Finite Group Databasebeta

← C2×#21456929 #30551409

Subgroups — C2×#21456929 #30551409

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×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840332C211yesmaximal, characteristic, complemented
3#21456929C2116yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic, complemented
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840114C211yesmaximal, characteristic, complemented
7C2×#16839983C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839966C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839908C211yesmaximal, characteristic
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839902C211yesmaximal, characteristic, complemented
15C2×#16839824C211yesmaximal, characteristic, complemented
16C2×C61×#489C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758190C2211yescharacteristic
24C22×#11758200C2211yescharacteristic
25C22×#11758201C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27#16840386—24no—
28#16840386C2218yescomplemented
29#16840332—24no—
30#16840332C2218yescomplemented
31C2×#14519777C2211yescharacteristic
32C2×#14519775C2211yescharacteristic
33C2×#14519772—21no—
34C2×#14519766—21no—
35C2×#14519765C2211yescharacteristic
36C2×#14519764C2211yescharacteristic
37C2×#14519762—21no—
38C2×#14519759—21no—
39C2×#14519759—21no—
40C2×#14519757C2211yescharacteristic
41C2×#14519754—21no—
42C2×#14519754—21no—
43C2×#14519753—21no—
44C2×#14519752C2211yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×#14519739C2211yescharacteristic
47C2×#14519734C2211yescharacteristic
48#16840156C2218yescomplemented
49#16840144C2218yescomplemented
50#16840114C2218yescomplemented
51#16839983C2218yescomplemented
52#16839976C2218yescomplemented
53#16839971C2218yescomplemented
54#16839966C2218yescomplemented
55#16839925C2218yescomplemented
56#16839919C2218yescomplemented
57#16839908C2218yes—
58#16839902C2218yescomplemented
59#16839824C2218yescomplemented
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C61×#489C2218yescomplemented
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—42no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2311yescharacteristic
85C2×Q8×D61—22no—
86C2×Q8×D61—42no—
87C2×Q8×D61—42no—
88C2×Q8×D61C2314yes—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96C2×Dic244—42no—
97C2×Dic244—42no—
98C2×Dic244C2314yes—
99C2×Dic244C2314yes—
100C2×#11758202—42no—
101C2×#11758202C2314yes—
102C2×#11758190—42no—
103C2×#11758190—42no—
104C2×#11758190C2314yes—
105C2×#11758190C2314yes—
106C2×#11758200—42no—
107C2×#11758200C2314yes—
108C2×#11758201—42no—
109C2×#11758201C2314yes—
110C2×#11758199—42no—
111C2×#11758199C2314yes—
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114#14519777—22no—
115#14519777C2314yes—
116#14519775—22no—
117#14519775C2314yes—
118#14519772—28no—
119#14519766—28no—
120#14519765—22no—
121#14519765C2314yes—
122#14519764—22no—
123#14519764C2314yes—
124#14519762—28no—
125#14519759—28no—
126#14519759—28no—
127#14519757—22no—
128#14519757C2314yes—
129#14519754—28no—
130#14519754—28no—
131#14519753—28no—
132#14519752—22no—
133#14519752C2314yes—
134#14519742—22no—
135#14519742C2314yes—
136#14519739—22no—
137#14519739C2314yes—
138#14519734D414yes—
139#14519734C2314yes—
140C2×C4⋊Dic61—21no—
141C2×C4⋊Dic61—21no—
142C2×C4⋊Dic61—21no—
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196—21no—
146C2×#11758196D411yescharacteristic
147C2×#11758196D411yescharacteristic
148C2×C22⋊Dic61—21no—
149C2×C22⋊Dic61—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198D411yescharacteristic
156C2×#11758198D411yescharacteristic
157C2×C4×Dic61—21no—
158C2×C4×Dic61C2311yescharacteristic
159#14519706C2314yes—
160#14519706C2314yes—
161#14519700C2314yes—
162#14519700C2314yes—
163#14519700C2314yes—
164#14519700C2314yes—
165#14519689C2314yes—
166#14519689C2314yes—
167C4×#92418C2314yes—
168C22×Q8×C61—21no—
169C22×Q8×C61C2311yescharacteristic
170C22×D4×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C4⋊Q8×C61—22no—
174C4⋊Q8×C61C2314yes—
175#124×C61—22no—
176#124×C61C2314yes—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C42×C61C2311yescharacteristic
183#103×C61C2314yes—
184#103×C61C2314yes—
185#102×C61C2314yes—
186#102×C61C2314yes—
187#97×C61C2314yes—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—24no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—82no—
196C2×Q8×C61C2412yes—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217Q8×D61—44no—
218Q8×D61—44no—
219Q8×D61—48no—
220#11758224—44no—
221#11758224—44no—
222#11758224—48no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—21no—
226C2×D244—24no—
227C2×D244—82no—
228C2×D244C2412yes—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—44no—
234C2×C4×D61—82no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2412yes—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—22no—
242C2×Dic122—22no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—44no—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C2×Dic122C2412yes—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61C2412yes—
254C2×C8×C61C2412yes—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C42×C61C2×D412yes—
263C42×C61C2412yes—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266#11758202—44no—
267#11758201—44no—
268#11758200—44no—
269#11758199—44no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198C2×D414yes—
276#11758198C2×D414yes—
277C4⋊Dic61—24no—
278C4⋊Dic61—24no—
279C4⋊Dic61—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196C2×D414yes—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418C2412yes—
291C2×#92418C2412yes—
292Dic244—44no—
293Dic244—44no—
294#11758190—44no—
295#11758190—44no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61C22×D412yes—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—42no—
312Q8×C61—84no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—42no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61H(5,𝔽2)12yes—
328C2×C4×C61H(5,𝔽2)12yes—
329C2×C4×C61C2511yescharacteristic
330C22⋊D61—48no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—48no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—42no—
347D244—84no—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—48no—
352C4×D61—84no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—48no—
360Dic122—42no—
361Dic122—42no—
362Dic122—42no—
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—84no—
372C22×C61#53512yes—
373C22×C61#57712yes—
374C22×C61#57812yes—
375C22×C61C23×D411yescharacteristic
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—44no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#53512yes—
390C4×C61C2×H(5,𝔽2)11yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—22no—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#542—611no—
399C2×#536—611no—
400#3225—6116no—
401C2×#497—611no—
402C2×#495—611no—
403C2×#489D6111yescharacteristic, complemented
404C2×#487—611no—
405C2×#464—611no—
406C2×#462—611no—
407C2×#463—611no—
408C2×#461—611no—
409C2×#452—611no—
410C2×#449—611no—
411C2×#451—611no—
412C2×#448—611no—
413C2×#433—611no—
414C2×C61—82no—
415C2×C61#322514yescomplemented
416C2×C61C2×#53511yescharacteristic
417C2×C61C2×#57711yescharacteristic
418C2×C61C2×#57811yescharacteristic
419D61—42no—
420D61—82no—
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×SD16—611no—
430C22×D8—611no—
431#542—618no—
432#542—1224no—
433#536—618no—
434#536—1224no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C4⋊Q8C2×D6111yescharacteristic
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×D4—611no—
453C2×#117—611no—
454#497—618no—
455#495—618no—
456#489C2×D6118yescomplemented
457#487—618no—
458#464—618no—
459#463—618no—
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⋊C8—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103C2×D6111yescharacteristic
474C2×#103C2×D6111yescharacteristic
475C2×#102C2×D6111yescharacteristic
476C2×#102C2×D6111yescharacteristic
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×#97C2×D6111yescharacteristic
480C2×C4×C8—611no—
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—2442no—
485C2×#41—2442no—
486C22×Q8—21no—
487C22×Q8—614no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—2442no—
494C22×Q8—2442no—
495C22×Q8C22×D6111yescharacteristic
496C22×D4—611no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C23×C4—611no—
501C23×C4—1221no—
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—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16—2442no—
517C2×SD16—2442no—
518C2×D8—614no—
519C2×D8—2442no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—614no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8C22×D6114yes—
530#126—1228no—
531#124—22no—
532#124—614no—
533#124—614no—
534#124—1222no—
535#124—1228no—
536#124—1222no—
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—614no—
551C4×D4—1222no—
552#117—614no—
553#117—614no—
554C2×C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—1221no—
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⋊C8—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103C22×D6114yes—
586#103C22×D6114yes—
587#102C22×D6114yes—
588#102C22×D6114yes—
589C22⋊C8—614no—
590C22⋊C8—614no—
591#97C22×D6114yes—
592C4×C8—614no—
593C24—21no—
594C24—611no—
595C24—1221no—
596#41—2444no—
597#41—2444no—
598#41—2448no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—612no—
605C2×Q8—612no—
606C2×Q8—612no—
607C2×Q8—1224no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—2444no—
618C2×Q8—2444no—
619C2×Q8—2444no—
620C2×Q8—2448no—
621C2×Q8C23×D6112yes—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—612no—
626C2×D4—1224no—
627C2×D4—1224no—
628C2×D4—1221no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—4882no—
632C2×D4—2444no—
633C2×D4C23×D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—4882no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658Q16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—2444no—
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—24no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—614no—
676C4⋊C4—614no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—614no—
688C22⋊C4—614no—
689C22⋊C4—1224no—
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—42no—
703C23—42no—
704C23—42no—
705C23—612no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—1222no—
724Q8—2448no—
725Q8—2442no—
726Q8—2442no—
727Q8—2442no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—1222no—
732D4—1222no—
733D4—4884no—
734D4—2448no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—4884no—
757C2×C4—2448no—
758C2×C4—2448no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4C2×D4×D6112yes—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4#1451982312yes—
766C2×C4#1451982312yes—
767C2×C4C24×D6111yescharacteristic
768C8—22no—
769C8—22no—
770C8—1222no—
771C8—1222no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22—1222no—
777C22—1222no—
778C22—1222no—
779C22—4884no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2444no—
784C22#1684033012yes—
785C22#1684057212yes—
786C22#1684057812yes—
787C22C22×D4×D6111yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—1222no—
794C4—1222no—
795C4—1222no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4#1684033012yes—
800C4C2×#1451982311yescharacteristic
801C4C2×#1451982311yescharacteristic
802C2—82no—
803C2—4882no—
804C2—2442no—
805C2#2145692914yesdirect product factor
806C2C2×#1684033011yescharacteristic
807C2C2×#1684057211yescharacteristic
808C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#489C2
socleC23×C61C22×D4
prime radicalC2×#16839908C2
hypercenterC2×#489D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840332C2semidirect
3. #21456929C2direct (N × H)
4. C2×#16840156C2semidirect
5. C2×#16840144C2semidirect
6. C2×#16840114C2semidirect
7. C2×#16839983C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839966C2semidirect
11. C2×#16839925C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839902C2semidirect
15. C2×#16839824C2semidirect
16. C2×C61×#489C2semidirect
28. #16840386C22semidirect
30. #16840332C22semidirect
48. #16840156C22semidirect
49. #16840144C22semidirect
50. #16840114C22semidirect
51. #16839983C22semidirect
52. #16839976C22semidirect
53. #16839971C22semidirect
54. #16839966C22semidirect
55. #16839925C22semidirect
56. #16839919C22semidirect
58. #16839902C22semidirect
59. #16839824C22semidirect
71. C61×#489C22semidirect
403. C2×#489D61semidirect
415. C2×C61#3225semidirect
456. #489C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403862
C2×#168403322
#214569292
C2×#168401562
C2×#168401442
C2×#168401142
C2×#168399832
C2×#168399712
C2×#168399762
C2×#168399662
C2×#168399252
C2×#168399082
C2×#168399192
C2×#168399022
C2×#168398242
C2×C61×#4892
C2×#322561