Finite Group Databasebeta

← #29695833

Subgroups — #29695833

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D61C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3C2×#16839842C211yesmaximal, characteristic, complemented
4#21448640C211yesmaximal, characteristic, complemented
5D4×#11758198C211yesmaximal, characteristic, complemented
6#21446684C211yesmaximal, characteristic, complemented
7#21446682C211yesmaximal, characteristic, complemented
8#21446169C211yesmaximal, characteristic, complemented
9#21446168C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21445847C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C2×D8×D61—24no—
22C2×D8×D61—24no—
23C2×D8×D61C418yescomplemented
24C22×C8×D61C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic, complemented
26C2×D4×Dic61C2211yescharacteristic, complemented
27C2×#14519739C2211yescharacteristic, complemented
28C22×#11758198—21no—
29C2×C22⋊C4×D61—21no—
30C4×#11758199—24no—
31#16839842—24no—
32C2×#14519710C2211yescharacteristic, complemented
33C2×#14519710C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic, complemented
36C2×#14519698C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic, complemented
42C2×C8×Dic61C2211yescharacteristic, complemented
43#16839665C2211yescharacteristic, complemented
44#16839664C2211yescharacteristic, complemented
45#16839663C2211yescharacteristic, complemented
46#16839641—21no—
47#16839639—21no—
48#16839638—21no—
49#16839638—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839617—21no—
53#16839617—21no—
54C4×#11758198C2211yescharacteristic
55#16839525C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C22×D8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C61×#390C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C24×D61—21no—
66C22×D244C2311yescharacteristic
67C22×D244C2311yescharacteristic
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61—22no—
76C2×D4×D61—41no—
77C2×D4×D61—41no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yescomplemented
81C2×D4×D61C2×C414yescomplemented
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×D488—22no—
87C2×D488—22no—
88C2×D488C2×C414yescomplemented
89C2×#11758199—22no—
90C2×#11758199—22no—
91C2×#11758199C2×C414yes—
92C2×#11758199C2×C414yescomplemented
93C2×#11758199D414yes—
94C2×#11758199D414yes—
95D8×D61—232no—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100C2×C8×D61C2×C414yescomplemented
101C4×D244—22no—
102C4×D244—41no—
103D4×Dic61—22no—
104D4×Dic61—41no—
105#14519739—22no—
106#14519739—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—44no—
121C2×#11758198D411yescharacteristic
122C2×#11758198D411yescharacteristic
123C22⋊C4×D61—44no—
124C2×C4×Dic61C2311yescharacteristic
125#14519710—22no—
126#14519710—22no—
127#14519699—22no—
128#14519699—41no—
129#14519698—22no—
130#14519698—41no—
131#14519697—22no—
132#14519697—41no—
133#14519689—22no—
134C4×#92418—22no—
135C8×Dic61—22no—
136#14519684—21no—
137#14519684—21no—
138#14519684D411yescharacteristic
139#14519684D411yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C2×D8×C61—22no—
144C2×D8×C61—22no—
145C2×D8×C61C2×C414yescomplemented
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C4×D4×C61—22no—
149C4×D4×C61—41no—
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#102×C61—22no—
157#102×C61—41no—
158C24×C61—21no—
159C24×C61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61—81no—
176C23×D61C2×D411yescharacteristic
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61C2×D412yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—81no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—81no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211D4×D61—28no—
212D4×D61—28no—
213D4×D61—44no—
214D4×D61—44no—
215D4×D61—44no—
216D4×D61—44no—
217D4×D61—44no—
218D4×D61—44no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244C22×C412yes—
228C2×D244C22×C412yes—
229C2×D244C2×D412yes—
230C2×D244C2×D412yes—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61—42no—
238C2×C4×D61—42no—
239C2×C4×D61—81no—
240C2×C4×D61—81no—
241C2×C4×D61C22×C412yes—
242C2×C4×D61#4112yes—
243D8×C61—28no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C22×C412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—81no—
257C42×C61—21no—
258C42×C61—21no—
259C22⋊Dic61—42no—
260C22⋊Dic61—42no—
261C22⋊Dic61—81no—
262#11758199—28no—
263#11758199C22⋊C4116yescomplemented
264#11758198—22no—
265#11758198—42no—
266#11758198—42no—
267#11758198—42no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—81no—
272#11758198—81no—
273#11758198D814yescomplemented
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418C22×C412yes—
284C2×#92418C2×D412yes—
285C2×#92418C2×D412yes—
286D488—28no—
287C8×D61—28no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61C22×D411yescharacteristic
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—48no—
312C22×D61—48no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—48no—
324C22×D61—48no—
325C22×D61—84no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61—84no—
329C22×D61—84no—
330C22×D61—84no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—84no—
334C22×D61—84no—
335C22×D61C4×D412yes—
336C22×D61C2×D812yes—
337C22×D61#13512yes—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—41no—
344D4×C61—41no—
345D4×C61C2×C22⋊C414yescomplemented
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—84no—
358C2×C4×C61C2×D812yescomplemented
359C2×C4×C61C23×C411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C2×#4111yescharacteristic
363C2×C4×C61H(5,𝔽2)11yescharacteristic
364C2×C4×C61H(5,𝔽2)11yescharacteristic
365C22⋊D61—48no—
366C22⋊D61—48no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—84no—
381C2×Dic61C4×D412yes—
382C2×Dic61C2×D812yescomplemented
383D244—22no—
384D244—22no—
385D244—22no—
386D244—22no—
387D244—22no—
388D244—41no—
389D244—41no—
390D244C2×C22⋊C414yescomplemented
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—84no—
396C4×D61—84no—
397C8×C61—22no—
398C8×C61—41no—
399#92418—41no—
400#92418C2×C22⋊C414yescomplemented
401C22⋊C4×D8—611nomaximal, Sylow
402C22×C61—24no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61C2×C4×D411yescharacteristic
417C22×C61D4211yescharacteristic
418C22×C61D4211yescharacteristic
419C22×C61C22×D811yescharacteristic
420C22×C61C2×#13511yescharacteristic
421C22×C61#57611yescharacteristic
422C22×C61#57611yescharacteristic
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—22no—
426C2×D61—22no—
427C2×D61—22no—
428C2×D61—22no—
429C2×D61—24no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—816no—
440C2×D61—816no—
441C2×D61—81no—
442C2×D61—81no—
443C2×D61—81no—
444C2×D61—81no—
445C2×D61C4×D814yescomplemented
446C4×C61—22no—
447C4×C61—41no—
448C4×C61—81no—
449C4×C61—81no—
450C4×C61C22×C22⋊C411yescharacteristic
451C4×C61#51811yescharacteristic
452C4×C61#54611yescharacteristic
453C4×C61#54611yescharacteristic
454Dic61—22no—
455Dic61—22no—
456Dic61—41no—
457Dic61—81no—
458Dic61—81no—
459C23×D8—611no—
460C2×C4×D8—611no—
461C2×C4×D8—611no—
462D4×C22⋊C4—611no—
463D4×C22⋊C4—611no—
464#1970—611no—
465#1970—611no—
466#1879—611no—
467#1879—611no—
468#1879—611no—
469#1879D6111yescharacteristic, complemented
470#1808—611no—
471#1786—611no—
472#1786—611no—
473C8×C22⋊C4—611no—
474C2×C61—44no—
475C2×C61—82no—
476C2×C61D4×C22⋊C411yescharacteristic
477C2×C61C2×C4×D811yescharacteristic
478C2×C61#294811yescharacteristic
479C2×C61D4×D811yescharacteristic
480C2×C61D4×D811yescharacteristic
481C2×C61#328011yescharacteristic
482C2×C61#328011yescharacteristic
483D61—24no—
484D61—44no—
485D61—82no—
486C23×D4—611no—
487C23×D4—611no—
488C22×D8—611no—
489C22×D8—611no—
490C22×D8—618no—
491C22×D8—611no—
492C22×D8—1224no—
493C22×D8—1224no—
494C22×D8C2×D6111yescharacteristic
495C23×C8—611no—
496C2×C4×D4—611no—
497C2×C4×D4—611no—
498C2×C4×D4—611no—
499C2×C4×D4C2×D6111yescharacteristic, complemented
500C22×C22⋊C4—1221no—
501C22×C22⋊C4—1221no—
502C4×D8—1224no—
503C4×D8—1224no—
504C2×#107—611no—
505C2×#107—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102C2×D6111yescharacteristic, complemented
513C2×#102C2×D6111yescharacteristic, complemented
514C2×C22⋊C8—611no—
515C2×C4×C8—611no—
516C2×C4×C8—611no—
517#390—611no—
518#390—611no—
519#390—611no—
520#390C2×D6111yescharacteristic, complemented
521#386—1221no—
522#386—1221no—
523#386—1221no—
524#386—1221no—
525#380—611no—
526#380—611no—
527#379—1221no—
528#379—1221no—
529C4×C22⋊C4—611no—
530#340—611no—
531#340C2×D6111yescharacteristic, complemented
532#336—611no—
533#336C2×D6111yescharacteristic, complemented
534C61C22⋊C4×D811yescharacteristic, complemented, Sylow
535C25—1221no—
536C25—1221no—
537C22×D4—614no—
538C22×D4—614no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1222no—
542C22×D4—1222no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1222no—
546C22×D4—1222no—
547C22×D4—1222no—
548C22×D4—1222no—
549C22×D4—2441no—
550C22×D4—2441no—
551C22×D4—2441no—
552C22×D4—2441no—
553C22×D4C22×D6111yescharacteristic
554C22×D4C22×D6111yescharacteristic
555C23×C4—21no—
556C23×C4—611no—
557C23×C4—1221no—
558C23×C4—1221no—
559C23×C4—1221no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—614no—
563C2×D8—614no—
564C2×D8—614no—
565C2×D8—614no—
566C2×D8—614no—
567C2×D8—1222no—
568C2×D8—1222no—
569C2×D8—1222no—
570C2×D8—1222no—
571C2×D8—12232no—
572C2×D8C4×D6114yescomplemented
573C22×C8—611no—
574C22×C8—614no—
575C22×C8—611no—
576C22×C8—1222no—
577C22×C8—1222no—
578C22×C8C22×D6111yescharacteristic
579C22×C8C22×D6111yescharacteristic
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—2441no—
586C4×D4—2441no—
587C4×D4—2441no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4C22×D6111yescharacteristic
591C2×C4⋊C4C22×D6111yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—611no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—2444no—
609C2×C22⋊C4—2444no—
610C2×C42—611no—
611C2×C42C22×D6111yescharacteristic
612#107—1222no—
613#107—1222no—
614#102—22no—
615#102—41no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—2441no—
620#102—2441no—
621#102—2441no—
622C22⋊C8—1222no—
623C4×C8—1222no—
624C4×C8—1222no—
625#95—611no—
626#95—611no—
627#95—1221no—
628#95—1221no—
629C24—21no—
630C24—21no—
631C24—611no—
632C24—1224no—
633C24—1224no—
634C24—1221no—
635C24—1221no—
636C24—4881no—
637C24—4881no—
638C24—4881no—
639C24—4881no—
640C24—2442no—
641C24—2442no—
642C24—2442no—
643C24—2442no—
644C24—2442no—
645C24—2442no—
646C24—2442no—
647C24—2442no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—612no—
657C2×D4—612no—
658C2×D4—612no—
659C2×D4—612no—
660C2×D4—1224no—
661C2×D4—1224no—
662C2×D4—1228no—
663C2×D4—1228no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—2444no—
673C2×D4—2444no—
674C2×D4—2444no—
675C2×D4—2444no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2442no—
679C2×D4—2442no—
680C2×D4—2442no—
681C2×D4—2442no—
682C2×D4C2×C4×D6112yes—
683C2×D4C2×C4×D6112yes—
684C2×D4D4×D6112yes—
685C2×D4D4×D6112yes—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—611no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—4881no—
703C22×C4—4881no—
704C22×C4—4881no—
705C22×C4—2442no—
706C22×C4—2442no—
707C22×C4—2442no—
708C22×C4—2442no—
709C22×C4—2442no—
710C22×C4—2442no—
711C22×C4D4×D6111yescharacteristic
712C22×C4D4×D6111yescharacteristic
713C22×C4C23×D6111yescharacteristic
714D8—28no—
715D8—6116no—
716D8—1228no—
717D8—1228no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—612no—
724C2×C8—612no—
725C2×C8—612no—
726C2×C8—1228no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8C2×C4×D6112yes—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—81no—
742C22⋊C4—614no—
743C22⋊C4—1222no—
744C22⋊C4—4881no—
745C22⋊C4—4881no—
746C22⋊C4—4881no—
747C22⋊C4—2442no—
748C22⋊C4—2442no—
749C22⋊C4—2442no—
750C22⋊C4—2442no—
751C22⋊C4—2442no—
752C22⋊C4—2442no—
753C22⋊C4—2442no—
754C22⋊C4—2442no—
755C42—21no—
756C42—21no—
757C42—1221no—
758C42—1221no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—612no—
774C23—612no—
775C23—612no—
776C23—1221no—
777C23—1221no—
778C23—1221no—
779C23—1221no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—4884no—
785C23—4884no—
786C23—4884no—
787C23—4884no—
788C23—4884no—
789C23—4884no—
790C23—4884no—
791C23—4884no—
792C23—4884no—
793C23—4884no—
794C23—2448no—
795C23—2448no—
796C23—2448no—
797C23—2448no—
798C23—2441no—
799C23—2441no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23C2×D4×D6111yescharacteristic
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—41no—
815D4—41no—
816D4—614no—
817D4—1222no—
818D4—1222no—
819D4—1222no—
820D4—1222no—
821D4—1222no—
822D4—2448no—
823D4—2448no—
824D4—2441no—
825D4—2441no—
826D4C22⋊C4×D6114yescomplemented
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—84no—
839C2×C4—612no—
840C2×C4—612no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—4884no—
853C2×C4—4884no—
854C2×C4—4884no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4D8×D6112yescomplemented
862C2×C4C22×C4×D6111yescharacteristic
863C2×C4C2×D4×D6111yescharacteristic
864C2×C4C2×D4×D6111yescharacteristic
865C2×C4#41×D6111yescharacteristic
866C2×C4#1451982211yescharacteristic
867C2×C4#1451982311yescharacteristic
868C8—22no—
869C8—41no—
870C8—614no—
871C8—2441no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—614no—
887C22—1222no—
888C22—1222no—
889C22—1222no—
890C22—1222no—
891C22—1222no—
892C22—1222no—
893C22—1224no—
894C22—48816no—
895C22—48816no—
896C22—4881no—
897C22—4881no—
898C22—4881no—
899C22—4881no—
900C22—2442no—
901C22—2442no—
902C22—2442no—
903C22—2442no—
904C22—2442no—
905C22—2442no—
906C22—2442no—
907C22—2442no—
908C22—2442no—
909C22C4×D4×D6111yescharacteristic
910C22#1684039411yescharacteristic
911C22#1684039611yescharacteristic
912C22C2×D8×D6111yescharacteristic
913C22#135×D6111yescharacteristic
914C22#1684056611yescharacteristic
915C22#1684056611yescharacteristic
916C4—22no—
917C4—41no—
918C4—81no—
919C4—81no—
920C4—1222no—
921C4—1222no—
922C4—4881no—
923C4—4881no—
924C4—2441no—
925C4C2×C22⋊C4×D6111yescharacteristic
926C4#1684023411yescharacteristic
927C4#1684040111yescharacteristic
928C4#1684040411yescharacteristic
929C2—44no—
930C2—82no—
931C2—1224no—
932C2—4882no—
933C2—2444no—
934C2#2144863711yescharacteristic
935C2C4×D8×D6111yescharacteristic
936C2#2145466811yescharacteristic
937C2#2145748911yescharacteristic
938C2#2145749111yescharacteristic
939C2#2145749911yescharacteristic
940C2#2145750211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×D61C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61C22⋊C4×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. C2×#16839842C2semidirect
4. #21448640C2semidirect
5. D4×#11758198C2semidirect
6. #21446684C2semidirect
7. #21446682C2semidirect
8. #21446169C2semidirect
9. #21446168C2semidirect
10. #21446166C2semidirect
11. #21445847C2semidirect
12. #21445748C2semidirect
13. #21445748C2semidirect
14. #21445589C2semidirect
15. C61×#1879C2semidirect
23. C2×D8×D61C4semidirect
25. C2×C4×D244C22semidirect
26. C2×D4×Dic61C22semidirect
27. C2×#14519739C22semidirect
32. C2×#14519710C22semidirect
33. C2×#14519710C22semidirect
34. C2×#14519699C22semidirect
35. C2×#14519699C22semidirect
36. C2×#14519698C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519697C22semidirect
39. C2×#14519697C22semidirect
41. C2×C4×#92418C22semidirect
42. C2×C8×Dic61C22semidirect
43. #16839665C22semidirect
44. #16839664C22semidirect
45. #16839663C22semidirect
55. #16839525C22semidirect
56. #16839516C22semidirect
58. C2×C4×D4×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C61×#390C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
80. C2×D4×D61C2×C4semidirect
81. C2×D4×D61C2×C4semidirect
88. C2×D488C2×C4semidirect
92. C2×#11758199C2×C4semidirect
100. C2×C8×D61C2×C4semidirect
145. C2×D8×C61C2×C4semidirect
263. #11758199C22⋊C4semidirect
273. #11758198D8semidirect
345. D4×C61C2×C22⋊C4semidirect
358. C2×C4×C61C2×D8semidirect
382. C2×Dic61C2×D8semidirect
390. D244C2×C22⋊C4semidirect
400. #92418C2×C22⋊C4semidirect
445. C2×D61C4×D8semidirect
469. #1879D61semidirect
499. C2×C4×D4C2×D61semidirect
512. C2×#102C2×D61semidirect
513. C2×#102C2×D61semidirect
520. #390C2×D61semidirect
531. #340C2×D61semidirect
533. #336C2×D61semidirect
534. C61C22⋊C4×D8semidirect
572. C2×D8C4×D61semidirect
826. D4C22⋊C4×D61semidirect
861. C2×C4D8×D61semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D612
C2×C4×#117581992
C2×#168398422
#214486402
D4×#117581982
#214466842
#214466822
#214461692
#214461682
#214461662
#214458472
#214457482
#214455892
C61×#18792
C22⋊C4×D861