Finite Group Databasebeta

← C2×#21457558 #30555276

Subgroups — C2×#21457558 #30555276

Order 15616.

2794 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×#14519797C211yesmaximal, characteristic, complemented
2C22×Q16×D61C211yesmaximal, characteristic, complemented
3C2×#16840422C211yesmaximal, characteristic, complemented
4C2×#16840419C211yesmaximal, characteristic, complemented
5#21457558C2116yesmaximal, direct product factor
6C2×#16840143C211yesmaximal, characteristic, complemented
7C2×#16840001C211yesmaximal, characteristic, complemented
8C2×#16839997C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839983C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839902C211yesmaximal, characteristic, complemented
13C2×#16839899C211yesmaximal, characteristic, complemented
14C2×#16839854C211yesmaximal, characteristic, complemented
15C2×#16839825C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519797—28no—
21C2×#14519797C2218yescomplemented
22C22×Dic244C2211yescharacteristic
23C22×#11758202C2211yescharacteristic
24C22×#11758202C2211yescharacteristic
25C2×Q16×D61—28no—
26C2×Q16×D61C2218yescomplemented
27C22×#11758190C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C23×#92418C2211yescharacteristic
32C22×C8×D61C2211yescharacteristic
33#16840422—24no—
34#16840422C2218yescomplemented
35#16840419—24no—
36#16840419C2218yescomplemented
37C2×#14519766C2211yescharacteristic
38C2×#14519764—21no—
39C2×#14519764C2211yescharacteristic
40C2×#14519763—21no—
41C2×#14519756—21no—
42C2×#14519756C2211yescharacteristic
43C2×#14519755—21no—
44C2×#14519752C2211yescharacteristic
45C2×#14519750—21no—
46C2×#14519748—21no—
47C2×#14519748C2211yescharacteristic
48C2×Q8×Dic61C2211yescharacteristic
49C2×#14519742C2211yescharacteristic
50C2×#14519739—21no—
51C2×C4×C22⋊D61—21no—
52C2×C4×C22⋊D61C2211yescharacteristic
53#16840143C2218yescomplemented
54#16840001C2218yescomplemented
55#16839997C2218yescomplemented
56#16839986C2218yescomplemented
57#16839983C2218yescomplemented
58#16839926C2218yescomplemented
59#16839902C2218yescomplemented
60#16839899C2218yescomplemented
61#16839854C2218yescomplemented
62#16839825C2218yescomplemented
63C2×#14519710C2211yescharacteristic
64C2×#14519706C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×C8×Dic61C2211yescharacteristic
71C22×#41×C61C2211yescharacteristic
72C22×Q16×C61C2211yescharacteristic
73C22×SD16×C61C2211yescharacteristic
74C2×C22⋊Q8×C61C2211yescharacteristic
75C61×#452C2218yescomplemented
76C2×#103×C61C2211yescharacteristic
77C2×#102×C61C2211yescharacteristic
78C2×C22⋊C8×C61C2211yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—24no—
81C2×#11758222—42no—
82C2×#11758222C2314yes—
83C22×Dic122—21no—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C2×Q8×D61—22no—
88C2×Q8×D61—22no—
89C2×Q8×D61—24no—
90C2×Q8×D61—24no—
91C2×Q8×D61—42no—
92C2×Q8×D61—42no—
93C2×Q8×D61C2314yes—
94C2×Q8×D61C2314yes—
95C22×D244—21no—
96C22×D244C2311yescharacteristic
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C22×C22⋊D61D411yescharacteristic
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104#14519797—232no—
105C2×Dic244—24no—
106C2×Dic244C2314yes—
107C2×#11758202—24no—
108C2×#11758202D418yescomplemented
109C2×#11758202C2314yes—
110C2×#11758202C2314yes—
111Q16×D61—232no—
112C2×#11758190—42no—
113C2×#11758190C2314yes—
114C2×#11758200—24no—
115C2×#11758200C2314yes—
116C2×#11758201—24no—
117C2×#11758201C2314yes—
118C2×#11758199—24no—
119C2×#11758199C2314yes—
120C22×#92418—24no—
121C22×#92418C2311yescharacteristic
122C22×#92418C2314yes—
123C22×#92418C2311yescharacteristic
124C2×C8×D61—24no—
125C2×C8×D61C2314yes—
126#14519766—22no—
127#14519766C2314yes—
128#14519764—28no—
129#14519764—22no—
130#14519764C2314yes—
131#14519763—28no—
132#14519756—22no—
133#14519756—28no—
134#14519756C2314yes—
135#14519755—28no—
136#14519752—22no—
137#14519752C2314yes—
138#14519750—28no—
139#14519748—28no—
140#14519748—22no—
141#14519748C2314yes—
142Q8×Dic61—22no—
143Q8×Dic61C2314yes—
144#14519742—22no—
145#14519742C2314yes—
146#14519739—28no—
147C4×C22⋊D61—28no—
148C4×C22⋊D61D414yes—
149C4×C22⋊D61C2314yes—
150C2×C4⋊Dic61—21no—
151C2×C4⋊Dic61C2311yescharacteristic
152C2×#11758196—21no—
153C2×#11758196—21no—
154C2×#11758196D411yescharacteristic
155C2×C22⋊Dic61—21no—
156C2×C22⋊Dic61—21no—
157C2×C22⋊Dic61—21no—
158C2×C22⋊Dic61—21no—
159C2×C22⋊Dic61D411yescharacteristic
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198D411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167#14519710C2314yes—
168#14519706C2314yes—
169#14519702C2314yes—
170#14519701C2314yes—
171#14519700C2314yes—
172#14519699C2314yes—
173#14519689C2314yes—
174C8×Dic61C2314yes—
175C2×#41×C61—22no—
176C2×#41×C61—24no—
177C2×#41×C61—42no—
178C2×#41×C61C2314yes—
179C22×Q8×C61C2311yescharacteristic
180C22×Q8×C61C2311yescharacteristic
181C22×D4×C61—21no—
182C22×D4×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61C2311yescharacteristic
185C2×Q16×C61—24no—
186C2×Q16×C61C2314yes—
187C2×SD16×C61—42no—
188C2×SD16×C61C2314yes—
189C22×C8×C61C2311yescharacteristic
190C22×C8×C61C2311yescharacteristic
191C22⋊Q8×C61—22no—
192C22⋊Q8×C61C2314yes—
193C2×C4⋊C4×C61—21no—
194C2×C4⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61—21no—
196#103×C61C2314yes—
197#102×C61C2314yes—
198C22⋊C8×C61C2314yes—
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203#41×C61—28no—
204#41×C61—44no—
205#41×C61—48no—
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61—22no—
211C2×Q8×C61C2×D414yes—
212C2×Q8×C61C2412yes—
213C2×Q8×C61C2412yes—
214C2×D4×C61—24no—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—22no—
218C2×D4×C61—44no—
219C2×D4×C61C2412yes—
220C22×C4×C61—21no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—24no—
226C22×C4×C61—44no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2412yes—
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—24no—
232C2×C22⋊D61—24no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—44no—
235C2×C22⋊D61—44no—
236C2×C22⋊D61C2×D414yes—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243Q8×D61—28no—
244Q8×D61—28no—
245Q8×D61—44no—
246Q8×D61—44no—
247Q8×D61—48no—
248Q8×D61—48no—
249#11758222—28no—
250#11758222—44no—
251#11758222—48no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—24no—
255C2×D244—21no—
256C2×D244—44no—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—24no—
261C2×C4×D61—24no—
262C2×C4×D61—24no—
263C2×C4×D61—44no—
264C2×C4×D61—44no—
265C2×C4×D61—44no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2412yes—
268C2×Dic122—21no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—22no—
272C2×Dic122—21no—
273C2×Dic122—24no—
274C2×Dic122—24no—
275C2×Dic122—44no—
276C2×Dic122—44no—
277C2×Dic122C2×D414yes—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280Q16×C61—28no—
281SD16×C61—44no—
282C2×C8×C61—22no—
283C2×C8×C61—22no—
284C2×C8×C61C2412yes—
285C2×C8×C61C2412yes—
286C4⋊C4×C61—24no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C2412yes—
289C22⋊C4×C61—24no—
290C22⋊Dic61—24no—
291C22⋊Dic61—24no—
292C22⋊Dic61—24no—
293C22⋊Dic61—24no—
294C22⋊Dic61C2×D414yes—
295#11758202—28no—
296#11758202C2×D4116yescomplemented
297#11758201—28no—
298#11758200—28no—
299#11758199—28no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198C2×D414yes—
304C4⋊Dic61—21no—
305C4⋊Dic61—24no—
306C4⋊Dic61C2412yes—
307#11758196—24no—
308#11758196—24no—
309#11758196C2×D414yes—
310C4×Dic61—24no—
311C4×Dic61—24no—
312C4×Dic61C2×D412yes—
313C4×Dic61C2412yes—
314C2×#92418—22no—
315C2×#92418—28no—
316C2×#92418C2×D414yes—
317C2×#92418C2412yes—
318C2×#92418C2412yes—
319Dic244—28no—
320#11758190—44no—
321C8×D61—28no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61#13514yescomplemented
338C22×D61C22×D412yes—
339Q8×C61—24no—
340Q8×C61—22no—
341Q8×C61—22no—
342Q8×C61—22no—
343Q8×C61—42no—
344Q8×C61C22×D414yes—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—48no—
348D4×C61—42no—
349C2×C4×C61—24no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—48no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D412yes—
363C2×C4×C61H(5,𝔽2)12yes—
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—28no—
366C22⋊D61—48no—
367C22⋊D61—48no—
368C2×Dic61—24no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61C22×D412yes—
378C2×Dic61C22×D412yes—
379C2×Dic61C22×D412yes—
380D244—22no—
381D244—22no—
382D244—48no—
383D244—42no—
384C4×D61—24no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—48no—
388C4×D61—48no—
389C4×D61—48no—
390Dic122—24no—
391Dic122—22no—
392Dic122—22no—
393Dic122—22no—
394Dic122—48no—
395Dic122—48no—
396Dic122—42no—
397Dic122C22×D414yes—
398C8×C61—22no—
399C8×C61—22no—
400#92418—22no—
401#92418C22×D414yes—
402C2×#3285—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—44no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—84no—
411C22×C61D4212yes—
412C22×C61C2×#13512yes—
413C22×C61#57812yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—22no—
416C2×D61—28no—
417C2×D61—22no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—84no—
422C2×D61C2×#13514yescomplemented
423C4×C61—24no—
424C4×C61—22no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61D4212yes—
428C4×C61C23×D411yescharacteristic
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430Dic61—24no—
431Dic61—22no—
432Dic61—22no—
433Dic61—22no—
434Dic61—42no—
435Dic61—42no—
436C22×#135—611no—
437C23×Q16—611no—
438C2×#548—611no—
439C2×#548—611no—
440#3285—6116no—
441C2×#495—611no—
442C2×#467—611no—
443C2×#466—611no—
444C2×#464—611no—
445C2×#464—611no—
446C2×#452—611no—
447C2×#452D6111yescharacteristic, complemented
448C2×#448—611no—
449C2×#448—611no—
450C2×C4×Q16—611no—
451C2×C8×D4—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61#328514yescomplemented
455C2×C61C2×D4211yescharacteristic
456C2×C61C22×#13511yescharacteristic
457C2×C61C2×#57811yescharacteristic
458D61—24no—
459D61—82no—
460C22×#41—611no—
461C22×#41C2×D6111yescharacteristic
462C23×Q8—611no—
463C23×Q8—611no—
464C2×#135—618no—
465C2×#135—1228no—
466C22×Q16—611no—
467C22×Q16—611no—
468C22×Q16—618no—
469C22×Q16—611no—
470C22×Q16—1228no—
471C22×Q16C2×D6111yescharacteristic
472C22×SD16—611no—
473C22×SD16—611no—
474C22×SD16—611no—
475C22×SD16C2×D6111yescharacteristic
476C22×D8—611no—
477C23×C8—611no—
478C23×C8—611no—
479#548—618no—
480#548—618no—
481#548—1224no—
482#548—1224no—
483C2×#124—611no—
484C2×#124—611no—
485C2×#124—1221no—
486C2×#124—1221no—
487C2×C22⋊Q8—611no—
488C2×C22⋊Q8—1221no—
489C2×C22⋊Q8—1221no—
490C2×C22⋊Q8C2×D6111yescharacteristic
491C2×#121—611no—
492C2×#121—611no—
493C2×#121—1221no—
494C2×#121—1221no—
495C2×C4×Q8—611no—
496C2×C4×Q8—611no—
497C2×C4×D4—611no—
498C2×C4×D4—1221no—
499C2×C4×D4—1221no—
500#495—618no—
501#467—618no—
502#466—618no—
503#464—618no—
504#464—618no—
505#452—618no—
506#452C2×D6118yescomplemented
507#448—618no—
508#448—618no—
509C4×Q16—618no—
510C8×D4—618no—
511C2×#107—611no—
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⋊C8C2×D6111yescharacteristic
521C2×C4×C8—611no—
522C61C2×#328511yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—614no—
527C2×#41—1224no—
528C2×#41—1222no—
529C2×#41—2442no—
530C2×#41C22×D6114yes—
531C22×Q8—614no—
532C22×Q8—614no—
533C22×Q8—611no—
534C22×Q8—611no—
535C22×Q8—1221no—
536C22×Q8—1221no—
537C22×Q8—1222no—
538C22×Q8—1222no—
539C22×Q8—1224no—
540C22×Q8—1224no—
541C22×Q8—2442no—
542C22×Q8—2442no—
543C22×Q8C22×D6111yescharacteristic
544C22×Q8C22×D6111yescharacteristic
545C22×D4—21no—
546C22×D4—611no—
547C22×D4—611no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4—1221no—
551C22×D4C22×D6111yescharacteristic
552C23×C4—21no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
557C23×C4C22×D6111yescharacteristic
558#135—12232no—
559C2×Q16—24no—
560C2×Q16—618no—
561C2×Q16—614no—
562C2×Q16—614no—
563C2×Q16—614no—
564C2×Q16—1224no—
565C2×Q16—1224no—
566C2×Q16—12232no—
567C2×Q16C22×D6114yes—
568C2×SD16—42no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—614no—
572C2×SD16—1224no—
573C2×SD16—1224no—
574C2×SD16—2442no—
575C2×SD16C22×D6114yes—
576C2×D8—614no—
577C2×D8—1224no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—614no—
581C22×C8—614no—
582C22×C8—1224no—
583C22×C8—1224no—
584C22×C8C22×D6111yescharacteristic
585C22×C8C22×D6111yescharacteristic
586#124—614no—
587#124—614no—
588#124—1222no—
589#124—1222no—
590#124—1228no—
591#124—1228no—
592C22⋊Q8—22no—
593C22⋊Q8—614no—
594C22⋊Q8—1228no—
595C22⋊Q8—1228no—
596C22⋊Q8—1222no—
597C22⋊Q8C22×D6114yes—
598#121—614no—
599#121—614no—
600#121—1228no—
601#121—1222no—
602#121—1222no—
603#121—1228no—
604C4×Q8—614no—
605C4×Q8—614no—
606C4×Q8—1222no—
607C4×Q8—1222no—
608C4×D4—614no—
609C4×D4—614no—
610C4×D4—1228no—
611C4×D4—1228no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C42—611no—
630C2×C42—1221no—
631C2×C42—1221no—
632#107—614no—
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⋊C8C22×D6114yes—
642C4×C8—614no—
643C24—21no—
644C24—611no—
645C24—1221no—
646C24D4×D6111yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—1228no—
651#41—2444no—
652#41—2448no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—22no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—614no—
659C2×Q8—612no—
660C2×Q8—612no—
661C2×Q8—1224no—
662C2×Q8—1224no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1222no—
666C2×Q8—1228no—
667C2×Q8—1228no—
668C2×Q8—1222no—
669C2×Q8—1222no—
670C2×Q8—2444no—
671C2×Q8—2444no—
672C2×Q8—2444no—
673C2×Q8—2444no—
674C2×Q8—2448no—
675C2×Q8—2448no—
676C2×Q8D4×D6114yes—
677C2×Q8C23×D6112yes—
678C2×Q8C23×D6112yes—
679C2×D4—24no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—44no—
684C2×D4—614no—
685C2×D4—612no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—1224no—
689C2×D4—1224no—
690C2×D4—1222no—
691C2×D4—1221no—
692C2×D4—1222no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4C23×D6112yes—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—44no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—1224no—
710C22×C4—1224no—
711C22×C4—1221no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1224no—
717C22×C4—2444no—
718C22×C4—2444no—
719C22×C4—2444no—
720C22×C4D4×D6112yes—
721C22×C4D4×D6111yescharacteristic
722C22×C4C23×D6112yes—
723C22×C4C23×D6111yescharacteristic
724Q16—28no—
725Q16—6116no—
726Q16—1228no—
727Q16—1228no—
728SD16—44no—
729SD16—1228no—
730SD16—1228no—
731SD16—2444no—
732D8—1228no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—614no—
736C2×C8—612no—
737C2×C8—612no—
738C2×C8—1228no—
739C2×C8—1228no—
740C2×C8—1222no—
741C2×C8C23×D6112yes—
742C2×C8C23×D6112yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—614no—
746C4⋊C4—612no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1221no—
750C4⋊C4—1224no—
751C4⋊C4C23×D6112yes—
752C22⋊C4—24no—
753C22⋊C4—614no—
754C22⋊C4—614no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C42—612no—
763C42—612no—
764C42—1224no—
765C42—1224no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—614no—
774C23—612no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—2442no—
779C23—2442no—
780C23—2442no—
781C23C2×D4×D6112yes—
782C23C2×D4×D6111yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—614no—
789Q8—1222no—
790Q8—1224no—
791Q8—1222no—
792Q8—1222no—
793Q8—2448no—
794Q8—2448no—
795Q8—2442no—
796Q8C2×D4×D6114yes—
797D4—22no—
798D4—22no—
799D4—48no—
800D4—42no—
801D4—1228no—
802D4—1222no—
803D4—1222no—
804D4—2448no—
805D4—2448no—
806D4—2448no—
807D4—2442no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—48no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—612no—
820C2×C4—612no—
821C2×C4—612no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1224no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1224no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—2448no—
833C2×C4—2448no—
834C2×C4—2448no—
835C2×C4—2442no—
836C2×C4—2442no—
837C2×C4C2×D4×D6112yes—
838C2×C4C2×D4×D6112yes—
839C2×C4C2×D4×D6111yescharacteristic
840C2×C4#1451982212yes—
841C2×C4C24×D6111yescharacteristic
842C8—22no—
843C8—22no—
844C8—614no—
845C8—1222no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—84no—
854C22—614no—
855C22—1222no—
856C22—1222no—
857C22—1228no—
858C22—4884no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22#1684039412yes—
863C22#135×D6112yes—
864C22#1684057812yes—
865C22C22×D4×D6111yescharacteristic
866C4—22no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—1222no—
871C4—1224no—
872C4—1222no—
873C4—1222no—
874C4—2442no—
875C4—2442no—
876C4#1684039412yes—
877C4C22×D4×D6111yescharacteristic
878C4C2×#1451982211yescharacteristic
879C2—42no—
880C2—82no—
881C2—1224no—
882C2—4882no—
883C2#2145755814yesdirect product factor
884C2C2×#1684039411yescharacteristic
885C2C2×#135×D6111yescharacteristic
886C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
hypercenterC2×#452D61
hypocenterC61C2×#3285
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#14519797C2semidirect
2. C22×Q16×D61C2semidirect
3. C2×#16840422C2semidirect
4. C2×#16840419C2semidirect
5. #21457558C2direct (N × H)
6. C2×#16840143C2semidirect
7. C2×#16840001C2semidirect
8. C2×#16839997C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839983C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839902C2semidirect
13. C2×#16839899C2semidirect
14. C2×#16839854C2semidirect
15. C2×#16839825C2semidirect
16. C2×C61×#452C2semidirect
21. C2×#14519797C22semidirect
26. C2×Q16×D61C22semidirect
34. #16840422C22semidirect
36. #16840419C22semidirect
53. #16840143C22semidirect
54. #16840001C22semidirect
55. #16839997C22semidirect
56. #16839986C22semidirect
57. #16839983C22semidirect
58. #16839926C22semidirect
59. #16839902C22semidirect
60. #16839899C22semidirect
61. #16839854C22semidirect
62. #16839825C22semidirect
75. C61×#452C22semidirect
108. C2×#11758202D4semidirect
296. #11758202C2×D4semidirect
337. C22×D61#135semidirect
422. C2×D61C2×#135semidirect
447. C2×#452D61semidirect
454. C2×C61#3285semidirect
506. #452C2×D61semidirect
522. C61C2×#3285semidirect
883. C2#21457558direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197972
C22×Q16×D612
C2×#168404222
C2×#168404192
#214575582
C2×#168401432
C2×#168400012
C2×#168399972
C2×#168399862
C2×#168399832
C2×#168399262
C2×#168399022
C2×#168398992
C2×#168398542
C2×#168398252
C2×C61×#4522
C2×#328561