Finite Group Databasebeta

← #29585297

Subgroups — #29585297

Order 15616.

1510 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
1C22×M16×D61C211yesmaximal, characteristic
2#21448198C211yesmaximal, characteristic
3C2×C4×#11758198C211yesmaximal, characteristic
4C2×#16839523C211yesmaximal, characteristic, complemented
5C2×#16839522C211yesmaximal, characteristic, complemented
6C2×#16839521C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758189—21no—
11C2×M16×D61—22no—
12C2×M16×D61—22no—
13C2×M16×D61—22no—
14C2×M16×D61—22no—
15C2×M16×D61—22no—
16C2×M16×D61C414yescomplemented
17C22×C8×D61—21no—
18C2×#14519736C2211yescharacteristic
19C22×#11758198—21no—
20C22×C4×Dic61C2211yescharacteristic
21#16839623—21no—
22#16839619C412yescomplemented
23#16839619C412yescomplemented
24#16839617—21no—
25C4×#11758198—21no—
26C4×#11758198—21no—
27C4×#11758198—22no—
28C4×#11758198C414yescomplemented
29C2×#14519684—21no—
30#16839523—22no—
31#16839522—22no—
32#16839521—22no—
33C22×M16×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C61×#339—22no—
37C24×D61D411yescharacteristic
38C23×Dic61—21no—
39C23×Dic61D411yescharacteristic
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61C2×C412yes—
49C22×C4×D61C2×C412yes—
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D412yes—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61Q812yes—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194C2×C412yes—
60C2×#11758194D412yes—
61C2×#11758194D412yes—
62C2×#11758189—24no—
63C2×#11758189—24no—
64C2×#11758189—24no—
65M16×D61—28no—
66M16×D61—28no—
67M16×D61—28no—
68M16×D61—28no—
69C22×#92418—21no—
70C2×C8×D61—24no—
71C2×C8×D61—24no—
72C2×C8×D61—24no—
73#14519736—21no—
74#14519736—21no—
75#14519736—21no—
76#14519736—21no—
77C2×C4⋊Dic61C2×C412yes—
78C2×C22⋊Dic61—21no—
79C2×#11758198—28no—
80C2×#11758198—24no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2×C412yes—
90#14519684—24no—
91#14519684—22no—
92#14519684—22no—
93C23×C4×C61—21no—
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61C2×C412yes—
99C2×M16×C61D412yes—
100C2×M16×C61D412yes—
101C22×C8×C61—21no—
102#117×C61—21no—
103#117×C61—21no—
104#117×C61—21no—
105#117×C61—21no—
106C2×C4⋊C4×C61C2×C412yes—
107C2×C22⋊C4×C61—21no—
108C2×C42×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2×C412yes—
115C24×C61C2×D411yescharacteristic
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—24no—
121C23×D61—42no—
122C23×D61C22⋊C411yescharacteristic
123C23×D61C22⋊C412yes—
124C23×D61C22⋊C411yescharacteristic
125C23×D61C4⋊C412yes—
126C22×C4×C61—24no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—42no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×Q811yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—24no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—42no—
154C22×Dic61—41no—
155C22×Dic61—41no—
156C22×Dic61C22⋊C412yes—
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C4⋊C412yes—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—21no—
187C2×C4×D61—22no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—22no—
191C2×C4×D61—21no—
192C2×C4×D61C4212yes—
193C2×C4×D61C4212yes—
194C2×C4×D61C22⋊C412yes—
195C2×C4×D61C22⋊C412yes—
196C2×C4×D61C4⋊C412yes—
197C2×C4×D61C4⋊C412yes—
198C2×C4×D61C4⋊C412yes—
199C2×C4×D61C4⋊C412yes—
200M16×C61—22no—
201M16×C61—22no—
202M16×C61—22no—
203M16×C61C22⋊C414yescomplemented
204C2×C8×C61—22no—
205C2×C8×C61—22no—
206C2×C8×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C42×C61—22no—
212C42×C61—22no—
213C42×C61—41no—
214C42×C61—41no—
215C42×C61—41no—
216C42×C61—41no—
217C22⋊Dic61—41no—
218C22⋊Dic61—41no—
219#11758198—216no—
220#11758198—44no—
221#11758198—44no—
222C4⋊Dic61—22no—
223C4⋊Dic61—22no—
224C4×Dic61—22no—
225C4×Dic61—22no—
226C4×Dic61—41no—
227C4×Dic61—41no—
228C4×Dic61—41no—
229C4×Dic61—41no—
230#11758194—22no—
231#11758194—22no—
232#11758194—22no—
233#11758194C22⋊C414yescomplemented
234C2×#92418—22no—
235C2×#92418—22no—
236C2×#92418—22no—
237#11758189—216no—
238C8×D61—216no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61C2×C22⋊C411yescharacteristic
242C23×C61C2×C22⋊C411yescharacteristic
243C23×C61C2×C4⋊C411yescharacteristic
244C23×C61#12111yescharacteristic
245C23×C61#12111yescharacteristic
246C23×C61#12111yescharacteristic
247C23×C61#12111yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61—44no—
267C22×D61#9512yes—
268C22×D61#9512yes—
269C22×D61#10414yes—
270C2×C4×C61—24no—
271C2×C4×C61—44no—
272C2×C4×C61—44no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61C2×C4211yescharacteristic
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C2×C22⋊C411yescharacteristic
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×C4×C61C2×C4⋊C411yescharacteristic
283C2×C4×C61C2×C4⋊C411yescharacteristic
284C2×C4×C61#11711yescharacteristic
285C2×C4×C61#11711yescharacteristic
286C2×C4×C61C4×D411yescharacteristic
287C2×C4×C61C4×D411yescharacteristic
288C2×C4×C61C4×D411yescharacteristic
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61C4×D411yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61#12011yescharacteristic
295C2×C4×C61#12011yescharacteristic
296C2×C4×C61#12011yescharacteristic
297C2×C4×C61#12011yescharacteristic
298C2×C4×C61C22⋊Q811yescharacteristic
299C2×C4×C61C22⋊Q811yescharacteristic
300C2×C4×C61C22⋊Q811yescharacteristic
301C2×C4×C61C22⋊Q811yescharacteristic
302C2×C4×C61#12311yescharacteristic
303C2×C4×C61#12311yescharacteristic
304C2×C4×C61#12311yescharacteristic
305C2×C4×C61#12311yescharacteristic
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—24no—
315C2×Dic61—44no—
316C2×Dic61—44no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61#9512yes—
323C2×Dic61#9512yes—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C8×C61—24no—
341#92418—24no—
342#10732—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61C2×#9511yescharacteristic
352C22×C61#38011yescharacteristic
353C22×C61#38011yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61#38611yescharacteristic
356C22×C61#38611yescharacteristic
357C22×C61#38611yescharacteristic
358C22×C61C2×#10412yes—
359C22×C61#42112yes—
360C2×D61—24no—
361C2×D61—24no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61#33914yescomplemented
374C4×C61—44no—
375C4×C61—82no—
376C4×C61C4×C22⋊C411yescharacteristic
377C4×C61C4×C22⋊C411yescharacteristic
378C4×C61#37911yescharacteristic
379C4×C61#38111yescharacteristic
380C4×C61#38511yescharacteristic
381C4×C61#38511yescharacteristic
382C4×C61#38511yescharacteristic
383C4×C61#38511yescharacteristic
384Dic61—22no—
385Dic61—22no—
386Dic61—44no—
387Dic61—82no—
388C23×M16—611no—
389#2280—611no—
390C2×C4×C22⋊C4—611no—
391C2×#339—611no—
392C2×#339—611no—
393C2×#339—611no—
394C2×#339D6111yescharacteristic, complemented
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—21no—
399C2×C61C22⋊#9511yescharacteristic
400C2×C61C2×#33911yescharacteristic
401C2×C61#173311yescharacteristic
402C2×C61#187112yes—
403C2×C61#187112yes—
404D61—24no—
405D61—42no—
406C24×C4—611no—
407C22×M16—611no—
408C22×M16—614no—
409C22×M16—1221no—
410C22×M16—1222no—
411C22×M16—1222no—
412C22×M16—1222no—
413C22×M16—1222no—
414C22×M16—1222no—
415C22×M16C2×D6111yescharacteristic
416C23×C8—1221no—
417C2×#117—611no—
418C2×#117C2×D6111yescharacteristic
419C22×C22⋊C4—1221no—
420C22×C42—611no—
421C22×C42C2×D6111yescharacteristic
422#381—1221no—
423#380—612no—
424#380—612no—
425#379—1221no—
426C4×C22⋊C4—614no—
427C4×C22⋊C4—1222no—
428C4×C22⋊C4—1221no—
429C4×C22⋊C4—1221no—
430C2×#95—1221no—
431#339—22no—
432#339—1222no—
433#339—1222no—
434#339—1222no—
435C61#1073211yescharacteristic, complemented, Sylow
436C25—611no—
437C23×C4—21no—
438C23×C4—611no—
439C23×C4—612no—
440C23×C4—612no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—612no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—612no—
447C23×C4—1221no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4C22×D6111yescharacteristic
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—612no—
461C2×M16—612no—
462C2×M16—612no—
463C2×M16—1224no—
464C2×M16—1224no—
465C2×M16—1224no—
466C2×M16—1228no—
467C2×M16—1228no—
468C2×M16—1228no—
469C2×M16—1221no—
470C2×M16—1221no—
471C2×M16—1221no—
472C2×M16—1228no—
473C2×M16C4×D6112yes—
474C2×M16D24412yes—
475C2×M16C22⋊D6112yes—
476C22×C8—21no—
477C22×C8—1224no—
478C22×C8—1224no—
479C22×C8—1224no—
480C22×C8—1221no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—21no—
485#117—1221no—
486#117—1221no—
487#117—1221no—
488#117—1221no—
489C2×C4⋊C4—612no—
490C2×C4⋊C4C4×D6112yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1224no—
493C2×C22⋊C4—1228no—
494C2×C22⋊C4—1222no—
495C2×C22⋊C4—1222no—
496C2×C22⋊C4—1221no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—612no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42—1221no—
509C2×C42—1221no—
510C2×C42C4×D6112yes—
511#95—1224no—
512#95—1222no—
513#95—1222no—
514C24—611no—
515C24—611no—
516C24—612no—
517C24—612no—
518C24—1224no—
519C24—1221no—
520C24—1221no—
521C24—1221no—
522C24—1221no—
523C24—2442no—
524C24D4×D6111yescharacteristic
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—612no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1222no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1222no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1222no—
568C22×C4—1221no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1224no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—2442no—
583C22×C4—2441no—
584C22×C4—2441no—
585C22×C4C2×C4×D6111yescharacteristic
586C22×C4C2×C4×D6111yescharacteristic
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×D24411yescharacteristic
589C22×C4#1175822211yescharacteristic
590C22×C4#1175822211yescharacteristic
591C22×C4D4×D6111yescharacteristic
592C22×C4D4×D6111yescharacteristic
593C22×C4D4×D6111yescharacteristic
594C22×C4D4×D6111yescharacteristic
595C22×C4#1175822411yescharacteristic
596C22×C4Q8×D6111yescharacteristic
597C22×C4#1175822611yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599M16—22no—
600M16—22no—
601M16—22no—
602M16—614no—
603M16—12216no—
604M16—1222no—
605M16—1222no—
606M16—1222no—
607M16#1175819814yescomplemented
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—12216no—
612C2×C8—1222no—
613C2×C8—1222no—
614C2×C8—1222no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—12216no—
622C22⋊C4—2444no—
623C22⋊C4—2444no—
624C22⋊C4—2441no—
625C22⋊C4—2441no—
626C42—22no—
627C42—22no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—1222no—
633C42—1222no—
634C42—2441no—
635C42—2441no—
636C42—2441no—
637C42—2441no—
638C23—22no—
639C23—22no—
640C23—614no—
641C23—612no—
642C23—612no—
643C23—1224no—
644C23—1224no—
645C23—1222no—
646C23—1221no—
647C23—1221no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1221no—
654C23—1222no—
655C23—1221no—
656C23—2442no—
657C23—2442no—
658C23—2444no—
659C23—2444no—
660C23—2444no—
661C23—2444no—
662C23C22⋊C4×D6111yescharacteristic
663C23C22⋊C4×D6111yescharacteristic
664C23C4⋊C4×D6111yescharacteristic
665C23#1451974811yescharacteristic
666C23#1451975011yescharacteristic
667C23#1451975011yescharacteristic
668C23#1451975211yescharacteristic
669C2×C4—24no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1222no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2442no—
711C2×C4C42×D6111yescharacteristic
712C2×C4C22⋊C4×D6111yescharacteristic
713C2×C4C22⋊C4×D6111yescharacteristic
714C2×C4C2×#1175819811yescharacteristic
715C2×C4C4⋊C4×D6111yescharacteristic
716C2×C4C4⋊C4×D6111yescharacteristic
717C2×C4#1451973411yescharacteristic
718C2×C4#1451973511yescharacteristic
719C2×C4#1451973711yescharacteristic
720C2×C4#1451973711yescharacteristic
721C2×C4C4×C22⋊D6111yescharacteristic
722C2×C4C4×C22⋊D6111yescharacteristic
723C2×C4#1451973911yescharacteristic
724C2×C4#1451973911yescharacteristic
725C2×C4C4×D24411yescharacteristic
726C2×C4C4×D24411yescharacteristic
727C2×C4#1451974511yescharacteristic
728C2×C4#1451974511yescharacteristic
729C2×C4#1451974711yescharacteristic
730C2×C4#1451974711yescharacteristic
731C2×C4#1451975311yescharacteristic
732C2×C4#1451975511yescharacteristic
733C2×C4#1451975511yescharacteristic
734C2×C4#1451975711yescharacteristic
735C2×C4#1451975911yescharacteristic
736C2×C4#1451975911yescharacteristic
737C2×C4#1451976211yescharacteristic
738C2×C4#1451976211yescharacteristic
739C8—24no—
740C8—1224no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—614no—
750C22—1222no—
751C22—1222no—
752C22—1224no—
753C22—1224no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—2444no—
758C22—2444no—
759C22—2444no—
760C22—2444no—
761C22—2442no—
762C22—2442no—
763C22#95×D6111yescharacteristic
764C22#1683961911yescharacteristic
765C22#1683962111yescharacteristic
766C22#1683963811yescharacteristic
767C22#1683963811yescharacteristic
768C22#1683964011yescharacteristic
769C22#1683964011yescharacteristic
770C22#104×D6112yes—
771C22#1683977712yes—
772C4—44no—
773C4—82no—
774C4—1222no—
775C4—1222no—
776C4—4882no—
777C4—2444no—
778C4#1683960911yescharacteristic
779C4C4×#1175819811yescharacteristic
780C4#1683961711yescharacteristic
781C4#1683962411yescharacteristic
782C4#1683963311yescharacteristic
783C4#1683963311yescharacteristic
784C4#1683963611yescharacteristic
785C4#1683963611yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—1224no—
791C2—2442no—
792C2#2144404011yescharacteristic
793C2#339×D6111yescharacteristic
794C2#2144552711yescharacteristic
795C2#2144611812yes—
796C2#2144612012yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#10732
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#16839523C2semidirect
5. C2×#16839522C2semidirect
6. C2×#16839521C2semidirect
7. C2×C61×#339C2semidirect
16. C2×M16×D61C4semidirect
22. #16839619C4semidirect
23. #16839619C4semidirect
28. C4×#11758198C4semidirect
203. M16×C61C22⋊C4semidirect
233. #11758194C22⋊C4semidirect
373. C2×D61#339semidirect
394. C2×#339D61semidirect
435. C61#10732semidirect
607. M16#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D612
#214481982
C2×C4×#117581982
C2×#168395232
C2×#168395222
C2×#168395212
C2×C61×#3392
#1073261