Finite Group Databasebeta

← #29717688

Subgroups — #29717688

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839991C211yesmaximal, characteristic, complemented
3C2×#16839914C211yesmaximal, characteristic, complemented
4C2×#16839913C211yesmaximal, characteristic, complemented
5#21449264C211yesmaximal, characteristic, complemented
6#21447052C211yesmaximal, characteristic, complemented
7#21447007C211yesmaximal, characteristic, complemented
8#21446908C211yesmaximal, characteristic, complemented
9#21446823C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446111C211yesmaximal, characteristic, complemented
13#21446082C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C22×#102×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic, complemented
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic, complemented
21D4×C22⋊D61—24no—
22D4×C22⋊D61—24no—
23C2×#14519773C2211yescharacteristic
24C2×#14519757C2211yescharacteristic, complemented
25C2×#14519756C2211yescharacteristic, complemented
26C2×#14519751C2211yescharacteristic
27C2×#14519749—21no—
28C2×#14519748C2211yescharacteristic
29C2×#14519746—21no—
30C2×#14519745—21no—
31C2×D4×Dic61C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33#16839991—24no—
34#16839914—24no—
35#16839913—24no—
36C2×#14519709C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×C22⋊#92418C2211yescharacteristic, complemented
44C2×#14519689C2211yescharacteristic, complemented
45C2×#14519689C2211yescharacteristic, complemented
46#16839692—21no—
47#16839684—21no—
48#16839667C2211yescharacteristic, complemented
49#16839661C2211yescharacteristic, complemented
50#16839641—21no—
51#16839622—21no—
52#16839619C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C23×C8×C61C2211yescharacteristic, complemented
59C22×C4⋊C4×C61C2211yescharacteristic, complemented
60C2×#102×C61—24no—
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic, complemented
64C2×#102×C61C2211yescharacteristic, complemented
65C24×D61—21no—
66C22×Dic122C2311yescharacteristic
67C22×D244C2311yescharacteristic
68C22×C22⋊D61—28no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—44no—
75C22×C22⋊D61—44no—
76C22×C22⋊D61D411yescharacteristic
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—41no—
82C2×D4×D61—41no—
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758190—22no—
86C2×#11758190—22no—
87C2×#11758190—41no—
88C2×#11758200—22no—
89C2×#11758200—22no—
90C2×#11758200—22no—
91C2×#11758200—22no—
92C2×#11758200—41no—
93C2×#11758200—41no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519773—22no—
97#14519773—22no—
98#14519757—22no—
99#14519757—41no—
100#14519756—22no—
101#14519756—22no—
102#14519751—22no—
103#14519751D414yes—
104#14519749—28no—
105#14519748—22no—
106#14519748—22no—
107#14519746—28no—
108#14519745—28no—
109D4×Dic61—22no—
110D4×Dic61—22no—
111C4×C22⋊D61—22no—
112C4×C22⋊D61—22no—
113C2×C4⋊Dic61—21no—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
117C2×#11758196—21no—
118C2×#11758196D411yescharacteristic
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×C22⋊Dic61—21no—
122C2×C22⋊Dic61D411yescharacteristic
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198D411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128#14519709—22no—
129#14519702—22no—
130#14519699—22no—
131#14519698—22no—
132#14519698—22no—
133#14519697—22no—
134#14519697—41no—
135C22⋊#92418—22no—
136#14519689—22no—
137#14519689—41no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142C25×C61—21no—
143C22×D4×C61—22no—
144C22×D4×C61—22no—
145C22×D4×C61—21no—
146C22×D4×C61—22no—
147C22×D4×C61—41no—
148C22×D4×C61—41no—
149C22×D4×C61D414yes—
150C22×D4×C61C2311yescharacteristic
151C22×D4×C61C2311yescharacteristic
152C23×C4×C61—21no—
153C23×C4×C61C2311yescharacteristic
154C22×C8×C61—22no—
155C22×C8×C61—22no—
156C22×C8×C61—41no—
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C2×C4⋊C4×C61—22no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61—41no—
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C4⋊C4×C61C2311yescharacteristic
164#102×C61—22no—
165#102×C61—22no—
166#102×C61—22no—
167#102×C61D414yescomplemented
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—24no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—42no—
175C24×C61—81no—
176C24×C61—81no—
177C24×C61C2×D411yescharacteristic
178C23×D61—21no—
179C23×D61—24no—
180C23×D61—42no—
181C23×D61—42no—
182C23×D61—42no—
183C23×D61—42no—
184C23×D61—81no—
185C23×D61—81no—
186C23×D61C2×D411yescharacteristic
187C2×D4×C61—28no—
188C2×D4×C61—24no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—44no—
198C2×D4×C61—44no—
199C2×D4×C61—44no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61C2×D412yes—
203C2×D4×C61C2×D412yes—
204C2×D4×C61C2×D412yes—
205C2×D4×C61#4112yes—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61—81no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—22no—
220C2×C22⋊D61—22no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61—42no—
228C2×C22⋊D61—42no—
229C2×C22⋊D61—432no—
230C2×C22⋊D61—42no—
231C2×C22⋊D61—42no—
232C2×C22⋊D61—42no—
233C2×C22⋊D61—42no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61—81no—
237C2×C22⋊D61SD1614yescomplemented
238C22×Dic61—24no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—42no—
243C22×Dic61—42no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247D4×D61—44no—
248D4×D61—44no—
249D4×D61—44no—
250D4×D61—44no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—21no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244C2×D412yes—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—44no—
275C2×C8×C61C2×D412yescomplemented
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—42no—
280C4⋊C4×C61C2×D412yescomplemented
281C22⋊Dic61—24no—
282C22⋊Dic61—24no—
283C22⋊Dic61—22no—
284C22⋊Dic61—42no—
285#11758200—44no—
286#11758200—44no—
287#11758198—24no—
288#11758198—22no—
289#11758198—42no—
290#11758198—81no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—42no—
295C4⋊Dic61—81no—
296C4⋊Dic61C2×D412yes—
297#11758196—22no—
298#11758196—42no—
299C4×Dic61—21no—
300C4×Dic61—21no—
301C2×#92418—21no—
302C2×#92418—21no—
303C2×#92418—21no—
304C2×#92418—21no—
305C2×#92418—21no—
306C2×#92418—21no—
307#11758190—44no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—48no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—48no—
328C23×C61—84no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61#12012yes—
334C23×C61C2×SD1612yes—
335C23×C61AGL(1,ℤ/8)12yes—
336C23×C61C22×D411yescharacteristic
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—22no—
344C22×D61—48no—
345C22×D61—48no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—84no—
353C22×D61—84no—
354C22×D61—84no—
355C22×D61—84no—
356C22×D61—84no—
357C22×D61C2×SD1612yes—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—22no—
361D4×C61—22no—
362D4×C61—22no—
363D4×C61—48no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61#12114yes—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—84no—
380C2×C4×C61#12012yes—
381C2×C4×C61C22×D411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C2×#4111yescharacteristic
385C2×C4×C61H(5,𝔽2)11yescharacteristic
386C2×C4×C61H(5,𝔽2)11yescharacteristic
387C22⋊D61—28no—
388C22⋊D61—48no—
389C22⋊D61—48no—
390C22⋊D61—48no—
391C22⋊D61—48no—
392C22⋊D61—84no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—22no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—48no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61C2×SD1612yes—
412D244—22no—
413D244—22no—
414D244—41no—
415D244—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420Dic122—41no—
421Dic122—41no—
422Dic122—41no—
423Dic122—41no—
424C8×C61—22no—
425C8×C61—41no—
426#92418—41no—
427#92418—41no—
428#24432—611nomaximal, Sylow
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—22no—
434C22×C61—22no—
435C22×C61—24no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—816no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61#45014yescomplemented
451C22×C61C2×#12011yescharacteristic
452C22×C61D4211yescharacteristic
453C22×C61#54611yescharacteristic
454C22×C61C22×SD1611yescharacteristic
455C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C61#57611yescharacteristic
457C22×C61#57711yescharacteristic
458C2×D61—22no—
459C2×D61—22no—
460C2×D61—22no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—42no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61—816no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61—81no—
473C4×C61—22no—
474C4×C61—42no—
475C4×C61—81no—
476C4×C61C2×#12111yescharacteristic
477C4×C61#53411yescharacteristic
478C4×C61D4211yescharacteristic
479C4×C61#54611yescharacteristic
480Dic61—22no—
481Dic61—41no—
482Dic61—42no—
483Dic61—41no—
484Dic61—81no—
485Dic61—81no—
486C2×D42—611no—
487C2×#465—611no—
488C2×#450—611no—
489C2×#450—611no—
490C22×#102D6111yescharacteristic, complemented
491#2417—611no—
492#2041—611no—
493#2034—611no—
494#2014—611no—
495#2000—611no—
496#1877—611no—
497#1874—611no—
498#1869—611no—
499#1864—611no—
500#1786—611no—
501C2×C61—24no—
502C2×C61—44no—
503C2×C61—82no—
504C2×C61#241011yescharacteristic
505C2×C61C2×#45011yescharacteristic
506C2×C61#301211yescharacteristic
507C2×C61#326411yescharacteristic
508C2×C61D4×SD1611yescharacteristic
509C2×C61#329511yescharacteristic
510C2×C61#331011yescharacteristic
511D61—42no—
512D61—82no—
513C23×D4—611no—
514C23×D4—1221no—
515C23×D4C2×D6111yescharacteristic
516C22×SD16—611no—
517C22×SD16—611no—
518C22×SD16—611no—
519C23×C8C2×D6111yescharacteristic, complemented
520D42—1224no—
521D42—1224no—
522C2×#127—611no—
523C2×C22⋊Q8—611no—
524C2×C22⋊Q8—611no—
525C2×#121—611no—
526C2×#121—611no—
527C2×#121—1221no—
528C2×#120—1221no—
529C2×#120—1221no—
530C2×C4×D4—611no—
531C2×C4×D4—611no—
532C22×C4⋊C4C2×D6111yescharacteristic, complemented
533#465—1224no—
534#450—1224no—
535#450—1224no—
536C2×#106—611no—
537C2×#103—611no—
538C2×#102—24no—
539C2×#102—611no—
540C2×#102—611no—
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×#102C2×D6111yescharacteristic
545C2×#102C2×D6111yescharacteristic
546C2×#102C2×D6111yescharacteristic, complemented
547C2×#102C2×D6111yescharacteristic, complemented
548C2×C22⋊C8—611no—
549C2×C22⋊C8—611no—
550C2×C22⋊C8—611no—
551#398—1221no—
552#396—1221no—
553#391—611no—
554#389—611no—
555#386—1221no—
556#380—611no—
557#380—1221no—
558#340—611no—
559#340—611no—
560#336—611no—
561#336—611no—
562C61#2443211yescharacteristic, complemented, Sylow
563C25—21no—
564C25—1221no—
565C22×Q8—611no—
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—21no—
569C22×D4—22no—
570C22×D4—41no—
571C22×D4—41no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4—1222no—
578C22×D4—1221no—
579C22×D4—1228no—
580C22×D4—1221no—
581C22×D4—1222no—
582C22×D4—1222no—
583C22×D4—1222no—
584C22×D4—2441no—
585C22×D4—2441no—
586C22×D4—2444no—
587C22×D4—2444no—
588C22×D4D24414yes—
589C22×D4C22×D6111yescharacteristic
590C22×D4C22×D6111yescharacteristic
591C23×C4—21no—
592C23×C4—611no—
593C23×C4—1221no—
594C23×C4C22×D6111yescharacteristic
595C2×SD16—1222no—
596C2×SD16—1222no—
597C2×SD16—1222no—
598C2×SD16—1222no—
599C2×SD16—1222no—
600C2×SD16—1222no—
601C2×SD16—2441no—
602C2×SD16—2441no—
603C2×SD16—2441no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8—611no—
608C22×C8—611no—
609C22×C8C22×D6111yescharacteristic
610C22×C8C22×D6111yescharacteristic
611#127—1222no—
612#127—1222no—
613C22⋊Q8—1222no—
614C22⋊Q8—1222no—
615C22⋊Q8—1222no—
616C22⋊Q8—2441no—
617#121—614no—
618#121—1222no—
619#121—1228no—
620#121—1222no—
621#121—1222no—
622#120—1228no—
623#120—1228no—
624C4×D4—1222no—
625C4×D4—1222no—
626C4×D4—1222no—
627C4×D4—1222no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4C22×D6111yescharacteristic
638C2×C4⋊C4C22×D6111yescharacteristic
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C42—611no—
648#106—1222no—
649#103—1222no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—1222no—
654#102—1222no—
655#102—1222no—
656#102—1222no—
657#102—2441no—
658#102C22⋊D6114yescomplemented
659C22⋊C8—1222no—
660C22⋊C8—1222no—
661C22⋊C8—2441no—
662#95—1221no—
663#95—1221no—
664#95—1221no—
665#95—1221no—
666C24—21no—
667C24—21no—
668C24—24no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—81no—
674C24—81no—
675C24—611no—
676C24—1224no—
677C24—1221no—
678C24—4881no—
679C24—4881no—
680C24—2442no—
681C24—2442no—
682C24—2442no—
683C24—2442no—
684C24D4×D6111yescharacteristic
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×D4—28no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—614no—
707C2×D4—612no—
708C2×D4—1222no—
709C2×D4—1222no—
710C2×D4—1224no—
711C2×D4—1224no—
712C2×D4—1224no—
713C2×D4—1224no—
714C2×D4—1224no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—4881no—
721C2×D4—4881no—
722C2×D4—2442no—
723C2×D4—2442no—
724C2×D4—2442no—
725C2×D4—2442no—
726C2×D4—2444no—
727C2×D4—2444no—
728C2×D4—2444no—
729C2×D4—24432no—
730C2×D4—2442no—
731C2×D4—2442no—
732C2×D4—2442no—
733C2×D4—2442no—
734C2×D4—2444no—
735C2×D4C2×D24412yes—
736C2×D4C2×D24412yes—
737C2×D4#1175822212yes—
738C2×D4C2×C22⋊D6112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—81no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—1224no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4C2×D24412yes—
764C22×C4D4×D6112yes—
765C22×C4D4×D6111yescharacteristic
766C22×C4C23×D6111yescharacteristic
767SD16—2444no—
768SD16—2444no—
769SD16—2444no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—44no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8C2×C22⋊D6112yescomplemented
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—42no—
787C4⋊C4—612no—
788C4⋊C4—1221no—
789C4⋊C4—1222no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—4881no—
793C4⋊C4—2442no—
794C4⋊C4—2442no—
795C4⋊C4C2×C22⋊D6112yescomplemented
796C22⋊C4—1224no—
797C22⋊C4—1224no—
798C22⋊C4—1222no—
799C22⋊C4—1222no—
800C22⋊C4—1224no—
801C22⋊C4—4881no—
802C22⋊C4—2442no—
803C22⋊C4—2442no—
804C42—1221no—
805C42—1221no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—48no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—48no—
826C23—84no—
827C23—84no—
828C23—84no—
829C23—84no—
830C23—84no—
831C23—612no—
832C23—1221no—
833C23—1221no—
834C23—1221no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1222no—
839C23—4884no—
840C23—4884no—
841C23—4884no—
842C23—4884no—
843C23—4884no—
844C23—2448no—
845C23—2448no—
846C23—2441no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23—2441no—
852C23#1451974712yes—
853C23SD16×D6112yes—
854C23#1451980112yes—
855C23C2×D4×D6111yescharacteristic
856Q8—2441no—
857Q8—2441no—
858Q8—2441no—
859Q8—2441no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—48no—
866D4—41no—
867D4—41no—
868D4—1228no—
869D4—1222no—
870D4—1222no—
871D4—4884no—
872D4—2448no—
873D4—2448no—
874D4—2448no—
875D4—2448no—
876D4—2441no—
877D4—2441no—
878D4#1451975114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—84no—
892C2×C4—612no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1222no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—2448no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4#1451974712yes—
916C2×C4C2×D4×D6111yescharacteristic
917C2×C4C22×C22⋊D6111yescharacteristic
918C2×C4C22×D24411yescharacteristic
919C2×C4C2×#1175822211yescharacteristic
920C2×C4#1451982211yescharacteristic
921C2×C4#1451982211yescharacteristic
922C8—22no—
923C8—41no—
924C8—2441no—
925C8—2441no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—816no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—1222no—
948C22—1222no—
949C22—1222no—
950C22—48816no—
951C22—4881no—
952C22—4881no—
953C22—4881no—
954C22—4881no—
955C22—2442no—
956C22—2442no—
957C22—2442no—
958C22—2441no—
959C22—2441no—
960C22—2441no—
961C22—2441no—
962C22#1683991414yescomplemented
963C22C2×#1451974711yescharacteristic
964C22D4×C22⋊D6111yescharacteristic
965C22#1684040211yescharacteristic
966C22C2×SD16×D6111yescharacteristic
967C22C2×#1451980111yescharacteristic
968C22#1684056311yescharacteristic
969C22#1684056811yescharacteristic
970C4—22no—
971C4—42no—
972C4—81no—
973C4—1222no—
974C4—4881no—
975C4—4881no—
976C4—2441no—
977C4—2442no—
978C4—2441no—
979C4C2×#1451975111yescharacteristic
980C4#1684032411yescharacteristic
981C4D4×C22⋊D6111yescharacteristic
982C4#1684040211yescharacteristic
983C2—24no—
984C2—44no—
985C2—82no—
986C2—4882no—
987C2—2442no—
988C2#2144918711yescharacteristic
989C2C2×#1683991411yescharacteristic
990C2#2145512811yescharacteristic
991C2#2145729911yescharacteristic
992C2SD16×C22⋊D6111yescharacteristic
993C2#2145763911yescharacteristic
994C2#2145783611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
hypercenterC22×#102D61
hypocenterC61#24432
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839991C2semidirect
3. C2×#16839914C2semidirect
4. C2×#16839913C2semidirect
5. #21449264C2semidirect
6. #21447052C2semidirect
7. #21447007C2semidirect
8. #21446908C2semidirect
9. #21446823C2semidirect
10. #21446151C2semidirect
11. #21446136C2semidirect
12. #21446111C2semidirect
13. #21446082C2semidirect
14. #21445748C2semidirect
15. C22×#102×C61C2semidirect
18. C22×#11758190C22semidirect
20. C22×#11758200C22semidirect
24. C2×#14519757C22semidirect
25. C2×#14519756C22semidirect
36. C2×#14519709C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519699C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519697C22semidirect
42. C2×#14519697C22semidirect
43. C2×C22⋊#92418C22semidirect
44. C2×#14519689C22semidirect
45. C2×#14519689C22semidirect
48. #16839667C22semidirect
49. #16839661C22semidirect
52. #16839619C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839516C22semidirect
56. #16839516C22semidirect
58. C23×C8×C61C22semidirect
59. C22×C4⋊C4×C61C22semidirect
63. C2×#102×C61C22semidirect
64. C2×#102×C61C22semidirect
167. #102×C61D4semidirect
237. C2×C22⋊D61SD16semidirect
275. C2×C8×C61C2×D4semidirect
280. C4⋊C4×C61C2×D4semidirect
450. C22×C61#450semidirect
490. C22×#102D61semidirect
519. C23×C8C2×D61semidirect
532. C22×C4⋊C4C2×D61semidirect
546. C2×#102C2×D61semidirect
547. C2×#102C2×D61semidirect
562. C61#24432semidirect
658. #102C22⋊D61semidirect
782. C2×C8C2×C22⋊D61semidirect
795. C4⋊C4C2×C22⋊D61semidirect
962. C22#16839914semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D612
C2×#168399912
C2×#168399142
C2×#168399132
#214492642
#214470522
#214470072
#214469082
#214468232
#214461512
#214461362
#214461112
#214460822
#214457482
C22×#102×C612
#2443261