Finite Group Databasebeta

← #29696937

Subgroups — #29696937

Order 15616.

1212 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839813C211yesmaximal, characteristic, complemented
2C2×#16839725C211yesmaximal, characteristic
3C4×C22⋊C4×D61C211yesmaximal, characteristic
4#21446432C211yesmaximal, characteristic, complemented
5#21446430C211yesmaximal, characteristic, complemented
6#21446425C211yesmaximal, characteristic, complemented
7#21446423C211yesmaximal, characteristic, complemented
8#21446002C211yesmaximal, characteristic, complemented
9#21446001C211yesmaximal, characteristic, complemented
10#21445886C211yesmaximal, characteristic, complemented
11#21445798C211yesmaximal, characteristic, complemented
12#21445728C211yesmaximal, characteristic
13#21445603C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×C22⋊C4×D61C411yescharacteristic
19C2×C22⋊C4×D61C411yescharacteristic
20C2×C42×D61C2211yescharacteristic
21C2×C42×D61C2211yescharacteristic
22#16839813—24no—
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×#14519706C2211yescharacteristic, complemented
26C2×#14519706C2211yescharacteristic, complemented
27#16839725—24no—
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519688C2211yescharacteristic, complemented
38C2×C4×#92418C2211yescharacteristic, complemented
39C22⋊C4×Dic61C411yescharacteristic
40C22⋊C4×Dic61C411yescharacteristic
41C4×#11758198C2211yescharacteristic
42C4×#11758198C2211yescharacteristic
43C4×C22⋊Dic61C2211yescharacteristic
44#16839609C411yescharacteristic
45#16839609C411yescharacteristic
46#95×D61C411yescharacteristic
47#95×D61C411yescharacteristic
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×M16×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic, complemented
57C2×C4×C8×C61C2211yescharacteristic, complemented
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—41no—
68C22×C4×D61—41no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C22⋊C4×D61—24no—
91C22⋊C4×D61—24no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100C42×D61—41no—
101C42×D61—41no—
102#14519706—22no—
103#14519706—22no—
104#14519706—41no—
105#14519706—41no—
106C22⋊#92418—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—22no—
110#14519689—22no—
111#14519689—22no—
112#14519689—41no—
113#14519689—41no—
114#14519689D414yes—
115#14519688—41no—
116C4×#92418—22no—
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—22no—
126C2×M16×C61—41no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C22⋊C8×C61—22no—
136#97×C61—41no—
137C4×C8×C61—22no—
138#95×C61C2×C411yescharacteristic
139#95×C61C2×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—22no—
145C23×D61—22no—
146C23×D61—41no—
147C23×D61—41no—
148C23×D61C22×C411yescharacteristic
149C23×D61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61#4112yes—
160C22×C4×C61#4112yes—
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—41no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—44no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—41no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61—41no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61M1614yescomplemented
203C2×C4×D61C2×D412yes—
204C2×C4×D61#4112yes—
205M16×C61—44no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
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×C61C2×D412yes—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198M1614yescomplemented
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C4×Dic61—41no—
237C4×Dic61—41no—
238#11758194—44no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—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×#92418C2×D412yes—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61#11712yes—
258C23×C61C23×C411yescharacteristic
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—28no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—44no—
275C22×D61—44no—
276C22×D61C4×D412yes—
277C22×D61C2×M1612yes—
278C22×D61C2×M1612yes—
279C22×D61#13112yes—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61#11712yes—
297C2×C4×C61C2×M1612yes—
298C2×C4×C61C2×M1612yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—44no—
321C2×Dic61C4×D412yes—
322C2×Dic61C2×M1612yes—
323C2×Dic61C2×M1612yes—
324C4×D61—28no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—44no—
330C4×D61—44no—
331C4×D61—44no—
332C4×D61—44no—
333C4×D61—44no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C8×C61—22no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—22no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#22553—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61C2×#11711yescharacteristic
355C22×C61C2×C4×D411yescharacteristic
356C22×C61#51811yescharacteristic
357C22×C61C22×M1611yescharacteristic
358C22×C61C22×M1611yescharacteristic
359C22×C61C2×#13111yescharacteristic
360C22×C61#56811yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—416no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61#43514yes—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61#54611yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#55111yescharacteristic
384C4×C61#55111yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—41no—
389Dic61—41no—
390Dic61—41no—
391C2×#431—611no—
392C2×#407—611no—
393C2×C4×C22⋊C4—611no—
394#1924—611no—
395#1924—611no—
396#1923—611no—
397#1923—611no—
398#1851—611no—
399#1851—611no—
400#1817—611no—
401#1797—611no—
402#1779—611no—
403#1753—611no—
404#1753D6111yescharacteristic, complemented
405#1749—611no—
406C2×C61—42no—
407C2×C61#234211yescharacteristic
408C2×C61#292011yescharacteristic
409C2×C61#292411yescharacteristic
410C2×C61C2×#43511yescharacteristic
411C2×C61D4×M1611yescharacteristic
412C2×C61#297411yescharacteristic
413C2×C61#297511yescharacteristic
414D61—24no—
415D61—42no—
416C24×C4—611no—
417C22×M16—611no—
418C22×M16C2×D6111yescharacteristic
419C22×C22⋊C4—611no—
420C22×C22⋊C4—611no—
421C22×C42—611no—
422C22×C42—611no—
423#431—1224no—
424C2×C4⋊C8—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—611no—
428#407—1224no—
429C2×C22⋊C8—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8—611no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8C2×D6111yescharacteristic
439C2×#97—611no—
440C2×#97C2×D6111yescharacteristic, complemented
441C2×C4×C8—611no—
442C2×C4×C8C2×D6111yescharacteristic, complemented
443C4×C22⋊C4—611no—
444C4×C22⋊C4—611no—
445C4×C22⋊C4—611no—
446C4×C22⋊C4—611no—
447C4×C22⋊C4—611no—
448C4×C22⋊C4—611no—
449C4×C22⋊C4—611no—
450C4×C22⋊C4C2×D6111yescharacteristic
451C2×#95—611no—
452C2×#95—611no—
453#336—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336C2×D6111yescharacteristic, complemented
460#336C2×D6111yescharacteristic, complemented
461C61#2255311yescharacteristic, complemented, Sylow
462C25—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—1222no—
473C23×C4—1222no—
474C23×C4—1222no—
475C23×C4—1222no—
476C23×C4—2441no—
477C23×C4—2441no—
478C23×C4C22×D6111yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C2×M16—1222no—
483C2×M16—1222no—
484C2×M16—2441no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8C22×D6111yescharacteristic
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C22×C8C22×D6111yescharacteristic
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4C4×D6111yescharacteristic
502C2×C22⋊C4C4×D6111yescharacteristic
503C2×C42—611no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—1222no—
510C2×C42—1222no—
511C2×C42—2441no—
512C2×C42—2441no—
513C2×C42C22×D6111yescharacteristic
514C2×C42C22×D6111yescharacteristic
515C4⋊C8—1222no—
516C4⋊C8—1222no—
517C4⋊C8—2441no—
518C4⋊C8—2441no—
519C22⋊C8—22no—
520C22⋊C8—614no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—2441no—
528C22⋊C8—2441no—
529#97—41no—
530#97—2441no—
531C4×C8—22no—
532C4×C8—1222no—
533#95—611no—
534#95—611no—
535#95—611no—
536#95—611no—
537#95—611no—
538#95—611no—
539#95C4×D6111yescharacteristic
540#95C4×D6111yescharacteristic
541C24—611no—
542C24—611no—
543C24—1222no—
544C24—1222no—
545C24—1222no—
546C24—1222no—
547C24—1222no—
548C24—2441no—
549C24—2441no—
550C24C2×C4×D6111yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—614no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4—2441no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2444no—
594C22×C4—2444no—
595C22×C4—2444no—
596C22×C4—2444no—
597C22×C4—2441no—
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4#1175822212yes—
604C22×C4#1175822212yes—
605C22×C4C23×D6111yescharacteristic
606M16—44no—
607M16—2444no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—612no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8D4×D6112yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—614no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—1222no—
645C42—1222no—
646C42—1221no—
647C42—1221no—
648C42—1221no—
649C42—1221no—
650C42—2441no—
651C42—2441no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—612no—
659C23—612no—
660C23—612no—
661C23—612no—
662C23—1228no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—2444no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2444no—
678C23—2444no—
679C23#1451973412yes—
680C23C22×C4×D6111yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—1228no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—2444no—
721C2×C4—2444no—
722C2×C4—2444no—
723C2×C4—2444no—
724C2×C4—2444no—
725C2×C4—2444no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4#1451973412yes—
731C2×C4M16×D6112yes—
732C2×C4M16×D6112yes—
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4C2×#1175822211yescharacteristic
736C2×C4C2×#1175822211yescharacteristic
737C2×C4#1451982211yescharacteristic
738C2×C4#1451982311yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C8—2441no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—614no—
755C22—1222no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—1222no—
764C22—24416no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22C2×#1451973411yescharacteristic
770C22C4×D4×D6111yescharacteristic
771C22#1684023411yescharacteristic
772C22C2×M16×D6111yescharacteristic
773C22C2×M16×D6111yescharacteristic
774C22#131×D6111yescharacteristic
775C22#1684052711yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—1222no—
782C4—1222no—
783C4—1222no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4#1684040211yescharacteristic
788C4#1684040811yescharacteristic
789C4#1684043611yescharacteristic
790C4#1684044111yescharacteristic
791C2—42no—
792C2—1224no—
793C2—2442no—
794C2#2144866211yescharacteristic
795C2#2145445011yescharacteristic
796C2#2145447411yescharacteristic
797C2#435×D6111yescharacteristic
798C2#2145455211yescharacteristic
799C2#2145485111yescharacteristic
800C2#2145485711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1753C2
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22553
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
4. #21446432C2semidirect
5. #21446430C2semidirect
6. #21446425C2semidirect
7. #21446423C2semidirect
8. #21446002C2semidirect
9. #21446001C2semidirect
10. #21445886C2semidirect
11. #21445798C2semidirect
13. #21445603C2semidirect
14. #21445582C2semidirect
15. C61×#1753C2semidirect
23. C2×#14519706C22semidirect
24. C2×#14519706C22semidirect
25. C2×#14519706C22semidirect
26. C2×#14519706C22semidirect
37. C2×#14519688C22semidirect
38. C2×C4×#92418C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
56. C2×#97×C61C22semidirect
57. C2×C4×C8×C61C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
202. C2×C4×D61M16semidirect
229. #11758198M16semidirect
404. #1753D61semidirect
440. C2×#97C2×D61semidirect
442. C2×C4×C8C2×D61semidirect
459. #336C2×D61semidirect
460. #336C2×D61semidirect
461. C61#22553semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C2×#168397252
C4×C22⋊C4×D612
#214464322
#214464302
#214464252
#214464232
#214460022
#214460012
#214458862
#214457982
#214457282
#214456032
#214455822
C61×#17532
#2255361