Finite Group Databasebeta

← C2×#21457361 #30555028

Subgroups — C2×#21457361 #30555028

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×#14519798C211yesmaximal, characteristic, complemented
3C2×#16840434C211yesmaximal, characteristic, complemented
4C2×#16840407C211yesmaximal, characteristic, complemented
5#21457361C2116yesmaximal, direct product factor
6C2×#16840151C211yesmaximal, characteristic, complemented
7C2×#16840009C211yesmaximal, characteristic, complemented
8C2×#16839999C211yesmaximal, characteristic, complemented
9C2×#16839984C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839910C211yesmaximal, characteristic, complemented
13C2×#16839908C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C2×#16839835C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic, complemented
19C22×#11758224C2211yescharacteristic
20C22×D4×D61C2211yescharacteristic
21C2×#14519804—28no—
22C2×#14519804C2218yescomplemented
23C2×#14519798—28no—
24C2×#14519798C2218yescomplemented
25C22×#11758202C2211yescharacteristic, complemented
26C22×#11758190C2211yescharacteristic, complemented
27C22×#11758190C2211yescharacteristic, complemented
28C22×#11758201C2211yescharacteristic
29C22×D488C2211yescharacteristic
30C22×D488C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758199C2211yescharacteristic
33C22×#11758189C2211yescharacteristic
34C22×C8×D61C2211yescharacteristic, complemented
35#16840434—24no—
36#16840434C2218yescomplemented
37#16840407—24no—
38#16840407C2218yescomplemented
39C2×#14519774—21no—
40C2×#14519774C2211yescharacteristic, complemented
41C2×#14519765C2211yescharacteristic
42C2×#14519761—21no—
43C2×#14519757C2211yescharacteristic
44C2×#14519752—21no—
45C2×#14519752—21no—
46C2×#14519752C2211yescharacteristic
47C2×#14519752C2211yescharacteristic
48C2×#14519752C2211yescharacteristic, complemented
49C2×#14519751—21no—
50C2×#14519747—21no—
51C2×C4×D244—21no—
52C2×C4×D244C2211yescharacteristic
53C22×#11758198—21no—
54#16840151C2218yescomplemented
55#16840009C2218yescomplemented
56#16839999C2218yescomplemented
57#16839984C2218yescomplemented
58#16839957C2218yescomplemented
59#16839927C2218yescomplemented
60#16839910C2218yescomplemented
61#16839908C2218yescomplemented
62#16839897C2218yescomplemented
63#16839835C2218yescomplemented
64C2×C4⋊#92418C2211yescharacteristic, complemented
65C2×#14519700C2211yescharacteristic, complemented
66C2×#14519697C2211yescharacteristic
67C2×#14519697C2211yescharacteristic, complemented
68C2×#14519697C2211yescharacteristic, complemented
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic, complemented
73C2×C4×D4×C61C2211yescharacteristic
74C61×#440C2218yescomplemented
75C2×#107×C61C2211yescharacteristic, complemented
76C2×#103×C61C2211yescharacteristic, complemented
77C2×#102×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C2×#11758226—22no—
81C2×#11758226—22no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226—42no—
85C2×#11758226—42no—
86C2×#11758226C2314yes—
87C2×#11758226C2314yescomplemented
88C2×#11758224—24no—
89C2×#11758224—22no—
90C2×#11758224—42no—
91C2×#11758224C2314yes—
92C22×Dic122C2311yescharacteristic
93C22×D244—21no—
94C22×D244—21no—
95C22×D244—21no—
96C22×D244—21no—
97C22×D244—21no—
98C22×D244—21no—
99C22×D244—21no—
100C22×D244D411yescharacteristic
101C22×D244C2311yescharacteristic
102C22×D244C2311yescharacteristic
103C22×D244C2311yescharacteristic
104C22×C22⋊D61—21no—
105C22×C22⋊D61—21no—
106C2×D4×D61—24no—
107C2×D4×D61—22no—
108C2×D4×D61—42no—
109C2×D4×D61C2314yes—
110C23×Dic61—21no—
111C22×C4×D61—21no—
112C22×C4×D61—21no—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519804—232no—
116#14519798—232no—
117C2×#11758202—24no—
118C2×#11758202C2314yescomplemented
119C2×#11758190—24no—
120C2×#11758190—42no—
121C2×#11758190C2314yescomplemented
122C2×#11758190C2314yescomplemented
123C2×#11758201—24no—
124C2×#11758201C2314yes—
125C2×D488—24no—
126C2×D488—42no—
127C2×D488C2314yes—
128C2×D488C2314yes—
129C2×#11758199—24no—
130C2×#11758199—24no—
131C2×#11758199C2314yes—
132C2×#11758199C2314yes—
133C2×#11758189—24no—
134C2×#11758189C2314yes—
135C22×#92418C2311yescharacteristic
136C22×#92418C2311yescharacteristic
137C2×C8×D61—24no—
138C2×C8×D61C2314yescomplemented
139#14519774—28no—
140#14519774—22no—
141#14519774C2314yescomplemented
142#14519765—22no—
143#14519765C2314yes—
144#14519761—28no—
145#14519757—22no—
146#14519757C2314yes—
147#14519752—22no—
148#14519752—22no—
149#14519752—22no—
150#14519752—28no—
151#14519752—28no—
152#14519752C2314yes—
153#14519752C2314yes—
154#14519752C2314yescomplemented
155#14519751—28no—
156#14519747—28no—
157C4×D244—28no—
158C4×D244D414yes—
159C4×D244C2314yes—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61D411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—28no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C4⋊#92418C2314yescomplemented
172#14519700C2314yescomplemented
173#14519697C2314yes—
174#14519697C2314yescomplemented
175#14519697C2314yescomplemented
176#14519689C2314yes—
177#14519689C2314yescomplemented
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61C2311yescharacteristic
180C23×C4×C61—21no—
181C2×SD16×C61D418yescomplemented
182C2×SD16×C61C2314yes—
183C22×C8×C61C2311yescharacteristic
184C22×C8×C61C2311yescharacteristic
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yescomplemented
187C4×D4×C61—22no—
188C4×D4×C61C2314yes—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61—21no—
193C2×C42×C61—21no—
194C2×C42×C61C2311yescharacteristic
195#107×C61C2314yescomplemented
196#103×C61C2314yescomplemented
197#102×C61C2314yes—
198#97×C61C2314yescomplemented
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—22no—
211C2×Q8×C61C2×D414yes—
212C2×Q8×C61C2412yes—
213C2×D4×C61—21no—
214C2×D4×C61—22no—
215C2×D4×C61C2×D414yes—
216C2×D4×C61C2412yes—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—24no—
221C22×C4×C61—82no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C22×Dic61—21no—
230C22×Dic61—24no—
231C22×Dic61—44no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234#11758226—28no—
235#11758226—28no—
236#11758226—44no—
237#11758226—44no—
238#11758226—48no—
239#11758226—48no—
240#11758224—28no—
241#11758224—44no—
242#11758224—48no—
243D4×D61—28no—
244D4×D61—44no—
245D4×D61—48no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—24no—
253C2×D244—24no—
254C2×D244—21no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—24no—
259C2×D244—24no—
260C2×D244—24no—
261C2×D244—24no—
262C2×D244—42no—
263C2×D244—44no—
264C2×D244—44no—
265C2×D244—44no—
266C2×D244—82no—
267C2×D244—82no—
268C2×D244—82no—
269C2×D244—82no—
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—44no—
281C2×C4×D61—44no—
282C2×C4×D61C2×D412yes—
283C2×C4×D61C2×D412yes—
284C2×C4×D61C2412yes—
285C2×C4×D61C2412yes—
286C2×Dic122—22no—
287C2×Dic122—22no—
288C2×Dic122—21no—
289C2×Dic122C2412yes—
290SD16×C61C2×D4116yescomplemented
291C2×C8×C61—22no—
292C2×C8×C61C2×D414yes—
293C2×C8×C61C2412yes—
294C2×C8×C61C2412yes—
295C4⋊C4×C61—24no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61C2412yes—
299C4⋊C4×C61C2412yes—
300C22⋊C4×C61—24no—
301C42×C61—24no—
302C42×C61C2×D412yes—
303C42×C61C2412yes—
304#11758202—28no—
305#11758201—28no—
306#11758199—28no—
307#11758199—28no—
308#11758198—24no—
309#11758198—24no—
310#11758198—24no—
311#11758198—24no—
312#11758198—24no—
313#11758198—24no—
314#11758198C2×D414yes—
315#11758198C2×D414yes—
316C4⋊Dic61—24no—
317C4⋊Dic61C2×D414yes—
318C2×#92418—22no—
319C2×#92418—22no—
320C2×#92418C2412yes—
321C2×#92418C2412yes—
322D488—28no—
323D488—44no—
324#11758190—28no—
325#11758190—44no—
326#11758189—28no—
327C8×D61—28no—
328C23×C61—24no—
329C23×C61—22no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—48no—
343C22×D61—48no—
344C22×D61—42no—
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×C61C22×D414yes—
360D4×C61—24no—
361D4×C61—22no—
362D4×C61C22×D414yes—
363C2×C4×C61—24no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—84no—
372C2×C4×C61C22×D412yes—
373C2×C4×C61C22×D412yes—
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D412yes—
376C2×C4×C61H(5,𝔽2)12yes—
377C2×C4×C61C2511yescharacteristic
378C22⋊D61—48no—
379C22⋊D61—48no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—48no—
384C2×Dic61—42no—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387D244—22no—
388D244—22no—
389D244—22no—
390D244—22no—
391D244—22no—
392D244—22no—
393D244—44no—
394D244—48no—
395D244—48no—
396D244—48no—
397D244—42no—
398D244—42no—
399D244—42no—
400D244—84no—
401D244—84no—
402D244—84no—
403D244—84no—
404C4×D61—24no—
405C4×D61—24no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—48no—
411C4×D61—48no—
412Dic122—22no—
413Dic122—22no—
414Dic122—42no—
415C8×C61—22no—
416C8×C61C22×D414yes—
417#92418—22no—
418#92418—22no—
419C2×#3268—611nomaximal, Sylow
420C22×C61—24no—
421C22×C61—48no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61D4212yes—
425C22×C61#57512yes—
426C22×C61#57612yes—
427C22×C61C23×D411yescharacteristic
428C2×D61—22no—
429C2×D61—22no—
430C2×D61—22no—
431C2×D61—22no—
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—44no—
435C2×D61—44no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—816no—
446C2×D61—84no—
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×#464—611no—
469C2×#459—611no—
470C2×#452—611no—
471C2×#449—611no—
472C2×#449—611no—
473C2×#447—611no—
474C2×#440D6111yescharacteristic, complemented
475C2×#435—611no—
476C2×C61—44no—
477C2×C61#326814yescomplemented
478C2×C61C2×D4211yescharacteristic
479C2×C61C2×#57511yescharacteristic
480C2×C61C2×#57611yescharacteristic
481D61—42no—
482D61—42no—
483D61—82no—
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×Q16—611no—
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×#124—611no—
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—1221no—
524C2×C4×D4C2×D6111yescharacteristic
525C22×C22⋊C4—1221no—
526#496—618no—
527#468—618no—
528#466—618no—
529#464—618no—
530#459—618no—
531#452—618no—
532#449—618no—
533#449—618no—
534#447—618no—
535#440C2×D6118yescomplemented
536#435—618no—
537C2×#107C2×D6111yescharacteristic, complemented
538C2×C4⋊C8—611no—
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×#97C2×D6111yescharacteristic, complemented
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×Q8—611no—
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—21no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4—1221no—
588AGL(1,ℤ/8)—12232no—
589#135—12232no—
590C2×Q16—614no—
591C2×Q16—1224no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×SD16—1224no—
596C2×SD16—1224no—
597C2×SD16—2442no—
598C2×SD16D24418yescomplemented
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—614no—
620#124—1222no—
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—22no—
637C4×D4—614no—
638C4×D4—614no—
639C4×D4—1228no—
640C4×D4C22×D6114yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4C22×D6111yescharacteristic
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—1228no—
650C2×C22⋊C4—1221no—
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#107C22×D6114yescomplemented
659C4⋊C8—614no—
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#97C22×D6114yescomplemented
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—2448no—
684#41—2444no—
685#41—2444no—
686#41—2448no—
687#41—2448no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—612no—
691C2×Q8—1221no—
692C2×Q8—1222no—
693C2×Q8—1222no—
694C2×Q8C2×D24414yes—
695C2×Q8C23×D6112yes—
696C2×D4—21no—
697C2×D4—22no—
698C2×D4—614no—
699C2×D4—612no—
700C2×D4—612no—
701C2×D4—612no—
702C2×D4—1224no—
703C2×D4—1224no—
704C2×D4—1224no—
705C2×D4—1224no—
706C2×D4—1224no—
707C2×D4—1224no—
708C2×D4—1228no—
709C2×D4—1224no—
710C2×D4—1224no—
711C2×D4—1224no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1222no—
716C2×D4—1222no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—4882no—
722C2×D4—4882no—
723C2×D4—4882no—
724C2×D4—4882no—
725C2×D4—2442no—
726C2×D4—2444no—
727C2×D4—2444no—
728C2×D4—2444no—
729C2×D4—2444no—
730C2×D4—2448no—
731C2×D4—2444no—
732C2×D4—2444no—
733C2×D4C2×D24414yes—
734C2×D4C23×D6112yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—82no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—612no—
745C22×C4—612no—
746C22×C4—1224no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—1222no—
750C22×C4—1222no—
751C22×C4—1222no—
752C22×C4—1222no—
753C22×C4—1221no—
754C22×C4—2444no—
755C22×C4—2444no—
756C22×C4—2444no—
757C22×C4D4×D6111yescharacteristic
758C22×C4D4×D6111yescharacteristic
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761SD16—1228no—
762SD16—1228no—
763SD16—2444no—
764SD16C2×D244116yescomplemented
765D8—1228no—
766D8—1228no—
767D8—1228no—
768D8—2444no—
769M16—1228no—
770C2×C8—22no—
771C2×C8—612no—
772C2×C8—612no—
773C2×C8—1222no—
774C2×C8—1222no—
775C2×C8—1228no—
776C2×C8C2×D24414yes—
777C2×C8C23×D6112yes—
778C2×C8C23×D6112yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—614no—
783C4⋊C4—1224no—
784C4⋊C4C23×D6112yes—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—614no—
788C22⋊C4—614no—
789C22⋊C4—1224no—
790C22⋊C4—1224no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4—1224no—
794C22⋊C4—1224no—
795C42—24no—
796C42D4×D6112yes—
797C42C23×D6112yes—
798C23—22no—
799C23—24no—
800C23—42no—
801C23—42no—
802C23—612no—
803C23—612no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—1222no—
809C23—1222no—
810C23—1222no—
811C23—1222no—
812C23—1222no—
813C23—4884no—
814C23—48816no—
815C23—2448no—
816C23—2448no—
817C23—2442no—
818C23—2442no—
819C23—2442no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23—2442no—
824C23—2442no—
825C23—2442no—
826C23C2×D4×D6111yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—1222no—
830Q8—1222no—
831Q8—2442no—
832Q8C22×D24414yes—
833D4—22no—
834D4—24no—
835D4—1222no—
836D4—1222no—
837D4—1222no—
838D4—1222no—
839D4—1222no—
840D4—1222no—
841D4—4884no—
842D4—4884no—
843D4—4884no—
844D4—4884no—
845D4—2444no—
846D4—2448no—
847D4—2448no—
848D4—2448no—
849D4—2448no—
850D4—2448no—
851D4—2442no—
852D4—2442no—
853D4—2442no—
854D4C22×D24414yes—
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—84no—
864C2×C4—612no—
865C2×C4—612no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1224no—
873C2×C4—1224no—
874C2×C4—1222no—
875C2×C4—2448no—
876C2×C4—2448no—
877C2×C4—2448no—
878C2×C4—2442no—
879C2×C4C2×D4×D6112yes—
880C2×C4C2×D4×D6112yes—
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×D24412yes—
883C2×C4#1451982312yes—
884C2×C4C24×D6111yescharacteristic
885C8—22no—
886C8—1222no—
887C8—1222no—
888C8C22×D24414yes—
889C22—24no—
890C22—42no—
891C22—42no—
892C22—48no—
893C22—1222no—
894C22—1222no—
895C22—1222no—
896C22—1222no—
897C22—1222no—
898C22—1222no—
899C22—48816no—
900C22—4884no—
901C22—4884no—
902C22—4884no—
903C22—2442no—
904C22—2442no—
905C22—2442no—
906C22—2442no—
907C22—2442no—
908C22—2442no—
909C22—2442no—
910C22—2442no—
911C22—2442no—
912C22—2444no—
913C22—2444no—
914C22D4×D24412yes—
915C22#1684056112yes—
916C22#1684056612yes—
917C22C22×D4×D6111yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—1222no—
924C4—1222no—
925C4—2442no—
926C4D4×D24412yes—
927C4C23×D24411yescharacteristic
928C4C2×#1451982311yescharacteristic
929C2—44no—
930C2—4882no—
931C2—4882no—
932C2—4882no—
933C2—2442no—
934C2—2442no—
935C2#2145736114yesdirect product factor
936C2C2×D4×D24411yescharacteristic
937C2C2×#1684056111yescharacteristic
938C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
hypercenterC2×#440D61
hypocenterC61C2×#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#14519804C2semidirect
2. C22×#14519798C2semidirect
3. C2×#16840434C2semidirect
4. C2×#16840407C2semidirect
5. #21457361C2direct (N × H)
6. C2×#16840151C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16839999C2semidirect
9. C2×#16839984C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839910C2semidirect
13. C2×#16839908C2semidirect
14. C2×#16839897C2semidirect
15. C2×#16839835C2semidirect
16. C2×C61×#440C2semidirect
18. C22×#11758226C22semidirect
22. C2×#14519804C22semidirect
24. C2×#14519798C22semidirect
25. C22×#11758202C22semidirect
26. C22×#11758190C22semidirect
27. C22×#11758190C22semidirect
34. C22×C8×D61C22semidirect
36. #16840434C22semidirect
38. #16840407C22semidirect
40. C2×#14519774C22semidirect
48. C2×#14519752C22semidirect
54. #16840151C22semidirect
55. #16840009C22semidirect
56. #16839999C22semidirect
57. #16839984C22semidirect
58. #16839957C22semidirect
59. #16839927C22semidirect
60. #16839910C22semidirect
61. #16839908C22semidirect
62. #16839897C22semidirect
63. #16839835C22semidirect
64. C2×C4⋊#92418C22semidirect
65. C2×#14519700C22semidirect
67. C2×#14519697C22semidirect
68. C2×#14519697C22semidirect
70. C2×#14519689C22semidirect
72. C2×C4×Q8×C61C22semidirect
74. C61×#440C22semidirect
75. C2×#107×C61C22semidirect
76. C2×#103×C61C22semidirect
78. C2×#97×C61C22semidirect
87. C2×#11758226C23semidirect
118. C2×#11758202C23semidirect
121. C2×#11758190C23semidirect
122. C2×#11758190C23semidirect
138. C2×C8×D61C23semidirect
141. #14519774C23semidirect
154. #14519752C23semidirect
171. C4⋊#92418C23semidirect
172. #14519700C23semidirect
174. #14519697C23semidirect
175. #14519697C23semidirect
177. #14519689C23semidirect
181. C2×SD16×C61D4semidirect
186. C4×Q8×C61C23semidirect
195. #107×C61C23semidirect
196. #103×C61C23semidirect
198. #97×C61C23semidirect
290. SD16×C61C2×D4semidirect
474. C2×#440D61semidirect
477. C2×C61#3268semidirect
521. C2×C4×Q8C2×D61semidirect
535. #440C2×D61semidirect
537. C2×#107C2×D61semidirect
540. C2×#103C2×D61semidirect
547. C2×#97C2×D61semidirect
548. C61C2×#3268semidirect
598. C2×SD16D244semidirect
635. C4×Q8C22×D61semidirect
658. #107C22×D61semidirect
661. #103C22×D61semidirect
668. #97C22×D61semidirect
764. SD16C2×D244semidirect
935. C2#21457361direct (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×#145197982
C2×#168404342
C2×#168404072
#214573612
C2×#168401512
C2×#168400092
C2×#168399992
C2×#168399842
C2×#168399572
C2×#168399272
C2×#168399102
C2×#168399082
C2×#168398972
C2×#168398352
C2×C61×#4402
C2×#326861