Finite Group Databasebeta

← C2×#21457826 #30556716

Subgroups — C2×#21457826 #30556716

Order 15616.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic, complemented
3#21457826C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840085C211yesmaximal, characteristic, complemented
6C2×#16840075C211yesmaximal, characteristic, complemented
7C2×#16840067C211yesmaximal, characteristic, complemented
8C2×#16840015C211yesmaximal, characteristic, complemented
9C2×#16839997C211yesmaximal, characteristic, complemented
10C2×#16839956C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic, complemented
13C2×#16839865C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×D488C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840460—24no—
23#16840460C2218yescomplemented
24#16840431—24no—
25#16840431C2218yescomplemented
26C2×#14519773—21no—
27C2×#14519773C2211yescharacteristic
28C2×#14519772—21no—
29C2×#14519768C2211yescharacteristic
30C2×#14519762—21no—
31C2×#14519752C2211yescharacteristic
32C2×#14519751—21no—
33C2×#14519751—21no—
34C2×#14519751C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519748—21no—
37C2×#14519748C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×#14519739C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C4×C22⋊D61—21no—
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×#14519735C2211yescharacteristic
44#16840125C2218yescomplemented
45#16840085C2218yescomplemented
46#16840075C2218yescomplemented
47#16840067C2218yescomplemented
48#16840015C2218yescomplemented
49#16839997C2218yescomplemented
50#16839956C2218yescomplemented
51#16839910C2218yescomplemented
52#16839907C2218yescomplemented
53#16839865C2218yescomplemented
54#16839831C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59#16839757C2218yescomplemented
60C2×#14519701C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61D411yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×#11758201—24no—
95C2×#11758201C2314yes—
96C2×D488—42no—
97C2×D488C2314yes—
98C2×#11758199—42no—
99C2×#11758199C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C2×C8×D61—42no—
103C2×C8×D61C2314yes—
104#14519773—28no—
105#14519773—22no—
106#14519773C2314yes—
107#14519772—28no—
108#14519768—22no—
109#14519768C2314yes—
110#14519762—28no—
111#14519752—22no—
112#14519752C2314yes—
113#14519751—22no—
114#14519751—22no—
115#14519751—28no—
116#14519751—28no—
117#14519751C2314yes—
118#14519751C2314yes—
119#14519748—22no—
120#14519748—28no—
121#14519748C2314yes—
122Q8×Dic61—22no—
123Q8×Dic61C2314yes—
124#14519739—22no—
125#14519739C2314yes—
126C4×C22⋊D61—28no—
127C4×C22⋊D61—28no—
128C4×C22⋊D61D414yes—
129C4×C22⋊D61C2314yes—
130#14519735—22no—
131#14519735C2314yes—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61D411yescharacteristic
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519710C2314yes—
151#14519709C2314yes—
152#14519706C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519687C2314yes—
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×M16×C61—42no—
173C2×M16×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C2×C4⋊C4×C61—22no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2314yes—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181#103×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61C2×D411yescharacteristic
190#41×C61—28no—
191#41×C61—44no—
192#41×C61—48no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61#4114yes—
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—44no—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—24no—
210C22×C4×C61—44no—
211C22×C4×C61—82no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61—82no—
227C2×C22⋊D61C2×D414yes—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758226—28no—
234#11758226—44no—
235#11758226—48no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—24no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—24no—
244C2×D244—44no—
245C2×D244—82no—
246C2×D244C2412yes—
247C2×D244C2412yes—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—44no—
253C2×C4×D61—82no—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2412yes—
256M16×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61C2412yes—
260C2×C8×C61C2412yes—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C22⋊Dic61—24no—
267C22⋊Dic61C2×D414yes—
268#11758201—28no—
269#11758199—44no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198C2×D414yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—24no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196C2×D414yes—
284C4×Dic61—24no—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418C2412yes—
291C2×#92418C2412yes—
292D488—44no—
293C8×D61—44no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61C22×D412yes—
315Q8×C61—24no—
316Q8×C61—22no—
317Q8×C61C2×#4114yes—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—48no—
321D4×C61—42no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—24no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—48no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—84no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4112yes—
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61C2511yescharacteristic
339C22⋊D61—44no—
340C22⋊D61—48no—
341C22⋊D61—48no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C22⋊D61—84no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355D244—22no—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—48no—
360D244—42no—
361D244—42no—
362D244—84no—
363C4×D61—24no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—48no—
367C4×D61—84no—
368C8×C61—22no—
369C8×C61—22no—
370#92418—22no—
371#92418—22no—
372C2×#3309—611nomaximal, Sylow
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—44no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—84no—
381C22×C61#54612yes—
382C22×C61#57512yes—
383C22×C61#57612yes—
384C22×C61C23×D411yescharacteristic
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—44no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—84no—
396C2×D61—84no—
397C4×C61—24no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61#54612yes—
402C4×C61C22×#4111yescharacteristic
403C4×C61C2×H(5,𝔽2)11yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—42no—
408Dic61—42no—
409C2×#553—611no—
410C2×#550—611no—
411#3309—6116no—
412C2×#490—611no—
413C2×#482—611no—
414C2×#480—611no—
415C2×#479—611no—
416C2×#469—611no—
417C2×#466—611no—
418C2×#459—611no—
419C2×#449—611no—
420C2×#449—611no—
421C2×#440—611no—
422C2×#435—611no—
423C2×#417D6111yescharacteristic, complemented
424C2×#416—611no—
425C2×C61—42no—
426C2×C61—82no—
427C2×C61#330914yescomplemented
428C2×C61C2×#54611yescharacteristic
429C2×C61C2×#57511yescharacteristic
430C2×C61C2×#57611yescharacteristic
431D61—42no—
432D61—82no—
433D61—82no—
434C22×#41—611no—
435C22×#41C2×D6111yescharacteristic
436C22×SD16—611no—
437C22×D8—611no—
438C22×D8—611no—
439C22×M16C2×D6111yescharacteristic
440C23×C8—611no—
441#553—618no—
442#553—1224no—
443#550—618no—
444#550—1224no—
445C2×#127—611no—
446C2×#127—1221no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#123—1221no—
450C2×#121—611no—
451C2×#121—611no—
452C2×#121—611no—
453C2×#121—611no—
454C2×#121—1221no—
455C2×#121—1221no—
456C2×#121—1221no—
457C2×C4×Q8—611no—
458C2×C4×D4—611no—
459C2×C4×D4—611no—
460C2×C4×D4—1221no—
461C2×C4×D4—1221no—
462C2×#117—611no—
463C22×C4⋊C4C2×D6111yescharacteristic
464#490—618no—
465#482—618no—
466#480—618no—
467#479—618no—
468#469—618no—
469#466—618no—
470#459—618no—
471#449—618no—
472#449—618no—
473#440—618no—
474#435—618no—
475C2×#107—611no—
476C2×#107—611no—
477C2×#106—611no—
478C2×C4⋊C8—611no—
479#417C2×D6118yescomplemented
480#416—618no—
481C2×#103—611no—
482C2×#103C2×D6111yescharacteristic
483C2×#103C2×D6111yescharacteristic
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102C2×D6111yescharacteristic
490C2×#102C2×D6111yescharacteristic
491C2×C22⋊C8—611no—
492C2×C22⋊C8—611no—
493C2×#97—611no—
494C61C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41—614no—
499C2×#41—1222no—
500C2×#41—1224no—
501C2×#41—2442no—
502C2×#41C22×D6114yes—
503C22×Q8C22×D6111yescharacteristic
504C22×D4—21no—
505C22×D4—611no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—1221no—
515C22×D4C22×D6111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—611no—
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522C2×SD16—614no—
523C2×SD16—1224no—
524C2×D8—614no—
525C2×D8—614no—
526C2×D8—2442no—
527C2×D8—2442no—
528C2×M16—42no—
529C2×M16C22×D6114yes—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—614no—
533C22×C8—2442no—
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#127—614no—
537#127—1222no—
538#127—1228no—
539#126—1228no—
540#125—614no—
541#125—1222no—
542#123—1228no—
543#121—614no—
544#121—614no—
545#121—614no—
546#121—614no—
547#121—1228no—
548#121—1228no—
549#121—1222no—
550#121—1228no—
551#121—1222no—
552#121—1222no—
553#121—1222no—
554C4×Q8—614no—
555C4×Q8—1222no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—614no—
559C4×D4—1222no—
560C4×D4—1228no—
561C4×D4—1228no—
562#117—614no—
563#117—1222no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C4⋊C4C22×D6114yes—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C42—611no—
584C2×C42—1221no—
585C2×C42—1221no—
586#107—614no—
587#107—614no—
588#106—614no—
589C4⋊C8—614no—
590#103—614no—
591#103C22×D6114yes—
592#103C22×D6114yes—
593#102—614no—
594#102—614no—
595#102—614no—
596#102—614no—
597#102—614no—
598#102C22×D6114yes—
599#102C22×D6114yes—
600C22⋊C8—614no—
601C22⋊C8—614no—
602#97—614no—
603C24—21no—
604C24—611no—
605C24—1221no—
606C24—1221no—
607C24D4×D6111yescharacteristic
608#41—28no—
609#41—44no—
610#41—48no—
611#41—1228no—
612#41—2444no—
613#41—2448no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1175822214yes—
617C2×Q8C23×D6112yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—614no—
624C2×D4—612no—
625C2×D4—612no—
626C2×D4—1224no—
627C2×D4—1224no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1222no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—4882no—
640C2×D4—4882no—
641C2×D4—4882no—
642C2×D4—4882no—
643C2×D4—2444no—
644C2×D4—2442no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4C23×D6112yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—4882no—
669C22×C4—2444no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—1228no—
675D8—2444no—
676D8—2444no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—612no—
681C2×C8—612no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—2444no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—614no—
691C4⋊C4—612no—
692C4⋊C4—612no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4C23×D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—614no—
701C22⋊C4—614no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C42—612no—
709C42—612no—
710C42—1224no—
711C42—1224no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—612no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—2442no—
726C23—2442no—
727C23—2442no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23C2×D4×D6112yes—
732C23C2×D4×D6111yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1175822214yes—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—42no—
740D4—1222no—
741D4—1222no—
742D4—1222no—
743D4—1222no—
744D4—4884no—
745D4—4884no—
746D4—4884no—
747D4—4884no—
748D4—2448no—
749D4—2444no—
750D4—2448no—
751D4—2448no—
752D4—2442no—
753D4—2442no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—2448no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4C2×D4×D6112yes—
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4C2×#1175822212yes—
784C2×C4#1451982212yes—
785C2×C4C24×D6111yescharacteristic
786C8—22no—
787C8—22no—
788C8—1222no—
789C8—1222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—84no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—4884no—
802C22—4884no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2444no—
810C22#1684040212yes—
811C22#1684056112yes—
812C22#1684056612yes—
813C22C22×D4×D6111yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—1222no—
819C4—1222no—
820C4—1222no—
821C4—2442no—
822C4—2442no—
823C4#1684040212yes—
824C4C22×#1175822211yescharacteristic
825C4C2×#1451982211yescharacteristic
826C2—42no—
827C2—82no—
828C2—4882no—
829C2—4882no—
830C2—2442no—
831C2#2145782614yesdirect product factor
832C2C2×#1684040211yescharacteristic
833C2C2×#1684056111yescharacteristic
834C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
hypercenterC2×#417D61
hypocenterC61C2×#3309
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840460C2semidirect
2. C2×#16840431C2semidirect
3. #21457826C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840085C2semidirect
6. C2×#16840075C2semidirect
7. C2×#16840067C2semidirect
8. C2×#16840015C2semidirect
9. C2×#16839997C2semidirect
10. C2×#16839956C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839907C2semidirect
13. C2×#16839865C2semidirect
14. C2×#16839831C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#417C2semidirect
23. #16840460C22semidirect
25. #16840431C22semidirect
44. #16840125C22semidirect
45. #16840085C22semidirect
46. #16840075C22semidirect
47. #16840067C22semidirect
48. #16840015C22semidirect
49. #16839997C22semidirect
50. #16839956C22semidirect
51. #16839910C22semidirect
52. #16839907C22semidirect
53. #16839865C22semidirect
54. #16839831C22semidirect
59. #16839757C22semidirect
72. C61×#417C22semidirect
423. C2×#417D61semidirect
427. C2×C61#3309semidirect
479. #417C2×D61semidirect
494. C61C2×#3309semidirect
831. C2#21457826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168404312
#214578262
C2×#168401252
C2×#168400852
C2×#168400752
C2×#168400672
C2×#168400152
C2×#168399972
C2×#168399562
C2×#168399102
C2×#168399072
C2×#168398652
C2×#168398312
C2×#168397572
C2×C61×#4172
C2×#330961