Finite Group Databasebeta

← C2×#21456861 #30551321

Subgroups — C2×#21456861 #30551321

Order 15616.

2198 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×#16840311C211yesmaximal, characteristic, complemented
2C2×#16840299C211yesmaximal, characteristic, complemented
3#21456861C2116yesmaximal, direct product factor
4C2×#16840155C211yesmaximal, characteristic, complemented
5C2×#16840148C211yesmaximal, characteristic, complemented
6C2×#16840129C211yesmaximal, characteristic, complemented
7C2×#16840125C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839921C211yesmaximal, characteristic, complemented
13C2×#16839910C211yesmaximal, characteristic, complemented
14C2×#16839908C211yesmaximal, characteristic, complemented
15C2×#16839818C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25#16840311—24no—
26#16840311C2218yescomplemented
27C2×#14519775C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29#16840299—24no—
30#16840299C2218yescomplemented
31C2×#14519772—21no—
32C2×#14519768C2211yescharacteristic
33C2×#14519766C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35C2×#14519762—21no—
36C2×#14519753C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519750—21no—
39C2×#14519750—21no—
40C2×C4×D244—21no—
41C2×C4×D244C2211yescharacteristic
42C2×#14519737—21no—
43C2×#14519737—21no—
44C2×#14519734—21no—
45C2×C42×D61C2211yescharacteristic
46#16840155C2218yescomplemented
47#16840148C2218yescomplemented
48#16840129C2218yescomplemented
49#16840125C2218yescomplemented
50#16839984C2218yescomplemented
51#16839978C2218yescomplemented
52#16839974C2218yescomplemented
53#16839923C2218yescomplemented
54#16839921C2218yescomplemented
55#16839910C2218yescomplemented
56#16839908C2218yescomplemented
57#16839818C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C2×#11758224—22no—
82C2×#11758224—42no—
83C2×#11758224—42no—
84C2×#11758224C2314yes—
85C22×Dic122C2311yescharacteristic
86C22×D244—21no—
87C22×D244—21no—
88C22×D244C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61D411yescharacteristic
97C22×C4×D61D411yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C2×#11758202—42no—
100C2×#11758202C2314yes—
101C2×#11758190—42no—
102C2×#11758190C2314yes—
103C2×#11758201—42no—
104C2×#11758201—42no—
105C2×#11758201C2314yes—
106C2×#11758201C2314yes—
107C2×D488—42no—
108C2×D488C2314yes—
109C2×#11758199—42no—
110C2×#11758199C2314yes—
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113#14519775—22no—
114#14519775C2314yes—
115#14519773—22no—
116#14519773C2314yes—
117#14519772—28no—
118#14519768—22no—
119#14519768C2314yes—
120#14519766—22no—
121#14519766C2314yes—
122#14519765—22no—
123#14519765C2314yes—
124#14519762—28no—
125#14519753—22no—
126#14519753C2314yes—
127#14519752—22no—
128#14519752C2314yes—
129#14519750—28no—
130#14519750—28no—
131C4×D244—28no—
132C4×D244—22no—
133C4×D244C2314yes—
134#14519737—28no—
135#14519737—28no—
136#14519734—28no—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61D411yescharacteristic
151C2×C4×Dic61D411yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153C42×D61D414yes—
154C42×D61C2314yes—
155C4⋊#92418C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519699C2314yes—
160#14519698C2314yes—
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yes—
165#14519687C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C2×Q16×C61—42no—
170C2×Q16×C61C2314yes—
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#124×C61—22no—
176#124×C61C2314yes—
177C4×Q8×C61—22no—
178C4×Q8×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yes—
186#103×C61C2314yes—
187#102×C61C2314yes—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61C2×D411yescharacteristic
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61C2412yes—
199C2×Q8×C61C2412yes—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61C2412yes—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—44no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758226—44no—
224#11758226—44no—
225#11758226—48no—
226#11758224—44no—
227#11758224—44no—
228#11758224—48no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—24no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244C2412yes—
240C2×D244C2412yes—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—44no—
248C2×C4×D61—44no—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2×D414yes—
251C2×C4×D61C2×D414yes—
252C2×C4×D61C2412yes—
253C2×Dic122—22no—
254C2×Dic122—22no—
255C2×Dic122—21no—
256C2×Dic122C2412yes—
257Q16×C61—44no—
258SD16×C61—44no—
259C2×C8×C61—22no—
260C2×C8×C61—22no—
261C2×C8×C61C2412yes—
262C2×C8×C61C2412yes—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61C2412yes—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C42×C61—24no—
269C42×C61C2×D412yes—
270C42×C61C2412yes—
271#11758202—44no—
272#11758201—44no—
273#11758201—44no—
274#11758199—44no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282C4⋊Dic61—21no—
283C4⋊Dic61—24no—
284C4⋊Dic61C2412yes—
285#11758196—24no—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289C4×Dic61C2×D412yes—
290C4×Dic61C2×D414yes—
291C4×Dic61C2×D414yes—
292C4×Dic61C2412yes—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297D488—44no—
298#11758190—44no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61C22×D412yes—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—42no—
321Q8×C61—42no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—42no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61H(5,𝔽2)12yes—
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61C2511yescharacteristic
339C22⋊D61—48no—
340C22⋊D61—48no—
341C22⋊D61—48no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—48no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353D244—22no—
354D244—22no—
355D244—22no—
356D244—22no—
357D244—48no—
358D244—48no—
359D244—42no—
360D244—42no—
361C4×D61—24no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—44no—
365C4×D61—44no—
366C4×D61—48no—
367C4×D61—48no—
368Dic122—22no—
369Dic122—22no—
370Dic122—42no—
371C8×C61—22no—
372C8×C61—22no—
373#92418—22no—
374#92418—22no—
375C2×#3219—611nomaximal, Sylow
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—84no—
380C22×C61#53512yes—
381C22×C61#57512yes—
382C22×C61#57512yes—
383C22×C61C23×D411yescharacteristic
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—44no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—84no—
395C2×D61—84no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—42no—
401C4×C61#53512yes—
402C4×C61C2×H(5,𝔽2)11yescharacteristic
403C4×C61C2×H(5,𝔽2)11yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—42no—
408Dic61—42no—
409C2×#532—611no—
410C2×#529—611no—
411#3219—6116no—
412C2×#497—611no—
413C2×#496—611no—
414C2×#491—611no—
415C2×#490—611no—
416C2×#464—611no—
417C2×#464D6111yescharacteristic, complemented
418C2×#463—611no—
419C2×#463—611no—
420C2×#452—611no—
421C2×#452—611no—
422C2×#449—611no—
423C2×#449—611no—
424C2×#432—611no—
425C2×C61—82no—
426C2×C61#321914yescomplemented
427C2×C61C2×#53511yescharacteristic
428C2×C61C2×#57511yescharacteristic
429C2×C61C2×#57511yescharacteristic
430D61—42no—
431D61—82no—
432D61—82no—
433C22×#41—611no—
434C22×#41—611no—
435C22×Q16—611no—
436C22×Q16C2×D6111yescharacteristic
437C22×SD16—611no—
438C22×SD16—611no—
439C22×SD16—611no—
440C22×SD16C2×D6111yescharacteristic
441C22×D8—611no—
442C22×D8—611no—
443#532—618no—
444#532—1224no—
445C2×C4⋊Q8—611no—
446C2×#127—611no—
447#529—618no—
448#529—1224no—
449C2×#126—1221no—
450C2×#125—611no—
451C2×#124—611no—
452C2×#124—611no—
453C2×#124C2×D6111yescharacteristic
454C2×#123—1221no—
455C2×C22⋊Q8—611no—
456C2×#121—611no—
457C2×#121—1221no—
458C2×#121—1221no—
459C2×C4×Q8C2×D6111yescharacteristic
460C2×C4×D4—611no—
461C2×C4×D4—1221no—
462C2×C4×D4—1221no—
463C2×C4×D4—1221no—
464C2×#117—1221no—
465C22×C42—611no—
466#497—618no—
467#496—618no—
468#491—618no—
469#490—618no—
470#464—618no—
471#464C2×D6118yescomplemented
472#463—618no—
473#463—618no—
474#452—618no—
475#452—618no—
476#449—618no—
477#449—618no—
478#432—618no—
479C2×C4⋊C8—611no—
480C2×C4⋊C8C2×D6111yescharacteristic
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102C2×D6111yescharacteristic
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492C2×#97—611no—
493C61C2×#321911yescharacteristic, complemented, Sylow
494C2×#41—614no—
495C2×#41—614no—
496C2×#41—1222no—
497C2×#41—1222no—
498C2×#41—2442no—
499C2×#41—2442no—
500C2×#41—2442no—
501C2×#41—2442no—
502C22×Q8—611no—
503C22×Q8C22×D6111yescharacteristic
504C22×Q8C22×D6111yescharacteristic
505C22×D4—611no—
506C22×D4—611no—
507C22×D4—1221no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4C22×D6111yescharacteristic
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×Q16—42no—
520C2×Q16—614no—
521C2×Q16—2442no—
522C2×Q16C22×D6114yes—
523C2×SD16—42no—
524C2×SD16—614no—
525C2×SD16—614no—
526C2×SD16—614no—
527C2×SD16—2442no—
528C2×SD16—2442no—
529C2×SD16—2442no—
530C2×SD16C22×D6114yes—
531C2×D8—614no—
532C2×D8—614no—
533C2×D8—2442no—
534C2×D8—2442no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539C4⋊Q8—614no—
540C4⋊Q8—1222no—
541#127—614no—
542#127—1222no—
543#126—1228no—
544#125—614no—
545#125—1222no—
546#124—22no—
547#124—614no—
548#124—614no—
549#124—1222no—
550#124—1222no—
551#124C22×D6114yes—
552#123—1228no—
553C22⋊Q8—614no—
554C22⋊Q8—1222no—
555#121—614no—
556#121—1228no—
557#121—1228no—
558#121—1222no—
559C4×Q8—22no—
560C4×Q8C22×D6114yes—
561C4×D4—614no—
562C4×D4—1228no—
563C4×D4—1228no—
564C4×D4—1228no—
565C4×D4—1222no—
566#117—1228no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
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×C22⋊C4—1221no—
584C2×C42—21no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—614no—
589C2×C42—614no—
590C2×C42C22×D6111yescharacteristic
591C4⋊C8—614no—
592C4⋊C8C22×D6114yes—
593#103—614no—
594#103—614no—
595#103—614no—
596#103C22×D6114yes—
597#102—614no—
598#102—614no—
599#102—614no—
600#102C22×D6114yes—
601C22⋊C8—614no—
602C22⋊C8—614no—
603#97—614no—
604#97—614no—
605C24—21no—
606C24—611no—
607C24—1221no—
608C24—1221no—
609#41—2444no—
610#41—2444no—
611#41—2448no—
612#41—2444no—
613#41—2444no—
614#41—2448no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—612no—
622C2×Q8—1221no—
623C2×Q8—1222no—
624C2×Q8—1222no—
625C2×Q8C23×D6112yes—
626C2×Q8C23×D6112yes—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1222no—
640C2×D4—1222no—
641C2×D4—1222no—
642C2×D4—1222no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4C23×D6112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—614no—
658C22×C4—614no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1224no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4—2444no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—44no—
675Q16—2444no—
676SD16—44no—
677SD16—2444no—
678SD16—2444no—
679SD16—2444no—
680D8—2444no—
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—24no—
691C4⋊C4—21no—
692C4⋊C4—612no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4—1221no—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C42—24no—
710C42—614no—
711C42—614no—
712C42—612no—
713C42—612no—
714C42D4×D6112yes—
715C42C23×D6112yes—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—612no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—2442no—
727C23—2442no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23—2442no—
732C23C2×D4×D6111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—1222no—
740Q8—1222no—
741Q8—2442no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—1222no—
746D4—1222no—
747D4—1222no—
748D4—1222no—
749D4—2448no—
750D4—2448no—
751D4—2448no—
752D4—2448no—
753D4—2448no—
754D4—2442no—
755D4—2442no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—612no—
765C2×C4—612no—
766C2×C4—612no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1224no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—2444no—
776C2×C4—2444no—
777C2×C4—2448no—
778C2×C4—2448no—
779C2×C4—2448no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4C2×D4×D6112yes—
783C2×C4C2×D4×D6112yes—
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4#1451982212yes—
786C2×C4#1451982312yes—
787C2×C4C24×D6111yescharacteristic
788C8—22no—
789C8—22no—
790C8—1222no—
791C8—1222no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—84no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—4884no—
800C22—4884no—
801C22—2442no—
802C22—2442no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2444no—
808C22#1684032812yes—
809C22#1684055912yes—
810C22#1684056112yes—
811C22C22×D4×D6111yescharacteristic
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—1222no—
818C4—1222no—
819C4—1222no—
820C4—2442no—
821C4—2442no—
822C4#1684032812yes—
823C4C2×#1451982211yescharacteristic
824C4C2×#1451982311yescharacteristic
825C2—82no—
826C2—4882no—
827C2—4882no—
828C2—2442no—
829C2#2145686114yesdirect product factor
830C2C2×#1684032811yescharacteristic
831C2C2×#1684055911yescharacteristic
832C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
hypercenterC2×#464D61
hypocenterC61C2×#3219
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840311C2semidirect
2. C2×#16840299C2semidirect
3. #21456861C2direct (N × H)
4. C2×#16840155C2semidirect
5. C2×#16840148C2semidirect
6. C2×#16840129C2semidirect
7. C2×#16840125C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839974C2semidirect
11. C2×#16839923C2semidirect
12. C2×#16839921C2semidirect
13. C2×#16839910C2semidirect
14. C2×#16839908C2semidirect
15. C2×#16839818C2semidirect
16. C2×C61×#464C2semidirect
26. #16840311C22semidirect
30. #16840299C22semidirect
46. #16840155C22semidirect
47. #16840148C22semidirect
48. #16840129C22semidirect
49. #16840125C22semidirect
50. #16839984C22semidirect
51. #16839978C22semidirect
52. #16839974C22semidirect
53. #16839923C22semidirect
54. #16839921C22semidirect
55. #16839910C22semidirect
56. #16839908C22semidirect
57. #16839818C22semidirect
73. C61×#464C22semidirect
417. C2×#464D61semidirect
426. C2×C61#3219semidirect
471. #464C2×D61semidirect
493. C61C2×#3219semidirect
829. C2#21456861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403112
C2×#168402992
#214568612
C2×#168401552
C2×#168401482
C2×#168401292
C2×#168401252
C2×#168399842
C2×#168399782
C2×#168399742
C2×#168399232
C2×#168399212
C2×#168399102
C2×#168399082
C2×#168398182
C2×C61×#4642
C2×#321961