋊C411yescharacteristic
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61C2×C22⋊C412yes—
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C4⋊C412yes—
307C2×Dic61C2×C4⋊C412yes—
308C2×Dic61C2×C4⋊C412yes—
309C2×Dic61#11712yes—
310C2×Dic61#11712yes—
311C2×Dic61#12114yes—
312C2×Dic61#12114yes—
313C2×Dic61C22⋊Q814yes—
314C2×Dic61C22⋊Q814yes—
315C4×D61—24no—
316C4×D61—24no—
317C4×D61—42no—
318C4×D61—42no—
319C4×D61—42no—
320C4×D61—42no—
321Dic122—28no—
322#20632—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—21no—
325C22×C61—22no—
326C22×C61—21no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61C22×C22⋊C411yescharacteristic
336C22×C61C22×C4⋊C411yescharacteristic
337C22×C61C2×#11711yescharacteristic
338C22×C61C2×#12112yes—
339C22×C61C2×C22⋊Q812yes—
340C2×D61—22no—
341C2×D61—42no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—42no—
345C4×C61—21no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—41no—
349C4×C61—41no—
350C4×C61—84no—
351C4×C61#41012yescomplemented
352Dic61—21no—
353Dic61—22no—
354Dic61—22no—
355Dic61—41no—
356Dic61—41no—
357Dic61—84no—
358Dic61#38014yes—
359Dic61#38012yes—
360Dic61#38012yes—
361Dic61#41012yescomplemented
362C2×C4×#41—611no—
363C2×#410—612no—
364#2285—612no—
365#1799—612no—
366#1799—612no—
367#1799—612no—
368#1799—611no—
369#1799D6111yescharacteristic, complemented
370#1740—612no—
371C2×C61—22no—
372C2×C61—21no—
373C2×C61—21no—
374C2×C61—22no—
375C2×C61—42no—
376C2×C61C2×#38011yescharacteristic
377C2×C61C2×#41011yescharacteristic
378C2×C61C2×#41011yescharacteristic
379D61—42no—
380C22×#41—611no—
381C4×#41—1222no—
382C4×#41—1222no—
383C4×#41—1222no—
384C4×#41—1222no—
385C2×C4×Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×C4×D4—611no—
392C2×C4×D4C2×D6111yescharacteristic
393C2×#117—611no—
394C2×#117—611no—
395C2×#117—611no—
396C2×#117—614no—
397C22×C42—611no—
398C22×C42—611no—
399C22×C42—611no—
400#410—1228no—
401C2×#99—612no—
402C2×#99—614no—
403C2×#99C2×D6112yes—
404#384—1222no—
405#382—1222no—
406#380—612no—
407#380—614no—
408#380C2×D6112yes—
409C4×C4⋊C4—1222no—
410C4×C4⋊C4—1222no—
411#342—614no—
412#342—612no—
413#342C2×D6112yes—
414C61#2063211yescharacteristic, complemented, Sylow
415C2×#41—614no—
416C2×#41—614no—
417C2×#41—1222no—
418C2×#41—1222no—
419C2×#41—1224no—
420C22×Q8—611no—
421C22×D4—611no—
422C22×D4—611no—
423C22×D4C22×D6111yescharacteristic
424C23×C4—611no—
425C23×C4—611no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4C4×D6111yescharacteristic
432C23×C4C22×D6111yescharacteristic
433C4×Q8—1222no—
434C4×Q8—1222no—
435C4×Q8—1222no—
436C4×Q8—1222no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—1222no—
440C4×D4—1222no—
441C4×D4—1222no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1222no—
447C4×D4—1222no—
448C4×D4—1222no—
449#117—1222no—
450#117—1222no—
451#117—1222no—
452#117—1222no—
453#117—1222no—
454#117—1222no—
455#117—1228no—
456#117—1228no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—1224no—
464C2×C4⋊C4—1224no—
465C2×C4⋊C4—1222no—
466C2×C4⋊C4C4×D6111yescharacteristic
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4—614no—
472C2×C22⋊C4C4×D6111yescharacteristic
473C2×C22⋊C4C22×D6114yes—
474C2×C22⋊C4C22×D6111yescharacteristic
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—612no—
480C2×C42—612no—
481C2×C42—612no—
482C2×C42—612no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42—1224no—
497C2×C42C4×D6111yescharacteristic
498#99—24no—
499#99—1228no—
500#99—1224no—
501#95—22no—
502#95—1224no—
503#95—1222no—
504C24—611no—
505C24C2×C4×D6111yescharacteristic
506C24C23×D6111yescharacteristic
507#41—1228no—
508#41—1228no—
509#41—1228no—
510#41—1228no—
511C2×Q8—614no—
512C2×Q8—1222no—
513C2×Q8—1222no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—612no—
517C2×D4—612no—
518C2×D4—614no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4D4×D6112yes—
524C2×D4Q8×D6112yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—612no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—614no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—612no—
540C22×C4—614no—
541C22×C4—611no—
542C22×C4—612no—
543C22×C4—614no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1222no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1224no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4C2×C4×D6111yescharacteristic
565C22×C4C2×C4×D6111yescharacteristic
566C22×C4C2×C4×D6111yescharacteristic
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4D4×D6112yes—
569C22×C4D4×D6112yes—
570C4⋊C4—22no—
571C4⋊C4—44no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—2444no—
578C4⋊C4—2448no—
579C4⋊C4—2448no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—1222no—
588C22⋊C4—1224no—
589C22⋊C4—1224no—
590C42—21no—
591C42—21no—
592C42—611no—
593C42—611no—
594C42—611no—
595C42—611no—
596C42—612no—
597C42—612no—
598C42—612no—
599C42—612no—
600C42—612no—
601C42—612no—
602C42—1221no—
603C42—1221no—
604C42—1221no—
605C42—1221no—
606C42—1221no—
607C42—1221no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—2448no—
613C23—21no—
614C23—21no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—612no—
620C23—1221no—
621C23—1221no—
622C23—2441no—
623C23—2441no—
624C23C4⋊C4×D6112yes—
625C23C22×C4×D6111yescharacteristic
626C23C2×D4×D6112yes—
627C23C2×D4×D6111yescharacteristic
628C23C2×Q8×D6111yescharacteristic
629C23#41×D6112yes—
630Q8—1228no—
631D4—24no—
632D4—24no—
633D4—1228no—
634D4—1224no—
635D4—1224no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—614no—
660C2×C4—614no—
661C2×C4—614no—
662C2×C4—614no—
663C2×C4—611no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—1224no—
667C2×C4—1224no—
668C2×C4—1224no—
669C2×C4—1224no—
670C2×C4—1224no—
671C2×C4—1222no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—2442no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2442no—
680C2×C4—2441no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2444no—
684C2×C4—2444no—
685C2×C4—2444no—
686C2×C4—2442no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4C22⋊C4×D6111yescharacteristic
690C2×C4C22⋊C4×D6112yes—
691C2×C4C22⋊C4×D6111yescharacteristic
692C2×C4C4⋊C4×D6112yes—
693C22—22no—
694C22—21no—
695C22—22no—
696C22—21no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—41no—
705C22—1222no—
706C22—2442no—
707C22—2442no—
708C22—2441no—
709C22—2441no—
710C22C2×C22⋊C4×D6111yescharacteristic
711C22C2×C4⋊C4×D6111yescharacteristic
712C22#117×D6111yescharacteristic
713C22#121×D6112yes—
714C22C22⋊Q8×D6112yes—
715C4—21no—
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—84no—
721C4—612no—
722C4—612no—
723C4—612no—
724C4—614no—
725C4—1222no—
726C4—1221no—
727C4—1222no—
728C4—4884no—
729C4—2441no—
730C4—2441no—
731C4#1683973412yescomplemented
732C2—22no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—42no—
737C2—2442no—
738C2#380×D6111yescharacteristic
739C2#410×D6111yescharacteristic
740C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C22
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#20632
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #21448221C2semidirect
4. #21445807C2semidirect
5. #21445806C2semidirect
6. #21445805C2semidirect
7. #21445804C2semidirect
8. #21445550C2semidirect
9. C61×#1799C2semidirect
15. C2×C4×Dic122C4semidirect
16. C2×#14519742C4semidirect
18. C2×C4×C22⋊D61C4semidirect
20. C2×#14519737C4semidirect
22. C2×#14519735C4semidirect
23. C2×#14519733C4semidirect
26. C22×C4×Dic61C4semidirect
28. C2×C42×D61C4semidirect
156. C2×C22⋊D61C4⋊C4semidirect
167. C22×Dic61C4⋊C4semidirect
195. C2×C4×D61C4⋊C4semidirect
198. C2×Dic122C4⋊C4semidirect
351. C4×C61#410semidirect
361. Dic61#410semidirect
369. #1799D61semidirect
414. C61#20632semidirect
731. C4#16839734semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
C2×#168397342
#214482212
#214458072
#214458062
#214458052
#214458042
#214455502
C61×#17992
#2063261