Finite Group Databasebeta

← C2×#21457534 #30555250

Subgroups — C2×#21457534 #30555250

Order 15616.

2806 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×#14519798C211yesmaximal, characteristic, complemented
2C22×#14519797C211yesmaximal, characteristic, complemented
3C2×#16840414C211yesmaximal, characteristic, complemented
4C2×#16840411C211yesmaximal, characteristic, complemented
5#21457534C2116yesmaximal, direct product factor
6C2×#16840140C211yesmaximal, characteristic, complemented
7C2×#16840002C211yesmaximal, characteristic, complemented
8C2×#16840001C211yesmaximal, characteristic, complemented
9C2×#16839966C211yesmaximal, characteristic, complemented
10C2×#16839965C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839925C211yesmaximal, characteristic, complemented
13C2×#16839923C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839825C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758224C2211yescharacteristic
20C2×#14519798—28no—
21C2×#14519798C2218yescomplemented
22C2×#14519797—28no—
23C2×#14519797C2218yescomplemented
24C22×Dic244C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758190C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C23×#92418C2211yescharacteristic
32C22×C8×D61C2211yescharacteristic
33#16840414—24no—
34#16840414C2218yescomplemented
35#16840411—24no—
36#16840411C2218yescomplemented
37C2×#14519775C2211yescharacteristic
38C2×#14519775C2211yescharacteristic
39C2×#14519762—21no—
40C2×#14519760—21no—
41C2×#14519759—21no—
42C2×#14519758—21no—
43C2×#14519757C2211yescharacteristic
44C2×#14519756C2211yescharacteristic
45C2×#14519753C2211yescharacteristic
46C2×#14519750—21no—
47C2×#14519749—21no—
48C2×D4×Dic61C2211yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×C4×C22⋊D61C2211yescharacteristic
51C22×#11758196—21no—
52C2×C4⋊C4×D61—21no—
53#16840140C2218yescomplemented
54#16840002C2218yescomplemented
55#16840001C2218yescomplemented
56#16839966C2218yescomplemented
57#16839965C2218yescomplemented
58#16839926C2218yescomplemented
59#16839925C2218yescomplemented
60#16839923C2218yescomplemented
61#16839842C2218yescomplemented
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×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C2×#11758222—22no—
84C2×#11758222—24no—
85C2×#11758222—42no—
86C2×#11758222C2314yes—
87C2×#11758224—24no—
88C2×#11758224—22no—
89C2×#11758224—42no—
90C2×#11758224C2314yes—
91C22×Dic122C2311yescharacteristic
92C22×Dic122C2311yescharacteristic
93C22×D244—21no—
94C22×D244C2311yescharacteristic
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61D411yescharacteristic
98C23×Dic61—21no—
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104#14519798—232no—
105#14519797—232no—
106C2×Dic244—42no—
107C2×Dic244C2314yes—
108C2×#11758202—24no—
109C2×#11758202—24no—
110C2×#11758202C2314yes—
111C2×#11758202C2314yes—
112C2×#11758190—24no—
113C2×#11758190C2314yes—
114C2×#11758200—24no—
115C2×#11758200C2314yes—
116C2×#11758201—24no—
117C2×#11758201C2314yes—
118C2×#11758199D418yescomplemented
119C2×#11758199C2314yes—
120C22×#92418—24no—
121C22×#92418C2311yescharacteristic
122C22×#92418C2314yes—
123C22×#92418C2311yescharacteristic
124C2×C8×D61—24no—
125C2×C8×D61C2314yes—
126#14519775—22no—
127#14519775—22no—
128#14519775C2314yes—
129#14519775C2314yes—
130#14519762—28no—
131#14519760—28no—
132#14519759—28no—
133#14519758—28no—
134#14519757—22no—
135#14519757C2314yes—
136#14519756—22no—
137#14519756C2314yes—
138#14519753—22no—
139#14519753C2314yes—
140#14519750—28no—
141#14519749—28no—
142D4×Dic61—22no—
143D4×Dic61C2314yes—
144#14519739—22no—
145#14519739C2314yes—
146C4×C22⋊D61D414yes—
147C4×C22⋊D61C2314yes—
148C2×C4⋊Dic61—21no—
149C2×C4⋊Dic61C2311yescharacteristic
150C2×#11758196—21no—
151C2×#11758196—21no—
152C2×#11758196—21no—
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196—28no—
157C2×#11758196D411yescharacteristic
158C4⋊C4×D61—28no—
159C2×C22⋊Dic61—21no—
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61D411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
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—42no—
186C2×Q16×C61C2314yes—
187C2×SD16×C61—24no—
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×C61—22no—
212C2×Q8×C61C2412yes—
213C2×Q8×C61C2412yes—
214C2×D4×C61—24no—
215C2×D4×C61—21no—
216C2×D4×C61—22no—
217C2×D4×C61—44no—
218C2×D4×C61C2×D414yes—
219C2×D4×C61C2412yes—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—21no—
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×Dic61—24no—
241C22×Dic61—24no—
242C22×Dic61—44no—
243C22×Dic61—44no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247#11758226—28no—
248#11758226—44no—
249#11758226—48no—
250#11758224—28no—
251#11758224—44no—
252#11758224—48no—
253#11758222—28no—
254#11758222—44no—
255#11758222—48no—
256C2×D244—21no—
257C2×D244—22no—
258C2×D244—24no—
259C2×D244—44no—
260C2×D244C2×D414yes—
261C2×D244C2412yes—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—24no—
267C2×C4×D61—44no—
268C2×C4×D61—44no—
269C2×C4×D61—44no—
270C2×C4×D61C2×D412yes—
271C2×C4×D61C2412yes—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—22no—
275C2×Dic122—22no—
276C2×Dic122—21no—
277C2×Dic122—21no—
278C2×Dic122C2412yes—
279C2×Dic122C2412yes—
280Q16×C61—44no—
281SD16×C61—28no—
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⋊Dic61C2×D414yes—
293#11758202—28no—
294#11758202—28no—
295#11758201—28no—
296#11758200—28no—
297#11758199C2×D4116yescomplemented
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198C2×D414yes—
302C4⋊Dic61—21no—
303C4⋊Dic61—24no—
304C4⋊Dic61C2412yes—
305#11758196—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196—24no—
309#11758196—24no—
310#11758196—24no—
311#11758196C2×D414yes—
312C4×Dic61C2×D412yes—
313C4×Dic61C2412yes—
314C2×#92418—22no—
315C2×#92418—28no—
316C2×#92418C2×D414yes—
317C2×#92418C2412yes—
318C2×#92418C2412yes—
319Dic244—44no—
320#11758190—28no—
321C8×D61—28no—
322C23×C61—24no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C22×D61—22no—
332C22×D61—24no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61C22×D412yes—
339Q8×C61—22no—
340Q8×C61—22no—
341Q8×C61—22no—
342Q8×C61—22no—
343Q8×C61—42no—
344Q8×C61—42no—
345D4×C61—24no—
346D4×C61—22no—
347D4×C61—48no—
348D4×C61C22×D414yes—
349C2×C4×C61—22no—
350C2×C4×C61—24no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—48no—
357C2×C4×C61—42no—
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—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—48no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61—48no—
378C2×Dic61#13514yescomplemented
379C2×Dic61C22×D412yes—
380C2×Dic61C22×D412yes—
381C2×Dic61C22×D412yes—
382D244—24no—
383D244—22no—
384D244—48no—
385D244C22×D414yes—
386C4×D61—24no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—48no—
390C4×D61—48no—
391C4×D61—48no—
392Dic122—22no—
393Dic122—22no—
394Dic122—22no—
395Dic122—22no—
396Dic122—42no—
397Dic122—42no—
398C8×C61—22no—
399C8×C61—22no—
400#92418—22no—
401#92418C22×D414yes—
402C2×#3283—611nomaximal, Sylow
403C22×C61—24no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—44no—
408C22×C61—48no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61D4212yes—
412C22×C61C2×#13512yes—
413C22×C61#57812yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—22no—
416C2×D61—24no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—44no—
420C2×D61—48no—
421C2×D61—42no—
422C2×D61—42no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61D4212yes—
428C4×C61C23×D411yescharacteristic
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61C2×#13514yescomplemented
436C22×#135—611no—
437C22×#135—611no—
438C2×#547—611no—
439C2×#547—611no—
440#3283—6116no—
441C2×#494—611no—
442C2×#467—611no—
443C2×#467—611no—
444C2×#461—611no—
445C2×#461—611no—
446C2×#452—611no—
447C2×#452—611no—
448C2×#452—611no—
449C2×#452D6111yescharacteristic, complemented
450C2×C4×D8—611no—
451C2×C8×D4—611no—
452C2×C61—42no—
453C2×C61—44no—
454C2×C61#328314yescomplemented
455C2×C61C2×D4211yescharacteristic
456C2×C61C22×#13511yescharacteristic
457C2×C61C2×#57811yescharacteristic
458D61—42no—
459D61—44no—
460C22×#41—611no—
461C22×#41—611no—
462C22×#41—611no—
463C22×#41C2×D6111yescharacteristic
464C2×#135—618no—
465C2×#135—618no—
466C2×#135—1228no—
467C2×#135—1228no—
468C22×Q16—611no—
469C22×Q16—611no—
470C22×Q16—611no—
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#547—618no—
480#547—618no—
481#547—1224no—
482#547—1224no—
483C2×C4⋊Q8—611no—
484C2×C4⋊Q8—611no—
485C2×#123—1221no—
486C2×#123—1221no—
487C2×#123—1221no—
488C2×#123—1221no—
489C2×C22⋊Q8—611no—
490C2×C22⋊Q8—611no—
491C2×C22⋊Q8—611no—
492C2×C22⋊Q8C2×D6111yescharacteristic
493C2×#121—1221no—
494C2×#121—1221no—
495C2×C4×D4—611no—
496C2×C4×D4—611no—
497C2×C4×D4—611no—
498C22×C4⋊C4—1221no—
499C22×C4⋊C4—1221no—
500#494—618no—
501#467—618no—
502#467—618no—
503#461—618no—
504#461—618no—
505#452—618no—
506#452—618no—
507#452—618no—
508#452C2×D6118yescomplemented
509C4×D8—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×#328311yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—614no—
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—1224no—
530C2×#41—1222no—
531C2×#41—1222no—
532C2×#41—1222no—
533C2×#41—1224no—
534C2×#41—1224no—
535C2×#41—2442no—
536C2×#41—2442no—
537C2×#41—2442no—
538C2×#41C22×D6114yes—
539C22×Q8—611no—
540C22×Q8—611no—
541C22×Q8C22×D6111yescharacteristic
542C22×Q8C22×D6111yescharacteristic
543C22×D4—21no—
544C22×D4—611no—
545C22×D4—611no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4C22×D6111yescharacteristic
550C23×C4—21no—
551C23×C4—611no—
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
557C23×C4C22×D6111yescharacteristic
558#135—12232no—
559#135—12232no—
560C2×Q16—42no—
561C2×Q16—614no—
562C2×Q16—614no—
563C2×Q16—614no—
564C2×Q16—1224no—
565C2×Q16—1224no—
566C2×Q16—2442no—
567C2×Q16C22×D6114yes—
568C2×SD16—24no—
569C2×SD16—614no—
570C2×SD16—614no—
571C2×SD16—614no—
572C2×SD16—1224no—
573C2×SD16—1224no—
574C2×SD16—1224no—
575C2×SD16C22×D6114yes—
576C2×D8—618no—
577C2×D8—614no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—614no—
581C22×C8—614no—
582C22×C8—1224no—
583C22×C8—1224no—
584C22×C8C22×D6111yescharacteristic
585C22×C8C22×D6111yescharacteristic
586C4⋊Q8—614no—
587C4⋊Q8—614no—
588C4⋊Q8—1222no—
589C4⋊Q8—1222no—
590#123—1228no—
591#123—1228no—
592#123—1228no—
593#123—1228no—
594C22⋊Q8—22no—
595C22⋊Q8—614no—
596C22⋊Q8—614no—
597C22⋊Q8—614no—
598C22⋊Q8—1222no—
599C22⋊Q8—1222no—
600C22⋊Q8—1222no—
601C22⋊Q8C22×D6114yes—
602#121—1228no—
603#121—1228no—
604C4×D4—614no—
605C4×D4—614no—
606C4×D4—614no—
607C4×D4—614no—
608C4×D4—1222no—
609C4×D4—1222no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1228no—
614C2×C4⋊C4—1228no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4C22×D6111yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—611no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C42—611no—
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—1228no—
652#41—1228no—
653#41—2444no—
654#41—2448no—
655#41—2444no—
656#41—2448no—
657#41—2444no—
658#41—2448no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—612no—
666C2×Q8—612no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1222no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8C23×D6112yes—
674C2×Q8C23×D6112yes—
675C2×D4—24no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—44no—
679C2×D4—614no—
680C2×D4—614no—
681C2×D4—612no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1221no—
687C2×D4—1222no—
688C2×D4—2444no—
689C2×D4—2444no—
690C2×D4—2444no—
691C2×D4D4×D6114yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—44no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—1224no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1224no—
715C22×C4—2444no—
716C22×C4—2444no—
717C22×C4—2444no—
718C22×C4—2444no—
719C22×C4—2444no—
720C22×C4D4×D6112yes—
721C22×C4D4×D6111yescharacteristic
722C22×C4C23×D6112yes—
723C22×C4C23×D6111yescharacteristic
724Q16—44no—
725Q16—1228no—
726Q16—1228no—
727Q16—2444no—
728SD16—28no—
729SD16—1228no—
730SD16—1228no—
731SD16—1228no—
732D8—6116no—
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—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1224no—
752C4⋊C4—1224no—
753C4⋊C4—1221no—
754C4⋊C4—1224no—
755C4⋊C4C23×D6112yes—
756C22⋊C4—24no—
757C22⋊C4—614no—
758C22⋊C4—614no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C42—612no—
765C42—612no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—42no—
772C23—42no—
773C23—612no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1224no—
779C23—2442no—
780C23—2442no—
781C23C2×D4×D6112yes—
782C23C2×D4×D6111yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—42no—
789Q8—1222no—
790Q8—1222no—
791Q8—1222no—
792Q8—1222no—
793Q8—2442no—
794Q8—2442no—
795D4—22no—
796D4—24no—
797D4—48no—
798D4—614no—
799D4—1228no—
800D4—1222no—
801D4—1224no—
802D4—2448no—
803D4—2448no—
804D4—2448no—
805D4C2×D4×D6114yes—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—48no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—614no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—612no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
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—2448no—
834C2×C4—2442no—
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—24no—
848C22—22no—
849C22—22no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—48no—
854C22—1222no—
855C22—1224no—
856C22—1222no—
857C22—1222no—
858C22—2442no—
859C22—2442no—
860C22—2444no—
861C22—2448no—
862C22#1684039412yes—
863C22#135×D6112yes—
864C22#1684057812yes—
865C22C22×D4×D6111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—614no—
871C4—1222no—
872C4—1222no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4#1684039412yes—
877C4C22×D4×D6111yescharacteristic
878C4C2×#1451982211yescharacteristic
879C2—42no—
880C2—44no—
881C2—2442no—
882C2—2444no—
883C2#2145753414yesdirect 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×#3283
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×#14519798C2semidirect
2. C22×#14519797C2semidirect
3. C2×#16840414C2semidirect
4. C2×#16840411C2semidirect
5. #21457534C2direct (N × H)
6. C2×#16840140C2semidirect
7. C2×#16840002C2semidirect
8. C2×#16840001C2semidirect
9. C2×#16839966C2semidirect
10. C2×#16839965C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839925C2semidirect
13. C2×#16839923C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839825C2semidirect
16. C2×C61×#452C2semidirect
21. C2×#14519798C22semidirect
23. C2×#14519797C22semidirect
34. #16840414C22semidirect
36. #16840411C22semidirect
53. #16840140C22semidirect
54. #16840002C22semidirect
55. #16840001C22semidirect
56. #16839966C22semidirect
57. #16839965C22semidirect
58. #16839926C22semidirect
59. #16839925C22semidirect
60. #16839923C22semidirect
61. #16839842C22semidirect
62. #16839825C22semidirect
75. C61×#452C22semidirect
118. C2×#11758199D4semidirect
297. #11758199C2×D4semidirect
378. C2×Dic61#135semidirect
435. Dic61C2×#135semidirect
449. C2×#452D61semidirect
454. C2×C61#3283semidirect
508. #452C2×D61semidirect
522. C61C2×#3283semidirect
883. C2#21457534direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197982
C22×#145197972
C2×#168404142
C2×#168404112
#214575342
C2×#168401402
C2×#168400022
C2×#168400012
C2×#168399662
C2×#168399652
C2×#168399262
C2×#168399252
C2×#168399232
C2×#168398422
C2×#168398252
C2×C61×#4522
C2×#328361