Finite Group Databasebeta

← C2×#21458840 #30560970

Subgroups — C2×#21458840 #30560970

Order 15616.

2250 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840484C211yesmaximal, characteristic, complemented
2C2×#16840433C211yesmaximal, characteristic, complemented
3#21458840C2116yesmaximal, direct product factor
4C2×#16840151C211yesmaximal, characteristic, complemented
5C2×#16840148C211yesmaximal, characteristic, complemented
6C2×#16840133C211yesmaximal, characteristic, complemented
7C2×#16839962C211yesmaximal, characteristic, complemented
8C2×#16839961C211yesmaximal, characteristic, complemented
9C2×#16839980C211yesmaximal, characteristic, complemented
10C2×#16839977C211yesmaximal, characteristic, complemented
11C2×#16839966C211yesmaximal, characteristic, complemented
12C2×#16839956C211yesmaximal, characteristic, complemented
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839861C211yesmaximal, characteristic, complemented
15C2×#16839844C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×D488C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26#16840484—24no—
27#16840484C2218yescomplemented
28#16840433—24no—
29#16840433C2218yescomplemented
30C2×#14519775C2211yescharacteristic
31C2×#14519774C2211yescharacteristic
32C2×#14519773C2211yescharacteristic
33C2×#14519773C2211yescharacteristic
34C2×#14519772—21no—
35C2×#14519771—21no—
36C2×#14519766C2211yescharacteristic
37C2×#14519765C2211yescharacteristic
38C2×#14519755—21no—
39C2×#14519751—21no—
40C2×#14519750—21no—
41C2×#14519750—21no—
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519739C2211yescharacteristic
47C2×#14519734—21no—
48#16840151C2218yescomplemented
49#16840148C2218yescomplemented
50#16840133C2218yescomplemented
51#16839980C2218yescomplemented
52#16839977C2218yescomplemented
53#16839966C2218yescomplemented
54#16839962C2218yescomplemented
55#16839961C2218yescomplemented
56#16839956C2218yescomplemented
57#16839890C2218yescomplemented
58#16839861C2218yescomplemented
59#16839844C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122D411yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×#11758190—24no—
94C2×#11758190—42no—
95C2×#11758190C2314yes—
96C2×#11758190C2314yes—
97C2×#11758200—42no—
98C2×#11758200C2314yes—
99C2×#11758201—42no—
100C2×#11758201—42no—
101C2×#11758201C2314yes—
102C2×#11758201C2314yes—
103C2×D488—24no—
104C2×D488—42no—
105C2×D488C2314yes—
106C2×D488C2314yes—
107C2×#11758199—42no—
108C2×#11758199C2314yes—
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111#14519775—22no—
112#14519775C2314yes—
113#14519774—22no—
114#14519774C2314yes—
115#14519773—22no—
116#14519773—22no—
117#14519773C2314yes—
118#14519773C2314yes—
119#14519772—28no—
120#14519771—28no—
121#14519766—22no—
122#14519766C2314yes—
123#14519765—22no—
124#14519765C2314yes—
125#14519755—28no—
126#14519751—28no—
127#14519750—28no—
128#14519750—28no—
129C4×Dic122D414yes—
130C4×Dic122C2314yes—
131#14519742—22no—
132#14519742C2314yes—
133#14519739—22no—
134#14519739—22no—
135#14519739—22no—
136#14519739C2314yes—
137#14519739C2314yes—
138#14519739C2314yes—
139#14519734—28no—
140C2×C4⋊Dic61D411yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196—21no—
144C2×#11758196D411yescharacteristic
145C2×#11758196D411yescharacteristic
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155C2×C4×Dic61C2311yescharacteristic
156C4⋊#92418C2314yes—
157#14519706C2314yes—
158#14519706C2314yes—
159#14519700C2314yes—
160#14519697C2314yes—
161#14519697C2314yes—
162#14519697C2314yes—
163#14519687C2314yes—
164C8×Dic61C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C2×SD16×C61—24no—
169C2×SD16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C4×Q8×C61—22no—
173C4×Q8×C61C2314yes—
174C4×D4×C61—22no—
175C4×D4×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182#107×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185#97×C61C2314yes—
186C24×C61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—44no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—82no—
213C2×C22⋊D61—82no—
214C22×Dic61—21no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758222—432no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—24no—
231C2×D244—44no—
232C2×D244—82no—
233C2×D244C2412yes—
234C2×D244C2412yes—
235C2×D244C2412yes—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×Dic122—24no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—21no—
246C2×Dic122C2×D414yes—
247C2×Dic122C2412yes—
248SD16×C61—28no—
249C2×C8×C61—22no—
250C2×C8×C61#4114yescomplemented
251C2×C8×C61C2412yes—
252C2×C8×C61C2412yes—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C42×C61—24no—
260C42×C61C2×D412yes—
261C42×C61C2412yes—
262#11758201—44no—
263#11758201—44no—
264#11758200—44no—
265#11758199—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273C4⋊Dic61C2×D414yes—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196C2×D414yes—
278#11758196C2×D414yes—
279C4×Dic61—24no—
280C4×Dic61C2×D412yes—
281C4×Dic61C2×D412yes—
282C4×Dic61C2412yes—
283C4×Dic61C2412yes—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288D488—28no—
289D488—44no—
290#11758190—28no—
291#11758190—44no—
292C23×C61—22no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—42no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—42no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—48no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4112yes—
328C2×C4×C61H(5,𝔽2)12yes—
329C2×C4×C61C2511yescharacteristic
330C22⋊D61—48no—
331C22⋊D61—48no—
332C22⋊D61—84no—
333C22⋊D61—84no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—42no—
339C2×Dic61AGL(1,ℤ/8)14yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—22no—
348D244—22no—
349D244—22no—
350D244—48no—
351D244—42no—
352D244—42no—
353D244—42no—
354D244—84no—
355C4×D61—48no—
356C4×D61—48no—
357C4×D61—48no—
358Dic122—28no—
359Dic122—22no—
360Dic122—22no—
361Dic122—42no—
362C8×C61—22no—
363C8×C61C2×#4114yescomplemented
364#92418—22no—
365#92418—22no—
366C2×#3397—611nomaximal, Sylow
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—84no—
371C22×C61#55012yes—
372C22×C61C2×AGL(1,ℤ/8)12yes—
373C22×C61#57712yes—
374C22×C61C23×D411yescharacteristic
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C2×D61—84no—
386C2×D61—84no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#55012yes—
393C4×C61C22×#4111yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—22no—
398Dic61—42no—
399Dic61C2×AGL(1,ℤ/8)14yes—
400C2×#556—611no—
401C2×#550—611no—
402#3397—6116no—
403C2×#496—611no—
404C2×#496—611no—
405C2×#492—611no—
406C2×#460—611no—
407C2×#460—611no—
408C2×#463—611no—
409C2×#463—611no—
410C2×#461—611no—
411C2×#459—611no—
412C2×#446—611no—
413C2×#440—611no—
414C2×#440D6111yescharacteristic, complemented
415C2×C4×D8—611no—
416C2×C61—82no—
417C2×C61#339714yescomplemented
418C2×C61C2×#55011yescharacteristic
419C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
420C2×C61C2×#57711yescharacteristic
421D61—82no—
422D61—82no—
423D61—82no—
424C22×#41—1221no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16—611no—
430C22×SD16C2×D6111yescharacteristic
431C22×D8—611no—
432C22×D8—611no—
433C22×D8—611no—
434#556—618no—
435#556—1224no—
436#550—618no—
437#550—1224no—
438C2×C4⋊Q8—611no—
439C2×#127—611no—
440C2×#127—611no—
441C2×#127—611no—
442C2×#126—1221no—
443C2×#126—1221no—
444C2×#124—611no—
445C2×#124—611no—
446C2×C22⋊Q8—1221no—
447C2×#121—1221no—
448C2×#121—1221no—
449C2×#121—1221no—
450C2×C4×Q8—611no—
451C2×C4×Q8—611no—
452C2×C4×Q8C2×D6111yescharacteristic
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4C2×D6111yescharacteristic
457C2×#117—1221no—
458#496—618no—
459#496—618no—
460#492—618no—
461#463—618no—
462#463—618no—
463#461—618no—
464#460—618no—
465#460—618no—
466#459—618no—
467#446—618no—
468#440—618no—
469#440C2×D6118yescomplemented
470C4×D8—618no—
471C2×#107C2×D6111yescharacteristic
472C2×C4⋊C8—611no—
473C2×C4⋊C8—611no—
474C2×C4⋊C8—611no—
475C2×#103—611no—
476C2×#103C2×D6111yescharacteristic
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102C2×D6111yescharacteristic
481C2×#97—611no—
482C2×#97C2×D6111yescharacteristic
483C2×C4×C8—611no—
484C61C2×#339711yescharacteristic, complemented, Sylow
485C2×#41—1228no—
486C2×#41—2448no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8C22×D6111yescharacteristic
490C22×D4—611no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—1221no—
494C22×D4—1221no—
495C22×D4—1221no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C23×C4—21no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×SD16—24no—
505C2×SD16—614no—
506C2×SD16—614no—
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—614no—
510C2×SD16—1224no—
511C2×SD16—2442no—
512C2×SD16—2442no—
513C2×SD16—2442no—
514C2×SD16—2442no—
515C2×SD16C22×D6114yes—
516C2×D8—614no—
517C2×D8—614no—
518C2×D8—614no—
519C2×D8—1224no—
520C2×D8—2442no—
521C2×D8—2442no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528#127—614no—
529#127—614no—
530#127—614no—
531#127—1222no—
532#127—1222no—
533#127—1222no—
534#126—1228no—
535#126—1228no—
536#124—614no—
537#124—614no—
538#124—1222no—
539#124—1222no—
540C22⋊Q8—1228no—
541#121—1228no—
542#121—1228no—
543#121—1228no—
544C4×Q8—22no—
545C4×Q8—614no—
546C4×Q8—614no—
547C4×Q8—614no—
548C4×Q8—1222no—
549C4×Q8C22×D6114yes—
550C4×D4—22no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—1222no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4C22×D6114yes—
558#117—1228no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C42—21no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581#107C22×D6114yes—
582C4⋊C8—614no—
583C4⋊C8—614no—
584C4⋊C8—614no—
585#103—614no—
586#103C22×D6114yes—
587#102—614no—
588#102—614no—
589#102—614no—
590#102C22×D6114yes—
591#97—614no—
592#97C22×D6114yes—
593C4×C8—614no—
594C24—21no—
595C24—1221no—
596C24—1221no—
597C24—1221no—
598#41—24432no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—614no—
603C2×Q8—612no—
604C2×Q8—1224no—
605C2×Q8—1221no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8C23×D6112yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—612no—
613C2×D4—612no—
614C2×D4—612no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1224no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1222no—
627C2×D4—1222no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—4882no—
631C2×D4—4882no—
632C2×D4—4882no—
633C2×D4—2444no—
634C2×D4—2444no—
635C2×D4—2444no—
636C2×D4C23×D6112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1221no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656SD16—28no—
657SD16—1228no—
658SD16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662D8—1228no—
663D8—2444no—
664D8—2444no—
665C2×C8—22no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8#1175822214yescomplemented
671C2×C8C23×D6112yes—
672C2×C8C23×D6112yes—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—614no—
677C4⋊C4—614no—
678C4⋊C4—614no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4C23×D6112yes—
683C4⋊C4C23×D6112yes—
684C22⋊C4—24no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—24no—
693C42—612no—
694C42—612no—
695C42—612no—
696C42—612no—
697C42—1224no—
698C42D4×D6112yes—
699C42C23×D6112yes—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—1228no—
721Q8—1222no—
722Q8—1222no—
723Q8—2442no—
724D4—22no—
725D4—22no—
726D4—42no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1222no—
732D4—1222no—
733D4—4884no—
734D4—4884no—
735D4—4884no—
736D4—2448no—
737D4—2448no—
738D4—2448no—
739D4—2442no—
740D4—2442no—
741D4—2442no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—614no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—2448no—
761C2×C4—2448no—
762C2×C4—2448no—
763C2×C4—2442no—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6112yes—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×#1175822212yes—
768C2×C4#1451982312yes—
769C2×C4C24×D6111yescharacteristic
770C8—22no—
771C8—1222no—
772C8—1222no—
773C8C2×#1175822214yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—4884no—
779C22—4884no—
780C22—4884no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22#1684043312yes—
791C22AGL(1,ℤ/8)×D6112yes—
792C22#1684057112yes—
793C22C22×D4×D6111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—614no—
800C4—1222no—
801C4—1222no—
802C4—1222no—
803C4—2442no—
804C4#1684043312yes—
805C4C22×#1175822211yescharacteristic
806C4C2×#1451982311yescharacteristic
807C2—82no—
808C2—4882no—
809C2—4882no—
810C2—4882no—
811C2#2145884014yesdirect product factor
812C2C2×#1684043311yescharacteristic
813C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
814C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
hypercenterC2×#440D61
hypocenterC61C2×#3397
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. C2×#16840484C2semidirect
2. C2×#16840433C2semidirect
3. #21458840C2direct (N × H)
4. C2×#16840151C2semidirect
5. C2×#16840148C2semidirect
6. C2×#16840133C2semidirect
7. C2×#16839962C2semidirect
8. C2×#16839961C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839977C2semidirect
11. C2×#16839966C2semidirect
12. C2×#16839956C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839861C2semidirect
15. C2×#16839844C2semidirect
16. C2×C61×#440C2semidirect
27. #16840484C22semidirect
29. #16840433C22semidirect
48. #16840151C22semidirect
49. #16840148C22semidirect
50. #16840133C22semidirect
51. #16839980C22semidirect
52. #16839977C22semidirect
53. #16839966C22semidirect
54. #16839962C22semidirect
55. #16839961C22semidirect
56. #16839956C22semidirect
57. #16839890C22semidirect
58. #16839861C22semidirect
59. #16839844C22semidirect
72. C61×#440C22semidirect
250. C2×C8×C61#41semidirect
363. C8×C61C2×#41semidirect
414. C2×#440D61semidirect
417. C2×C61#3397semidirect
469. #440C2×D61semidirect
484. C61C2×#3397semidirect
670. C2×C8#11758222semidirect
773. C8C2×#11758222semidirect
811. C2#21458840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404842
C2×#168404332
#214588402
C2×#168401512
C2×#168401482
C2×#168401332
C2×#168399622
C2×#168399612
C2×#168399802
C2×#168399772
C2×#168399662
C2×#168399562
C2×#168398902
C2×#168398612
C2×#168398442
C2×C61×#4402
C2×#339761