Finite Group Databasebeta

← #29585301

Subgroups — #29585301

Order 15616.

1550 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, 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
10C2×#14519736C2211yescharacteristic
11C2×#14519735C412yescomplemented
12C2×#14519734—21no—
13C2×#14519733—21no—
14#117×D61—22no—
15#117×D61—22no—
16#117×D61—22no—
17#117×D61—22no—
18C2×C4⋊C4×D61C412yescomplemented
19C22×#11758198—21no—
20C2×C22⋊C4×D61—21no—
21C22×C4×Dic61C2211yescharacteristic
22C2×C42×D61—21no—
23#16839725—22no—
24#16839725C414yescomplemented
25C2×#14519689—21no—
26C2×#14519689—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×D61—22no—
49C22×C4×D61C2×C412yes—
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C412yes—
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D412yes—
56C22×C4×D61Q812yes—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194C2×C412yescomplemented
63C22×#92418—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736D412yes—
67#14519736D412yes—
68#14519735—24no—
69#14519735—24no—
70#14519734—24no—
71#14519734—24no—
72#14519733—24no—
73#14519733—24no—
74C2×C4⋊Dic61C2×C412yes—
75C2×#11758196—22no—
76C4⋊C4×D61—24no—
77C4⋊C4×D61—24no—
78C2×C22⋊Dic61—21no—
79C2×#11758198—28no—
80C2×#11758198—22no—
81C2×#11758198—24no—
82C22⋊C4×D61—24no—
83C22⋊C4×D61—24no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2×C412yescomplemented
92C42×D61—24no—
93C42×D61—24no—
94#14519689—24no—
95#14519689—24no—
96#14519684—24no—
97C23×C4×C61—21no—
98C23×C4×C61C2311yescharacteristic
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C2×M16×C61—21no—
104C2×M16×C61C2×C412yescomplemented
105C22×C8×C61—21no—
106#117×C61—21no—
107#117×C61—21no—
108#117×C61D412yes—
109#117×C61D412yes—
110C2×C4⋊C4×C61C2×C412yes—
111C2×C22⋊C4×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61—21no—
118C2×C42×C61C2×C412yescomplemented
119C24×C61C2×D411yescharacteristic
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—24no—
125C23×D61—42no—
126C23×D61C22⋊C411yescharacteristic
127C23×D61C22⋊C412yes—
128C23×D61C22⋊C411yescharacteristic
129C23×D61C4⋊C412yes—
130C22×C4×C61—24no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—42no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×Q811yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—24no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—42no—
158C22×Dic61—41no—
159C22×Dic61—41no—
160C22×Dic61C22⋊C412yes—
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C4⋊C412yes—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—28no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61C4212yes—
200C2×C4×D61C4212yes—
201C2×C4×D61C22⋊C412yes—
202C2×C4×D61C22⋊C412yes—
203C2×C4×D61C4⋊C412yes—
204C2×C4×D61C4⋊C412yes—
205C2×C4×D61C4⋊C412yes—
206C2×C4×D61C4⋊C412yes—
207M16×C61—22no—
208M16×C61—22no—
209M16×C61—41no—
210M16×C61—41no—
211C2×C8×C61—22no—
212C2×C8×C61—41no—
213C2×C8×C61—41no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61C22⋊C414yescomplemented
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C42×C61—22no—
219C42×C61—22no—
220C42×C61—22no—
221C42×C61—22no—
222C42×C61—41no—
223C42×C61—41no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226#11758198—28no—
227#11758198—216no—
228C4⋊Dic61—22no—
229C4⋊Dic61C22⋊C414yescomplemented
230#11758196—28no—
231C4×Dic61—28no—
232C4×Dic61—22no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C4×Dic61—41no—
237C4×Dic61—41no—
238#11758194—22no—
239#11758194—22no—
240#11758194—41no—
241#11758194—41no—
242C2×#92418—22no—
243C2×#92418—41no—
244C2×#92418—41no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61C2×C22⋊C411yescharacteristic
248C23×C61C2×C22⋊C411yescharacteristic
249C23×C61C2×C4⋊C411yescharacteristic
250C23×C61#12011yescharacteristic
251C23×C61#12011yescharacteristic
252C23×C61#12311yescharacteristic
253C23×C61#12311yescharacteristic
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—22no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—44no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61#9512yes—
274C22×D61#9512yes—
275C22×D61#10414yes—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—44no—
279C2×C4×C61—42no—
280C2×C4×C61—44no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61C2×C4211yescharacteristic
285C2×C4×C61C2×C22⋊C411yescharacteristic
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C2×C4⋊C411yescharacteristic
289C2×C4×C61C2×C4⋊C411yescharacteristic
290C2×C4×C61#11711yescharacteristic
291C2×C4×C61#11711yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61#12011yescharacteristic
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61C22⋊Q811yescharacteristic
307C2×C4×C61C22⋊Q811yescharacteristic
308C2×C4×C61C22⋊Q811yescharacteristic
309C2×C4×C61C22⋊Q811yescharacteristic
310C2×C4×C61#12311yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—44no—
323C2×Dic61—42no—
324C2×Dic61—44no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61#9512yes—
329C2×Dic61#9512yes—
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—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—416no—
347C8×C61—42no—
348#92418—42no—
349#10733—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61C2×#9511yescharacteristic
359C22×C61#37911yescharacteristic
360C22×C61#38111yescharacteristic
361C22×C61#38511yescharacteristic
362C22×C61#38511yescharacteristic
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61C2×#10412yes—
366C22×C61#42112yes—
367C2×D61—24no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—24no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61#33914yescomplemented
381C4×C61—44no—
382C4×C61—44no—
383C4×C61C4×C22⋊C411yescharacteristic
384C4×C61C4×C22⋊C411yescharacteristic
385C4×C61#38011yescharacteristic
386C4×C61#38011yescharacteristic
387C4×C61#38511yescharacteristic
388C4×C61#38511yescharacteristic
389C4×C61#38611yescharacteristic
390C4×C61#38611yescharacteristic
391Dic61—22no—
392Dic61—22no—
393Dic61—44no—
394Dic61—44no—
395C22×#117—611no—
396C2×#407—611no—
397C2×C4×C22⋊C4—611no—
398C2×#339—611no—
399C2×#339—611no—
400C2×#339—611no—
401C2×#339D6111yescharacteristic, complemented
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61C22⋊#9511yescharacteristic
407C2×C61C2×#33911yescharacteristic
408C2×C61#173311yescharacteristic
409C2×C61#178912yes—
410C2×C61#182612yes—
411D61—24no—
412D61—42no—
413C24×C4—611no—
414C22×M16—611no—
415C22×M16C2×D6111yescharacteristic
416C2×#117—611no—
417C2×#117—612no—
418C2×#117—1221no—
419C2×#117—1221no—
420C2×#117—1222no—
421C2×#117—1222no—
422C2×#117—1222no—
423C2×#117—1222no—
424C2×#117C2×D6111yescharacteristic
425C22×C4⋊C4—612no—
426C22×C22⋊C4—1221no—
427C22×C22⋊C4—1221no—
428C22×C42—611no—
429C22×C42—1221no—
430C22×C42C2×D6111yescharacteristic
431#407—614no—
432#407—1222no—
433C2×C22⋊C8—1221no—
434C2×C22⋊C8—1221no—
435C4×C22⋊C4—614no—
436C4×C22⋊C4—1222no—
437C2×#95—1221no—
438#339—22no—
439#339—1222no—
440#339—1222no—
441#339—1222no—
442C61#1073311yescharacteristic, complemented, Sylow
443C25—611no—
444C23×C4—21no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—612no—
449C23×C4—612no—
450C23×C4—612no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—612no—
454C23×C4—1222no—
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—612no—
471C2×M16—1221no—
472C2×M16—1221no—
473C2×M16—1221no—
474C2×M16—1221no—
475C2×M16—1221no—
476C2×M16C4×D6112yescomplemented
477C22×C8—21no—
478C22×C8—1221no—
479#117—21no—
480#117—21no—
481#117—612no—
482#117—612no—
483#117—1224no—
484#117—1224no—
485#117—1224no—
486#117—1224no—
487#117—1224no—
488#117—1221no—
489#117—1221no—
490#117—1224no—
491#117D24412yes—
492#117C22⋊D6112yes—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4C4×D6112yes—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1228no—
504C2×C22⋊C4—1221no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—612no—
512C2×C42—1224no—
513C2×C42—1224no—
514C2×C42—1222no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42C4×D6112yescomplemented
522C22⋊C8—1224no—
523C22⋊C8—1224no—
524#95—1224no—
525C24—611no—
526C24—611no—
527C24—612no—
528C24—612no—
529C24—1224no—
530C24—1221no—
531C24—1221no—
532C24—1221no—
533C24—1221no—
534C24—2442no—
535C24D4×D6111yescharacteristic
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—612no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—1228no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1224no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—2444no—
595C22×C4—2444no—
596C22×C4—2442no—
597C22×C4—2441no—
598C22×C4—2441no—
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×D24411yescharacteristic
603C22×C4#1175822211yescharacteristic
604C22×C4#1175822211yescharacteristic
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4#1175822411yescharacteristic
610C22×C4Q8×D6111yescharacteristic
611C22×C4#1175822611yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613M16—22no—
614M16—22no—
615M16—41no—
616M16—41no—
617M16—1222no—
618M16—1222no—
619M16—2441no—
620M16—2441no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—1222no—
625C2×C8—2441no—
626C2×C8—2441no—
627C4⋊C4—22no—
628C4⋊C4—614no—
629C4⋊C4—1228no—
630C4⋊C4—1222no—
631C4⋊C4#1175819814yescomplemented
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—1228no—
635C22⋊C4—12216no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—41no—
643C42—41no—
644C42—1228no—
645C42—1222no—
646C42—1222no—
647C42—1222no—
648C42—1222no—
649C42—2441no—
650C42—2441no—
651C23—22no—
652C23—22no—
653C23—614no—
654C23—612no—
655C23—612no—
656C23—1224no—
657C23—1224no—
658C23—1222no—
659C23—1221no—
660C23—1221no—
661C23—1222no—
662C23—1222no—
663C23—1221no—
664C23—1221no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—2442no—
670C23—2442no—
671C23—2444no—
672C23—2444no—
673C23—2444no—
674C23—2444no—
675C23C22⋊C4×D6111yescharacteristic
676C23C22⋊C4×D6111yescharacteristic
677C23C4⋊C4×D6111yescharacteristic
678C23#1451974511yescharacteristic
679C23#1451974711yescharacteristic
680C23#1451975911yescharacteristic
681C23#1451976211yescharacteristic
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1224no—
717C2×C4—1224no—
718C2×C4—24416no—
719C2×C4—2444no—
720C2×C4—2444no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4C42×D6111yescharacteristic
726C2×C4C22⋊C4×D6111yescharacteristic
727C2×C4C22⋊C4×D6111yescharacteristic
728C2×C4C2×#1175819811yescharacteristic
729C2×C4C4⋊C4×D6111yescharacteristic
730C2×C4C4⋊C4×D6111yescharacteristic
731C2×C4#1451973411yescharacteristic
732C2×C4#1451973511yescharacteristic
733C2×C4#1451973711yescharacteristic
734C2×C4#1451973711yescharacteristic
735C2×C4C4×C22⋊D6111yescharacteristic
736C2×C4C4×C22⋊D6111yescharacteristic
737C2×C4#1451973911yescharacteristic
738C2×C4#1451973911yescharacteristic
739C2×C4C4×D24411yescharacteristic
740C2×C4C4×D24411yescharacteristic
741C2×C4#1451974511yescharacteristic
742C2×C4#1451974711yescharacteristic
743C2×C4#1451974811yescharacteristic
744C2×C4#1451975011yescharacteristic
745C2×C4#1451975011yescharacteristic
746C2×C4#1451975211yescharacteristic
747C2×C4#1451975311yescharacteristic
748C2×C4#1451975511yescharacteristic
749C2×C4#1451975511yescharacteristic
750C2×C4#1451975711yescharacteristic
751C2×C4#1451975911yescharacteristic
752C2×C4#1451976211yescharacteristic
753C8—42no—
754C8—2442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—614no—
764C22—1224no—
765C22—1224no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2442no—
776C22—2442no—
777C22#95×D6111yescharacteristic
778C22#1683961711yescharacteristic
779C22#1683962411yescharacteristic
780C22#1683963311yescharacteristic
781C22#1683963611yescharacteristic
782C22#1683963811yescharacteristic
783C22#1683964011yescharacteristic
784C22#104×D6112yes—
785C22#1683977712yes—
786C4—44no—
787C4—44no—
788C4—1222no—
789C4—1222no—
790C4—2444no—
791C4—2444no—
792C4#1683960911yescharacteristic
793C4C4×#1175819811yescharacteristic
794C4#1683961911yescharacteristic
795C4#1683962111yescharacteristic
796C4#1683963311yescharacteristic
797C4#1683963611yescharacteristic
798C4#1683963811yescharacteristic
799C4#1683964011yescharacteristic
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—1224no—
805C2—2442no—
806C2#2144404011yescharacteristic
807C2#339×D6111yescharacteristic
808C2#2144552711yescharacteristic
809C2#2144576112yes—
810C2#2144591712yes—
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#10733
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
11. C2×#14519735C4semidirect
18. C2×C4⋊C4×D61C4semidirect
24. #16839725C4semidirect
28. C4×#11758198C4semidirect
62. C2×#11758194C2×C4semidirect
91. C2×C4×Dic61C2×C4semidirect
104. C2×M16×C61C2×C4semidirect
118. C2×C42×C61C2×C4semidirect
215. C4⋊C4×C61C22⋊C4semidirect
229. C4⋊Dic61C22⋊C4semidirect
380. C2×D61#339semidirect
401. C2×#339D61semidirect
442. C61#10733semidirect
476. C2×M16C4×D61semidirect
521. C2×C42C4×D61semidirect
631. C4⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
C2×#168397252
C2×C4×#117581982
C2×#168395232
C2×#168395222
C2×#168395212
C2×C61×#3392
#1073361