Finite Group Databasebeta

← C2×#21457354 #30555021

Subgroups — C2×#21457354 #30555021

Order 15616.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic, complemented
2C22×#14519800C211yesmaximal, characteristic, complemented
3C2×#16840434C211yesmaximal, characteristic, complemented
4C2×#16840405C211yesmaximal, characteristic, complemented
5#21457354C2116yesmaximal, direct product factor
6C2×#16840152C211yesmaximal, characteristic, complemented
7C2×#16840011C211yesmaximal, characteristic, complemented
8C2×#16839997C211yesmaximal, characteristic, complemented
9C2×#16839958C211yesmaximal, characteristic, complemented
10C2×#16839923C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic, complemented
13C2×#16839897C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839832C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic
19C22×#11758226C2211yescharacteristic, complemented
20C22×D4×D61C2211yescharacteristic
21C2×#14519804—28no—
22C2×#14519804C2218yescomplemented
23C2×#14519800—28no—
24C2×#14519800C2218yescomplemented
25C22×#11758201C2211yescharacteristic
26C22×#11758201C2211yescharacteristic, complemented
27C22×#11758201C2211yescharacteristic, complemented
28C22×D488C2211yescharacteristic
29C22×D488C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758189C2211yescharacteristic
33C22×C8×D61C2211yescharacteristic, complemented
34#16840434—24no—
35#16840434C2218yescomplemented
36#16840405—24no—
37#16840405C2218yescomplemented
38C2×#14519774—21no—
39C2×#14519774C2211yescharacteristic, complemented
40C2×#14519759—21no—
41C2×#14519753C2211yescharacteristic
42C2×#14519752—21no—
43C2×#14519752—21no—
44C2×#14519752C2211yescharacteristic
45C2×#14519752C2211yescharacteristic, complemented
46C2×#14519750—21no—
47C2×#14519748C2211yescharacteristic
48C2×#14519747—21no—
49C2×C4×D244—21no—
50C2×C4×D244C2211yescharacteristic
51C2×C4×D244C2211yescharacteristic
52C2×C22⋊C4×D61—21no—
53#16840152C2218yescomplemented
54#16840011C2218yescomplemented
55#16839997C2218yescomplemented
56#16839958C2218yescomplemented
57#16839923C2218yescomplemented
58#16839910C2218yescomplemented
59#16839906C2218yescomplemented
60#16839897C2218yescomplemented
61#16839860C2218yescomplemented
62#16839832C2218yescomplemented
63C2×#14519710C2211yescharacteristic, complemented
64C2×#14519701C2211yescharacteristic, complemented
65C2×#14519699C2211yescharacteristic, complemented
66C2×#14519699C2211yescharacteristic, complemented
67C2×#14519697C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#14519689C2211yescharacteristic, complemented
70C2×#14519688C2211yescharacteristic, complemented
71C22×Q16×C61C2211yescharacteristic, complemented
72C22×SD16×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic, complemented
75C61×#464C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#102×C61C2211yescharacteristic
79C24×D61—21no—
80C2×#11758226—22no—
81C2×#11758226—22no—
82C2×#11758226—22no—
83C2×#11758226—24no—
84C2×#11758226—24no—
85C2×#11758226—24no—
86C2×#11758226—42no—
87C2×#11758226—42no—
88C2×#11758226—42no—
89C2×#11758226C2314yes—
90C2×#11758226C2314yes—
91C2×#11758226C2314yescomplemented
92C22×D244—21no—
93C22×D244—21no—
94C22×D244—21no—
95C22×D244—21no—
96C22×D244—21no—
97C22×D244—21no—
98C22×D244—21no—
99C22×D244D411yescharacteristic
100C22×D244C2311yescharacteristic
101C22×D244C2311yescharacteristic
102C22×D244C2311yescharacteristic
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C2×D4×D61—24no—
106C2×D4×D61—22no—
107C2×D4×D61—42no—
108C2×D4×D61C2314yes—
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61—21no—
112C22×C4×D61—21no—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519804—232no—
116#14519800—232no—
117C2×#11758201—24no—
118C2×#11758201—42no—
119C2×#11758201D418yescomplemented
120C2×#11758201C2314yes—
121C2×#11758201C2314yescomplemented
122C2×#11758201C2314yescomplemented
123C2×D488—24no—
124C2×D488—24no—
125C2×D488C2314yes—
126C2×D488C2314yes—
127C2×#11758199—24no—
128C2×#11758199—42no—
129C2×#11758199C2314yes—
130C2×#11758199C2314yes—
131C2×#11758189—24no—
132C2×#11758189C2314yes—
133C22×#92418C2311yescharacteristic
134C22×#92418C2311yescharacteristic
135C2×C8×D61—24no—
136C2×C8×D61C2314yescomplemented
137#14519774—28no—
138#14519774—22no—
139#14519774C2314yescomplemented
140#14519759—28no—
141#14519753—22no—
142#14519753C2314yes—
143#14519752—22no—
144#14519752—22no—
145#14519752—28no—
146#14519752—28no—
147#14519752C2314yes—
148#14519752C2314yescomplemented
149#14519750—28no—
150#14519748—22no—
151#14519748C2314yes—
152#14519747—28no—
153C4×D244—22no—
154C4×D244—28no—
155C4×D244D414yes—
156C4×D244C2314yes—
157C4×D244C2314yes—
158C2×C4⋊Dic61D411yescharacteristic
159C2×C4⋊Dic61C2311yescharacteristic
160C2×#11758196—21no—
161C2×C22⋊Dic61—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—28no—
169#14519710C2314yescomplemented
170#14519701C2314yescomplemented
171#14519699C2314yescomplemented
172#14519699C2314yescomplemented
173#14519697C2314yes—
174#14519689C2314yes—
175#14519689C2314yescomplemented
176#14519688C2314yescomplemented
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61C2311yescharacteristic
180C2×Q16×C61—24no—
181C2×Q16×C61C2314yescomplemented
182C2×SD16×C61—24no—
183C2×SD16×C61C2314yes—
184C22×C8×C61C2311yescharacteristic
185C22×C8×C61C2311yescharacteristic
186#124×C61—22no—
187#124×C61C2314yes—
188C4×Q8×C61—22no—
189C4×Q8×C61C2314yescomplemented
190C2×C4⋊C4×C61—21no—
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C42×C61—21no—
195C2×C42×C61C2311yescharacteristic
196C4⋊C8×C61C2314yescomplemented
197#103×C61C2314yescomplemented
198#102×C61C2314yes—
199C24×C61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—24no—
204C23×D61—44no—
205C23×D61—44no—
206C23×D61—82no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C2×Q8×C61—21no—
210C2×Q8×C61—21no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—22no—
214C2×Q8×C61C2×D414yes—
215C2×Q8×C61C2412yes—
216C2×Q8×C61C2412yes—
217C2×D4×C61—22no—
218C2×D4×C61—21no—
219C2×D4×C61—22no—
220C2×D4×C61C2412yes—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—82no—
231C22×Dic61—21no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234#11758226—28no—
235#11758226—28no—
236#11758226—28no—
237#11758226—44no—
238#11758226—44no—
239#11758226—44no—
240#11758226—48no—
241#11758226—48no—
242#11758226—48no—
243D4×D61—28no—
244D4×D61—44no—
245D4×D61—48no—
246C2×D244—21no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—24no—
253C2×D244—24no—
254C2×D244—24no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—24no—
259C2×D244—24no—
260C2×D244—24no—
261C2×D244—42no—
262C2×D244—44no—
263C2×D244—44no—
264C2×D244—44no—
265C2×D244—44no—
266C2×D244—82no—
267C2×D244—82no—
268C2×D244—82no—
269C2×D244C2×D414yes—
270C2×D244C2×D414yes—
271C2×D244C2412yes—
272C2×D244C2412yes—
273C2×D244C2412yes—
274C2×C4×D61—22no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—22no—
278C2×C4×D61—24no—
279C2×C4×D61—24no—
280C2×C4×D61—24no—
281C2×C4×D61—24no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—82no—
286C2×C4×D61C2×D412yes—
287C2×C4×D61C2×D412yes—
288C2×C4×D61C2412yes—
289C2×C4×D61C2412yes—
290Q16×C61—28no—
291SD16×C61—28no—
292C2×C8×C61—22no—
293C2×C8×C61—22no—
294C2×C8×C61C2412yes—
295C2×C8×C61C2412yes—
296C4⋊C4×C61—24no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61C2412yes—
299C22⋊C4×C61—24no—
300C22⋊C4×C61—24no—
301C42×C61—24no—
302C42×C61C2×D412yes—
303C42×C61C2412yes—
304C22⋊Dic61—24no—
305#11758201—28no—
306#11758201—44no—
307#11758201C2×D4116yescomplemented
308#11758199—28no—
309#11758199—44no—
310#11758198—24no—
311#11758198—24no—
312#11758198—24no—
313#11758198—24no—
314#11758198C2×D414yes—
315#11758198C2×D414yes—
316C4⋊Dic61—21no—
317C4⋊Dic61C2×D414yes—
318C4⋊Dic61C2412yes—
319#11758196—24no—
320C2×#92418—22no—
321C2×#92418C2×D414yes—
322C2×#92418C2412yes—
323C2×#92418C2412yes—
324D488—28no—
325D488—28no—
326#11758189—28no—
327C8×D61—28no—
328C23×C61—22no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—24no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—48no—
344C22×D61—48no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—84no—
354C22×D61—816no—
355C22×D61C22×D412yes—
356C22×D61C22×D412yes—
357Q8×C61—24no—
358Q8×C61—22no—
359Q8×C61—22no—
360Q8×C61—22no—
361Q8×C61—42no—
362Q8×C61C22×D414yes—
363D4×C61—22no—
364D4×C61—22no—
365D4×C61—42no—
366C2×C4×C61—24no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61C22×D412yes—
375C2×C4×C61C22×D412yes—
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D412yes—
378C2×C4×C61H(5,𝔽2)12yes—
379C2×C4×C61C2511yescharacteristic
380C22⋊D61—48no—
381C22⋊D61—84no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—42no—
386C2×Dic61C22×D412yes—
387C2×Dic61C22×D412yes—
388D244—24no—
389D244—22no—
390D244—22no—
391D244—22no—
392D244—22no—
393D244—22no—
394D244—44no—
395D244—48no—
396D244—48no—
397D244—48no—
398D244—48no—
399D244—42no—
400D244—42no—
401D244—84no—
402D244—84no—
403D244—84no—
404D244C22×D414yes—
405C4×D61—24no—
406C4×D61—24no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—48no—
412C4×D61—48no—
413C4×D61—48no—
414C4×D61—84no—
415C8×C61—22no—
416C8×C61—22no—
417#92418—22no—
418#92418C22×D414yes—
419C2×#3268—611nomaximal, Sylow
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—84no—
424C22×C61D4212yes—
425C22×C61#57512yes—
426C22×C61#57612yes—
427C22×C61C23×D411yescharacteristic
428C2×D61—22no—
429C2×D61—22no—
430C2×D61—24no—
431C2×D61—22no—
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—44no—
436C2×D61—44no—
437C2×D61—48no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—816no—
447C2×D61—84no—
448C2×D61—84no—
449C4×C61—24no—
450C4×C61—22no—
451C4×C61—22no—
452C4×C61—42no—
453C4×C61—42no—
454C4×C61D4212yes—
455C4×C61C23×D411yescharacteristic
456C4×C61C2×H(5,𝔽2)11yescharacteristic
457Dic61—22no—
458Dic61—22no—
459Dic61—42no—
460C22×AGL(1,ℤ/8)—611no—
461C22×#135—611no—
462C2×#550—611no—
463C2×#546—611no—
464#3268—6116no—
465C2×#496—611no—
466C2×#468—611no—
467C2×#466—611no—
468C2×#464D6111yescharacteristic, complemented
469C2×#459—611no—
470C2×#452—611no—
471C2×#449—611no—
472C2×#449—611no—
473C2×#447—611no—
474C2×#440—611no—
475C2×#435—611no—
476C2×C61—82no—
477C2×C61#326814yescomplemented
478C2×C61C2×D4211yescharacteristic
479C2×C61C2×#57511yescharacteristic
480C2×C61C2×#57611yescharacteristic
481D61—42no—
482D61—42no—
483D61—44no—
484D61—82no—
485D61—82no—
486C22×#41—611no—
487C22×#41—611no—
488C22×#41—611no—
489C23×D4—611no—
490C2×AGL(1,ℤ/8)—618no—
491C2×AGL(1,ℤ/8)—1228no—
492C2×#135—618no—
493C2×#135—1228no—
494C22×Q16C2×D6111yescharacteristic, complemented
495C22×SD16—611no—
496C22×SD16—611no—
497C22×SD16—611no—
498C22×SD16C2×D6111yescharacteristic
499C22×D8—611no—
500C22×D8—611no—
501C22×D8—611no—
502C22×D8—611no—
503C22×M16—611no—
504C23×C8—611no—
505#550—618no—
506#550—1224no—
507#546—618no—
508#546—1224no—
509C2×#127—611no—
510C2×#127—1221no—
511C2×#124C2×D6111yescharacteristic
512C2×#123—1221no—
513C2×C22⋊Q8—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#121—611no—
517C2×#121—1221no—
518C2×#121—1221no—
519C2×#121—1221no—
520C2×#120—1221no—
521C2×C4×Q8C2×D6111yescharacteristic, complemented
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×C4×D4—1221no—
525C22×C22⋊C4—1221no—
526#496—618no—
527#468—618no—
528#466—618no—
529#464C2×D6118yescomplemented
530#459—618no—
531#452—618no—
532#449—618no—
533#449—618no—
534#447—618no—
535#440—618no—
536#435—618no—
537C2×#107—611no—
538C2×C4⋊C8C2×D6111yescharacteristic, complemented
539C2×#103—611no—
540C2×#103C2×D6111yescharacteristic, complemented
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×#102C2×D6111yescharacteristic
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×#97—611no—
548C61C2×#326811yescharacteristic, complemented, Sylow
549C25—1221no—
550C2×#41—614no—
551C2×#41—614no—
552C2×#41—614no—
553C2×#41—1222no—
554C2×#41—1222no—
555C2×#41—1222no—
556C2×#41—1224no—
557C2×#41—1224no—
558C2×#41—1224no—
559C2×#41—2442no—
560C2×#41—2442no—
561C2×#41—2442no—
562C22×Q8C22×D6111yescharacteristic
563C22×Q8C22×D6111yescharacteristic
564C22×D4—614no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4—1221no—
570C22×D4—1221no—
571C22×D4—1221no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1222no—
575C22×D4—1221no—
576C22×D4—1224no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4—1221no—
580C22×D4—2442no—
581C22×D4C22×D6111yescharacteristic
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4—1221no—
588AGL(1,ℤ/8)—12232no—
589#135—12232no—
590C2×Q16—24no—
591C2×Q16C22×D6114yescomplemented
592C2×SD16—24no—
593C2×SD16—618no—
594C2×SD16—614no—
595C2×SD16—614no—
596C2×SD16—614no—
597C2×SD16—1224no—
598C2×SD16—2442no—
599C2×SD16C22×D6114yes—
600C2×D8—614no—
601C2×D8—614no—
602C2×D8—614no—
603C2×D8—614no—
604C2×D8—1224no—
605C2×D8—1224no—
606C2×D8—1224no—
607C2×D8—2442no—
608C2×M16—614no—
609C2×M16—1224no—
610C22×C8—611no—
611C22×C8—611no—
612C22×C8—614no—
613C22×C8—1224no—
614C22×C8C22×D6111yescharacteristic
615C22×C8C22×D6111yescharacteristic
616#127—614no—
617#127—1228no—
618#127—1222no—
619#124—22no—
620#124C22×D6114yes—
621#123—1228no—
622C22⋊Q8—614no—
623C22⋊Q8—1222no—
624#121—614no—
625#121—614no—
626#121—614no—
627#121—1228no—
628#121—1228no—
629#121—1228no—
630#121—1222no—
631#121—1222no—
632#121—1222no—
633#120—1228no—
634C4×Q8—22no—
635C4×Q8C22×D6114yescomplemented
636C4×D4—614no—
637C4×D4—614no—
638C4×D4—614no—
639C4×D4—1228no—
640C4×D4—1222no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—1228no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C42—21no—
657C2×C42C22×D6111yescharacteristic
658#107—614no—
659C4⋊C8C22×D6114yescomplemented
660#103—614no—
661#103C22×D6114yescomplemented
662#102—614no—
663#102—614no—
664#102—614no—
665#102C22×D6114yes—
666C22⋊C8—614no—
667C22⋊C8—614no—
668#97—614no—
669C24—21no—
670C24—611no—
671C24—611no—
672C24—1224no—
673C24—1221no—
674C24—1221no—
675C24—1221no—
676C24—4882no—
677C24—2444no—
678C24—2444no—
679#41—1228no—
680#41—1228no—
681#41—1228no—
682#41—2444no—
683#41—2444no—
684#41—2444no—
685#41—2448no—
686#41—2448no—
687#41—2448no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—22no—
691C2×Q8—22no—
692C2×Q8—22no—
693C2×Q8D4×D6114yes—
694C2×Q8C23×D6112yes—
695C2×Q8C23×D6112yes—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—22no—
699C2×D4—614no—
700C2×D4—614no—
701C2×D4—612no—
702C2×D4—612no—
703C2×D4—612no—
704C2×D4—1224no—
705C2×D4—1224no—
706C2×D4—1224no—
707C2×D4—1224no—
708C2×D4—1224no—
709C2×D4—1224no—
710C2×D4—1228no—
711C2×D4—1224no—
712C2×D4—1221no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1224no—
716C2×D4—1224no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1222no—
722C2×D4—4882no—
723C2×D4—4882no—
724C2×D4—4882no—
725C2×D4—4882no—
726C2×D4—2442no—
727C2×D4—2444no—
728C2×D4—2444no—
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4—2444no—
732C2×D4—2448no—
733C2×D4—2444no—
734C2×D4C23×D6112yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—612no—
741C22×C4—612no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—1224no—
745C22×C4—1224no—
746C22×C4—1224no—
747C22×C4—1222no—
748C22×C4—1222no—
749C22×C4—1222no—
750C22×C4—1222no—
751C22×C4—1221no—
752C22×C4—1224no—
753C22×C4—4882no—
754C22×C4—2444no—
755C22×C4—2444no—
756C22×C4—2444no—
757C22×C4D4×D6111yescharacteristic
758C22×C4D4×D6111yescharacteristic
759C22×C4C23×D6111yescharacteristic
760Q16—28no—
761SD16—28no—
762SD16—6116no—
763SD16—1228no—
764SD16—2444no—
765D8—1228no—
766D8—1228no—
767D8—1228no—
768D8—2444no—
769M16—1228no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—614no—
773C2×C8—612no—
774C2×C8—612no—
775C2×C8—1228no—
776C2×C8—1222no—
777C2×C8C23×D6112yes—
778C2×C8C23×D6112yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—614no—
782C4⋊C4—612no—
783C4⋊C4—1224no—
784C4⋊C4—1221no—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—614no—
789C22⋊C4—614no—
790C22⋊C4—1224no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4—1224no—
794C22⋊C4—1224no—
795C42—24no—
796C42D4×D6112yes—
797C42C23×D6112yes—
798C23—22no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—612no—
803C23—612no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1224no—
812C23—1222no—
813C23—1222no—
814C23—4884no—
815C23—48816no—
816C23—2448no—
817C23—2448no—
818C23—2442no—
819C23—2442no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23—2442no—
824C23—2442no—
825C23—2442no—
826C23C2×D4×D6111yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—22no—
830Q8—22no—
831Q8—42no—
832Q8C2×D4×D6114yes—
833D4—22no—
834D4—22no—
835D4—42no—
836D4—614no—
837D4—1222no—
838D4—1222no—
839D4—1222no—
840D4—1222no—
841D4—1222no—
842D4—1224no—
843D4—4884no—
844D4—4884no—
845D4—4884no—
846D4—4884no—
847D4—2444no—
848D4—2448no—
849D4—2448no—
850D4—2448no—
851D4—2448no—
852D4—2448no—
853D4—2442no—
854D4—2442no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—612no—
864C2×C4—612no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1224no—
872C2×C4—1224no—
873C2×C4—1222no—
874C2×C4—4884no—
875C2×C4—2448no—
876C2×C4—2448no—
877C2×C4—2448no—
878C2×C4—2442no—
879C2×C4C2×D4×D6112yes—
880C2×C4C2×D4×D6112yes—
881C2×C4C2×D4×D6112yes—
882C2×C4C2×D4×D6111yescharacteristic
883C2×C4#1451982312yes—
884C2×C4C24×D6111yescharacteristic
885C8—22no—
886C8—22no—
887C8—614no—
888C8—1222no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—84no—
893C22—1222no—
894C22—1222no—
895C22—1224no—
896C22—1222no—
897C22—1222no—
898C22—1222no—
899C22—1222no—
900C22—48816no—
901C22—4884no—
902C22—4884no—
903C22—2442no—
904C22—2442no—
905C22—2442no—
906C22—2442no—
907C22—2442no—
908C22—2442no—
909C22—2442no—
910C22—2442no—
911C22—2444no—
912C22—2444no—
913C22—2448no—
914C22#1684039612yes—
915C22#1684056112yes—
916C22#1684056412yes—
917C22C22×D4×D6111yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—1222no—
924C4—1222no—
925C4—2442no—
926C4#1684039612yes—
927C4C22×D4×D6111yescharacteristic
928C4C2×#1451982311yescharacteristic
929C2—82no—
930C2—4882no—
931C2—4882no—
932C2—2442no—
933C2—2442no—
934C2—2444no—
935C2#2145735414yesdirect product factor
936C2C2×#1684039611yescharacteristic
937C2C2×#1684056111yescharacteristic
938C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
hypercenterC2×#464D61
hypocenterC61C2×#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#14519804C2semidirect
2. C22×#14519800C2semidirect
3. C2×#16840434C2semidirect
4. C2×#16840405C2semidirect
5. #21457354C2direct (N × H)
6. C2×#16840152C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16839997C2semidirect
9. C2×#16839958C2semidirect
10. C2×#16839923C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839906C2semidirect
13. C2×#16839897C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839832C2semidirect
16. C2×C61×#464C2semidirect
19. C22×#11758226C22semidirect
22. C2×#14519804C22semidirect
24. C2×#14519800C22semidirect
26. C22×#11758201C22semidirect
27. C22×#11758201C22semidirect
33. C22×C8×D61C22semidirect
35. #16840434C22semidirect
37. #16840405C22semidirect
39. C2×#14519774C22semidirect
45. C2×#14519752C22semidirect
53. #16840152C22semidirect
54. #16840011C22semidirect
55. #16839997C22semidirect
56. #16839958C22semidirect
57. #16839923C22semidirect
58. #16839910C22semidirect
59. #16839906C22semidirect
60. #16839897C22semidirect
61. #16839860C22semidirect
62. #16839832C22semidirect
63. C2×#14519710C22semidirect
64. C2×#14519701C22semidirect
65. C2×#14519699C22semidirect
66. C2×#14519699C22semidirect
69. C2×#14519689C22semidirect
70. C2×#14519688C22semidirect
71. C22×Q16×C61C22semidirect
74. C2×C4×Q8×C61C22semidirect
75. C61×#464C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
91. C2×#11758226C23semidirect
119. C2×#11758201D4semidirect
121. C2×#11758201C23semidirect
122. C2×#11758201C23semidirect
136. C2×C8×D61C23semidirect
139. #14519774C23semidirect
148. #14519752C23semidirect
169. #14519710C23semidirect
170. #14519701C23semidirect
171. #14519699C23semidirect
172. #14519699C23semidirect
175. #14519689C23semidirect
176. #14519688C23semidirect
181. C2×Q16×C61C23semidirect
189. C4×Q8×C61C23semidirect
196. C4⋊C8×C61C23semidirect
197. #103×C61C23semidirect
307. #11758201C2×D4semidirect
468. C2×#464D61semidirect
477. C2×C61#3268semidirect
494. C22×Q16C2×D61semidirect
521. C2×C4×Q8C2×D61semidirect
529. #464C2×D61semidirect
538. C2×C4⋊C8C2×D61semidirect
540. C2×#103C2×D61semidirect
548. C61C2×#3268semidirect
591. C2×Q16C22×D61semidirect
635. C4×Q8C22×D61semidirect
659. C4⋊C8C22×D61semidirect
661. #103C22×D61semidirect
935. C2#21457354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198042
C22×#145198002
C2×#168404342
C2×#168404052
#214573542
C2×#168401522
C2×#168400112
C2×#168399972
C2×#168399582
C2×#168399232
C2×#168399102
C2×#168399062
C2×#168398972
C2×#168398602
C2×#168398322
C2×C61×#4642
C2×#326861