Finite Group Databasebeta

← #29691123

Subgroups — #29691123

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839841C211yesmaximal, characteristic, complemented
2C2×#16839724C211yesmaximal, characteristic, complemented
3C4×#14519747C211yesmaximal, characteristic
4#21446616C211yesmaximal, characteristic, complemented
5#21446611C211yesmaximal, characteristic, complemented
6#21446434C211yesmaximal, characteristic, complemented
7#21446426C211yesmaximal, characteristic, complemented
8#21446425C211yesmaximal, characteristic, complemented
9#21446115C211yesmaximal, characteristic, complemented
10#21446115C211yesmaximal, characteristic, complemented
11#21446113C211yesmaximal, characteristic, complemented
12#21446000C211yesmaximal, characteristic, complemented
13#21445728C211yesmaximal, characteristic, complemented
14#21445601C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic, complemented
20C2×#14519747C411yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24#16839841—24no—
25C2×C4⋊#92418C2211yescharacteristic, complemented
26C2×#14519706C2211yescharacteristic, complemented
27#16839724—24no—
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic, complemented
37C2×#14519689C2211yescharacteristic, complemented
38C2×#14519689C2211yescharacteristic, complemented
39C2×#14519688C2211yescharacteristic, complemented
40C2×C8×Dic61C2211yescharacteristic, complemented
41#16839640C411yescharacteristic
42#16839640C411yescharacteristic
43#16839639C411yescharacteristic
44#16839637C411yescharacteristic
45#16839636C411yescharacteristic
46#16839636C411yescharacteristic
47#16839617C411yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×#11758198C2211yescharacteristic
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×C4⋊C8×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic, complemented
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61C2×C411yescharacteristic
62C22×D244C2×C411yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C23×Dic61C2×C411yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—41no—
69C22×C4×D61—41no—
70C22×C4×D61—41no—
71C22×C4×D61—41no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—41no—
80C2×#11758189—41no—
81C2×#11758189—41no—
82C2×#11758189—41no—
83C2×#11758189—41no—
84C2×#11758189—41no—
85C2×#11758189D414yescomplemented
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519747—24no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—41no—
94C4×D244—41no—
95C4×C22⋊D61—41no—
96C4×C22⋊D61—41no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C4⋊#92418—22no—
112#14519706—41no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—41no—
121#14519689—41no—
122#14519689—41no—
123#14519689—41no—
124#14519688—41no—
125C8×Dic61—41no—
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
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
139C4⋊C8×C61—41no—
140C22⋊C8×C61—22no—
141C22⋊C8×C61—41no—
142C4×C8×C61—22no—
143#95×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—41no—
150C23×D61—41no—
151C23×D61—41no—
152C23×D61—41no—
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—41no—
171C22×Dic61—22no—
172C22×Dic61—41no—
173C22×Dic61—41no—
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—41no—
183C2×D244—41no—
184C2×D244—41no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
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—22no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61—41no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—41no—
211C2×C4×D61C2×D412yes—
212C2×C4×D61#4112yes—
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×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61C2×D412yes—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—22no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C22⋊Dic61—41no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—41no—
236#11758198—41no—
237#11758198—41no—
238#11758198—41no—
239#11758198—41no—
240#11758198M1614yescomplemented
241C4⋊Dic61—22no—
242C4⋊Dic61—41no—
243#11758196—41no—
244C4×Dic61—21no—
245C4×Dic61—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—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418C2×D412yes—
258#11758189—44no—
259#11758189—44no—
260#11758189—44no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61#13112yes—
268C23×C61C23×C411yescharacteristic
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—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61—44no—
291C22×D61—44no—
292C22×D61—44no—
293C22×D61—44no—
294C22×D61—44no—
295C22×D61C4×D412yes—
296C22×D61C2×M1612yes—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61C2×M1612yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—44no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—44no—
337C2×Dic61C4×D412yes—
338C2×Dic61C2×M1612yes—
339D244—44no—
340D244—44no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—44no—
346C4×D61—44no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C8×C61—22no—
356C8×C61—41no—
357C8×C61—41no—
358C8×C61—41no—
359#92418—22no—
360#92418—41no—
361#92418—41no—
362#92418—41no—
363#22038—611nomaximal, Sylow
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61C2×C4×D411yescharacteristic
372C22×C61#51811yescharacteristic
373C22×C61#51811yescharacteristic
374C22×C61C22×M1611yescharacteristic
375C22×C61C2×#13111yescharacteristic
376C22×C61#56811yescharacteristic
377C22×C61#56811yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—416no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C4×C61—22no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61#53411yescharacteristic
406C4×C61#53511yescharacteristic
407C4×C61#53811yescharacteristic
408C4×C61#53811yescharacteristic
409Dic61—22no—
410Dic61—22no—
411Dic61—41no—
412Dic61—41no—
413Dic61—41no—
414C2×#436—611no—
415C2×#407—611no—
416C4×#120—611no—
417#1955—611no—
418#1954—611no—
419#1924—611no—
420#1923—611no—
421#1923—611no—
422#1923D6111yescharacteristic, complemented
423#1870—611no—
424#1870—611no—
425#1870—611no—
426#1851—611no—
427#1779—611no—
428#1753—611no—
429C2×C61—42no—
430C2×C61#232111yescharacteristic
431C2×C61#293311yescharacteristic
432C2×C61D4×M1611yescharacteristic
433C2×C61#297411yescharacteristic
434C2×C61#297511yescharacteristic
435C2×C61#297611yescharacteristic
436C2×C61#297811yescharacteristic
437D61—42no—
438D61—42no—
439D61—81no—
440C24×C4—611no—
441C22×M16—611no—
442C22×M16—611no—
443C22×M16—611no—
444C2×#120—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448#436—1224no—
449C2×C4⋊C8—611no—
450C2×C4⋊C8—611no—
451C2×C4⋊C8C2×D6111yescharacteristic, complemented
452#407—1224no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×C22⋊C8—611no—
464C2×C22⋊C8C2×D6111yescharacteristic
465C2×C22⋊C8C2×D6111yescharacteristic
466C2×#97—611no—
467C2×C4×C8—611no—
468C2×C4×C8C2×D6111yescharacteristic, complemented
469#386—611no—
470#386—611no—
471#386—611no—
472#385—611no—
473#385—611no—
474#385—611no—
475#379—611no—
476C4×C22⋊C4—611no—
477C4×C22⋊C4—611no—
478C4×C22⋊C4C2×D6111yescharacteristic
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483#336C2×D6111yescharacteristic, complemented
484#336C2×D6111yescharacteristic, complemented
485C61#2203811yescharacteristic, complemented, Sylow
486C25—611no—
487C22×D4—611no—
488C22×D4—611no—
489C22×D4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—1222no—
497C23×C4—1222no—
498C23×C4—2441no—
499C23×C4—2441no—
500C23×C4—2441no—
501C23×C4—2441no—
502C23×C4C22×D6111yescharacteristic
503C2×M16—614no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—2441no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C2×M16—2441no—
511C2×M16—2441no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6111yescharacteristic
520#120—1224no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—2441no—
524C4×D4—2441no—
525C4×D4—2441no—
526C4×D4—2441no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4C4×D6111yescharacteristic
541C2×C22⋊C4C4×D6111yescharacteristic
542C2×C42—611no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—41no—
546C4⋊C8—1222no—
547C4⋊C8—2441no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—1222no—
551C22⋊C8—1222no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—2441no—
557C22⋊C8—2441no—
558C22⋊C8—2441no—
559C22⋊C8—2441no—
560C22⋊C8—2441no—
561#97—2441no—
562C4×C8—22no—
563C4×C8—2441no—
564#95—611no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95C4×D6111yescharacteristic
569#95C4×D6111yescharacteristic
570C24—611no—
571C24—611no—
572C24—611no—
573C24—1222no—
574C24—1222no—
575C24—1222no—
576C24—2441no—
577C24—2441no—
578C24—2441no—
579C24—2441no—
580C24C2×C4×D6111yescharacteristic
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—2441no—
587C2×D4—2441no—
588C2×D4—2441no—
589C2×D4—2441no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2441no—
625C22×C4—2441no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2441no—
631C22×C4—2441no—
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4C2×C4×D6111yescharacteristic
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638M16—2444no—
639M16—2444no—
640M16—2444no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—612no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8D4×D6112yes—
665C4⋊C4—1222no—
666C4⋊C4—2441no—
667C4⋊C4—2441no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—614no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—2441no—
675C22⋊C4—2441no—
676C22⋊C4—2441no—
677C22⋊C4—2441no—
678C22⋊C4—2441no—
679C22⋊C4—2441no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—1221no—
685C42—1221no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—612no—
693C23—612no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—2444no—
714C23—2444no—
715C23—2444no—
716C23—2444no—
717C23—2444no—
718C23—2444no—
719C23—2444no—
720C23#1451978312yes—
721C23C22×C4×D6111yescharacteristic
722D4—2444no—
723D4—2444no—
724D4—2444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—2444no—
763C2×C4—2444no—
764C2×C4—2444no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4M16×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4#41×D6111yescharacteristic
776C2×C4#1451982211yescharacteristic
777C2×C4#1451982311yescharacteristic
778C2×C4#1451982311yescharacteristic
779C2×C4#1451982311yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—1222no—
785C8—2441no—
786C8—2441no—
787C8—2441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—24416no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22—2441no—
812C22—2441no—
813C22—2441no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22C4×D4×D6111yescharacteristic
818C22#1684023411yescharacteristic
819C22#1684023611yescharacteristic
820C22C2×M16×D6111yescharacteristic
821C22C2×#1451978311yescharacteristic
822C22#1684052711yescharacteristic
823C22#1684052711yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—1222no—
830C4—1222no—
831C4—2441no—
832C4—2441no—
833C4—2441no—
834C4#1684032311yescharacteristic
835C4#1684032811yescharacteristic
836C4#1684034611yescharacteristic
837C4#1684035111yescharacteristic
838C2—42no—
839C2—4881no—
840C2—2442no—
841C2—2442no—
842C2#2144848111yescharacteristic
843C2#2145453911yescharacteristic
844C2#2145455211yescharacteristic
845C2#2145485311yescharacteristic
846C2#2145485711yescharacteristic
847C2#2145486111yescharacteristic
848C2#2145488011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1923C2
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1923D61
hypocenterC61#22038
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16839841C2semidirect
2. C2×#16839724C2semidirect
4. #21446616C2semidirect
5. #21446611C2semidirect
6. #21446434C2semidirect
7. #21446426C2semidirect
8. #21446425C2semidirect
9. #21446115C2semidirect
10. #21446115C2semidirect
11. #21446113C2semidirect
12. #21446000C2semidirect
13. #21445728C2semidirect
14. #21445601C2semidirect
15. C61×#1923C2semidirect
19. C22×#11758189C22semidirect
25. C2×C4⋊#92418C22semidirect
26. C2×#14519706C22semidirect
36. C2×#14519689C22semidirect
37. C2×#14519689C22semidirect
38. C2×#14519689C22semidirect
39. C2×#14519688C22semidirect
40. C2×C8×Dic61C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
54. C2×C4⋊C8×C61C22semidirect
57. C2×C4×C8×C61C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
85. C2×#11758189D4semidirect
240. #11758198M16semidirect
422. #1923D61semidirect
451. C2×C4⋊C8C2×D61semidirect
468. C2×C4×C8C2×D61semidirect
483. #336C2×D61semidirect
484. #336C2×D61semidirect
485. C61#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#168398412
C2×#168397242
C4×#145197472
#214466162
#214466112
#214464342
#214464262
#214464252
#214461152
#214461132
#214460002
#214457282
#214456012
C61×#19232
#2203861