Finite Group Databasebeta

← #29700263

Subgroups — #29700263

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×#16839915C211yesmaximal, characteristic
2C2×#16839861C211yesmaximal, characteristic, complemented
3C22×#14519697C211yesmaximal, characteristic
4#21448824C211yesmaximal, characteristic, complemented
5#21448639C211yesmaximal, characteristic
6#21446698C211yesmaximal, characteristic, complemented
7#21446514C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic, complemented
9#21446240C211yesmaximal, characteristic, complemented
10#21446175C211yesmaximal, characteristic, complemented
11#21446154C211yesmaximal, characteristic, complemented
12#21446063C211yesmaximal, characteristic, complemented
13#21445643C211yesmaximal, characteristic, complemented
14#21445598C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519742C2211yescharacteristic, complemented
22C2×#14519739C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25#16839915C418yescomplemented
26#16839861—24no—
27C2×#14519700C2211yescharacteristic, complemented
28C2×#14519700C2211yescharacteristic, complemented
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519697—24no—
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519687C2211yescharacteristic, complemented
37C2×#14519687C2211yescharacteristic, complemented
38#16839667C2211yescharacteristic, complemented
39#16839663C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839658C2211yescharacteristic, complemented
42#16839657—21no—
43#16839643—21no—
44#16839640—21no—
45#16839640—21no—
46#16839635—21no—
47#16839617—21no—
48C4⋊C4×Dic61C2211yescharacteristic, complemented
49C4×C22⋊Dic61—21no—
50C4×C22⋊Dic61C2211yescharacteristic
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic, complemented
57C2×#107×C61C2211yescharacteristic, complemented
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×Dic122C2311yescharacteristic
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—21no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2×C414yes—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758190—22no—
76C2×#11758190—22no—
77C2×#11758190—41no—
78C2×#11758190—41no—
79C2×#11758190C2×C414yescomplemented
80C2×#11758190C2×C414yescomplemented
81C22×#92418—22no—
82C22×#92418—22no—
83C22×#92418—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519756—22no—
87#14519756C2×C414yescomplemented
88#14519742—22no—
89#14519742—41no—
90#14519739—22no—
91#14519739—22no—
92#14519739—41no—
93#14519739—41no—
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61D411yescharacteristic
100C2×C22⋊Dic61D411yescharacteristic
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C22⋊C4×D61—44no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519700—22no—
113#14519700—41no—
114#14519699C2×C414yescomplemented
115#14519699C2×C414yescomplemented
116#14519697—22no—
117#14519697—22no—
118#14519697—22no—
119#14519697D414yes—
120#14519687—22no—
121#14519687—41no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684D411yescharacteristic
127#14519684D411yescharacteristic
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140#107×C61—22no—
141#107×C61—41no—
142C22⋊C8×C61C2×C414yescomplemented
143#95×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—81no—
153C23×D61—81no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
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×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—81no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61#4112yes—
168C22×C4×C61C2411yescharacteristic
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—28no—
183C2×D244—24no—
184C2×D244—21no—
185C2×D244—44no—
186C2×D244—44no—
187C2×D244—44no—
188C2×D244—42no—
189C2×D244—42no—
190C2×D244C22×C412yes—
191C2×D244C22×C412yes—
192C2×D244C2×D412yes—
193C2×D244#4112yes—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—81no—
199C2×C4×D61—81no—
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×C61C22×C412yes—
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—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—42no—
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—42no—
222C22⋊Dic61—24no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—42no—
229#11758198—81no—
230#11758198—81no—
231C4⋊Dic61—21no—
232C4⋊Dic61C22×C412yes—
233#11758196—24no—
234#11758196—42no—
235#11758196—81no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—42no—
241C4×Dic61—81no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—44no—
248C2×#92418C2×D412yes—
249#11758190—28no—
250#11758190—44no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C4×D412yes—
256C23×C61AGL(1,ℤ/8)12yes—
257C23×C61#13712yes—
258C23×C61C22×D411yescharacteristic
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—48no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—48no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
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—84no—
299C2×C4×C61C4×D412yes—
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
306C2×Dic61—22no—
307C2×Dic61—22no—
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—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324D244—22no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—22no—
329D244—48no—
330D244—41no—
331D244—41no—
332D244C4×D414yes—
333C4×D61—84no—
334C4×D61—84no—
335Dic122—22no—
336Dic122—22no—
337Dic122—41no—
338Dic122—41no—
339C8×C61—22no—
340C8×C61—22no—
341#92418—22no—
342#92418—41no—
343#22854—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61#44014yescomplemented
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—24no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—816no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C4×C61—22no—
374C4×C61—42no—
375C4×C61—81no—
376C4×C61—81no—
377C4×C61—81no—
378C4×C61C2×C4×D411yescharacteristic
379C4×C61#51811yescharacteristic
380C4×C61#54611yescharacteristic
381C4×C61#55111yescharacteristic
382Dic61—42no—
383Dic61—42no—
384Dic61—41no—
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
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#1862—611no—
400#1852D6111yescharacteristic, complemented
401#1762—611no—
402#1752—611no—
403C2×C61—24no—
404C2×C61#235811yescharacteristic
405C2×C61C2×#44011yescharacteristic
406C2×C61#294611yescharacteristic
407C2×C61#326411yescharacteristic
408C2×C61#326611yescharacteristic
409C2×C61#331011yescharacteristic
410C2×C61#331411yescharacteristic
411D61—44no—
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×D4—611no—
421C22×C4⋊C4C2×D6111yescharacteristic
422C22×C22⋊C4—1221no—
423#450—618no—
424#440—1224no—
425C2×#107C2×D6111yescharacteristic, complemented
426C2×#107C2×D6111yescharacteristic, complemented
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—1224no—
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97—611no—
438C2×#97—611no—
439#391—611no—
440#390—611no—
441#390—611no—
442#389—611no—
443#389—1221no—
444#387—1221no—
445#386—1221no—
446#386—1221no—
447#385—1221no—
448#380C2×D6111yescharacteristic
449#379—1221no—
450C4×C4⋊C4—611no—
451C4×C22⋊C4—611no—
452C4×C22⋊C4—1221no—
453#340—611no—
454#340—611no—
455#340C2×D6111yescharacteristic, complemented
456#340C2×D6111yescharacteristic, complemented
457#336—611no—
458#336—611no—
459C61#2285411yescharacteristic, complemented, Sylow
460C25—1221no—
461C22×Q8—611no—
462C22×D4—614no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4—2441no—
470C22×D4—2441no—
471C23×C4—21no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4C22×D6111yescharacteristic
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—1222no—
493C4×D4—1222no—
494C4×D4—2441no—
495C4×D4—2441no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
520C2×C42—1221no—
521C2×C42—1221no—
522#107—22no—
523#107—41no—
524#103—1222no—
525#103—2441no—
526#102—614no—
527#102—614no—
528#102—614no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532C22⋊C8C4×D6114yescomplemented
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—1221no—
543C24—1224no—
544C24—1221no—
545C24—4881no—
546C24—4881no—
547C24—2442no—
548C24—2442no—
549C24—2442no—
550C24—2442no—
551C24D4×D6111yescharacteristic
552C2×Q8—612no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—1228no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1224no—
572C2×D4—2444no—
573C2×D4—2444no—
574C2×D4—2444no—
575C2×D4—2442no—
576C2×D4—2442no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—4881no—
595C22×C4—4881no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4C2×C4×D6112yes—
601C22×C4D4×D6111yescharacteristic
602C22×C4#1175822612yes—
603C22×C4C23×D6111yescharacteristic
604SD16—1228no—
605SD16—2444no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—612no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—2444no—
617C2×C8C2×C4×D6112yes—
618C2×C8C2×C4×D6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—612no—
628C4⋊C4—1221no—
629C4⋊C4—1224no—
630C4⋊C4—4881no—
631C4⋊C4—2442no—
632C4⋊C4D4×D6112yes—
633C22⋊C4—42no—
634C22⋊C4—1222no—
635C22⋊C4—1224no—
636C22⋊C4—1222no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—1221no—
644C42—1221no—
645C42—1221no—
646C42—1221no—
647C42—4881no—
648C42—2442no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—4884no—
658C23—4884no—
659C23—4884no—
660C23—4884no—
661C23—4884no—
662C23—2448no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2448no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23#1451973912yes—
675C23#1451980112yes—
676C23#1451980912yes—
677C23C2×D4×D6111yescharacteristic
678Q8—1222no—
679Q8—1222no—
680Q8—2441no—
681Q8—2441no—
682D4—614no—
683D4—1222no—
684D4—1222no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—2448no—
689D4—2441no—
690D4—2441no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
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—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—1222no—
711C2×C4—1222no—
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—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—4884no—
725C2×C4—4884no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4#1451973912yes—
731C2×C4C22×C4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6111yescharacteristic
734C2×C4C2×#1175822611yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982311yescharacteristic
737C8—22no—
738C8—22no—
739C8—1222no—
740C8—2441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—1224no—
748C22—48816no—
749C22—4881no—
750C22—4881no—
751C22—4881no—
752C22—4881no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22#1683986114yescomplemented
763C22C2×#1451973911yescharacteristic
764C22#1684039411yescharacteristic
765C22#1684040411yescharacteristic
766C22C2×#1451980111yescharacteristic
767C22C2×#1451980911yescharacteristic
768C22#1684056611yescharacteristic
769C22#1684057111yescharacteristic
770C4—22no—
771C4—42no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4—2442no—
776C4—2442no—
777C4—2441no—
778C4—2441no—
779C4—2441no—
780C4—2441no—
781C4C4×D4×D6111yescharacteristic
782C4#1684023411yescharacteristic
783C4#1684040311yescharacteristic
784C4#1684043911yescharacteristic
785C2—24no—
786C2—4882no—
787C2—2444no—
788C2#2144879511yescharacteristic
789C2C2×#1683986111yescharacteristic
790C2#2145464911yescharacteristic
791C2#2145729211yescharacteristic
792C2#2145732211yescharacteristic
793C2#2145783811yescharacteristic
794C2#2145789811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1852C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#1852D61
hypocenterC61#22854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#16839861C2semidirect
4. #21448824C2semidirect
6. #21446698C2semidirect
7. #21446514C2semidirect
8. #21446438C2semidirect
9. #21446240C2semidirect
10. #21446175C2semidirect
11. #21446154C2semidirect
12. #21446063C2semidirect
13. #21445643C2semidirect
14. #21445598C2semidirect
15. C61×#1852C2semidirect
21. C2×#14519742C22semidirect
25. #16839915C4semidirect
27. C2×#14519700C22semidirect
28. C2×#14519700C22semidirect
36. C2×#14519687C22semidirect
37. C2×#14519687C22semidirect
38. #16839667C22semidirect
41. #16839658C22semidirect
48. C4⋊C4×Dic61C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839516C22semidirect
54. #16839516C22semidirect
56. C2×#107×C61C22semidirect
57. C2×#107×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
79. C2×#11758190C2×C4semidirect
80. C2×#11758190C2×C4semidirect
87. #14519756C2×C4semidirect
114. #14519699C2×C4semidirect
115. #14519699C2×C4semidirect
142. C22⋊C8×C61C2×C4semidirect
350. C22×C61#440semidirect
400. #1852D61semidirect
425. C2×#107C2×D61semidirect
426. C2×#107C2×D61semidirect
455. #340C2×D61semidirect
456. #340C2×D61semidirect
459. C61#22854semidirect
532. C22⋊C8C4×D61semidirect
762. C22#16839861semidirect

Maximal subgroups

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

subgroupindex
C2×#168399152
C2×#168398612
C22×#145196972
#214488242
#214486392
#214466982
#214465142
#214464382
#214462402
#214461752
#214461542
#214460632
#214456432
#214455982
C61×#18522
#2285461