Finite Group Databasebeta

← #29585325

Subgroups — #29585325

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic
3C2×#16839619C211yesmaximal, characteristic
4C2×#16839531C211yesmaximal, characteristic, complemented
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×C61×#343C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758189—21no—
12C2×M16×D61—22no—
13C2×M16×D61—22no—
14C2×M16×D61—22no—
15C2×M16×D61—22no—
16C2×M16×D61—22no—
17C2×M16×D61C414yescomplemented
18C22×C8×D61—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758198C412yes—
21#16839725—22no—
22#16839725C414yescomplemented
23C2×#14519689—21no—
24C2×#14519689—21no—
25#16839619—21no—
26#16839619—21no—
27#16839619—21no—
28#16839619—21no—
29C2×#14519684C412yes—
30#16839531—22no—
31#16839530—22no—
32#16839530—22no—
33C22×M16×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#343—22no—
37C24×D61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C412yes—
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×D61D412yes—
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61Q812yes—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194—21no—
64C2×#11758194C2×C412yes—
65C2×#11758194C2×C412yes—
66C2×#11758194D412yes—
67C2×#11758194D412yes—
68C2×#11758189—24no—
69C2×#11758189—24no—
70C2×#11758189—24no—
71M16×D61—28no—
72M16×D61—28no—
73M16×D61—28no—
74M16×D61—28no—
75C22×#92418—21no—
76C22×#92418—21no—
77C2×C8×D61—24no—
78C2×C8×D61—24no—
79C2×C8×D61—24no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—44no—
89#14519689—24no—
90#14519689—24no—
91#14519684—22no—
92#14519684—22no—
93C23×C4×C61C2×C412yes—
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C2×M16×C61C2×C412yes—
104C2×M16×C61C2×C412yes—
105C2×M16×C61D412yes—
106C2×M16×C61D412yes—
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C24×C61C22×C411yescharacteristic
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—41no—
123C23×D61—41no—
124C23×D61C4212yes—
125C23×D61C22⋊C411yescharacteristic
126C23×D61C22⋊C411yescharacteristic
127C23×D61C4⋊C412yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
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×D411yescharacteristic
142C22×C4×C61C2×Q811yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—42no—
155C22×Dic61—42no—
156C22×Dic61C4212yes—
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—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
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—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61C22⋊C412yes—
193C2×C4×D61C22⋊C412yes—
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×C61—22no—
204M16×C61—22no—
205M16×C61—41no—
206M16×C61—41no—
207M16×C61C22⋊C414yescomplemented
208C2×C8×C61—22no—
209C2×C8×C61—22no—
210C2×C8×C61—22no—
211C2×C8×C61—22no—
212C2×C8×C61—41no—
213C2×C8×C61—41no—
214C4⋊C4×C61—41no—
215C4⋊C4×C61—41no—
216C4⋊C4×C61—41no—
217C4⋊C4×C61—41no—
218#11758198—44no—
219#11758198—44no—
220C4⋊Dic61—41no—
221C4⋊Dic61—41no—
222C4⋊Dic61—41no—
223C4⋊Dic61—41no—
224#11758194—22no—
225#11758194—22no—
226#11758194—22no—
227#11758194—22no—
228#11758194—22no—
229#11758194—41no—
230#11758194—41no—
231#11758194C22⋊C414yescomplemented
232C2×#92418—22no—
233C2×#92418—22no—
234C2×#92418—22no—
235C2×#92418—22no—
236C2×#92418—41no—
237C2×#92418—41no—
238#11758189—216no—
239C8×D61—216no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61C2×C4211yescharacteristic
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C2×C4⋊C411yescharacteristic
247C23×C61C4×D411yescharacteristic
248C23×C61C4×D411yescharacteristic
249C23×C61C4×D411yescharacteristic
250C23×C61C4×D411yescharacteristic
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61#9512yes—
278C22×D61#9512yes—
279C22×D61#10012yes—
280C22×D61#10112yes—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—82no—
285C2×C4×C61—82no—
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C4⋊C411yescharacteristic
291C2×C4×C61C2×C4⋊C411yescharacteristic
292C2×C4×C61#11711yescharacteristic
293C2×C4×C61#11711yescharacteristic
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61#12011yescharacteristic
299C2×C4×C61#12011yescharacteristic
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×C4×C61#12311yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—82no—
326C2×Dic61—82no—
327C2×Dic61#9512yes—
328C2×Dic61#9512yes—
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—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C8×C61—24no—
346C8×C61—42no—
347#92418—24no—
348#92418—42no—
349#10739—611nomaximal, Sylow
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—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61C2×#9511yescharacteristic
363C22×C61C4×C22⋊C411yescharacteristic
364C22×C61C4×C22⋊C411yescharacteristic
365C22×C61#38511yescharacteristic
366C22×C61#38511yescharacteristic
367C22×C61#38611yescharacteristic
368C22×C61#38611yescharacteristic
369C22×C61C2×#10011yescharacteristic
370C22×C61C2×#10111yescharacteristic
371C22×C61#41311yescharacteristic
372C22×C61#41311yescharacteristic
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61#34314yescomplemented
391C4×C61—82no—
392C4×C61#37911yescharacteristic
393C4×C61#38011yescharacteristic
394C4×C61#38011yescharacteristic
395C4×C61#38111yescharacteristic
396C4×C61#38511yescharacteristic
397C4×C61#38511yescharacteristic
398C4×C61#38611yescharacteristic
399C4×C61#38611yescharacteristic
400Dic61—22no—
401Dic61—22no—
402Dic61—82no—
403C23×M16—611no—
404C2×#407—611no—
405C2×#380—611no—
406C2×#343—611no—
407C2×#343—611no—
408C2×#343—611no—
409C2×#343D6111yescharacteristic, complemented
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61C22⋊#9511yescharacteristic
415C2×C61C2×#34311yescharacteristic
416C2×C61#174211yescharacteristic
417C2×C61#190011yescharacteristic
418C2×C61#190011yescharacteristic
419C2×C61#190111yescharacteristic
420C2×C61#190111yescharacteristic
421D61—24no—
422D61—42no—
423C24×C4—611no—
424C22×M16—611no—
425C22×M16—611no—
426C22×M16—614no—
427C22×M16—1221no—
428C22×M16—1222no—
429C22×M16—1222no—
430C22×M16—1222no—
431C22×M16—1222no—
432C22×M16—1222no—
433C22×M16C2×D6111yescharacteristic
434C22×M16C2×D6111yescharacteristic
435C23×C8—1221no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4C2×D6111yescharacteristic
438C22×C22⋊C4—612no—
439#407—614no—
440#407—1222no—
441C2×C22⋊C8—1221no—
442C2×C22⋊C8—1221no—
443#380—1221no—
444#380—1221no—
445#380—1221no—
446#380—1221no—
447C2×#95—612no—
448#343—22no—
449#343—1222no—
450#343—1222no—
451#343—1222no—
452C61#1073911yescharacteristic, complemented, Sylow
453C25—611no—
454C23×C4—611no—
455C23×C4—612no—
456C23×C4—612no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—612no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—612no—
463C23×C4—612no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4—1221no—
471C23×C4—1221no—
472C23×C4C4×D6112yes—
473C23×C4C22×D6111yescharacteristic
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—612no—
483C2×M16—612no—
484C2×M16—612no—
485C2×M16—612no—
486C2×M16—1224no—
487C2×M16—1224no—
488C2×M16—1224no—
489C2×M16—1228no—
490C2×M16—1228no—
491C2×M16—1228no—
492C2×M16—1221no—
493C2×M16—1221no—
494C2×M16—1221no—
495C2×M16—1228no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16C4×D6112yes—
502C2×M16C4×D6112yes—
503C2×M16D24412yes—
504C2×M16C22⋊D6112yes—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—1224no—
508C22×C8—1224no—
509C22×C8—1224no—
510C22×C8—1221no—
511C22×C8—1221no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—2444no—
527C22⋊C8—1224no—
528C22⋊C8—1224no—
529#95—1222no—
530#95—1222no—
531C24—611no—
532C24—611no—
533C24—612no—
534C24—612no—
535C24—1222no—
536C24—1222no—
537C24—1221no—
538C24—1221no—
539C24—1221no—
540C24—1221no—
541C24—2441no—
542C24—2441no—
543C24C2×C4×D6111yescharacteristic
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—612no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1221no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4C2×D24411yescharacteristic
605C22×C4#1175822211yescharacteristic
606C22×C4#1175822211yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610C22×C4D4×D6111yescharacteristic
611C22×C4D4×D6111yescharacteristic
612C22×C4#1175822411yescharacteristic
613C22×C4Q8×D6111yescharacteristic
614C22×C4#1175822611yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616M16—22no—
617M16—22no—
618M16—22no—
619M16—22no—
620M16—22no—
621M16—41no—
622M16—41no—
623M16—614no—
624M16—12216no—
625M16—1222no—
626M16—1222no—
627M16—1222no—
628M16—1222no—
629M16—1222no—
630M16—2441no—
631M16—2441no—
632M16#1175819814yescomplemented
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—12216no—
640C2×C8—1222no—
641C2×C8—1222no—
642C2×C8—1222no—
643C2×C8—1222no—
644C2×C8—2441no—
645C2×C8—2441no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—2441no—
651C4⋊C4—2441no—
652C4⋊C4—2441no—
653C4⋊C4—2441no—
654C22⋊C4—2444no—
655C22⋊C4—2444no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—612no—
661C23—612no—
662C23—612no—
663C23—612no—
664C23—1224no—
665C23—1224no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—1221no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23C42×D6111yescharacteristic
691C23C22⋊C4×D6111yescharacteristic
692C23C4⋊C4×D6111yescharacteristic
693C23#1451973711yescharacteristic
694C23C4×C22⋊D6111yescharacteristic
695C23#1451973911yescharacteristic
696C23C4×D24411yescharacteristic
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—4882no—
729C2×C4—4882no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4C22⋊C4×D6111yescharacteristic
734C2×C4C22⋊C4×D6111yescharacteristic
735C2×C4C22⋊C4×D6111yescharacteristic
736C2×C4C2×#1175819811yescharacteristic
737C2×C4C4⋊C4×D6111yescharacteristic
738C2×C4C4⋊C4×D6111yescharacteristic
739C2×C4#1451973411yescharacteristic
740C2×C4#1451973511yescharacteristic
741C2×C4#1451973711yescharacteristic
742C2×C4C4×C22⋊D6111yescharacteristic
743C2×C4#1451973911yescharacteristic
744C2×C4C4×D24411yescharacteristic
745C2×C4#1451974511yescharacteristic
746C2×C4#1451974511yescharacteristic
747C2×C4#1451974711yescharacteristic
748C2×C4#1451974711yescharacteristic
749C2×C4#1451974811yescharacteristic
750C2×C4#1451975011yescharacteristic
751C2×C4#1451975011yescharacteristic
752C2×C4#1451975211yescharacteristic
753C2×C4#1451975311yescharacteristic
754C2×C4#1451975511yescharacteristic
755C2×C4#1451975511yescharacteristic
756C2×C4#1451975711yescharacteristic
757C2×C4#1451975911yescharacteristic
758C2×C4#1451975911yescharacteristic
759C2×C4#1451976211yescharacteristic
760C2×C4#1451976211yescharacteristic
761C8—24no—
762C8—42no—
763C8—1224no—
764C8—2442no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—614no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—2444no—
788C22—2444no—
789C22—2444no—
790C22—2444no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22#95×D6111yescharacteristic
796C22#1683960911yescharacteristic
797C22C4×#1175819811yescharacteristic
798C22#1683963311yescharacteristic
799C22#1683963611yescharacteristic
800C22#1683963811yescharacteristic
801C22#1683964011yescharacteristic
802C22#100×D6111yescharacteristic
803C22#101×D6111yescharacteristic
804C22#1683974311yescharacteristic
805C22#1683974511yescharacteristic
806C4—82no—
807C4—1222no—
808C4—1222no—
809C4—4882no—
810C4#1683961711yescharacteristic
811C4#1683961911yescharacteristic
812C4#1683962111yescharacteristic
813C4#1683962411yescharacteristic
814C4#1683963311yescharacteristic
815C4#1683963611yescharacteristic
816C4#1683963811yescharacteristic
817C4#1683964011yescharacteristic
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—1224no—
823C2—2442no—
824C2#2144404011yescharacteristic
825C2#343×D6111yescharacteristic
826C2#2144555611yescharacteristic
827C2#2144627911yescharacteristic
828C2#2144628111yescharacteristic
829C2#2144628411yescharacteristic
830C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#343C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenterC2×#343D61
hypocenterC61#10739
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#16839531C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839530C2semidirect
7. C2×C61×#343C2semidirect
17. C2×M16×D61C4semidirect
22. #16839725C4semidirect
207. M16×C61C22⋊C4semidirect
231. #11758194C22⋊C4semidirect
390. C2×D61#343semidirect
409. C2×#343D61semidirect
452. C61#10739semidirect
632. 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
C2×#168397252
C2×#168396192
C2×#168395312
C2×#168395302
C2×C61×#3432
#1073961