Finite Group Databasebeta

← #29686179

Subgroups — #29686179

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×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839830C211yesmaximal, characteristic, complemented
4C2×#16839717C211yesmaximal, characteristic, complemented
5#21449061C211yesmaximal, characteristic
6#21446611C211yesmaximal, characteristic, complemented
7#21446536C211yesmaximal, characteristic, complemented
8#21446433C211yesmaximal, characteristic, complemented
9#21446429C211yesmaximal, characteristic, complemented
10#21446111C211yesmaximal, characteristic, complemented
11#21445801C211yesmaximal, characteristic, complemented
12#21445692C211yesmaximal, characteristic, complemented
13#21445601C211yesmaximal, characteristic, complemented
14#21445593C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16839837—24no—
23#16839834—24no—
24#16839830—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839717—24no—
35C2×#14519688C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839695C411yescharacteristic
42#16839690C411yescharacteristic
43#16839685C411yescharacteristic
44#16839684C411yescharacteristic
45#16839678C411yescharacteristic
46#16839677C411yescharacteristic
47#16839676C411yescharacteristic
48#16839670C411yescharacteristic
49C4×#11758196C2211yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×C22⋊Dic61C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194D414yescomplemented
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519736—22no—
84#14519736—22no—
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C4⋊#92418—22no—
105#14519706—22no—
106#14519706—22no—
107#14519706—22no—
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—22no—
113#14519688—22no—
114#14519687—22no—
115#14519687D414yescomplemented
116C8×Dic61—22no—
117C8×Dic61—22no—
118C8×Dic61—22no—
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C22×C8×C61—22no—
130C22×C8×C61—22no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C4×D4×C61—22no—
136C4×D4×C61—22no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C22⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61—22no—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—41no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
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—28no—
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×C61C2×D412yes—
198C2×C8×C61#4112yes—
199C4⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C42×C61—21no—
203C42×C61—21no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—41no—
213#11758198—41no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—41no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61C2×D412yes—
225C4×Dic61#4112yes—
226#11758194—28no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—44no—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238C2×#92418C2×D412yes—
239C2×#92418#4112yes—
240#11758189—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61C4×D412yes—
254C23×C61#13112yes—
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263D4×C61—44no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
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×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C22⋊D61—44no—
291C22⋊D61—44no—
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—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61C4×D412yes—
311C2×Dic61C4×D412yes—
312C2×Dic61#13112yes—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—22no—
318C8×C61—22no—
319C8×C61—41no—
320C8×C61—41no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#92418#12114yes—
325#21496—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C4×#4111yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61#56811yescharacteristic
346C22×C61#56811yescharacteristic
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—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61C2×#12111yescharacteristic
359C4×C61#52511yescharacteristic
360C4×C61#52911yescharacteristic
361C4×C61#53211yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
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#1869D6111yescharacteristic, complemented
380#1798—611no—
381#1771—611no—
382#1753—611no—
383C8×C22⋊C4—611no—
384C2×C61—42no—
385C2×C61—42no—
386C2×C61C4×#12111yescharacteristic
387C2×C61#293311yescharacteristic
388C2×C61#293311yescharacteristic
389C2×C61#293311yescharacteristic
390C2×C61#293511yescharacteristic
391C2×C61#296611yescharacteristic
392C2×C61#296711yescharacteristic
393D61—81no—
394C22×M16—611no—
395C22×M16—611no—
396C23×C8—611no—
397C23×C8C2×D6111yescharacteristic
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4C2×D6111yescharacteristic
401C2×#117—611no—
402#436—1224no—
403#435—1224no—
404#435—1224no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8C2×D6111yescharacteristic
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×D4C4×D6111yescharacteristic
445C23×C4—611no—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C2×M16—614no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
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×C42—611no—
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
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—
524C24C2×C4×D6111yescharacteristic
525C24C2×C4×D6111yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—1222no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4D4×D6112yes—
563C22×C4#1175822412yes—
564C22×C4C23×D6111yescharacteristic
565M16—1228no—
566M16—2444no—
567C2×C8—28no—
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—612no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—2444no—
591C2×C8D4×D6112yes—
592C2×C8#1175822412yes—
593C4⋊C4—22no—
594C4⋊C4—1222no—
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—612no—
615C42—612no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23#1451973712yes—
640C23#1451978312yes—
641C23C22×C4×D6111yescharacteristic
642D4—44no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
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—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4#1451973712yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822411yescharacteristic
695C2×C4C2×#1175822411yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—614no—
701C8—1222no—
702C8—2441no—
703C8—2441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C4×D4×D6111yescharacteristic
726C22C2×#1451973711yescharacteristic
727C22C4×#1175822411yescharacteristic
728C22#131×D6111yescharacteristic
729C22C2×#1451978311yescharacteristic
730C22#1684052711yescharacteristic
731C22#1684052811yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—1222no—
737C4—1222no—
738C4—1222no—
739C4—2441no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4#121×D6111yescharacteristic
744C4#1684026811yescharacteristic
745C4#1684028911yescharacteristic
746C4#1684030711yescharacteristic
747C2—42no—
748C2—42no—
749C2—4881no—
750C2#2144832911yescharacteristic
751C2#2145453911yescharacteristic
752C2#2145454011yescharacteristic
753C2#2145454911yescharacteristic
754C2#2145456011yescharacteristic
755C2#2145478711yescharacteristic
756C2#2145480111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1869C2
prime radical#16839670C4
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#21496
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#16839837C2semidirect
2. C2×#16839834C2semidirect
3. C2×#16839830C2semidirect
4. C2×#16839717C2semidirect
6. #21446611C2semidirect
7. #21446536C2semidirect
8. #21446433C2semidirect
9. #21446429C2semidirect
10. #21446111C2semidirect
11. #21445801C2semidirect
12. #21445692C2semidirect
13. #21445601C2semidirect
14. #21445593C2semidirect
15. C61×#1869C2semidirect
68. C2×#11758194D4semidirect
115. #14519687D4semidirect
379. #1869D61semidirect
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×#168398342
C2×#168398302
C2×#168397172
#214490612
#214466112
#214465362
#214464332
#214464292
#214461112
#214458012
#214456922
#214456012
#214455932
C61×#18692
#2149661