Finite Group Databasebeta

← C2×#21456878 #30551382

Subgroups — C2×#21456878 #30551382

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840365C211yesmaximal, characteristic, complemented
2C2×#16840333C211yesmaximal, characteristic, complemented
3#21456878C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840129C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839976C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839966C211yesmaximal, characteristic, complemented
11C2×#16839965C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic, complemented
13C2×#16839903C211yesmaximal, characteristic, complemented
14C2×#16839900C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840365—24no—
25#16840365C2218yescomplemented
26#16840333—24no—
27#16840333C2218yescomplemented
28C2×#14519775C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31C2×#14519768C2211yescharacteristic
32C2×#14519764C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519761—21no—
35C2×#14519759—21no—
36C2×#14519758—21no—
37C2×#14519758—21no—
38C2×#14519756—21no—
39C2×#14519756—21no—
40C2×#14519751C2211yescharacteristic
41C2×#14519749—21no—
42C2×#14519748—21no—
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519736C2211yescharacteristic
46#16840150C2218yescomplemented
47#16840133C2218yescomplemented
48#16840129C2218yescomplemented
49#16840115C2218yescomplemented
50#16839976C2218yescomplemented
51#16839975C2218yescomplemented
52#16839966C2218yescomplemented
53#16839965C2218yescomplemented
54#16839907C2218yescomplemented
55#16839903C2218yescomplemented
56#16839900C2218yescomplemented
57#16839820C2218yescomplemented
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—22no—
79C22×Dic122—42no—
80C22×Dic122—42no—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2314yes—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61—21no—
89C23×Dic61—21no—
90C22×C4×D61—21no—
91C2×#11758190—42no—
92C2×#11758190—42no—
93C2×#11758190C2314yes—
94C2×#11758190C2314yes—
95C2×#11758200—42no—
96C2×#11758200—42no—
97C2×#11758200C2314yes—
98C2×#11758200C2314yes—
99C2×#11758201—42no—
100C2×#11758201C2314yes—
101C2×#11758199—42no—
102C2×#11758199C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519775—22no—
106#14519775—22no—
107#14519775C2314yes—
108#14519775C2314yes—
109#14519773—22no—
110#14519773C2314yes—
111#14519768—22no—
112#14519768C2314yes—
113#14519764—22no—
114#14519764—22no—
115#14519764C2314yes—
116#14519764C2314yes—
117#14519761—28no—
118#14519759—28no—
119#14519758—28no—
120#14519758—28no—
121#14519756—28no—
122#14519756—28no—
123#14519751—22no—
124#14519751C2314yes—
125#14519749—28no—
126#14519748—28no—
127D4×Dic61—22no—
128D4×Dic61C2314yes—
129#14519739—22no—
130#14519739C2314yes—
131#14519736D414yes—
132#14519736C2314yes—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61D411yescharacteristic
135C2×C4⋊Dic61D411yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61D411yescharacteristic
148C2×C22⋊Dic61D411yescharacteristic
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519706C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519698C2314yes—
161C22⋊#92418C2314yes—
162#14519687C2314yes—
163C8×Dic61C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C2×SD16×C61—42no—
176C2×SD16×C61C2314yes—
177C2×D8×C61—42no—
178C2×D8×C61C2314yes—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—48no—
195C2×Q8×C61—21no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61C2412yes—
199C2×D4×C61—24no—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—44no—
208C2×D4×C61—82no—
209C2×D4×C61C2412yes—
210C2×D4×C61C2412yes—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—44no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61—82no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—24no—
231C22×Dic61—24no—
232C22×Dic61—44no—
233C22×Dic61—82no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—21no—
241C2×D244C2412yes—
242C2×C4×D61—24no—
243C2×C4×D61—82no—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—24no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—44no—
252C2×Dic122—44no—
253C2×Dic122—44no—
254C2×Dic122—48no—
255C2×Dic122C2412yes—
256C2×Dic122C2412yes—
257SD16×C61—44no—
258D8×C61—44no—
259C2×C8×C61—22no—
260C2×C8×C61—22no—
261C2×C8×C61C2412yes—
262C2×C8×C61C2412yes—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61C2×D414yes—
272C22⋊Dic61C2×D414yes—
273#11758201—44no—
274#11758200—44no—
275#11758200—44no—
276#11758199—44no—
277#11758198—24no—
278#11758198—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61C2×D414yes—
282C4⋊Dic61C2×D414yes—
283C4⋊Dic61C2412yes—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289C4×Dic61C2×D412yes—
290C4×Dic61C2×D412yes—
291C4×Dic61C2412yes—
292C4×Dic61C2412yes—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297#11758190—44no—
298#11758190—44no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61C22×D412yes—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—42no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—48no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—84no—
327C2×C4×C61—22no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—48no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61H(5,𝔽2)12yes—
340C2×C4×C61C2511yescharacteristic
341C22⋊D61—84no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—48no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—84no—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360D244—22no—
361D244—22no—
362D244—42no—
363C4×D61—84no—
364Dic122—22no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368Dic122—48no—
369Dic122—42no—
370Dic122—42no—
371C8×C61—22no—
372C8×C61—22no—
373#92418—22no—
374#92418—22no—
375C2×#3221—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—44no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—84no—
387C22×C61—84no—
388C22×C61#53512yes—
389C22×C61#57712yes—
390C22×C61#57712yes—
391C22×C61C23×D411yescharacteristic
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—84no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—42no—
399C4×C61#53512yes—
400C4×C61C2×H(5,𝔽2)11yescharacteristic
401C4×C61C2×H(5,𝔽2)11yescharacteristic
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409C2×#540—611no—
410C2×#536—611no—
411#3221—6116no—
412C2×#496—611no—
413C2×#492—611no—
414C2×#491—611no—
415C2×#488—611no—
416C2×#463—611no—
417C2×#463—611no—
418C2×#461—611no—
419C2×#461—611no—
420C2×#449—611no—
421C2×#449D6111yescharacteristic, complemented
422C2×#448—611no—
423C2×#448—611no—
424C2×#433—611no—
425C2×C61—42no—
426C2×C61—82no—
427C2×C61—82no—
428C2×C61#322114yescomplemented
429C2×C61C2×#53511yescharacteristic
430C2×C61C2×#57711yescharacteristic
431C2×C61C2×#57711yescharacteristic
432D61—82no—
433C22×#41C2×D6111yescharacteristic
434C23×Q8—611no—
435C22×SD16—611no—
436C22×SD16—611no—
437C22×SD16—611no—
438C22×SD16—611no—
439C22×SD16—611no—
440C22×SD16C2×D6111yescharacteristic
441C22×D8—611no—
442C22×D8C2×D6111yescharacteristic
443#540—618no—
444#540—1224no—
445#536—618no—
446#536—1224no—
447C2×C4⋊Q8—611no—
448C2×C4⋊Q8—611no—
449C2×#127—611no—
450C2×#125—611no—
451C2×#124—611no—
452C2×#124—611no—
453C2×#123—1221no—
454C2×#123—1221no—
455C2×#123—1221no—
456C2×#123—1221no—
457C2×C22⋊Q8—1221no—
458C2×C22⋊Q8—1221no—
459C2×#121—611no—
460C2×#121—1221no—
461C2×#121—1221no—
462C2×#121C2×D6111yescharacteristic
463C2×C4×D4—611no—
464C2×C4×D4—611no—
465C2×#117—611no—
466#496—618no—
467#492—618no—
468#491—618no—
469#488—618no—
470#463—618no—
471#463—618no—
472#461—618no—
473#461—618no—
474#449—618no—
475#449C2×D6118yescomplemented
476#448—618no—
477#448—618no—
478#433—618no—
479C2×C4⋊C8—611no—
480C2×C4⋊C8—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103C2×D6111yescharacteristic
487C2×#102—611no—
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8C2×D6111yescharacteristic
491C2×#97—611no—
492C2×C4×C8—611no—
493C61C2×#322111yescharacteristic, complemented, Sylow
494C2×#41—22no—
495C2×#41—42no—
496C2×#41—42no—
497C2×#41C22×D6114yes—
498C22×Q8—611no—
499C22×Q8—611no—
500C22×Q8—614no—
501C22×Q8—1221no—
502C22×Q8—1222no—
503C22×Q8—2442no—
504C22×Q8—2442no—
505C22×Q8C22×D6111yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—611no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4C22×D6111yescharacteristic
513C22×D4C22×D6111yescharacteristic
514C23×C4—21no—
515C23×C4—1221no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4C22×D6111yescharacteristic
519C2×SD16—42no—
520C2×SD16—614no—
521C2×SD16—614no—
522C2×SD16—614no—
523C2×SD16—614no—
524C2×SD16—614no—
525C2×SD16—2442no—
526C2×SD16—2442no—
527C2×SD16—2442no—
528C2×SD16—2442no—
529C2×SD16—2442no—
530C2×SD16C22×D6114yes—
531C2×D8—42no—
532C2×D8—614no—
533C2×D8—2442no—
534C2×D8C22×D6114yes—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539C4⋊Q8—614no—
540C4⋊Q8—614no—
541C4⋊Q8—1222no—
542C4⋊Q8—1222no—
543#127—614no—
544#127—1222no—
545#125—614no—
546#125—1222no—
547#124—614no—
548#124—614no—
549#124—1222no—
550#124—1222no—
551#123—1228no—
552#123—1228no—
553#123—1228no—
554#123—1228no—
555C22⋊Q8—1228no—
556C22⋊Q8—1228no—
557#121—22no—
558#121—614no—
559#121—1228no—
560#121—1228no—
561#121—1222no—
562#121C22×D6114yes—
563C4×D4—614no—
564C4×D4—614no—
565C4×D4—1222no—
566C4×D4—1222no—
567#117—614no—
568#117—614no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—611no—
590C2×C42—611no—
591C4⋊C8—614no—
592C4⋊C8—614no—
593#103—614no—
594#103—614no—
595#103—614no—
596#103—614no—
597#103—614no—
598#103C22×D6114yes—
599#102—614no—
600#102C22×D6114yes—
601C22⋊C8—614no—
602C22⋊C8C22×D6114yes—
603#97—614no—
604C4×C8—614no—
605C24—21no—
606C24—21no—
607C24—1221no—
608C24D4×D6111yescharacteristic
609#41—44no—
610#41—44no—
611#41—48no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—612no—
616C2×Q8—612no—
617C2×Q8—1224no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1222no—
621C2×Q8—1222no—
622C2×Q8—1222no—
623C2×Q8—1222no—
624C2×Q8—2444no—
625C2×Q8—2444no—
626C2×Q8—2444no—
627C2×Q8—2448no—
628C2×Q8C23×D6112yes—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—44no—
638C2×D4—82no—
639C2×D4—612no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1221no—
644C2×D4—1222no—
645C2×D4—1222no—
646C2×D4—4882no—
647C2×D4—4882no—
648C2×D4—4882no—
649C2×D4C23×D6112yes—
650C2×D4C23×D6112yes—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4882no—
668C22×C4—4882no—
669C22×C4—2444no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—44no—
675SD16—2444no—
676SD16—2444no—
677SD16—2444no—
678SD16—2444no—
679SD16—2444no—
680D8—44no—
681D8—2444no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—612no—
685C2×C8—612no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8C23×D6112yes—
689C2×C8C23×D6112yes—
690C4⋊C4—21no—
691C4⋊C4—614no—
692C4⋊C4—614no—
693C4⋊C4—612no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4—1224no—
700C4⋊C4—1221no—
701C4⋊C4C23×D6112yes—
702C22⋊C4—24no—
703C22⋊C4—614no—
704C22⋊C4—614no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C42—612no—
713C42—612no—
714C42—612no—
715C42—612no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—1222no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23C2×D4×D6112yes—
732C23C2×D4×D6111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—42no—
736Q8—1222no—
737Q8—1222no—
738Q8—1222no—
739Q8—1222no—
740Q8—2448no—
741Q8—2442no—
742Q8—2442no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—48no—
748D4—42no—
749D4—42no—
750D4—84no—
751D4—1222no—
752D4—1222no—
753D4—4884no—
754D4—4884no—
755D4—4884no—
756D4—2442no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4C2×D4×D6112yes—
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4#1451982212yes—
786C2×C4#1451982212yes—
787C2×C4C24×D6111yescharacteristic
788C8—22no—
789C8—22no—
790C8—1222no—
791C8—1222no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—84no—
804C22—4884no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22#1684032712yes—
809C22#1684056912yes—
810C22#1684057212yes—
811C22C22×D4×D6111yescharacteristic
812C4—22no—
813C4—42no—
814C4—42no—
815C4—1222no—
816C4—1222no—
817C4—1222no—
818C4—1222no—
819C4—2442no—
820C4—2442no—
821C4—2442no—
822C4#1684032712yes—
823C4C2×#1451982211yescharacteristic
824C4C2×#1451982211yescharacteristic
825C2—42no—
826C2—82no—
827C2—82no—
828C2—4882no—
829C2#2145687814yesdirect product factor
830C2C2×#1684032711yescharacteristic
831C2C2×#1684056911yescharacteristic
832C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3221
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. C2×#16840333C2semidirect
3. #21456878C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16840129C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839976C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839966C2semidirect
11. C2×#16839965C2semidirect
12. C2×#16839907C2semidirect
13. C2×#16839903C2semidirect
14. C2×#16839900C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#449C2semidirect
25. #16840365C22semidirect
27. #16840333C22semidirect
46. #16840150C22semidirect
47. #16840133C22semidirect
48. #16840129C22semidirect
49. #16840115C22semidirect
50. #16839976C22semidirect
51. #16839975C22semidirect
52. #16839966C22semidirect
53. #16839965C22semidirect
54. #16839907C22semidirect
55. #16839903C22semidirect
56. #16839900C22semidirect
57. #16839820C22semidirect
73. C61×#449C22semidirect
421. C2×#449D61semidirect
428. C2×C61#3221semidirect
475. #449C2×D61semidirect
493. C61C2×#3221semidirect
829. C2#21456878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403652
C2×#168403332
#214568782
C2×#168401502
C2×#168401332
C2×#168401292
C2×#168401152
C2×#168399762
C2×#168399752
C2×#168399662
C2×#168399652
C2×#168399072
C2×#168399032
C2×#168399002
C2×#168398202
C2×C61×#4492
C2×#322161