Finite Group Databasebeta

← C2×#21456925 #30551407

Subgroups — C2×#21456925 #30551407

Order 15616.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840377C211yesmaximal, characteristic, complemented
2C2×#16840332C211yesmaximal, characteristic, complemented
3#21456925C2116yesmaximal, direct product factor
4C2×#16840153C211yesmaximal, characteristic, complemented
5C2×#16840145C211yesmaximal, characteristic, complemented
6C2×#16840120C211yesmaximal, characteristic, complemented
7C2×#16840111C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839973C211yesmaximal, characteristic, complemented
10C2×#16839967C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839904C211yesmaximal, characteristic
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839899C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758200C2211yescharacteristic
25#16840377—24no—
26#16840377C2218yescomplemented
27#16840332—24no—
28#16840332C2218yescomplemented
29C2×#14519777C2211yescharacteristic
30C2×#14519776C2211yescharacteristic
31C2×#14519775C2211yescharacteristic
32C2×#14519770—21no—
33C2×#14519764C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519760—21no—
37C2×#14519759—21no—
38C2×#14519759—21no—
39C2×#14519757C2211yescharacteristic
40C2×#14519756—21no—
41C2×#14519754—21no—
42C2×#14519754—21no—
43C2×#14519748C2211yescharacteristic
44C2×C4×Dic122C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840153C2218yescomplemented
47#16840145C2218yescomplemented
48#16840120C2218yescomplemented
49#16840111C2218yescomplemented
50#16839981C2218yescomplemented
51#16839973C2218yescomplemented
52#16839967C2218yescomplemented
53#16839925C2218yescomplemented
54#16839919C2218yescomplemented
55#16839904C2218yes—
56#16839899C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—42no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2311yescharacteristic
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—22no—
87C2×Q8×D61—42no—
88C2×Q8×D61—42no—
89C2×Q8×D61C2314yes—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×Dic244—42no—
96C2×Dic244—42no—
97C2×Dic244C2314yes—
98C2×Dic244C2314yes—
99C2×#11758202—42no—
100C2×#11758202C2314yes—
101C2×#11758200—42no—
102C2×#11758200—42no—
103C2×#11758200—42no—
104C2×#11758200C2314yes—
105C2×#11758200C2314yes—
106C2×#11758200C2314yes—
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109#14519777—22no—
110#14519777C2314yes—
111#14519776—22no—
112#14519776C2314yes—
113#14519775—22no—
114#14519775C2314yes—
115#14519770—28no—
116#14519764—22no—
117#14519764—22no—
118#14519764C2314yes—
119#14519764C2314yes—
120#14519763—28no—
121#14519760—28no—
122#14519759—28no—
123#14519759—28no—
124#14519757—22no—
125#14519757C2314yes—
126#14519756—28no—
127#14519754—28no—
128#14519754—28no—
129#14519748—22no—
130#14519748C2314yes—
131C4×Dic122—22no—
132C4×Dic122C2314yes—
133#14519734D414yes—
134#14519734C2314yes—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C2×#11758196D411yescharacteristic
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×C22⋊Dic61—21no—
150C2×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×#11758198D411yescharacteristic
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519698C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yes—
165C8×Dic61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C2×SD16×C61—42no—
171C2×SD16×C61C2314yes—
172C2×D8×C61—42no—
173C2×D8×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176#124×C61—22no—
177#124×C61C2314yes—
178C4×D4×C61—22no—
179C4×D4×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yes—
186#103×C61C2314yes—
187#102×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61C2412yes—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—24no—
206C22×C4×C61—82no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—44no—
213C2×C22⋊D61—82no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—44no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223Q8×D61—44no—
224Q8×D61—44no—
225Q8×D61—48no—
226#11758224—44no—
227#11758224—44no—
228#11758224—48no—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—24no—
232C2×C4×D61—44no—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2412yes—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—24no—
245C2×Dic122—24no—
246C2×Dic122—44no—
247C2×Dic122—82no—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C2×Dic122C2412yes—
251SD16×C61—44no—
252D8×C61—44no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61C2412yes—
256C2×C8×C61C2412yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C42×C61C2×D412yes—
263C42×C61C2412yes—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269#11758202—44no—
270#11758200—44no—
271#11758200—44no—
272#11758200—44no—
273#11758198—24no—
274#11758198C2×D414yes—
275#11758198C2×D414yes—
276C4⋊Dic61—24no—
277C4⋊Dic61—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196C2×D414yes—
286#11758196C2×D414yes—
287C4×Dic61—24no—
288C4×Dic61C2×D412yes—
289C4×Dic61C2412yes—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294Dic244—44no—
295Dic244—44no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61C22×D411yescharacteristic
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61C22×D412yes—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—42no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—42no—
317D4×C61—42no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—84no—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61H(5,𝔽2)12yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—48no—
332C22⋊D61—84no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—48no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—48no—
352Dic122—22no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—48no—
359Dic122—42no—
360Dic122—42no—
361Dic122—42no—
362Dic122—84no—
363C8×C61—22no—
364C8×C61—22no—
365#92418—22no—
366#92418—22no—
367C2×#3225—611nomaximal, Sylow
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—84no—
375C22×C61—84no—
376C22×C61#53512yes—
377C22×C61#57712yes—
378C22×C61#57812yes—
379C22×C61C23×D411yescharacteristic
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—44no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61#53512yes—
389C4×C61C2×H(5,𝔽2)11yescharacteristic
390C4×C61C2×H(5,𝔽2)11yescharacteristic
391Dic61—22no—
392Dic61—22no—
393Dic61—22no—
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#542—611no—
399C2×#536—611no—
400#3225—6116no—
401C2×#497—611no—
402C2×#495—611no—
403C2×#489—611no—
404C2×#487—611no—
405C2×#464—611no—
406C2×#462—611no—
407C2×#463D6111yescharacteristic, complemented
408C2×#461—611no—
409C2×#452—611no—
410C2×#449—611no—
411C2×#451—611no—
412C2×#448—611no—
413C2×#433—611no—
414C2×C61—82no—
415C2×C61—82no—
416C2×C61#322514yescomplemented
417C2×C61C2×#53511yescharacteristic
418C2×C61C2×#57711yescharacteristic
419C2×C61C2×#57811yescharacteristic
420D61—42no—
421C22×#41—611no—
422C23×Q8—611no—
423C22×Q16—611no—
424C22×Q16—611no—
425C22×Q16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16C2×D6111yescharacteristic
430C22×D8C2×D6111yescharacteristic
431#542—618no—
432#542—1224no—
433#536—618no—
434#536—1224no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C4⋊Q8—611no—
438C2×#126—1221no—
439C2×#124—611no—
440C2×#124—611no—
441C2×#124—1221no—
442C2×#124C2×D6111yescharacteristic
443C2×#123—1221no—
444C2×#123—1221no—
445C2×#123—1221no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8—1221no—
449C2×C22⋊Q8—1221no—
450C2×#121—611no—
451C2×C4×Q8—611no—
452C2×C4×D4C2×D6111yescharacteristic
453C2×#117—611no—
454#497—618no—
455#495—618no—
456#489—618no—
457#487—618no—
458#464—618no—
459#463C2×D6118yescomplemented
460#462—618no—
461#461—618no—
462#452—618no—
463#451—618no—
464#449—618no—
465#448—618no—
466#433—618no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8C2×D6111yescharacteristic
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103C2×D6111yescharacteristic
475C2×#102—611no—
476C2×#102C2×D6111yescharacteristic
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×#97—611no—
480C2×C4×C8—611no—
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—2442no—
485C2×#41—2442no—
486C22×Q8—614no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—1221no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—2442no—
494C22×Q8—2442no—
495C22×Q8C22×D6111yescharacteristic
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4C22×D6111yescharacteristic
499C22×D4C22×D6111yescharacteristic
500C23×C4—21no—
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×Q16—614no—
505C2×Q16—614no—
506C2×Q16—614no—
507C2×Q16—2442no—
508C2×Q16—2442no—
509C2×Q16—2442no—
510C2×SD16—42no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16—2442no—
517C2×SD16C22×D6114yes—
518C2×D8—42no—
519C2×D8C22×D6114yes—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4⋊Q8—614no—
525C4⋊Q8—614no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8—1222no—
530#126—1228no—
531#124—22no—
532#124—614no—
533#124—614no—
534#124—1222no—
535#124—1222no—
536#124—1228no—
537#124C22×D6114yes—
538#123—1228no—
539#123—1228no—
540#123—1228no—
541C22⋊Q8—614no—
542C22⋊Q8—1228no—
543C22⋊Q8—1228no—
544C22⋊Q8—1222no—
545C22⋊Q8—1228no—
546#121—614no—
547#121—1222no—
548C4×Q8—614no—
549C4×Q8—1222no—
550C4×D4—22no—
551C4×D4C22×D6114yes—
552#117—614no—
553#117—614no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
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—611no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—614no—
580C4⋊C8C22×D6114yes—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103—614no—
586#103C22×D6114yes—
587#102—614no—
588#102C22×D6114yes—
589C22⋊C8—614no—
590C22⋊C8—614no—
591#97—614no—
592C4×C8—614no—
593C24—21no—
594C24—21no—
595C24—611no—
596#41—2444no—
597#41—2444no—
598#41—2448no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—612no—
603C2×Q8—612no—
604C2×Q8—612no—
605C2×Q8—1224no—
606C2×Q8—1224no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1222no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—4882no—
617C2×Q8—2444no—
618C2×Q8—2444no—
619C2×Q8—2444no—
620C2×Q8—2448no—
621C2×Q8C23×D6112yes—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—4882no—
631C2×D4—2444no—
632C2×D4C23×D6112yes—
633C2×D4C23×D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658Q16—2444no—
659SD16—44no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—44no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8C23×D6112yes—
671C2×C8C23×D6112yes—
672C4⋊C4—21no—
673C4⋊C4—614no—
674C4⋊C4—614no—
675C4⋊C4—612no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1221no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1224no—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—614no—
689C22⋊C4—614no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1224no—
696C42—612no—
697C42—612no—
698C42—1224no—
699C42D4×D6112yes—
700C42C23×D6112yes—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—612no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—1222no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—4884no—
724Q8—2448no—
725Q8—2442no—
726Q8—2442no—
727Q8—2442no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—42no—
733D4—42no—
734D4—4884no—
735D4—2448no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—84no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—2448no—
757C2×C4—2448no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4C2×D4×D6112yes—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4#1451982212yes—
766C2×C4#1451982312yes—
767C2×C4C24×D6111yescharacteristic
768C8—22no—
769C8—22no—
770C8—1222no—
771C8—1222no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—84no—
779C22—84no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—2444no—
784C22#1684032812yes—
785C22#1684057212yes—
786C22#1684057612yes—
787C22C22×D4×D6111yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—1222no—
793C4—1222no—
794C4—1222no—
795C4—2442no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4#1684032812yes—
800C4C2×#1451982211yescharacteristic
801C4C2×#1451982311yescharacteristic
802C2—82no—
803C2—82no—
804C2—2442no—
805C2#2145692514yesdirect product factor
806C2C2×#1684032811yescharacteristic
807C2C2×#1684057211yescharacteristic
808C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC2×#16839904C2
hypercenterC2×#463D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840377C2semidirect
2. C2×#16840332C2semidirect
3. #21456925C2direct (N × H)
4. C2×#16840153C2semidirect
5. C2×#16840145C2semidirect
6. C2×#16840120C2semidirect
7. C2×#16840111C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839973C2semidirect
10. C2×#16839967C2semidirect
11. C2×#16839925C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839899C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#463C2semidirect
26. #16840377C22semidirect
28. #16840332C22semidirect
46. #16840153C22semidirect
47. #16840145C22semidirect
48. #16840120C22semidirect
49. #16840111C22semidirect
50. #16839981C22semidirect
51. #16839973C22semidirect
52. #16839967C22semidirect
53. #16839925C22semidirect
54. #16839919C22semidirect
56. #16839899C22semidirect
57. #16839822C22semidirect
73. C61×#463C22semidirect
407. C2×#463D61semidirect
416. C2×C61#3225semidirect
459. #463C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403772
C2×#168403322
#214569252
C2×#168401532
C2×#168401452
C2×#168401202
C2×#168401112
C2×#168399812
C2×#168399732
C2×#168399672
C2×#168399252
C2×#168399042
C2×#168399192
C2×#168398992
C2×#168398222
C2×C61×#4632
C2×#322561