Finite Group Databasebeta

← C2×#21456773 #30551221

Subgroups — C2×#21456773 #30551221

Order 15616.

2186 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#16840308C211yesmaximal, characteristic
3#21456773C2116yesmaximal, direct product factor
4C2×#16840140C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840111C211yesmaximal, characteristic, complemented
7C2×#16840107C211yesmaximal, characteristic, complemented
8C2×#16839987C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839983C211yesmaximal, characteristic, complemented
11C2×#16839982C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839924C211yesmaximal, characteristic, complemented
14C2×#16839922C211yesmaximal, characteristic, complemented
15C2×#16839812C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24#16840314—24no—
25#16840314C2218yescomplemented
26#16840308—24no—
27#16840308C2218yes—
28C2×#14519776C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519773C2211yescharacteristic
32C2×#14519767—21no—
33C2×#14519766C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519754—21no—
37C2×#14519749—21no—
38C2×#14519749—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×#14519742—21no—
41C2×#14519742C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43C2×C4×C22⋊D61—21no—
44C2×#14519733—21no—
45C22×C4×Dic61C2211yescharacteristic
46#16840140C2218yescomplemented
47#16840133C2218yescomplemented
48#16840111C2218yescomplemented
49#16840107C2218yescomplemented
50#16839987C2218yescomplemented
51#16839986C2218yescomplemented
52#16839983C2218yescomplemented
53#16839982C2218yescomplemented
54#16839926C2218yescomplemented
55#16839924C2218yescomplemented
56#16839922C2218yescomplemented
57#16839812C2218yescomplemented
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61D411yescharacteristic
89C23×Dic61D411yescharacteristic
90C22×C4×D61—21no—
91C2×Dic244—42no—
92C2×Dic244C2314yes—
93C2×#11758202—42no—
94C2×#11758202—42no—
95C2×#11758202C2314yes—
96C2×#11758202C2314yes—
97C2×#11758190—42no—
98C2×#11758190C2314yes—
99C2×#11758200—42no—
100C2×#11758200C2314yes—
101C2×#11758201—42no—
102C2×#11758201C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519776—22no—
106#14519776C2314yes—
107#14519775—22no—
108#14519775—22no—
109#14519775C2314yes—
110#14519775C2314yes—
111#14519773—22no—
112#14519773C2314yes—
113#14519767—28no—
114#14519766—22no—
115#14519766C2314yes—
116#14519764—22no—
117#14519764C2314yes—
118#14519756—22no—
119#14519756C2314yes—
120#14519754—28no—
121#14519749—28no—
122#14519749—28no—
123Q8×Dic61—22no—
124Q8×Dic61C2314yes—
125#14519742—28no—
126#14519742—22no—
127#14519742C2314yes—
128C4×C22⋊D61—28no—
129C4×C22⋊D61—28no—
130#14519733—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C2×C4×Dic61D414yes—
150C2×C4×Dic61C2311yescharacteristic
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2314yes—
153#14519706C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161C22⋊#92418C2314yes—
162C8×Dic61C2314yes—
163C8×Dic61C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×Q8×C61C2311yescharacteristic
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C23×C4×C61—21no—
173C23×C4×C61C2311yescharacteristic
174C2×Q16×C61—42no—
175C2×Q16×C61C2314yes—
176C2×SD16×C61—42no—
177C2×SD16×C61C2314yes—
178C22×C8×C61C2311yescharacteristic
179C22×C8×C61C2311yescharacteristic
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61C2314yes—
182C2×C4⋊C4×C61—21no—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191#41×C61—44no—
192#41×C61—44no—
193#41×C61—48no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×Q8×C61C2412yes—
202C2×D4×C61—24no—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—44no—
207C2×D4×C61C2412yes—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—44no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—44no—
225C22×Dic61—24no—
226C22×Dic61—24no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D414yes—
233C22×Dic61C2×D414yes—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758222—44no—
237#11758222—44no—
238#11758222—48no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—21no—
242C2×D244C2412yes—
243C2×C4×D61—24no—
244C2×C4×D61—44no—
245C2×Dic122—22no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—22no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—24no—
252C2×Dic122—44no—
253C2×Dic122C2412yes—
254C2×Dic122C2412yes—
255Q16×C61—44no—
256SD16×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61C2412yes—
260C2×C8×C61C2412yes—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268#11758202—44no—
269#11758202—44no—
270#11758201—44no—
271#11758200—44no—
272#11758198—24no—
273#11758198—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61C2412yes—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284C4×Dic61—24no—
285C4×Dic61—24no—
286C4×Dic61C2×D414yes—
287C4×Dic61C2×D414yes—
288C4×Dic61C2×D412yes—
289C4×Dic61C2×D412yes—
290C4×Dic61C2412yes—
291C4×Dic61C2412yes—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296Dic244—44no—
297#11758190—44no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—42no—
316Q8×C61—42no—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—48no—
320D4×C61—42no—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61H(5,𝔽2)12yes—
335C2×C4×C61H(5,𝔽2)12yes—
336C2×C4×C61C2511yescharacteristic
337C22⋊D61—48no—
338C22⋊D61—48no—
339C22⋊D61—48no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—28no—
343C2×Dic61—28no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61#13514yes—
351C2×Dic61#13714yes—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356D244—22no—
357D244—22no—
358D244—42no—
359C4×D61—48no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—42no—
365Dic122—42no—
366Dic122—48no—
367C8×C61—22no—
368C8×C61—22no—
369#92418—22no—
370#92418—22no—
371C2×#3210—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—44no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—84no—
380C22×C61#53512yes—
381C22×C61C2×#13512yes—
382C22×C61C2×#13712yes—
383C22×C61C23×D411yescharacteristic
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—84no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#53512yes—
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400Dic61C2×#13514yes—
401Dic61C2×#13714yes—
402C2×#533—611no—
403C2×#532—611no—
404#3210—6116no—
405C2×#494—611no—
406C2×#492—611no—
407C2×#487—611no—
408C2×#486—611no—
409C2×#464—611no—
410C2×#464—611no—
411C2×#464—611no—
412C2×#464—611no—
413C2×#452—611no—
414C2×#452—611no—
415C2×#452—611no—
416C2×#452D6111yescharacteristic, complemented
417C2×#431—611no—
418C2×C61—42no—
419C2×C61—82no—
420C2×C61#321014yescomplemented
421C2×C61C2×#53511yescharacteristic
422C2×C61C22×#13511yescharacteristic
423C2×C61C22×#13711yescharacteristic
424D61—82no—
425C22×#41—611no—
426C22×#41C2×D6111yescharacteristic
427C22×Q16—611no—
428C22×Q16—611no—
429C22×Q16—611no—
430C22×Q16C2×D6111yescharacteristic
431C22×SD16—611no—
432C22×SD16—611no—
433C22×SD16—611no—
434C22×SD16C2×D6111yescharacteristic
435#533—618no—
436#533—1224no—
437#532—618no—
438#532—1224no—
439C2×C4⋊Q8—611no—
440C2×C4⋊Q8—611no—
441C2×C4⋊Q8—611no—
442C2×#127—611no—
443C2×#125—1221no—
444C2×#124—611no—
445C2×#124—611no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8C2×D6111yescharacteristic
449C2×#121—1221no—
450C2×#121—1221no—
451C2×C4×Q8—611no—
452C2×C4×Q8—611no—
453C2×C4×Q8—1221no—
454C2×C4×D4—1221no—
455C2×C4×D4—1221no—
456C2×#117—1221no—
457C22×C42—611no—
458#494—618no—
459#492—618no—
460#487—618no—
461#486—618no—
462#464—618no—
463#464—618no—
464#464—618no—
465#464—618no—
466#452—618no—
467#452—618no—
468#452—618no—
469#452C2×D6118yescomplemented
470#431—618no—
471C2×C4⋊C8—611no—
472C2×C4⋊C8—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103C2×D6111yescharacteristic
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102C2×D6111yescharacteristic
481C2×C22⋊C8—611no—
482C2×C22⋊C8C2×D6111yescharacteristic
483C2×C4×C8—611no—
484C2×C4×C8—611no—
485C61C2×#321011yescharacteristic, complemented, Sylow
486C2×#41—22no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41—614no—
490C2×#41—1222no—
491C2×#41—2442no—
492C2×#41—2442no—
493C2×#41C22×D6114yes—
494C22×Q8—611no—
495C22×Q8—611no—
496C22×Q8—1221no—
497C22×Q8C22×D6111yescharacteristic
498C22×Q8C22×D6111yescharacteristic
499C22×D4—21no—
500C22×D4—611no—
501C22×D4—1221no—
502C22×D4—1221no—
503C22×D4—1221no—
504C22×D4C22×D6111yescharacteristic
505C23×C4—21no—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—1221no—
509C23×C4C22×D6111yescharacteristic
510C2×Q16—42no—
511C2×Q16—614no—
512C2×Q16—614no—
513C2×Q16—614no—
514C2×Q16—2442no—
515C2×Q16—2442no—
516C2×Q16—2442no—
517C2×Q16C22×D6114yes—
518C2×SD16—42no—
519C2×SD16—614no—
520C2×SD16—614no—
521C2×SD16—614no—
522C2×SD16—2442no—
523C2×SD16—2442no—
524C2×SD16—2442no—
525C2×SD16C22×D6114yes—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8C22×D6111yescharacteristic
529C22×C8C22×D6111yescharacteristic
530C4⋊Q8—614no—
531C4⋊Q8—614no—
532C4⋊Q8—614no—
533C4⋊Q8—1222no—
534C4⋊Q8—1222no—
535C4⋊Q8—1222no—
536#127—614no—
537#127—1222no—
538#125—1228no—
539#124—614no—
540#124—614no—
541#124—1222no—
542#124—1222no—
543C22⋊Q8—22no—
544C22⋊Q8—614no—
545C22⋊Q8—1228no—
546C22⋊Q8—1222no—
547C22⋊Q8C22×D6114yes—
548#121—1228no—
549#121—1228no—
550C4×Q8—614no—
551C4×Q8—614no—
552C4×Q8—1222no—
553C4×Q8—1228no—
554C4×Q8—1222no—
555C4×D4—1228no—
556C4×D4—1228no—
557#117—1228no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—614no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—614no—
581C2×C42—1221no—
582C2×C42—1221no—
583C4⋊C8—614no—
584C4⋊C8—614no—
585#103—614no—
586#103—614no—
587#103—614no—
588#103C22×D6114yes—
589#102—614no—
590#102—614no—
591#102—614no—
592#102C22×D6114yes—
593C22⋊C8—614no—
594C22⋊C8C22×D6114yes—
595C4×C8—614no—
596C4×C8—614no—
597C24—21no—
598C24—1221no—
599C24D4×D6111yescharacteristic
600#41—44no—
601#41—44no—
602#41—48no—
603#41—2444no—
604#41—2444no—
605#41—2448no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—612no—
613C2×Q8—612no—
614C2×Q8—1224no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1222no—
618C2×Q8—1222no—
619C2×Q8—1222no—
620C2×Q8—1222no—
621C2×Q8—2444no—
622C2×Q8C23×D6112yes—
623C2×Q8C23×D6112yes—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—612no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1221no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—2444no—
637C2×D4—2444no—
638C2×D4—2444no—
639C2×D4C23×D6112yes—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—44no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—614no—
650C22×C4—614no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—1224no—
654C22×C4—1224no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1224no—
659C22×C4—2444no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664Q16—44no—
665Q16—2444no—
666Q16—2444no—
667Q16—2444no—
668SD16—44no—
669SD16—2444no—
670SD16—2444no—
671SD16—2444no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—612no—
675C2×C8—612no—
676C2×C8—1222no—
677C2×C8—1222no—
678C2×C8C23×D6112yes—
679C2×C8C23×D6112yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—612no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1221no—
691C4⋊C4—1224no—
692C4⋊C4C23×D6112yes—
693C22⋊C4—24no—
694C22⋊C4—1224no—
695C22⋊C4—1224no—
696C22⋊C4—1224no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C42—614no—
700C42—614no—
701C42—612no—
702C42—612no—
703C42—612no—
704C42—612no—
705C42—1224no—
706C42—1224no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—1222no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23C2×D4×D6112yes—
719C23C2×D4×D6111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—1222no—
727Q8—1222no—
728Q8—1222no—
729Q8—1222no—
730Q8—2448no—
731Q8—2442no—
732Q8—2442no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—42no—
737D4—1222no—
738D4—1222no—
739D4—2448no—
740D4—2448no—
741D4—2448no—
742D4—2442no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—614no—
755C2×C4—614no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—1228no—
761C2×C4—1228no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—2448no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4C2×D4×D6112yes—
772C2×C4C2×D4×D6111yescharacteristic
773C2×C4#1451982212yes—
774C2×C4#1451982212yes—
775C2×C4C24×D6111yescharacteristic
776C8—22no—
777C8—22no—
778C8—1222no—
779C8—1222no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22—4884no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22#1684032712yes—
793C22#135×D6112yes—
794C22#137×D6112yes—
795C22C22×D4×D6111yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—614no—
801C4—614no—
802C4—1222no—
803C4—1222no—
804C4—2442no—
805C4—2442no—
806C4—2442no—
807C4#1684032712yes—
808C4C2×#1451982211yescharacteristic
809C4C2×#1451982211yescharacteristic
810C2—42no—
811C2—82no—
812C2—4882no—
813C2#2145677314yesdirect product factor
814C2C2×#1684032711yescharacteristic
815C2C2×#135×D6111yescharacteristic
816C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC2×#16840308C2
hypercenterC2×#452D61
hypocenterC61C2×#3210
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. C2×#16840314C2semidirect
3. #21456773C2direct (N × H)
4. C2×#16840140C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16840111C2semidirect
7. C2×#16840107C2semidirect
8. C2×#16839987C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839983C2semidirect
11. C2×#16839982C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839924C2semidirect
14. C2×#16839922C2semidirect
15. C2×#16839812C2semidirect
16. C2×C61×#452C2semidirect
25. #16840314C22semidirect
46. #16840140C22semidirect
47. #16840133C22semidirect
48. #16840111C22semidirect
49. #16840107C22semidirect
50. #16839987C22semidirect
51. #16839986C22semidirect
52. #16839983C22semidirect
53. #16839982C22semidirect
54. #16839926C22semidirect
55. #16839924C22semidirect
56. #16839922C22semidirect
57. #16839812C22semidirect
73. C61×#452C22semidirect
416. C2×#452D61semidirect
420. C2×C61#3210semidirect
469. #452C2×D61semidirect
485. C61C2×#3210semidirect
813. C2#21456773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#168403082
#214567732
C2×#168401402
C2×#168401332
C2×#168401112
C2×#168401072
C2×#168399872
C2×#168399862
C2×#168399832
C2×#168399822
C2×#168399262
C2×#168399242
C2×#168399222
C2×#168398122
C2×C61×#4522
C2×#321061