Finite Group Databasebeta

← #29700268

Subgroups — #29700268

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839914C211yesmaximal, characteristic
2C2×#16839862C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic
4#21448823C211yesmaximal, characteristic, complemented
5D4×#11758198C211yesmaximal, characteristic
6#21446698C211yesmaximal, characteristic, complemented
7#21446515C211yesmaximal, characteristic, complemented
8#21446437C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446151C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445594C211yesmaximal, characteristic, complemented
15C61×#1862C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic, complemented
22C2×D4×Dic61C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24C22×#11758198—21no—
25#16839914C418yescomplemented
26#16839862—24no—
27C2×#14519710C2211yescharacteristic, complemented
28C2×#14519702C2211yescharacteristic, complemented
29C2×#14519700C2211yescharacteristic, complemented
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34#102×D61—24no—
35C2×#14519689C2211yescharacteristic
36C2×#14519688C2211yescharacteristic, complemented
37C2×#14519687C2211yescharacteristic, complemented
38#16839667C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839658—21no—
42#16839645—21no—
43#16839641—21no—
44#16839639—21no—
45#16839633—21no—
46#16839619C2211yescharacteristic
47#16839617—21no—
48C4⋊C4×Dic61C2211yescharacteristic, complemented
49C4×#11758198C2211yescharacteristic
50#16839609—21no—
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C2×C4×D4×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#389C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C2×D4×D61C2×C414yes—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758190—41no—
76C2×#11758190—41no—
77C2×#11758190C2×C414yescomplemented
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86#14519757—22no—
87#14519757C2×C414yescomplemented
88C4×Dic122—22no—
89C4×Dic122—41no—
90D4×Dic61—22no—
91D4×Dic61—41no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—41no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—44no—
107C2×#11758198D411yescharacteristic
108C2×#11758198D411yescharacteristic
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519710—22no—
113#14519702—41no—
114#14519700—22no—
115#14519699—22no—
116#14519698D414yes—
117#14519697—22no—
118#14519697C2×C414yescomplemented
119#14519689C2×C414yescomplemented
120#14519688—22no—
121#14519687—41no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684D411yescharacteristic
127#14519684D411yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—41no—
141#102×C61—22no—
142#102×C61C2×C414yescomplemented
143#95×C61—21no—
144C24×C61—21no—
145C23×D61—21no—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—81no—
152C23×D61—81no—
153C23×D61C2×D411yescharacteristic
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61C22×C412yes—
158C2×D4×C61C2×D412yes—
159C2×D4×C61#4112yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61—81no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—24no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—81no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181D4×D61—28no—
182D4×D61—44no—
183D4×D61—44no—
184D4×D61—44no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C412yes—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—81no—
198C2×C4×D61C22×C412yes—
199C2×C4×D61#4112yes—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C22×C412yes—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61C22×C412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—81no—
218C4⋊C4×C61C22×C412yes—
219C22⋊C4×C61—42no—
220C42×C61—21no—
221C42×C61—21no—
222C22⋊Dic61—42no—
223#11758200—28no—
224#11758198—24no—
225#11758198—22no—
226#11758198—22no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230#11758198—81no—
231#11758198—81no—
232C4⋊Dic61—21no—
233C4⋊Dic61—24no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—42no—
242C4×Dic61—81no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C22×C412yes—
248C2×#92418C2×D412yes—
249#11758190—44no—
250C8×D61—44no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C22×D411yescharacteristic
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—48no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—48no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61C4×D412yes—
278C22×D61AGL(1,ℤ/8)12yes—
279C22×D61#13712yes—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61C4×D414yes—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—84no—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C22⋊D61—48no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—84no—
325C2×Dic61C4×D412yes—
326D244—22no—
327D244—22no—
328D244—41no—
329D244—41no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—84no—
335Dic122—22no—
336Dic122—22no—
337Dic122—41no—
338Dic122—41no—
339C8×C61—22no—
340C8×C61—41no—
341#92418—22no—
342#92418—22no—
343#22854—611nomaximal, Sylow
344C22×C61—24no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61C2×C4×D411yescharacteristic
352C22×C61D4211yescharacteristic
353C22×C61#54611yescharacteristic
354C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C61C2×#13711yescharacteristic
356C22×C61#57611yescharacteristic
357C22×C61#57711yescharacteristic
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—816no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61#44014yescomplemented
373C4×C61—42no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—81no—
377C4×C61—81no—
378C4×C61C2×C4×D411yescharacteristic
379C4×C61#51811yescharacteristic
380C4×C61#54611yescharacteristic
381C4×C61#55111yescharacteristic
382Dic61—22no—
383Dic61—42no—
384Dic61—42no—
385Dic61—41no—
386Dic61—41no—
387Dic61—81no—
388C2×#450—611no—
389C2×#440—611no—
390C22×#102—611no—
391#2360—611no—
392D4×C22⋊C4—611no—
393#1973—611no—
394#1936—611no—
395#1925—611no—
396#1892—611no—
397#1880—611no—
398#1877—611no—
399#1862D6111yescharacteristic, complemented
400#1852—611no—
401#1762—611no—
402#1752—611no—
403C2×C61—44no—
404C2×C61#235811yescharacteristic
405C2×C61C2×#44011yescharacteristic
406C2×C61#294611yescharacteristic
407C2×C61#326411yescharacteristic
408C2×C61#326611yescharacteristic
409C2×C61#331011yescharacteristic
410C2×C61#331411yescharacteristic
411D61—24no—
412D61—82no—
413C23×D4—611no—
414C22×SD16—611no—
415C22×SD16—611no—
416C23×C8—611no—
417C2×C22⋊Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×D4—611no—
420C2×C4×D4C2×D6111yescharacteristic
421C22×C4⋊C4—611no—
422C22×C22⋊C4—1221no—
423#450—618no—
424#440—1224no—
425C2×#107—611no—
426C2×#107C2×D6111yescharacteristic, complemented
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—1224no—
434C2×#102C2×D6111yescharacteristic
435C2×#102C2×D6111yescharacteristic
436C2×C22⋊C8—611no—
437C2×#97—611no—
438C2×#97—611no—
439#391—611no—
440#390—611no—
441#390—611no—
442#389—1221no—
443#389C2×D6111yescharacteristic, complemented
444#387—1221no—
445#386—1221no—
446#386—1221no—
447#385—1221no—
448#380—611no—
449#379—1221no—
450C4×C4⋊C4—611no—
451C4×C22⋊C4—611no—
452C4×C22⋊C4—1221no—
453#340—611no—
454#340—611no—
455#340—611no—
456#340C2×D6111yescharacteristic, complemented
457#336—611no—
458#336C2×D6111yescharacteristic, complemented
459C61#2285411yescharacteristic, complemented, Sylow
460C25—1221no—
461C22×Q8—611no—
462C22×D4—614no—
463C22×D4—611no—
464C22×D4—1222no—
465C22×D4—1221no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—2441no—
469C22×D4—2441no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1221no—
475C2×SD16—614no—
476C2×SD16—614no—
477C2×SD16—1222no—
478C2×SD16—1222no—
479C2×SD16—2441no—
480C2×SD16—2441no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—2441no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C22⋊Q8—614no—
489C22⋊Q8—1222no—
490C4×Q8—1222no—
491C4×Q8—2441no—
492C4×D4—22no—
493C4×D4—41no—
494C4×D4—1222no—
495C4×D4—2441no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—2441no—
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—2444no—
518C2×C42—611no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42C22×D6111yescharacteristic
522#107—41no—
523#107—1222no—
524#103—1222no—
525#103—2441no—
526#102—22no—
527#102—614no—
528#102—614no—
529#102—1222no—
530#102—1222no—
531#102C4×D6114yescomplemented
532C22⋊C8—614no—
533#97—1222no—
534#97—2441no—
535#95—21no—
536#95—611no—
537#95—611no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24—611no—
544C24—1224no—
545C24—1221no—
546C24—4881no—
547C24—4881no—
548C24—2442no—
549C24—2442no—
550C24—2442no—
551C24—2442no—
552C2×Q8—612no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1228no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—2444no—
570C2×D4—2444no—
571C2×D4—2444no—
572C2×D4—2442no—
573C2×D4—2442no—
574C2×D4C2×C4×D6112yes—
575C2×D4D4×D6112yes—
576C2×D4#1175822612yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—81no—
583C22×C4—611no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—4881no—
596C22×C4—4881no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4D4×D6111yescharacteristic
602C22×C4D4×D6111yescharacteristic
603C22×C4C23×D6111yescharacteristic
604SD16—1228no—
605SD16—2444no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—2444no—
618C2×C8C2×C4×D6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—81no—
625C4⋊C4—612no—
626C4⋊C4—1224no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—2442no—
631C4⋊C4—2442no—
632C4⋊C4C2×C4×D6112yes—
633C22⋊C4—42no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1224no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—21no—
644C42—21no—
645C42—1221no—
646C42—1221no—
647C42—4881no—
648C42—2442no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—612no—
657C23—612no—
658C23—612no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1222no—
664C23—4884no—
665C23—4884no—
666C23—4884no—
667C23—4884no—
668C23—4884no—
669C23—2448no—
670C23—2448no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23C2×D4×D6111yescharacteristic
678Q8—1222no—
679Q8—1222no—
680Q8—2441no—
681Q8—2441no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—1222no—
686D4—1222no—
687D4—2448no—
688D4—2441no—
689D4—2441no—
690D4#1451973914yes—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—84no—
707C2×C4—612no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—4884no—
723C2×C4—4884no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4C22×C4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6111yescharacteristic
734C2×C4C2×#1175822611yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982311yescharacteristic
737C8—22no—
738C8—41no—
739C8—1222no—
740C8—1222no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—614no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—48816no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22C4×D4×D6111yescharacteristic
764C22#1684039411yescharacteristic
765C22#1684040311yescharacteristic
766C22AGL(1,ℤ/8)×D6111yescharacteristic
767C22#137×D6111yescharacteristic
768C22#1684056311yescharacteristic
769C22#1684056911yescharacteristic
770C4—42no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4—1222no—
776C4—4881no—
777C4—2442no—
778C4—2442no—
779C4—2441no—
780C4—2441no—
781C4C2×#1451973911yescharacteristic
782C4#1684023411yescharacteristic
783C4#1684040411yescharacteristic
784C4#1684043911yescharacteristic
785C2—44no—
786C2—1224no—
787C2—4882no—
788C2#2144879511yescharacteristic
789C2#440×D6111yescharacteristic
790C2#2145464411yescharacteristic
791C2#2145729711yescharacteristic
792C2#2145732711yescharacteristic
793C2#2145783711yescharacteristic
794C2#2145789711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1862C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1862D61
hypocenterC61#22854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#16839862C2semidirect
4. #21448823C2semidirect
6. #21446698C2semidirect
7. #21446515C2semidirect
8. #21446437C2semidirect
9. #21446241C2semidirect
10. #21446173C2semidirect
11. #21446151C2semidirect
12. #21446005C2semidirect
13. #21445646C2semidirect
14. #21445594C2semidirect
15. C61×#1862C2semidirect
21. C2×C4×Dic122C22semidirect
25. #16839914C4semidirect
27. C2×#14519710C22semidirect
28. C2×#14519702C22semidirect
29. C2×#14519700C22semidirect
36. C2×#14519688C22semidirect
37. C2×#14519687C22semidirect
38. #16839667C22semidirect
48. C4⋊C4×Dic61C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
56. C2×#107×C61C22semidirect
59. C61×#389C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
77. C2×#11758190C2×C4semidirect
80. C2×#11758200C2×C4semidirect
87. #14519757C2×C4semidirect
118. #14519697C2×C4semidirect
119. #14519689C2×C4semidirect
142. #102×C61C2×C4semidirect
372. C2×D61#440semidirect
399. #1862D61semidirect
426. C2×#107C2×D61semidirect
443. #389C2×D61semidirect
456. #340C2×D61semidirect
458. #336C2×D61semidirect
459. C61#22854semidirect
531. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399142
C2×#168398622
C2×#102×D612
#214488232
D4×#117581982
#214466982
#214465152
#214464372
#214462412
#214461732
#214461512
#214460052
#214456462
#214455942
C61×#18622
#2285461