Finite Group Databasebeta

← C2×#21457376 #30555044

Subgroups — C2×#21457376 #30555044

Order 15616.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic, complemented
2C22×#14519798C211yesmaximal, characteristic, complemented
3C2×#16840424C211yesmaximal, characteristic, complemented
4C2×#16840416C211yesmaximal, characteristic, complemented
5#21457376C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840009C211yesmaximal, characteristic, complemented
8C2×#16840004C211yesmaximal, characteristic, complemented
9C2×#16839972C211yesmaximal, characteristic, complemented
10C2×#16839977C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839925C211yesmaximal, characteristic, complemented
13C2×#16839908C211yesmaximal, characteristic, complemented
14C2×#16839919C211yesmaximal, characteristic, complemented
15C2×#16839835C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×#11758224C2211yescharacteristic
20C22×Q8×D61C2211yescharacteristic
21C2×#14519806—28no—
22C2×#14519806C2218yescomplemented
23C2×#14519798—28no—
24C2×#14519798C2218yescomplemented
25C22×Dic244C2211yescharacteristic
26C22×Dic244C2211yescharacteristic
27C22×#11758202C2211yescharacteristic
28C22×#11758202C2211yescharacteristic
29C22×#11758190C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758200C2211yescharacteristic
32C22×#11758199C2211yescharacteristic
33C22×#11758189C2211yescharacteristic
34C22×C8×D61C2211yescharacteristic
35#16840424—24no—
36#16840424C2218yescomplemented
37#16840416—24no—
38#16840416C2218yescomplemented
39C2×#14519777C2211yescharacteristic
40C2×#14519765—21no—
41C2×#14519765C2211yescharacteristic
42C2×#14519761—21no—
43C2×#14519761—21no—
44C2×#14519757—21no—
45C2×#14519757C2211yescharacteristic
46C2×#14519757C2211yescharacteristic
47C2×#14519757C2211yescharacteristic
48C2×#14519752—21no—
49C2×#14519752C2211yescharacteristic
50C2×#14519751—21no—
51C2×C4×D244—21no—
52C2×C4×D244C2211yescharacteristic
53C22×C4⋊Dic61—21no—
54#16840156C2218yescomplemented
55#16840009C2218yescomplemented
56#16840004C2218yescomplemented
57#16839977C2218yescomplemented
58#16839972C2218yescomplemented
59#16839927C2218yescomplemented
60#16839925C2218yescomplemented
61#16839919C2218yescomplemented
62#16839908C2218yescomplemented
63#16839835C2218yescomplemented
64C2×C4⋊#92418C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C61×#440C2218yescomplemented
75C2×#107×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#102×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C2×#11758224—24no—
84C2×#11758224—24no—
85C2×#11758224—22no—
86C2×#11758224—22no—
87C2×#11758224—42no—
88C2×#11758224—42no—
89C2×#11758224C2314yes—
90C2×#11758224C2314yes—
91C22×Dic122—21no—
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2311yescharacteristic
95C2×Q8×D61—22no—
96C2×Q8×D61—24no—
97C2×Q8×D61—42no—
98C2×Q8×D61C2314yes—
99C22×D244—21no—
100C22×D244—21no—
101C22×D244D411yescharacteristic
102C22×D244C2311yescharacteristic
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C23×Dic61—21no—
106C23×Dic61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111#14519806—232no—
112#14519798—232no—
113C2×Dic244—24no—
114C2×Dic244—42no—
115C2×Dic244C2314yes—
116C2×Dic244C2314yes—
117C2×#11758202—24no—
118C2×#11758202—24no—
119C2×#11758202C2314yes—
120C2×#11758202C2314yes—
121C2×#11758190—24no—
122C2×#11758190—42no—
123C2×#11758190C2314yes—
124C2×#11758190C2314yes—
125C2×#11758200—24no—
126C2×#11758200C2314yes—
127C2×#11758199—24no—
128C2×#11758199C2314yes—
129C2×#11758189—24no—
130C2×#11758189C2314yes—
131C22×#92418C2311yescharacteristic
132C22×#92418C2311yescharacteristic
133C2×C8×D61—24no—
134C2×C8×D61C2314yes—
135#14519777—22no—
136#14519777C2314yes—
137#14519765—22no—
138#14519765—28no—
139#14519765C2314yes—
140#14519761—28no—
141#14519761—28no—
142#14519757—22no—
143#14519757—22no—
144#14519757—22no—
145#14519757—28no—
146#14519757C2314yes—
147#14519757C2314yes—
148#14519757C2314yes—
149#14519752—28no—
150#14519752—22no—
151#14519752C2314yes—
152#14519751—28no—
153C4×D244—28no—
154C4×D244D414yes—
155C4×D244C2314yes—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61—28no—
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C4⋊#92418C2314yes—
172#14519700C2314yes—
173#14519700C2314yes—
174#14519700C2314yes—
175#14519697C2314yes—
176#14519689C2314yes—
177#14519689C2314yes—
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×C61C2314yes—
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×C61C2314yes—
196#103×C61C2314yes—
197#102×C61C2314yes—
198#97×C61C2314yes—
199C24×C61—21no—
200C23×D61—21no—
201C23×D61C2×D411yescharacteristic
202C23×D61C2×D411yescharacteristic
203C2×Q8×C61—21no—
204C2×Q8×C61—22no—
205C2×Q8×C61C2×D414yes—
206C2×Q8×C61C2412yes—
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61C2×D414yes—
210C2×D4×C61C2412yes—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—44no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—24no—
227C22×Dic61—24no—
228C22×Dic61—44no—
229C22×Dic61—44no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758226—28no—
233#11758226—44no—
234#11758226—48no—
235Q8×D61—28no—
236Q8×D61—44no—
237Q8×D61—48no—
238#11758224—28no—
239#11758224—28no—
240#11758224—44no—
241#11758224—44no—
242#11758224—48no—
243#11758224—48no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—24no—
247C2×D244—24no—
248C2×D244—21no—
249C2×D244—42no—
250C2×D244—44no—
251C2×D244—44no—
252C2×D244C2×D414yes—
253C2×D244C2412yes—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—22no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—24no—
276C2×Dic122—44no—
277C2×Dic122C2412yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280SD16×C61C2×D4116yescomplemented
281C2×C8×C61—22no—
282C2×C8×C61C2×D414yes—
283C2×C8×C61C2412yes—
284C2×C8×C61C2412yes—
285C4⋊C4×C61—24no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C2412yes—
289C4⋊C4×C61C2412yes—
290C22⋊C4×C61—24no—
291C42×C61—24no—
292C42×C61C2×D412yes—
293C42×C61C2412yes—
294#11758202—28no—
295#11758202—28no—
296#11758200—28no—
297#11758199—28no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—24no—
304#11758198C2×D414yes—
305#11758198C2×D414yes—
306C4⋊Dic61—24no—
307C4⋊Dic61—24no—
308C4⋊Dic61—24no—
309C4⋊Dic61—24no—
310C4⋊Dic61—24no—
311C4⋊Dic61C2×D414yes—
312C2×#92418—22no—
313C2×#92418—22no—
314C2×#92418C2412yes—
315C2×#92418C2412yes—
316Dic244—28no—
317Dic244—44no—
318#11758190—28no—
319#11758190—44no—
320#11758189—28no—
321C8×D61—28no—
322C23×C61—24no—
323C23×C61—22no—
324C23×C61—42no—
325C23×C61—42no—
326C23×C61C22×D411yescharacteristic
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61C22×D412yes—
338C22×D61C22×D412yes—
339Q8×C61—24no—
340Q8×C61—22no—
341Q8×C61C22×D414yes—
342D4×C61—24no—
343D4×C61—22no—
344D4×C61C22×D414yes—
345C2×C4×C61—24no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—48no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D412yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D412yes—
358C2×C4×C61H(5,𝔽2)12yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—48no—
361C22⋊D61—48no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—48no—
368C2×Dic61—48no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61C22×D412yes—
373C2×Dic61C22×D412yes—
374D244—22no—
375D244—22no—
376D244—44no—
377D244—48no—
378D244—48no—
379D244—42no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—48no—
387C4×D61—48no—
388Dic122—22no—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122—22no—
393Dic122—22no—
394Dic122—48no—
395Dic122—42no—
396Dic122—42no—
397Dic122—42no—
398C8×C61—22no—
399C8×C61C22×D414yes—
400#92418—22no—
401#92418—22no—
402C2×#3269—611nomaximal, Sylow
403C22×C61—24no—
404C22×C61—48no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61D4212yes—
408C22×C61#57512yes—
409C22×C61#57812yes—
410C22×C61C23×D411yescharacteristic
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—44no—
418C2×D61—44no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—84no—
423C4×C61—24no—
424C4×C61—22no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61D4212yes—
429C4×C61C23×D411yescharacteristic
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431Dic61—22no—
432Dic61—22no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436C22×#137—611no—
437C22×#135—611no—
438C2×#548—611no—
439C2×#547—611no—
440#3269—6116no—
441C2×#497—611no—
442C2×#468—611no—
443C2×#467—611no—
444C2×#462—611no—
445C2×#463—611no—
446C2×#452—611no—
447C2×#452—611no—
448C2×#449—611no—
449C2×#451—611no—
450C2×#440D6111yescharacteristic, complemented
451C2×#435—611no—
452C2×C61—44no—
453C2×C61#326914yescomplemented
454C2×C61C2×D4211yescharacteristic
455C2×C61C2×#57511yescharacteristic
456C2×C61C2×#57811yescharacteristic
457D61—42no—
458D61—42no—
459D61—82no—
460C22×#41—611no—
461C22×#41—611no—
462C22×#41—611no—
463C23×Q8—611no—
464C2×#137—618no—
465C2×#137—1228no—
466C2×#135—618no—
467C2×#135—1228no—
468C22×Q16—611no—
469C22×Q16—611no—
470C22×Q16—611no—
471C22×Q16—611no—
472C22×SD16—611no—
473C22×SD16—611no—
474C22×SD16—611no—
475C22×SD16C2×D6111yescharacteristic
476C22×D8—611no—
477C22×M16—611no—
478C23×C8—611no—
479#548—618no—
480#548—1224no—
481#547—618no—
482#547—1224no—
483C2×C4⋊Q8—611no—
484C2×#124—611no—
485C2×#124—1221no—
486C2×#123—1221no—
487C2×#123—1221no—
488C2×C22⋊Q8—611no—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8—611no—
491C2×C22⋊Q8—1221no—
492C2×#121—611no—
493C2×#121—1221no—
494C2×#121—1221no—
495C2×C4×Q8C2×D6111yescharacteristic
496C2×C4×D4—611no—
497C2×C4×D4—1221no—
498C2×C4×D4C2×D6111yescharacteristic
499C22×C4⋊C4—1221no—
500#497—618no—
501#468—618no—
502#467—618no—
503#463—618no—
504#462—618no—
505#452—618no—
506#452—618no—
507#451—618no—
508#449—618no—
509#440C2×D6118yescomplemented
510#435—618no—
511C2×#107C2×D6111yescharacteristic
512C2×C4⋊C8—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×#103C2×D6111yescharacteristic
517C2×#102—611no—
518C2×#102C2×D6111yescharacteristic
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×#97C2×D6111yescharacteristic
522C61C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—614no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41—1224no—
530C2×#41—1224no—
531C2×#41—1224no—
532C2×#41—2442no—
533C2×#41—2442no—
534C2×#41—2442no—
535C22×Q8—614no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—611no—
539C22×Q8—1221no—
540C22×Q8—1222no—
541C22×Q8—1224no—
542C22×Q8—2442no—
543C22×Q8C22×D6111yescharacteristic
544C22×D4—611no—
545C22×D4—611no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4C22×D6111yescharacteristic
551C23×C4—21no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
557C23×C4—1221no—
558#137—12232no—
559#135—12232no—
560C2×Q16—614no—
561C2×Q16—614no—
562C2×Q16—614no—
563C2×Q16—614no—
564C2×Q16—1224no—
565C2×Q16—1224no—
566C2×Q16—1224no—
567C2×Q16—2442no—
568C2×SD16—614no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—1224no—
572C2×SD16—1224no—
573C2×SD16—2442no—
574C2×SD16D24418yescomplemented
575C2×SD16C22×D6114yes—
576C2×D8—614no—
577C2×D8—1224no—
578C2×M16—614no—
579C2×M16—1224no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—614no—
583C22×C8—1224no—
584C22×C8C22×D6111yescharacteristic
585C22×C8C22×D6111yescharacteristic
586C4⋊Q8—614no—
587C4⋊Q8—1222no—
588#124—614no—
589#124—1228no—
590#124—1222no—
591#123—1228no—
592#123—1228no—
593C22⋊Q8—614no—
594C22⋊Q8—614no—
595C22⋊Q8—614no—
596C22⋊Q8—1228no—
597C22⋊Q8—1222no—
598C22⋊Q8—1222no—
599C22⋊Q8—1222no—
600#121—614no—
601#121—1222no—
602#121—1228no—
603#121—1228no—
604C4×Q8—22no—
605C4×Q8C22×D6114yes—
606C4×D4—22no—
607C4×D4—614no—
608C4×D4—614no—
609C4×D4—1228no—
610C4×D4C22×D6114yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1228no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C42—21no—
631C2×C42C22×D6111yescharacteristic
632#107C22×D6114yes—
633C4⋊C8—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103C22×D6114yes—
638#102—614no—
639#102C22×D6114yes—
640C22⋊C8—614no—
641C22⋊C8—614no—
642#97C22×D6114yes—
643C24—21no—
644C24—611no—
645C24—611no—
646C24—1221no—
647#41—1228no—
648#41—1228no—
649#41—1228no—
650#41—2444no—
651#41—2444no—
652#41—2448no—
653#41—2448no—
654#41—2444no—
655#41—2448no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—612no—
659C2×Q8—612no—
660C2×Q8—612no—
661C2×Q8—1224no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1228no—
666C2×Q8—1222no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—1222no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—2444no—
673C2×Q8—2444no—
674C2×Q8—2448no—
675C2×Q8C2×D24414yes—
676C2×Q8C23×D6112yes—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—614no—
680C2×D4—612no—
681C2×D4—1224no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1221no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—2442no—
689C2×D4—2444no—
690C2×D4—2444no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4C2×D24414yes—
694C2×D4C23×D6112yes—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—44no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—1224no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—2444no—
718C22×C4—2444no—
719C22×C4—2444no—
720C22×C4—2444no—
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724Q16—1228no—
725Q16—1228no—
726Q16—1228no—
727Q16—2444no—
728SD16—1228no—
729SD16—1228no—
730SD16—2444no—
731SD16C2×D244116yescomplemented
732D8—1228no—
733M16—1228no—
734C2×C8—22no—
735C2×C8—612no—
736C2×C8—612no—
737C2×C8—1222no—
738C2×C8—1222no—
739C2×C8—1228no—
740C2×C8C2×D24414yes—
741C2×C8C23×D6112yes—
742C2×C8C23×D6112yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—614no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1224no—
752C4⋊C4C23×D6112yes—
753C4⋊C4C23×D6112yes—
754C22⋊C4—24no—
755C22⋊C4—614no—
756C22⋊C4—614no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C22⋊C4—1224no—
763C42—24no—
764C42D4×D6112yes—
765C42C23×D6112yes—
766C23—22no—
767C23—24no—
768C23—42no—
769C23—42no—
770C23—612no—
771C23—612no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1222no—
779C23—2442no—
780C23—2442no—
781C23—2442no—
782C23C2×D4×D6111yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—1222no—
786Q8—1222no—
787Q8—1222no—
788Q8—1222no—
789Q8—1222no—
790Q8—1222no—
791Q8—2448no—
792Q8—2442no—
793Q8—2442no—
794Q8—2442no—
795Q8C22×D24414yes—
796D4—22no—
797D4—24no—
798D4—1222no—
799D4—1222no—
800D4—2444no—
801D4—2448no—
802D4—2448no—
803D4—2448no—
804D4—2448no—
805D4—2442no—
806D4C22×D24414yes—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—612no—
817C2×C4—612no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1224no—
825C2×C4—1224no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—2448no—
830C2×C4—2448no—
831C2×C4—2448no—
832C2×C4—2448no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4C2×D4×D6112yes—
837C2×C4C2×D4×D6112yes—
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4C22×D24412yes—
840C2×C4#1451982312yes—
841C2×C4C24×D6111yescharacteristic
842C8—22no—
843C8—1222no—
844C8—1222no—
845C8C22×D24414yes—
846C22—24no—
847C22—42no—
848C22—42no—
849C22—48no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—4884no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22—2444no—
861C22—2444no—
862C22D4×D24412yes—
863C22#1684055812yes—
864C22#1684057812yes—
865C22C22×D4×D6111yescharacteristic
866C4—24no—
867C4—22no—
868C4—22no—
869C4—42no—
870C4—42no—
871C4—1222no—
872C4—1222no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4D4×D24412yes—
877C4C23×D24411yescharacteristic
878C4C2×#1451982311yescharacteristic
879C2—44no—
880C2—4882no—
881C2—2442no—
882C2—2442no—
883C2#2145737614yesdirect product factor
884C2C2×D4×D24411yescharacteristic
885C2C2×#1684055811yescharacteristic
886C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
hypercenterC2×#440D61
hypocenterC61C2×#3269
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×#14519806C2semidirect
2. C22×#14519798C2semidirect
3. C2×#16840424C2semidirect
4. C2×#16840416C2semidirect
5. #21457376C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16840004C2semidirect
9. C2×#16839972C2semidirect
10. C2×#16839977C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839925C2semidirect
13. C2×#16839908C2semidirect
14. C2×#16839919C2semidirect
15. C2×#16839835C2semidirect
16. C2×C61×#440C2semidirect
22. C2×#14519806C22semidirect
24. C2×#14519798C22semidirect
36. #16840424C22semidirect
38. #16840416C22semidirect
54. #16840156C22semidirect
55. #16840009C22semidirect
56. #16840004C22semidirect
57. #16839977C22semidirect
58. #16839972C22semidirect
59. #16839927C22semidirect
60. #16839925C22semidirect
61. #16839919C22semidirect
62. #16839908C22semidirect
63. #16839835C22semidirect
74. C61×#440C22semidirect
181. C2×SD16×C61D4semidirect
280. SD16×C61C2×D4semidirect
450. C2×#440D61semidirect
453. C2×C61#3269semidirect
509. #440C2×D61semidirect
522. C61C2×#3269semidirect
574. C2×SD16D244semidirect
731. SD16C2×D244semidirect
883. C2#21457376direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198062
C22×#145197982
C2×#168404242
C2×#168404162
#214573762
C2×#168401562
C2×#168400092
C2×#168400042
C2×#168399722
C2×#168399772
C2×#168399272
C2×#168399252
C2×#168399082
C2×#168399192
C2×#168398352
C2×C61×#4402
C2×#326961