Finite Group Databasebeta

← #29700172

Subgroups — #29700172

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839832C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839724C211yesmaximal, characteristic, complemented
4C22×#14519689C211yesmaximal, characteristic, complemented
5C4×#14519747C211yesmaximal, characteristic
6#21446616C211yesmaximal, characteristic, complemented
7#21446430C211yesmaximal, characteristic, complemented
8#21446424C211yesmaximal, characteristic, complemented
9#21446115C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446109C211yesmaximal, characteristic, complemented
12#21446000C211yesmaximal, characteristic, complemented
13#21445601C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#1850C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic, complemented
21C2×#14519747C411yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C4×C22⋊D61C2211yescharacteristic
25#16839832—24no—
26C8×C22⋊D61—24no—
27C2×#14519706C2211yescharacteristic, complemented
28#16839724—24no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689—24no—
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic, complemented
38C2×#14519689C2211yescharacteristic, complemented
39C2×#14519689C2211yescharacteristic, complemented
40C2×#14519688C2211yescharacteristic, complemented
41C2×#14519688C2211yescharacteristic, complemented
42C2×C8×Dic61C2211yescharacteristic, complemented
43#16839640C411yescharacteristic
44#16839640C411yescharacteristic
45#16839639C411yescharacteristic
46#16839637C411yescharacteristic
47#16839636C411yescharacteristic
48#16839636C411yescharacteristic
49#16839617C411yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C23×C8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic, complemented
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×C22⋊C8×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C24×D61C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—41no—
84C2×#11758189—41no—
85C22×#92418—22no—
86C22×#92418—22no—
87C22×#92418—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—41no—
95#14519747—24no—
96C4×D244—22no—
97C4×D244—22no—
98C4×D244—41no—
99C4×D244—41no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—22no—
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117C22⋊#92418D414yescomplemented
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519689—22no—
124#14519689—22no—
125#14519689—41no—
126#14519689D414yescomplemented
127#14519688—22no—
128#14519688—41no—
129C8×Dic61—22no—
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C22×C8×C61—22no—
136C22×C8×C61—22no—
137C22×C8×C61—41no—
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—22no—
147C4⋊C8×C61—41no—
148C22⋊C8×C61—22no—
149#95×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—41no—
158C23×D61—41no—
159C23×D61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C23×D61C22×C411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C2×D412yes—
172C22×C4×C61#4112yes—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61M1614yescomplemented
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—41no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—41no—
190C2×D244—41no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
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—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—22no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61C2×D412yes—
218C2×C4×D61#4112yes—
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—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—44no—
231C2×C8×C61C2×D412yes—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C22⋊Dic61—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—41no—
246#11758198—41no—
247#11758198—41no—
248C4⋊Dic61—22no—
249C4⋊Dic61—41no—
250#11758196—22no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—44no—
263C2×#92418C2×D412yes—
264C2×#92418C2×D412yes—
265C2×#92418C2×D412yes—
266#11758189—44no—
267#11758189—44no—
268C8×D61—44no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61C4×D412yes—
274C23×C61C2×M1612yes—
275C23×C61#13112yes—
276C23×C61C23×C411yescharacteristic
277C22×D61—28no—
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—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61C4×D412yes—
303C22×D61C2×M1612yes—
304C22×D61#13112yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61C4×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C22⋊D61—28no—
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—21no—
344C2×Dic61—44no—
345C2×Dic61C4×D412yes—
346C2×Dic61C2×M1612yes—
347D244—44no—
348D244—44no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—44no—
354C4×D61—44no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C8×C61—22no—
364C8×C61—41no—
365C8×C61—41no—
366C8×C61—41no—
367#92418—22no—
368#92418—22no—
369#92418—22no—
370#92418—41no—
371#22846—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61#43514yescomplemented
379C22×C61C2×C4×D411yescharacteristic
380C22×C61C2×C4×D411yescharacteristic
381C22×C61#51811yescharacteristic
382C22×C61C22×M1611yescharacteristic
383C22×C61C2×#13111yescharacteristic
384C22×C61C2×#13111yescharacteristic
385C22×C61#56811yescharacteristic
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—416no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—22no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61D4211yescharacteristic
414C4×C61#54611yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#55111yescharacteristic
417Dic61—22no—
418Dic61—22no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422C2×#435—611no—
423C2×C8×D4—611no—
424C2×#407—611no—
425C22×C22⋊C8—611no—
426C4×#120—611no—
427#1955—611no—
428#1924—611no—
429#1923—611no—
430#1870—611no—
431#1869—611no—
432#1869—611no—
433#1851—611no—
434#1850D6111yescharacteristic, complemented
435#1753—611no—
436#1752—611no—
437C2×C61—24no—
438C2×C61#235811yescharacteristic
439C2×C61C2×#43511yescharacteristic
440C2×C61#292911yescharacteristic
441C2×C61#293311yescharacteristic
442C2×C61D4×M1611yescharacteristic
443C2×C61#297411yescharacteristic
444C2×C61#297611yescharacteristic
445D61—42no—
446D61—42no—
447D61—42no—
448C24×C4—611no—
449C22×M16—611no—
450C22×M16—611no—
451C23×C8—611no—
452C23×C8—611no—
453C23×C8C2×D6111yescharacteristic
454C2×#120—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458#435—1224no—
459C8×D4—1224no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8C2×D6111yescharacteristic, complemented
462C2×C4⋊C8C2×D6111yescharacteristic, complemented
463#407—1224no—
464C2×C22⋊C8—611no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—1224no—
475C2×C22⋊C8C2×D6111yescharacteristic
476C2×#97—611no—
477C2×#97—611no—
478C2×C4×C8—611no—
479#386—611no—
480#386—611no—
481#386—611no—
482#385—611no—
483#385—611no—
484#385—611no—
485#379—611no—
486C4×C22⋊C4—611no—
487C4×C22⋊C4—611no—
488C4×C22⋊C4C2×D6111yescharacteristic
489#336—611no—
490#336—611no—
491#336—611no—
492#336—611no—
493#336C2×D6111yescharacteristic, complemented
494#336C2×D6111yescharacteristic, complemented
495C61#2284611yescharacteristic, complemented, Sylow
496C25—611no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1222no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—2441no—
511C23×C4—2441no—
512C23×C4C22×D6111yescharacteristic
513C2×M16—1222no—
514C2×M16—1222no—
515C2×M16—1222no—
516C2×M16—1222no—
517C2×M16—2441no—
518C2×M16—2441no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—1222no—
527C22×C8—1222no—
528C22×C8—1222no—
529C22×C8—1222no—
530C22×C8—2441no—
531C22×C8—2441no—
532C22×C8C22×D6111yescharacteristic
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#120—1224no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—2441no—
542C4×D4—2441no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4C4×D6111yescharacteristic
557C2×C22⋊C4C4×D6111yescharacteristic
558C2×C42—611no—
559C2×C42C22×D6111yescharacteristic
560C2×C42C22×D6111yescharacteristic
561C4⋊C8—22no—
562C4⋊C8—41no—
563C4⋊C8—1222no—
564C22⋊C8—22no—
565C22⋊C8—614no—
566C22⋊C8—614no—
567C22⋊C8—1222no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—2441no—
575#97—1222no—
576#97—2441no—
577C4×C8—1222no—
578#95—611no—
579#95—611no—
580#95—611no—
581#95—611no—
582#95C4×D6111yescharacteristic
583#95C4×D6111yescharacteristic
584C24—611no—
585C24—611no—
586C24—611no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—2441no—
593C24—2441no—
594C24C2×C4×D6111yescharacteristic
595C2×D4—614no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—2441no—
603C2×D4—2441no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1222no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—2441no—
638C22×C4—2441no—
639C22×C4—2444no—
640C22×C4—2444no—
641C22×C4—2444no—
642C22×C4—2444no—
643C22×C4—2441no—
644C22×C4C2×C4×D6111yescharacteristic
645C22×C4C2×C4×D6111yescharacteristic
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4D4×D6112yes—
650C22×C4#1175822612yes—
651C22×C4C23×D6111yescharacteristic
652M16—2444no—
653M16—2444no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—44no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—612no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—2444no—
679C2×C8—2444no—
680C2×C8D4×D6112yes—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—2441no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—2441no—
694C22⋊C4—2441no—
695C22⋊C4—2441no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—1221no—
701C42—1221no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—612no—
707C23—612no—
708C23—612no—
709C23—1228no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—2444no—
729C23—2444no—
730C23—2444no—
731C23—2444no—
732C23—2444no—
733C23—2444no—
734C23#1451973912yes—
735C23M16×D6112yes—
736C23#1451978312yes—
737C23C22×C4×D6111yescharacteristic
738D4—1228no—
739D4—2444no—
740D4—2444no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4—2444no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4#1451973912yes—
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4#41×D6111yescharacteristic
793C2×C4C2×#1175822611yescharacteristic
794C2×C4#1451982211yescharacteristic
795C2×C4#1451982311yescharacteristic
796C8—22no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—1222no—
801C8—1222no—
802C8—1222no—
803C8—2441no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—1222no—
811C22—1222no—
812C22—1222no—
813C22—1222no—
814C22—1222no—
815C22—1222no—
816C22—1222no—
817C22—1222no—
818C22—1222no—
819C22—24416no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22#1683983214yescomplemented
833C22C4×D4×D6111yescharacteristic
834C22C2×#1451973911yescharacteristic
835C22#1684023411yescharacteristic
836C22C2×M16×D6111yescharacteristic
837C22#131×D6111yescharacteristic
838C22C2×#1451978311yescharacteristic
839C22#1684052711yescharacteristic
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—1222no—
846C4—1222no—
847C4—2441no—
848C4—2441no—
849C4—2441no—
850C4#1684039411yescharacteristic
851C4#1684040311yescharacteristic
852C4#1684040411yescharacteristic
853C4#1684043911yescharacteristic
854C2—24no—
855C2—2442no—
856C2—2442no—
857C2—2442no—
858C2#2144879511yescharacteristic
859C2C2×#1683983211yescharacteristic
860C2#2145450811yescharacteristic
861C2#2145454311yescharacteristic
862C2#2145455211yescharacteristic
863C2#2145484911yescharacteristic
864C2#2145486111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1850C2
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1850D61
hypocenterC61#22846
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#16839832C2semidirect
2. C2×C8×C22⋊D61C2semidirect
3. C2×#16839724C2semidirect
4. C22×#14519689C2semidirect
6. #21446616C2semidirect
7. #21446430C2semidirect
8. #21446424C2semidirect
9. #21446115C2semidirect
10. #21446110C2semidirect
11. #21446109C2semidirect
12. #21446000C2semidirect
13. #21445601C2semidirect
14. #21445597C2semidirect
15. C61×#1850C2semidirect
20. C22×C8×D61C22semidirect
27. C2×#14519706C22semidirect
37. C2×#14519689C22semidirect
38. C2×#14519689C22semidirect
39. C2×#14519689C22semidirect
40. C2×#14519688C22semidirect
41. C2×#14519688C22semidirect
42. C2×C8×Dic61C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
57. C2×C4⋊C8×C61C22semidirect
58. C2×C4⋊C8×C61C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
117. C22⋊#92418D4semidirect
126. #14519689D4semidirect
176. C2×C22⋊D61M16semidirect
378. C22×C61#435semidirect
434. #1850D61semidirect
461. C2×C4⋊C8C2×D61semidirect
462. C2×C4⋊C8C2×D61semidirect
493. #336C2×D61semidirect
494. #336C2×D61semidirect
495. C61#22846semidirect
832. C22#16839832semidirect

Maximal subgroups

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

subgroupindex
C2×#168398322
C2×C8×C22⋊D612
C2×#168397242
C22×#145196892
C4×#145197472
#214466162
#214464302
#214464242
#214461152
#214461102
#214461092
#214460002
#214456012
#214455972
C61×#18502
#2284661