Finite Group Databasebeta

← #29691122

Subgroups — #29691122

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×#16839840C211yesmaximal, characteristic, complemented
2C2×#16839725C211yesmaximal, characteristic, complemented
3C4×#14519745C211yesmaximal, characteristic
4#21446615C211yesmaximal, characteristic, complemented
5#21446611C211yesmaximal, characteristic, complemented
6#21446433C211yesmaximal, characteristic, complemented
7#21446426C211yesmaximal, characteristic, complemented
8#21446423C211yesmaximal, characteristic, complemented
9#21446423C211yesmaximal, characteristic, complemented
10#21446114C211yesmaximal, characteristic, complemented
11#21446114C211yesmaximal, characteristic, complemented
12#21446002C211yesmaximal, characteristic, complemented
13#21445728C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C2×#14519745C411yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16839840—24no—
23C2×C4⋊#92418C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×#14519706C2211yescharacteristic, complemented
26#16839725—24no—
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic, complemented
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic, complemented
38C2×C4×#92418C2211yescharacteristic, complemented
39C2×C8×Dic61C2211yescharacteristic, complemented
40#16839642C411yescharacteristic
41#16839638C411yescharacteristic
42#16839638C411yescharacteristic
43#16839634C411yescharacteristic
44#16839633C411yescharacteristic
45#16839633C411yescharacteristic
46#16839617C411yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×C22⋊Dic61C2211yescharacteristic
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×M16×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic, complemented
58C2×C22⋊C8×C61C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C23×Dic61C2×C411yescharacteristic
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—41no—
68C22×C4×D61—41no—
69C22×C4×D61—41no—
70C22×C4×D61—41no—
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758194—22no—
76C2×#11758194—41no—
77C2×#11758194—41no—
78C2×#11758194—41no—
79C2×#11758194—41no—
80C2×#11758194D414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519745—24no—
86C4×C22⋊D61—41no—
87C4×C22⋊D61—41no—
88C4×C22⋊D61—41no—
89C4×C22⋊D61—41no—
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C4⋊#92418—22no—
105#14519706—41no—
106#14519706—41no—
107C22⋊#92418—22no—
108C22⋊#92418—22no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—22no—
113#14519689—41no—
114#14519689—41no—
115#14519689—41no—
116#14519689—41no—
117#14519687—41no—
118C4×#92418—22no—
119C8×Dic61—41no—
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—22no—
130C2×M16×C61—41no—
131C2×M16×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C4×D4×C61—22no—
137C4×D4×C61—22no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C22⋊C8×C61—22no—
143C22⋊C8×C61—41no—
144C22⋊C8×C61—41no—
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—22no—
150C23×D61—41no—
151C23×D61—41no—
152C23×D61—41no—
153C23×D61—41no—
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C411yescharacteristic
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—41no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61#4112yes—
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C2×C22⋊D61—41no—
182C22×Dic61—22no—
183C22×Dic61—41no—
184C22×Dic61—41no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C2×C4×D61—22no—
192C2×C4×D61—22no—
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×C4×D61—41no—
206C2×C4×D61—41no—
207C2×C4×D61—41no—
208C2×C4×D61—41no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213M16×C61—44no—
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×C61—21no—
225C2×C8×C61—21no—
226C4⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C42×C61—21no—
230C42×C61—21no—
231C22⋊Dic61—22no—
232C22⋊Dic61—41no—
233C22⋊Dic61—41no—
234C22⋊Dic61—41no—
235#11758198—22no—
236#11758198—22no—
237#11758198—41no—
238#11758198—41no—
239#11758198—41no—
240#11758198M1614yescomplemented
241#11758196—41no—
242#11758196—41no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247#11758194—44no—
248#11758194—44no—
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×#92418—21no—
258C2×#92418—21no—
259C2×#92418C2×D412yes—
260C2×#92418C2×D412yes—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61C4×D412yes—
275C23×C61C23×C411yescharacteristic
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×D61C2×M1612yes—
296C22×D61#13112yes—
297D4×C61—44no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C4×D412yes—
317C2×C4×C61C2×M1612yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C22⋊D61—44no—
325C22⋊D61—44no—
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—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—44no—
344C2×Dic61C2×M1612yes—
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—41no—
356C8×C61—41no—
357C8×C61—41no—
358C8×C61—41no—
359#92418—22no—
360#92418—22no—
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×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61C2×C4×D411yescharacteristic
379C22×C61#51811yescharacteristic
380C22×C61#51811yescharacteristic
381C22×C61C22×M1611yescharacteristic
382C22×C61C2×#13111yescharacteristic
383C22×C61#56811yescharacteristic
384C22×C61#56811yescharacteristic
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—416no—
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—22no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61#53411yescharacteristic
405C4×C61#53511yescharacteristic
406C4×C61#53811yescharacteristic
407C4×C61#53811yescharacteristic
408Dic61—22no—
409Dic61—41no—
410Dic61—41no—
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#1923—611no—
423#1870—611no—
424#1870—611no—
425#1870D6111yescharacteristic, complemented
426#1851—611no—
427#1779—611no—
428#1753—611no—
429C2×C61—42no—
430C2×C61—81no—
431C2×C61#232111yescharacteristic
432C2×C61#293311yescharacteristic
433C2×C61D4×M1611yescharacteristic
434C2×C61#297411yescharacteristic
435C2×C61#297511yescharacteristic
436C2×C61#297611yescharacteristic
437C2×C61#297811yescharacteristic
438D61—42no—
439D61—42no—
440C24×C4—611no—
441C22×M16—611no—
442C22×M16—611no—
443C22×M16C2×D6111yescharacteristic
444C2×#120—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4C2×D6111yescharacteristic
448#436—1224no—
449C2×C4⋊C8—611no—
450C2×C4⋊C8—611no—
451C2×C4⋊C8—611no—
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⋊C8C2×D6111yescharacteristic
464C2×C22⋊C8C2×D6111yescharacteristic, complemented
465C2×C22⋊C8C2×D6111yescharacteristic, complemented
466C2×#97—611no—
467C2×C4×C8—611no—
468C2×C4×C8—611no—
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⋊C4—611no—
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×D4C4×D6111yescharacteristic
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1222no—
496C23×C4—1222no—
497C23×C4—2441no—
498C23×C4—2441no—
499C23×C4—2441no—
500C23×C4—2441no—
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—614no—
507C2×M16—1222no—
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—22no—
522C4×D4—22no—
523C4×D4—2441no—
524C4×D4—2441no—
525C4×D4—2441no—
526C4×D4—2441no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4C4×D6111yescharacteristic
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×C42—611no—
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—1222no—
546C4⋊C8—2441no—
547C4⋊C8—2441no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C22⋊C8—1222no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—2441no—
558C22⋊C8—2441no—
559C22⋊C8—2441no—
560C22⋊C8—2441no—
561#97—2441no—
562C4×C8—1222no—
563C4×C8—2441no—
564#95—611no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95—611no—
569#95—611no—
570C24—611no—
571C24—611no—
572C24—1222no—
573C24—1222no—
574C24—1222no—
575C24—2441no—
576C24—2441no—
577C24—2441no—
578C24—2441no—
579C24C2×C4×D6111yescharacteristic
580C24C2×C4×D6111yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—41no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
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—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1222no—
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—1222no—
620C22×C4—1222no—
621C22×C4—2441no—
622C22×C4—2441no—
623C22×C4—2441no—
624C22×C4—2441no—
625C22×C4—2444no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4—2441no—
630C22×C4—2441no—
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4D4×D6112yes—
636C22×C4#1175822412yes—
637C22×C4C23×D6111yescharacteristic
638M16—44no—
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—21no—
653C2×C8—612no—
654C2×C8—612no—
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×C8—1221no—
665C4⋊C4—22no—
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—1221no—
683C42—1221no—
684C42—1221no—
685C42—1221no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—612no—
700C23—612no—
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#1451973712yes—
721C23C22×C4×D6111yescharacteristic
722D4—44no—
723D4—2444no—
724D4—2444no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
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—2444no—
762C2×C4—2444no—
763C2×C4—2444no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4#1451973712yes—
773C2×C4M16×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×#1175822411yescharacteristic
776C2×C4#1451982211yescharacteristic
777C2×C4#1451982211yescharacteristic
778C2×C4#1451982311yescharacteristic
779C2×C4#1451982311yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—1222no—
785C8—1222no—
786C8—2441no—
787C8—2441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—24416no—
809C22—2441no—
810C22—2441no—
811C22—2441no—
812C22—2441no—
813C22—2441no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22C2×#1451973711yescharacteristic
818C22#1684023411yescharacteristic
819C22#1684023411yescharacteristic
820C22C2×M16×D6111yescharacteristic
821C22#131×D6111yescharacteristic
822C22#1684052711yescharacteristic
823C22#1684052811yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—1222no—
829C4—2441no—
830C4—2441no—
831C4—2441no—
832C4—2441no—
833C4—2441no—
834C4#1684032311yescharacteristic
835C4#1684032711yescharacteristic
836C4#1684034911yescharacteristic
837C4#1684034911yescharacteristic
838C2—42no—
839C2—81no—
840C2—2442no—
841C2—2442no—
842C2#2144848211yescharacteristic
843C2#2145454911yescharacteristic
844C2#2145455111yescharacteristic
845C2#2145485111yescharacteristic
846C2#2145485711yescharacteristic
847C2#2145486611yescharacteristic
848C2#2145487811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC2×#14519745C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#22038
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#16839840C2semidirect
2. C2×#16839725C2semidirect
4. #21446615C2semidirect
5. #21446611C2semidirect
6. #21446433C2semidirect
7. #21446426C2semidirect
8. #21446423C2semidirect
9. #21446423C2semidirect
10. #21446114C2semidirect
11. #21446114C2semidirect
12. #21446002C2semidirect
13. #21445728C2semidirect
14. #21445605C2semidirect
15. C61×#1870C2semidirect
18. C22×#11758194C22semidirect
23. C2×C4⋊#92418C22semidirect
24. C2×#14519706C22semidirect
25. C2×#14519706C22semidirect
28. C2×C22⋊#92418C22semidirect
37. C2×#14519687C22semidirect
38. C2×C4×#92418C22semidirect
39. C2×C8×Dic61C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
57. C2×C22⋊C8×C61C22semidirect
58. C2×C22⋊C8×C61C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
80. C2×#11758194D4semidirect
240. #11758198M16semidirect
425. #1870D61semidirect
464. C2×C22⋊C8C2×D61semidirect
465. C2×C22⋊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×#168398402
C2×#168397252
C4×#145197452
#214466152
#214466112
#214464332
#214464262
#214464232
#214461142
#214460022
#214457282
#214456052
C61×#18702
#2203861