Finite Group Databasebeta

← #29691133

Subgroups — #29691133

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839838C211yesmaximal, characteristic, complemented
2C2×#16839730C211yesmaximal, characteristic, complemented
3#21449035C211yesmaximal, characteristic
4#21446617C211yesmaximal, characteristic, complemented
5#21446613C211yesmaximal, characteristic, complemented
6#21446432C211yesmaximal, characteristic, complemented
7#21446426C211yesmaximal, characteristic, complemented
8#21446426C211yesmaximal, characteristic, complemented
9#21446425C211yesmaximal, characteristic, complemented
10#21446115C211yesmaximal, characteristic, complemented
11#21446115C211yesmaximal, characteristic, complemented
12#21446109C211yesmaximal, characteristic, complemented
13#21445999C211yesmaximal, characteristic, complemented
14#21445730C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16839838—24no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26#16839730—24no—
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839683C411yescharacteristic
41#16839680C411yescharacteristic
42#16839678C411yescharacteristic
43#16839678C411yescharacteristic
44#16839675C411yescharacteristic
45#16839672C411yescharacteristic
46#16839671C411yescharacteristic
47#16839671C411yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×#11758198C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×D244C2×C411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—41no—
79C2×#11758189—41no—
80C22×#92418—22no—
81C22×#92418—41no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C4×D244—41no—
88C4×D244—41no—
89C4×D244—41no—
90C4×D244—41no—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196C2×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×#11758198C2×C411yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C4⋊#92418—41no—
108C4⋊#92418—41no—
109#14519706—22no—
110C22⋊#92418—22no—
111#14519689—22no—
112#14519689—22no—
113#14519689—22no—
114#14519689—22no—
115#14519689—22no—
116#14519689—41no—
117#14519689—41no—
118#14519689—41no—
119#14519689—41no—
120#14519689—41no—
121#14519689—41no—
122C8×Dic61—22no—
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—41no—
129C2×M16×C61—41no—
130C2×M16×C61D414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61—22no—
140#97×C61—41no—
141C4×C8×C61—41no—
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61#4112yes—
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174#11758222—44no—
175#11758222—44no—
176#11758222—44no—
177#11758222—44no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—41no—
181C2×D244—41no—
182C2×D244—41no—
183C2×D244—41no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×Dic122—22no—
206C2×Dic122—41no—
207C2×Dic122—41no—
208M16×C61—44no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61C2×D412yes—
220C2×C8×C61C2×D412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—41no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C22⋊Dic61—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—41no—
233#11758198—41no—
234#11758198—41no—
235#11758198—41no—
236#11758198—41no—
237C4⋊Dic61—41no—
238C4⋊Dic61—41no—
239#11758196—22no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—44no—
255#11758189—44no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61C4×D412yes—
263C23×C61C23×C411yescharacteristic
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61C4×D412yes—
303C2×C4×C61#13112yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C22⋊D61—44no—
311C22⋊D61—44no—
312C22⋊D61—44no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61#13112yes—
328D244—44no—
329D244—44no—
330D244—44no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343Dic122—44no—
344C8×C61—22no—
345C8×C61—22no—
346C8×C61—41no—
347C8×C61—41no—
348#92418—41no—
349#92418—41no—
350#92418—41no—
351#92418—41no—
352#22039—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61C2×C4×D411yescharacteristic
361C22×C61#51811yescharacteristic
362C22×C61#51811yescharacteristic
363C22×C61C2×#13111yescharacteristic
364C22×C61C2×#13111yescharacteristic
365C22×C61#56811yescharacteristic
366C22×C61#56811yescharacteristic
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C4×C61—22no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61#53411yescharacteristic
394C4×C61#53511yescharacteristic
395C4×C61#53811yescharacteristic
396C4×C61#53811yescharacteristic
397Dic61—22no—
398Dic61—41no—
399Dic61—41no—
400Dic61—41no—
401Dic61—41no—
402C2×#436—611no—
403C2×#408—611no—
404#2388—611no—
405#1955—611no—
406#1954—611no—
407#1924—611no—
408#1923—611no—
409#1923—611no—
410#1923—611no—
411#1870—611no—
412#1870—611no—
413#1869—611no—
414#1850—611no—
415#1780—611no—
416#1753D6111yescharacteristic, complemented
417C2×C61—42no—
418C2×C61#232111yescharacteristic
419C2×C61#293311yescharacteristic
420C2×C61#293511yescharacteristic
421C2×C61#297611yescharacteristic
422C2×C61#297811yescharacteristic
423C2×C61#297911yescharacteristic
424C2×C61#298111yescharacteristic
425D61—81no—
426D61—81no—
427D61—81no—
428C22×#41—611no—
429C22×M16—611no—
430C22×M16C2×D6111yescharacteristic
431C23×C8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435#436—1224no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8—611no—
439#408—1224no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8C2×D6111yescharacteristic
453C2×#97C2×D6111yescharacteristic
454C2×C4×C8—611no—
455C2×C4×C8C2×D6111yescharacteristic
456#395—611no—
457#394—611no—
458#394—611no—
459#394—611no—
460#393—611no—
461#392—611no—
462#392—611no—
463#392—611no—
464C4×C22⋊C4—611no—
465C4×C22⋊C4—611no—
466C4×C22⋊C4C2×D6111yescharacteristic
467#336—611no—
468#336—611no—
469#336—611no—
470#336—611no—
471#336C2×D6111yescharacteristic
472#336C2×D6111yescharacteristic
473C61#2203911yescharacteristic, complemented, Sylow
474C2×#41—1222no—
475C2×#41—1222no—
476C2×#41—2441no—
477C2×#41—2441no—
478C2×#41—2441no—
479C2×#41—2441no—
480C22×Q8—611no—
481C22×D4—611no—
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4C22×D6111yescharacteristic
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—1222no—
494C2×M16—2441no—
495C2×M16—2441no—
496C2×M16D24414yescomplemented
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—1222no—
502C22×C8—2441no—
503C22×C8—2441no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513C4×D4—2441no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4C4×D6111yescharacteristic
528C2×C22⋊C4C4×D6111yescharacteristic
529C2×C42—611no—
530C2×C42C22×D6111yescharacteristic
531C2×C42C22×D6111yescharacteristic
532C4⋊C8—1222no—
533C4⋊C8—2441no—
534C4⋊C8—2441no—
535C22⋊C8—22no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C22⋊C8—2441no—
547C22⋊C8—2441no—
548#97—41no—
549C4×C8—41no—
550C4×C8—1222no—
551#95—611no—
552#95—611no—
553#95—611no—
554#95—611no—
555#95C4×D6111yescharacteristic
556#95C4×D6111yescharacteristic
557C24—611no—
558C24—611no—
559C24—611no—
560C24C2×C4×D6111yescharacteristic
561#41—2444no—
562#41—2444no—
563#41—2444no—
564#41—2444no—
565C2×Q8—1222no—
566C2×Q8—2441no—
567C2×Q8—2441no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C2×D4—2441no—
580C2×D4—2441no—
581C2×D4—2441no—
582C2×D4—2441no—
583C2×D4—2441no—
584C2×D4—2441no—
585C2×D4—2441no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4C2×C4×D6111yescharacteristic
614C22×C4C2×C4×D6111yescharacteristic
615C22×C4C2×C4×D6111yescharacteristic
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4C2×D24412yes—
619C22×C4#1175822212yes—
620C22×C4C23×D6111yescharacteristic
621M16—44no—
622M16—2444no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—2444no—
646C2×C8C2×D24412yes—
647C2×C8C2×D24412yes—
648C4⋊C4—1222no—
649C4⋊C4—2441no—
650C4⋊C4—2441no—
651C22⋊C4—22no—
652C22⋊C4—41no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—2441no—
659C22⋊C4—2441no—
660C22⋊C4—2441no—
661C22⋊C4—2441no—
662C22⋊C4—2441no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—1221no—
668C42—1221no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23C4×D24412yes—
697C23C22×C4×D6111yescharacteristic
698Q8—2444no—
699D4—2444no—
700D4—2444no—
701D4—2444no—
702D4—2444no—
703D4—2444no—
704D4—2444no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—612no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4C4×D24412yes—
750C2×C4#1451978512yes—
751C2×C4C22×D24411yescharacteristic
752C2×C4C2×#1175822211yescharacteristic
753C2×C4#1451982211yescharacteristic
754C2×C4#1451982211yescharacteristic
755C2×C4#1451982311yescharacteristic
756C2×C4#1451982311yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—2441no—
762C8—2441no—
763C8—2441no—
764C8—2441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—2441no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22C2×C4×D24411yescharacteristic
794C22#1684023411yescharacteristic
795C22#1684023411yescharacteristic
796C22#131×D6111yescharacteristic
797C22C2×#1451978511yescharacteristic
798C22#1684052711yescharacteristic
799C22#1684052811yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—1222no—
806C4—2441no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C4#1684032411yescharacteristic
811C4#1684033111yescharacteristic
812C4#1684034511yescharacteristic
813C4#1684034511yescharacteristic
814C2—42no—
815C2—4881no—
816C2—4881no—
817C2—4881no—
818C2#2144847911yescharacteristic
819C2#2145454711yescharacteristic
820C2#2145456511yescharacteristic
821C2#2145486811yescharacteristic
822C2#2145487611yescharacteristic
823C2#2145488411yescharacteristic
824C2#2145489111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1753C2
prime radical#21449035C2
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22039
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#16839838C2semidirect
2. C2×#16839730C2semidirect
4. #21446617C2semidirect
5. #21446613C2semidirect
6. #21446432C2semidirect
7. #21446426C2semidirect
8. #21446426C2semidirect
9. #21446425C2semidirect
10. #21446115C2semidirect
11. #21446115C2semidirect
12. #21446109C2semidirect
13. #21445999C2semidirect
14. #21445730C2semidirect
15. C61×#1753C2semidirect
130. C2×M16×C61D4semidirect
416. #1753D61semidirect
473. C61#22039semidirect
496. C2×M16D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
C2×#168397302
#214490352
#214466172
#214466132
#214464322
#214464262
#214464252
#214461152
#214461092
#214459992
#214457302
C61×#17532
#2203961