Finite Group Databasebeta

← C2×#21456923 #30551403

Subgroups — C2×#21456923 #30551403

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×#16840381C211yesmaximal, characteristic, complemented
2C2×#16840337C211yesmaximal, characteristic, complemented
3#21456923C2116yesmaximal, direct product factor
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840122C211yesmaximal, characteristic, complemented
6C2×#16840112C211yesmaximal, characteristic, complemented
7C2×#16839986C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839965C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic
13C2×#16839916C211yesmaximal, characteristic, complemented
14C2×#16839899C211yesmaximal, characteristic, complemented
15C2×#16839824C211yesmaximal, characteristic, complemented
16C2×C61×#497C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23#16840381—24no—
24#16840381C2218yescomplemented
25#16840337—24no—
26#16840337C2218yescomplemented
27C2×#14519777C2211yescharacteristic
28C2×#14519775C2211yescharacteristic
29C2×#14519770—21no—
30C2×#14519766C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519763—21no—
33C2×#14519762—21no—
34C2×#14519762—21no—
35C2×#14519761—21no—
36C2×#14519755—21no—
37C2×#14519755—21no—
38C2×#14519754—21no—
39C2×#14519753C2211yescharacteristic
40C2×#14519748C2211yescharacteristic
41C2×Q8×Dic61C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519734C2211yescharacteristic
44#16840144C2218yescomplemented
45#16840122C2218yescomplemented
46#16840112C2218yescomplemented
47#16839986C2218yescomplemented
48#16839979C2218yescomplemented
49#16839970C2218yescomplemented
50#16839965C2218yescomplemented
51#16839923C2218yescomplemented
52#16839916C2218yescomplemented
53#16839906C2218yes—
54#16839899C2218yescomplemented
55#16839824C2218yescomplemented
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C2×C4⋊Q8×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#497C2218yescomplemented
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—42no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×#11758202—42no—
96C2×#11758202C2314yes—
97C2×#11758200—42no—
98C2×#11758200C2314yes—
99C2×#11758201—42no—
100C2×#11758201C2314yes—
101C2×#11758199—42no—
102C2×#11758199C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519777—22no—
106#14519777C2314yes—
107#14519775—22no—
108#14519775C2314yes—
109#14519770—28no—
110#14519766—22no—
111#14519766C2314yes—
112#14519765—22no—
113#14519765C2314yes—
114#14519763—28no—
115#14519762—28no—
116#14519762—28no—
117#14519761—28no—
118#14519755—28no—
119#14519755—28no—
120#14519754—28no—
121#14519753—22no—
122#14519753C2314yes—
123#14519748—22no—
124#14519748C2314yes—
125Q8×Dic61—22no—
126Q8×Dic61C2314yes—
127D4×Dic61—22no—
128D4×Dic61C2314yes—
129#14519734D414yes—
130#14519734C2314yes—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196D411yescharacteristic
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61C2311yescharacteristic
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519701C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519689C2314yes—
162#14519689C2314yes—
163C4×#92418C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×Q8×C61C2311yescharacteristic
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×Q16×C61—42no—
169C2×Q16×C61—42no—
170C2×Q16×C61C2314yes—
171C2×Q16×C61C2314yes—
172C2×SD16×C61—42no—
173C2×SD16×C61—42no—
174C2×SD16×C61C2314yes—
175C2×SD16×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178C4⋊Q8×C61—22no—
179C4⋊Q8×C61C2314yes—
180#124×C61—22no—
181#124×C61C2314yes—
182C2×C4⋊C4×C61—21no—
183C2×C4⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C42×C61C2311yescharacteristic
187#97×C61C2314yes—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
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×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×Q8×C61C2412yes—
202C2×Q8×C61C2412yes—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61C2412yes—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—82no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—82no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758226—44no—
224#11758226—44no—
225#11758226—48no—
226Q8×D61—44no—
227Q8×D61—44no—
228Q8×D61—48no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—24no—
232C2×D244—21no—
233C2×D244—44no—
234C2×D244C2412yes—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61C2×D412yes—
242C2×C4×D61C2412yes—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—24no—
248C2×Dic122—44no—
249C2×Dic122—82no—
250C2×Dic122C2412yes—
251Q16×C61—44no—
252Q16×C61—44no—
253SD16×C61—44no—
254SD16×C61—44no—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61—24no—
260C4⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C42×C61C2×D412yes—
264C42×C61C2412yes—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267#11758202—44no—
268#11758201—44no—
269#11758200—44no—
270#11758199—44no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198C2×D414yes—
277#11758198C2×D414yes—
278C4⋊Dic61—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—24no—
282C4⋊Dic61C2412yes—
283C4⋊Dic61C2412yes—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287#11758196C2×D414yes—
288#11758196C2×D414yes—
289C4×Dic61—24no—
290C4×Dic61C2×D412yes—
291C4×Dic61C2412yes—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
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—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—42no—
316Q8×C61—42no—
317Q8×C61—42no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—42no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D412yes—
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61H(5,𝔽2)12yes—
333C2×C4×C61H(5,𝔽2)12yes—
334C2×C4×C61C2511yescharacteristic
335C22⋊D61—84no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—84no—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349D244—22no—
350D244—22no—
351D244—48no—
352D244—42no—
353C4×D61—24no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357C4×D61—48no—
358Dic122—22no—
359Dic122—22no—
360Dic122—48no—
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—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×#497D6111yescharacteristic, complemented
402C2×#495—611no—
403C2×#489—611no—
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×Q16C2×D6111yescharacteristic
425C22×Q16C2×D6111yescharacteristic
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16C2×D6111yescharacteristic
429C22×SD16C2×D6111yescharacteristic
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#497C2×D6118yescomplemented
455#495—618no—
456#489—618no—
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×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
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—614no—
487C22×Q8—611no—
488C22×Q8—1221no—
489C22×Q8—1222no—
490C22×Q8—1221no—
491C22×Q8—2442no—
492C22×Q8—2442no—
493C22×Q8C22×D6111yescharacteristic
494C22×Q8C22×D6111yescharacteristic
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—42no—
505C2×Q16—42no—
506C2×Q16—614no—
507C2×Q16—2442no—
508C2×Q16C22×D6114yes—
509C2×Q16C22×D6114yes—
510C2×SD16—42no—
511C2×SD16—42no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16C22×D6114yes—
517C2×SD16C22×D6114yes—
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—1228no—
545C22⋊Q8—1222no—
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—21no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
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×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#103—614no—
586#103—614no—
587#102—614no—
588#102—614no—
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—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—612no—
609C2×Q8—1224no—
610C2×Q8—1224no—
611C2×Q8—1221no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—4882no—
615C2×Q8—2444no—
616C2×Q8—2444no—
617C2×Q8—2444no—
618C2×Q8—2448no—
619C2×Q8C23×D6112yes—
620C2×Q8C23×D6112yes—
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—44no—
657Q16—44no—
658Q16—2444no—
659SD16—44no—
660SD16—44no—
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—24no—
674C4⋊C4—614no—
675C4⋊C4—614no—
676C4⋊C4—612no—
677C4⋊C4—612no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1224no—
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—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—1222no—
724Q8—1222no—
725Q8—4884no—
726Q8—2448no—
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#1451982212yes—
766C2×C4#1451982212yes—
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#1684032512yes—
785C22#1684057112yes—
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#1684032512yes—
800C4C2×#1451982211yescharacteristic
801C4C2×#1451982211yescharacteristic
802C2—82no—
803C2—4882no—
804C2—2442no—
805C2#2145692314yesdirect product factor
806C2C2×#1684032511yescharacteristic
807C2C2×#1684057111yescharacteristic
808C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#497C2
socleC23×C61C22×D4
prime radicalC2×#16839906C2
hypercenterC2×#497D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#16840381C2semidirect
2. C2×#16840337C2semidirect
3. #21456923C2direct (N × H)
4. C2×#16840144C2semidirect
5. C2×#16840122C2semidirect
6. C2×#16840112C2semidirect
7. C2×#16839986C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839965C2semidirect
11. C2×#16839923C2semidirect
13. C2×#16839916C2semidirect
14. C2×#16839899C2semidirect
15. C2×#16839824C2semidirect
16. C2×C61×#497C2semidirect
24. #16840381C22semidirect
26. #16840337C22semidirect
44. #16840144C22semidirect
45. #16840122C22semidirect
46. #16840112C22semidirect
47. #16839986C22semidirect
48. #16839979C22semidirect
49. #16839970C22semidirect
50. #16839965C22semidirect
51. #16839923C22semidirect
52. #16839916C22semidirect
54. #16839899C22semidirect
55. #16839824C22semidirect
75. C61×#497C22semidirect
401. C2×#497D61semidirect
415. C2×C61#3225semidirect
454. #497C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403812
C2×#168403372
#214569232
C2×#168401442
C2×#168401222
C2×#168401122
C2×#168399862
C2×#168399702
C2×#168399792
C2×#168399652
C2×#168399232
C2×#168399062
C2×#168399162
C2×#168398992
C2×#168398242
C2×C61×#4972
C2×#322561