Finite Group Databasebeta

← C2×#21456907 #30551362

Subgroups — C2×#21456907 #30551362

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840331C211yesmaximal, characteristic, complemented
2#21456907C2116yesmaximal, direct product factor
3C2×#16840152C211yesmaximal, characteristic, complemented
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840124C211yesmaximal, characteristic, complemented
6C2×#16840110C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839962C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839922C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839912C211yesmaximal, characteristic, complemented
14C2×#16839895C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758200C2211yescharacteristic, complemented
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758201C2211yescharacteristic, complemented
24C22×#11758199C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26C22×#11758199C2211yescharacteristic, complemented
27#16840331—24no—
28#16840331C2218yescomplemented
29C2×#14519774C2211yescharacteristic
30C2×#14519774C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519752—21no—
34C2×#14519752—21no—
35C2×#14519747—21no—
36C2×#14519747—21no—
37#16840152C2218yescomplemented
38#16840144C2218yescomplemented
39#16840124C2218yescomplemented
40#16840110C2218yescomplemented
41#16839984C2218yescomplemented
42#16839977C2218yescomplemented
43#16839962C2218yescomplemented
44#16839957C2218yescomplemented
45#16839922C2218yescomplemented
46#16839912C2218yescomplemented
47#16839905C2218yescomplemented
48#16839895C2218yescomplemented
49#16839823C2218yescomplemented
50C2×C4⋊#92418C2211yescharacteristic, complemented
51C2×C4⋊#92418C2211yescharacteristic, complemented
52C2×#14519700C2211yescharacteristic, complemented
53C2×#14519700C2211yescharacteristic, complemented
54C2×#14519697C2211yescharacteristic
55C2×#14519697C2211yescharacteristic
56C2×#14519697C2211yescharacteristic
57C2×#14519697C2211yescharacteristic
58C2×#14519697C2211yescharacteristic, complemented
59C2×#14519697C2211yescharacteristic, complemented
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic, complemented
63C2×C4×#92418C2211yescharacteristic, complemented
64C61×#542—24no—
65C61×#542C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic, complemented
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic, complemented
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic, complemented
75C2×C4×D4×C61C2211yescharacteristic, complemented
76C2×#117×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—42no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244—22no—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—42no—
90C22×D244—42no—
91C22×D244C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×D244C2314yes—
95C22×C22⋊D61—21no—
96C22×C4×D61—21no—
97C2×#11758202—42no—
98C2×#11758202C2314yescomplemented
99C2×#11758200—42no—
100C2×#11758200C2314yescomplemented
101C2×#11758201—42no—
102C2×#11758201—42no—
103C2×#11758201—42no—
104C2×#11758201C2314yes—
105C2×#11758201C2314yes—
106C2×#11758201C2314yescomplemented
107C2×#11758199—42no—
108C2×#11758199—42no—
109C2×#11758199—42no—
110C2×#11758199C2314yes—
111C2×#11758199C2314yes—
112C2×#11758199C2314yescomplemented
113C22×#92418C2311yescharacteristic
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116C22×#92418C2311yescharacteristic
117#14519774—22no—
118#14519774—22no—
119#14519774C2314yes—
120#14519774C2314yes—
121#14519765—22no—
122#14519765—22no—
123#14519765C2314yes—
124#14519765C2314yes—
125#14519752—28no—
126#14519752—28no—
127#14519747—28no—
128#14519747—28no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C4⋊#92418C2314yescomplemented
134C4⋊#92418C2314yescomplemented
135#14519700C2314yescomplemented
136#14519700C2314yescomplemented
137#14519697C2314yes—
138#14519697C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141#14519697C2314yescomplemented
142#14519697C2314yescomplemented
143C22⋊#92418C2314yes—
144C22⋊#92418C2314yes—
145#14519688C2314yescomplemented
146C4×#92418C2314yescomplemented
147C22×Q8×C61—21no—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61—21no—
150C22×D4×C61C2311yescharacteristic
151C23×C4×C61—21no—
152C23×C4×C61C2311yescharacteristic
153C4⋊Q8×C61—22no—
154C4⋊Q8×C61C2314yescomplemented
155#126×C61—28no—
156#124×C61—28no—
157#124×C61—22no—
158#124×C61C2314yescomplemented
159#123×C61—28no—
160C22⋊Q8×C61—22no—
161C22⋊Q8×C61—28no—
162C22⋊Q8×C61C2314yes—
163#121×C61—22no—
164#121×C61C2314yes—
165C4×Q8×C61—22no—
166C4×Q8×C61C2314yescomplemented
167C4×D4×C61—22no—
168C4×D4×C61C2314yescomplemented
169#117×C61D414yes—
170#117×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D411yescharacteristic
175C2×C4⋊C4×C61D411yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C22⋊C4×C61D411yescharacteristic
185C2×C42×C61—21no—
186C2×C42×C61C2311yescharacteristic
187C2×C42×C61C2311yescharacteristic
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—24no—
194C23×D61—44no—
195C23×D61—82no—
196C23×D61—82no—
197C2×Q8×C61—21no—
198C2×Q8×C61—24no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—82no—
202C2×Q8×C61C2412yes—
203C2×D4×C61—24no—
204C2×D4×C61—21no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—82no—
208C2×D4×C61C2412yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—82no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—44no—
226C22×Dic61—21no—
227#11758222—44no—
228#11758222—44no—
229#11758222—48no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—24no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—24no—
243C2×D244—24no—
244C2×D244—44no—
245C2×D244—44no—
246C2×D244—44no—
247C2×D244—48no—
248C2×D244—82no—
249C2×D244—82no—
250C2×D244—82no—
251C2×D244—82no—
252C2×D244C2412yes—
253C2×D244C2412yes—
254C2×D244C2412yes—
255C2×C4×D61—24no—
256C2×C4×D61—44no—
257C2×Dic122—22no—
258C2×Dic122—22no—
259C2×Dic122—21no—
260C2×Dic122C2412yes—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C2×D414yes—
267C4⋊C4×C61C2×D414yes—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C22⋊C4×C61—24no—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—24no—
273C22⋊C4×C61—24no—
274C22⋊C4×C61—24no—
275C22⋊C4×C61C2×D414yes—
276C22⋊C4×C61C2×D414yes—
277C42×C61—24no—
278C42×C61C2×D412yes—
279C42×C61C2×D412yes—
280C42×C61C2412yes—
281C42×C61C2412yes—
282#11758202—44no—
283#11758201—44no—
284#11758201—44no—
285#11758201—44no—
286#11758200—44no—
287#11758199—44no—
288#11758199—44no—
289#11758199—44no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294C2×#92418—22no—
295C2×#92418—22no—
296C2×#92418—22no—
297C2×#92418—22no—
298C2×#92418C2412yes—
299C2×#92418C2412yes—
300C2×#92418C2412yes—
301C2×#92418C2412yes—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61C22×D412yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—84no—
325C22×D61—84no—
326C22×D61—816no—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—42no—
330Q8×C61—84no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—42no—
334D4×C61—84no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—24no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—84no—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61H(5,𝔽2)12yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—48no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—48no—
369D244—42no—
370D244—42no—
371D244—42no—
372D244—84no—
373D244—84no—
374D244—84no—
375D244—84no—
376C4×D61—48no—
377Dic122—22no—
378Dic122—22no—
379Dic122—42no—
380#92418—22no—
381#92418—22no—
382#92418—22no—
383#92418—22no—
384C2×#3224—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—44no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—84no—
393C22×C61#53512yes—
394C22×C61#57612yes—
395C22×C61#57712yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—816no—
407C2×D61—84no—
408C2×D61—84no—
409C2×D61—84no—
410C4×C61—22no—
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61#53512yes—
419C4×C61C2×H(5,𝔽2)11yescharacteristic
420C4×C61C2×H(5,𝔽2)11yescharacteristic
421Dic61—42no—
422C2×#542D6111yescharacteristic, complemented
423C2×#535—611no—
424#3224—6116no—
425C2×#496—611no—
426C2×#495—611no—
427C2×#489—611no—
428C2×#486—611no—
429C2×#464—611no—
430C2×#460—611no—
431C2×#463—611no—
432C2×#459—611no—
433C2×#452—611no—
434C2×#449—611no—
435C2×#450—611no—
436C2×#447—611no—
437C2×#433—611no—
438C2×C61—42no—
439C2×C61—82no—
440C2×C61#322414yescomplemented
441C2×C61C2×#53511yescharacteristic
442C2×C61C2×#57611yescharacteristic
443C2×C61C2×#57711yescharacteristic
444D61—82no—
445D61—82no—
446D61—82no—
447C22×#41—611no—
448C23×D4—611no—
449C22×Q16—611no—
450C22×SD16—611no—
451C22×SD16—611no—
452C22×SD16—611no—
453C22×SD16—611no—
454C22×D8—611no—
455C22×D8—611no—
456C22×D8—611no—
457#542—24no—
458#542C2×D6118yescomplemented
459#535—618no—
460#535—1224no—
461C2×C4⋊Q8C2×D6111yescharacteristic, complemented
462C2×#127—611no—
463C2×#127—611no—
464C2×#126—21no—
465C2×#124—21no—
466C2×#124—611no—
467C2×#124—611no—
468C2×#124C2×D6111yescharacteristic, complemented
469C2×#123—21no—
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8C2×D6111yescharacteristic
472C2×#121—1221no—
473C2×#121—1221no—
474C2×#121C2×D6111yescharacteristic
475C2×#120—1221no—
476C2×#120—1221no—
477C2×C4×Q8C2×D6111yescharacteristic, complemented
478C2×C4×D4C2×D6111yescharacteristic, complemented
479C2×#117C2×D6111yescharacteristic
480#496—618no—
481#495—618no—
482#489—618no—
483#486—618no—
484#464—618no—
485#463—618no—
486#460—618no—
487#459—618no—
488#452—618no—
489#450—618no—
490#449—618no—
491#447—618no—
492#433—618no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102—611no—
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×C22⋊C8—611no—
504C2×C22⋊C8—611no—
505C2×#97—611no—
506C2×C4×C8—611no—
507C61C2×#322411yescharacteristic, complemented, Sylow
508C25—1221no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—2442no—
512C2×#41—2442no—
513C22×Q8—21no—
514C22×Q8—611no—
515C22×Q8C22×D6111yescharacteristic
516C22×D4—21no—
517C22×D4—611no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—614no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—1222no—
528C22×D4—2442no—
529C22×D4—2442no—
530C22×D4C22×D6111yescharacteristic
531C23×C4—21no—
532C23×C4—1221no—
533C23×C4C22×D6111yescharacteristic
534C2×Q16—614no—
535C2×Q16—2442no—
536C2×SD16—614no—
537C2×SD16—614no—
538C2×SD16—614no—
539C2×SD16—614no—
540C2×SD16—2442no—
541C2×SD16—2442no—
542C2×SD16—2442no—
543C2×SD16—2442no—
544C2×D8—614no—
545C2×D8—614no—
546C2×D8—614no—
547C2×D8—2442no—
548C2×D8—2442no—
549C2×D8—2442no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—611no—
554C4⋊Q8—22no—
555C4⋊Q8C22×D6114yescomplemented
556#127—614no—
557#127—614no—
558#127—1222no—
559#127—1222no—
560#126—28no—
561#124—28no—
562#124—22no—
563#124—614no—
564#124—614no—
565#124—1222no—
566#124—1222no—
567#124C22×D6114yescomplemented
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—28no—
571C22⋊Q8C22×D6114yes—
572#121—22no—
573#121—1228no—
574#121—1228no—
575#121C22×D6114yes—
576#120—1228no—
577#120—1228no—
578C4×Q8—22no—
579C4×Q8C22×D6114yescomplemented
580C4×D4—22no—
581C4×D4C22×D6114yescomplemented
582#117C22⋊D6114yes—
583#117C22×D6114yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4C22⋊D6111yescharacteristic
588C2×C4⋊C4C22⋊D6111yescharacteristic
589C2×C4⋊C4C22×D6111yescharacteristic
590C2×C4⋊C4C22×D6111yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4C22⋊D6111yescharacteristic
601C2×C22⋊C4C22⋊D6111yescharacteristic
602C2×C42—21no—
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C4⋊C8—614no—
606C4⋊C8—614no—
607#103—614no—
608#103—614no—
609#102—614no—
610#102—614no—
611#102—614no—
612#102—614no—
613#102—614no—
614#102—614no—
615C22⋊C8—614no—
616C22⋊C8—614no—
617#97—614no—
618C4×C8—614no—
619C24—21no—
620C24—1224no—
621C24—1221no—
622C24—1221no—
623C24—1221no—
624C24—4882no—
625C24—4882no—
626C24—2444no—
627C24C2×C22⋊D6111yescharacteristic
628#41—2444no—
629#41—2444no—
630#41—2448no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—612no—
637C2×Q8—1221no—
638C2×Q8—1222no—
639C2×Q8—1222no—
640C2×Q8C23×D6112yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—82no—
646C2×D4—612no—
647C2×D4—612no—
648C2×D4—612no—
649C2×D4—1224no—
650C2×D4—1224no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1222no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1222no—
664C2×D4—4882no—
665C2×D4—4882no—
666C2×D4—4882no—
667C2×D4—4882no—
668C2×D4—2444no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2448no—
672C2×D4—2444no—
673C2×D4C23×D6112yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—82no—
681C22×C4—1221no—
682C22×C4—1224no—
683C22×C4—2444no—
684C22×C4C2×C22⋊D6112yes—
685C22×C4C2×C22⋊D6111yescharacteristic
686C22×C4C2×C22⋊D6111yescharacteristic
687C22×C4C2×C22⋊D6111yescharacteristic
688C22×C4C2×C22⋊D6111yescharacteristic
689C22×C4C2×C22⋊D6111yescharacteristic
690C22×C4C23×D6112yes—
691C22×C4C23×D6111yescharacteristic
692Q16—2444no—
693SD16—2444no—
694SD16—2444no—
695SD16—2444no—
696SD16—2444no—
697D8—2444no—
698D8—2444no—
699D8—2444no—
700C2×C8—612no—
701C2×C8—612no—
702C2×C8—612no—
703C2×C8—612no—
704C2×C8—1222no—
705C2×C8—1222no—
706C2×C8—1222no—
707C2×C8—1222no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4C2×C22⋊D6114yes—
714C4⋊C4C2×C22⋊D6114yes—
715C4⋊C4C23×D6112yes—
716C4⋊C4C23×D6112yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4C2×C22⋊D6114yes—
727C22⋊C4C2×C22⋊D6114yes—
728C42—24no—
729C42C2×C22⋊D6112yes—
730C42C2×C22⋊D6112yes—
731C42C23×D6112yes—
732C42C23×D6112yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23—4884no—
744C23—4884no—
745C23—48816no—
746C23—2448no—
747C23—2442no—
748C23—2442no—
749C23—2442no—
750C23—2442no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23—2442no—
755C23—2442no—
756C23C22×C22⋊D6112yes—
757C23C22×C22⋊D6111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—1222no—
763Q8—1222no—
764Q8—2442no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—84no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—1222no—
775D4—4884no—
776D4—4884no—
777D4—4884no—
778D4—4884no—
779D4—2448no—
780D4—2448no—
781D4—2442no—
782D4—2442no—
783D4—2442no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—1222no—
800C2×C4—2448no—
801C2×C4—2442no—
802C2×C4C22×C22⋊D6112yes—
803C2×C4C22×C22⋊D6112yes—
804C2×C4C22×C22⋊D6112yes—
805C2×C4C22×C22⋊D6112yes—
806C2×C4C22×C22⋊D6112yes—
807C2×C4C22×C22⋊D6111yescharacteristic
808C2×C4#1451982312yes—
809C2×C4#1451982312yes—
810C2×C4C24×D6111yescharacteristic
811C8—1222no—
812C8—1222no—
813C8—1222no—
814C8—1222no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—48816no—
824C22—4884no—
825C22—4884no—
826C22—4884no—
827C22—2442no—
828C22—2442no—
829C22—2442no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22#1684032612yes—
837C22#1684056512yes—
838C22#1684057012yes—
839C22C23×C22⋊D6111yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—2442no—
849C4#1684032612yes—
850C4C2×#1451982311yescharacteristic
851C4C2×#1451982311yescharacteristic
852C2—42no—
853C2—82no—
854C2—4882no—
855C2—4882no—
856C2—4882no—
857C2#2145690714yesdirect product factor
858C2C2×#1684032611yescharacteristic
859C2C2×#1684056511yescharacteristic
860C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
hypercenterC2×#542D61
hypocenterC61C2×#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840331C2semidirect
2. #21456907C2direct (N × H)
3. C2×#16840152C2semidirect
4. C2×#16840144C2semidirect
5. C2×#16840124C2semidirect
6. C2×#16840110C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839962C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839922C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839912C2semidirect
14. C2×#16839895C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#542C2semidirect
19. C22×#11758202C22semidirect
20. C22×#11758200C22semidirect
23. C22×#11758201C22semidirect
26. C22×#11758199C22semidirect
28. #16840331C22semidirect
37. #16840152C22semidirect
38. #16840144C22semidirect
39. #16840124C22semidirect
40. #16840110C22semidirect
41. #16839984C22semidirect
42. #16839977C22semidirect
43. #16839962C22semidirect
44. #16839957C22semidirect
45. #16839922C22semidirect
46. #16839912C22semidirect
47. #16839905C22semidirect
48. #16839895C22semidirect
49. #16839823C22semidirect
50. C2×C4⋊#92418C22semidirect
51. C2×C4⋊#92418C22semidirect
52. C2×#14519700C22semidirect
53. C2×#14519700C22semidirect
58. C2×#14519697C22semidirect
59. C2×#14519697C22semidirect
62. C2×#14519688C22semidirect
63. C2×C4×#92418C22semidirect
65. C61×#542C22semidirect
66. C2×C4⋊Q8×C61C22semidirect
69. C2×#124×C61C22semidirect
74. C2×C4×Q8×C61C22semidirect
75. C2×C4×D4×C61C22semidirect
98. C2×#11758202C23semidirect
100. C2×#11758200C23semidirect
106. C2×#11758201C23semidirect
112. C2×#11758199C23semidirect
133. C4⋊#92418C23semidirect
134. C4⋊#92418C23semidirect
135. #14519700C23semidirect
136. #14519700C23semidirect
141. #14519697C23semidirect
142. #14519697C23semidirect
145. #14519688C23semidirect
146. C4×#92418C23semidirect
154. C4⋊Q8×C61C23semidirect
158. #124×C61C23semidirect
166. C4×Q8×C61C23semidirect
168. C4×D4×C61C23semidirect
422. C2×#542D61semidirect
440. C2×C61#3224semidirect
458. #542C2×D61semidirect
461. C2×C4⋊Q8C2×D61semidirect
468. C2×#124C2×D61semidirect
477. C2×C4×Q8C2×D61semidirect
478. C2×C4×D4C2×D61semidirect
507. C61C2×#3224semidirect
555. C4⋊Q8C22×D61semidirect
567. #124C22×D61semidirect
579. C4×Q8C22×D61semidirect
581. C4×D4C22×D61semidirect
857. C2#21456907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403312
#214569072
C2×#168401522
C2×#168401442
C2×#168401242
C2×#168401102
C2×#168399842
C2×#168399622
C2×#168399772
C2×#168399572
C2×#168399222
C2×#168399052
C2×#168399122
C2×#168398952
C2×#168398232
C2×C61×#5422
C2×#322461