Finite Group Databasebeta

← #29686167

Subgroups — #29686167

Order 15616.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839837C211yesmaximal, characteristic, complemented
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839832C211yesmaximal, characteristic, complemented
4C2×#16839718C211yesmaximal, characteristic, complemented
5#21449055C211yesmaximal, characteristic
6#21446612C211yesmaximal, characteristic, complemented
7#21446535C211yesmaximal, characteristic, complemented
8#21446430C211yesmaximal, characteristic, complemented
9#21446430C211yesmaximal, characteristic, complemented
10#21446109C211yesmaximal, characteristic, complemented
11#21446109C211yesmaximal, characteristic, complemented
12#21445696C211yesmaximal, characteristic, complemented
13#21445599C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1798C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23#16839837—24no—
24#16839836—24no—
25#16839832—24no—
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839718—24no—
35C2×#14519688C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839692C411yescharacteristic
42#16839687C411yescharacteristic
43#16839684C411yescharacteristic
44#16839684C411yescharacteristic
45#16839679C411yescharacteristic
46#16839678C411yescharacteristic
47#16839678C411yescharacteristic
48#16839671C411yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194D414yescomplemented
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C22×#92418—22no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C4×D244—22no—
85C4×D244—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107#14519706—22no—
108#14519706—22no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—22no—
113#14519689—22no—
114#14519689—22no—
115#14519688—22no—
116#14519688D414yescomplemented
117#14519687—22no—
118C4×#92418—22no—
119C4×#92418—22no—
120C8×Dic61—22no—
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132#117×C61—22no—
133#117×C61—22no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61—22no—
141C4⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61—22no—
144C24×C61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D412yes—
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—41no—
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—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61C2×D412yes—
205C42×C61#4112yes—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198—41no—
215#11758198—41no—
216C4⋊Dic61—22no—
217C4⋊Dic61—22no—
218C4⋊Dic61—41no—
219#11758196—22no—
220#11758196—22no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225#11758194—28no—
226C2×#92418—28no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418C2×D412yes—
234C2×#92418C2×D412yes—
235C2×#92418C2×D412yes—
236C2×#92418C2×D412yes—
237C2×#92418#4112yes—
238C2×#92418#4112yes—
239#11758189—44no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61C4×D412yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61#13112yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61C4×D412yes—
280C2×C4×C61C4×D412yes—
281C2×C4×C61C4×D412yes—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C22⋊D61—44no—
289C22⋊D61—44no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61#13112yes—
308D244—44no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—41no—
318C8×C61—41no—
319C8×C61—41no—
320C8×C61—41no—
321#92418—22no—
322#92418—22no—
323#92418—22no—
324#92418#12114yes—
325#21496—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×D411yescharacteristic
335C22×C61C4×#4111yescharacteristic
336C22×C61C2×#13111yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61#56811yescharacteristic
339C22×C61#56811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61C2×#12111yescharacteristic
360C4×C61#52511yescharacteristic
361C4×C61#52911yescharacteristic
362C4×C61#53211yescharacteristic
363Dic61—22no—
364Dic61—41no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369C2×#436—611no—
370C2×#435—611no—
371C2×#435—611no—
372C2×#405—611no—
373#2392—611no—
374#1954—611no—
375#1939—611no—
376#1924—611no—
377#1924—611no—
378#1869—611no—
379#1869—611no—
380#1798D6111yescharacteristic, complemented
381#1771—611no—
382#1753—611no—
383C8×C22⋊C4—611no—
384C2×C61—42no—
385C2×C61C4×#12111yescharacteristic
386C2×C61#293311yescharacteristic
387C2×C61#293311yescharacteristic
388C2×C61#293311yescharacteristic
389C2×C61#293511yescharacteristic
390C2×C61#296611yescharacteristic
391C2×C61#296711yescharacteristic
392D61—42no—
393D61—81no—
394C22×M16—611no—
395C22×M16—611no—
396C23×C8—611no—
397C23×C8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×#117C2×D6111yescharacteristic
402#436—1224no—
403#435—1224no—
404#435—1224no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8C2×D6111yescharacteristic
408C2×C4⋊C8C2×D6111yescharacteristic
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8C2×D6111yescharacteristic
416C2×C22⋊C8C2×D6111yescharacteristic
417#405—1224no—
418C2×#97—611no—
419C2×#97—611no—
420C2×#97—611no—
421C2×C4×C8—611no—
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424#398—611no—
425#397—611no—
426#396—611no—
427#396—611no—
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—611no—
434C4×C22⋊C4—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336C2×D6111yescharacteristic
440#336C2×D6111yescharacteristic
441C61#2149611yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4C22×D6111yescharacteristic
448C2×M16—614no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4C4×D6111yescharacteristic
482C2×C4⋊C4C4×D6111yescharacteristic
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C4×D6111yescharacteristic
494C2×C22⋊C4C4×D6111yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511#97—614no—
512#97—1222no—
513#97—1222no—
514C4×C8—1222no—
515C4×C8—1222no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523C24—611no—
524C24—611no—
525C24C2×C4×D6111yescharacteristic
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4C2×C4×D6111yescharacteristic
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4D4×D6112yes—
563C22×C4#1175822612yes—
564C22×C4C23×D6111yescharacteristic
565M16—1228no—
566M16—2444no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—1228no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—2444no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C42—21no—
613C42—21no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42D4×D6112yes—
619C42#1175822412yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—612no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23#1451973912yes—
641C23C22×C4×D6111yescharacteristic
642D4—2444no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—612no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4#1451973712yes—
688C2×C4#1451973712yes—
689C2×C4#1451973912yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4C2×#1175822611yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—614no—
701C8—1222no—
702C8—1222no—
703C8—1222no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C2×#1451973711yescharacteristic
726C22C2×#1451973911yescharacteristic
727C22#1684023011yescharacteristic
728C22#131×D6111yescharacteristic
729C22#131×D6111yescharacteristic
730C22#1684052711yescharacteristic
731C22#1684052711yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—1222no—
738C4—2441no—
739C4—2441no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4#121×D6111yescharacteristic
744C4#1684027511yescharacteristic
745C4#1684029811yescharacteristic
746C4#1684030711yescharacteristic
747C2—42no—
748C2—4881no—
749C2—2442no—
750C2#2144832511yescharacteristic
751C2#2145454311yescharacteristic
752C2#2145454311yescharacteristic
753C2#2145454911yescharacteristic
754C2#2145455911yescharacteristic
755C2#2145479211yescharacteristic
756C2#2145480211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1798C2
prime radical#16839671C4
cosocleC22×C4×C61C24
hypercenter#1798D61
hypocenterC61#21496
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
1. C2×#16839837C2semidirect
2. C2×#16839836C2semidirect
3. C2×#16839832C2semidirect
4. C2×#16839718C2semidirect
6. #21446612C2semidirect
7. #21446535C2semidirect
8. #21446430C2semidirect
9. #21446430C2semidirect
10. #21446109C2semidirect
11. #21446109C2semidirect
12. #21445696C2semidirect
13. #21445599C2semidirect
14. #21445589C2semidirect
15. C61×#1798C2semidirect
70. C2×#11758194D4semidirect
116. #14519688D4semidirect
380. #1798D61semidirect
441. C61#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#168398372
C2×#168398362
C2×#168398322
C2×#168397182
#214490552
#214466122
#214465352
#214464302
#214461092
#214456962
#214455992
#214455892
C61×#17982
#2149661