Finite Group Databasebeta

← C2×#21456915 #30551370

Subgroups — C2×#21456915 #30551370

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×#16840383C211yesmaximal, characteristic, complemented
2C2×#16840331C211yesmaximal, characteristic, complemented
3#21456915C2116yesmaximal, direct product factor
4C2×#16840151C211yesmaximal, characteristic, complemented
5C2×#16840146C211yesmaximal, characteristic, complemented
6C2×#16840122C211yesmaximal, characteristic, complemented
7C2×#16840109C211yesmaximal, characteristic, complemented
8C2×#16839985C211yesmaximal, characteristic, complemented
9C2×#16839963C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839958C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839909C211yesmaximal, characteristic, complemented
14C2×#16839915C211yesmaximal, characteristic, complemented
15C2×#16839898C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758190C2211yescharacteristic, complemented
23C22×#11758190C2211yescharacteristic, complemented
24C22×D488C2211yescharacteristic
25C22×D488C2211yescharacteristic
26C22×D488C2211yescharacteristic, complemented
27#16840383—24no—
28#16840383C2218yescomplemented
29#16840331—24no—
30#16840331C2218yescomplemented
31C2×#14519777C2211yescharacteristic, complemented
32C2×#14519774C2211yescharacteristic
33C2×#14519774C2211yescharacteristic
34C2×#14519772—21no—
35C2×#14519765C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519765C2211yescharacteristic, complemented
38C2×#14519763—21no—
39C2×#14519759—21no—
40C2×#14519756C2211yescharacteristic
41C2×#14519755—21no—
42C2×#14519752—21no—
43C2×#14519752—21no—
44C2×#14519751C2211yescharacteristic
45C2×#14519747—21no—
46C2×#14519747—21no—
47C2×C4×Dic122C2211yescharacteristic, complemented
48C2×C4×D244C2211yescharacteristic, complemented
49#16840151C2218yescomplemented
50#16840146C2218yescomplemented
51#16840122C2218yescomplemented
52#16840109C2218yescomplemented
53#16839985C2218yescomplemented
54#16839978C2218yescomplemented
55#16839963C2218yescomplemented
56#16839958C2218yescomplemented
57#16839926C2218yescomplemented
58#16839915C2218yescomplemented
59#16839909C2218yescomplemented
60#16839898C2218yescomplemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519702C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic, complemented
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic, complemented
72C2×C4⋊C8×C61C2211yescharacteristic, complemented
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—42no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2311yescharacteristic
85C22×D244—21no—
86C22×D244—22no—
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244—21no—
91C22×D244—42no—
92C22×D244—42no—
93C22×D244C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×D244C2311yescharacteristic
96C22×D244C2311yescharacteristic
97C22×D244C2314yes—
98C22×C22⋊D61—21no—
99C22×C22⋊D61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C2×Dic244—42no—
103C2×Dic244C2314yescomplemented
104C2×#11758190—42no—
105C2×#11758190—42no—
106C2×#11758190—42no—
107C2×#11758190—42no—
108C2×#11758190C2314yes—
109C2×#11758190C2314yes—
110C2×#11758190C2314yescomplemented
111C2×#11758190C2314yescomplemented
112C2×D488—42no—
113C2×D488—42no—
114C2×D488—42no—
115C2×D488C2314yes—
116C2×D488C2314yes—
117C2×D488C2314yescomplemented
118#14519777—22no—
119#14519777C2314yescomplemented
120#14519774—22no—
121#14519774—22no—
122#14519774C2314yes—
123#14519774C2314yes—
124#14519772—28no—
125#14519765—22no—
126#14519765—22no—
127#14519765—22no—
128#14519765C2314yes—
129#14519765C2314yes—
130#14519765C2314yescomplemented
131#14519763—28no—
132#14519759—28no—
133#14519756—22no—
134#14519756C2314yes—
135#14519755—28no—
136#14519752—28no—
137#14519752—28no—
138#14519751—22no—
139#14519751C2314yes—
140#14519747—28no—
141#14519747—28no—
142C4×Dic122—22no—
143C4×Dic122C2314yescomplemented
144C4×D244—22no—
145C4×D244C2314yescomplemented
146C2×C4⋊Dic61—21no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×C4⋊Dic61C2311yescharacteristic
149C2×#11758196—21no—
150C2×#11758196—21no—
151C2×C22⋊Dic61—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×C4×Dic61—21no—
161#14519702C2314yescomplemented
162#14519702C2314yescomplemented
163#14519699C2314yes—
164#14519699C2314yes—
165#14519699C2314yes—
166#14519699C2314yes—
167#14519699C2314yescomplemented
168#14519699C2314yescomplemented
169C23×C4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#117×C61D414yes—
175#117×C61C2314yes—
176C2×C4⋊C4×C61D411yescharacteristic
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yescomplemented
183C4⋊C8×C61C2314yescomplemented
184C22⋊C8×C61C2314yes—
185C22⋊C8×C61C2314yes—
186#97×C61C2314yescomplemented
187C4×C8×C61C2314yescomplemented
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—24no—
194C23×D61—44no—
195C23×D61—82no—
196C23×D61—82no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—82no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215#11758222—44no—
216#11758222—44no—
217#11758222—48no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—24no—
232C2×D244—24no—
233C2×D244—24no—
234C2×D244—24no—
235C2×D244—44no—
236C2×D244—44no—
237C2×D244—44no—
238C2×D244—48no—
239C2×D244—82no—
240C2×D244—82no—
241C2×D244—82no—
242C2×D244—82no—
243C2×D244C2412yes—
244C2×D244C2412yes—
245C2×D244C2412yes—
246C2×D244C2412yes—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—44no—
250C2×C4×D61—82no—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—22no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—24no—
258C2×Dic122—82no—
259C2×Dic122C2412yes—
260C2×Dic122C2412yes—
261C2×C8×C61—22no—
262C2×C8×C61—22no—
263C2×C8×C61—22no—
264C2×C8×C61—22no—
265C2×C8×C61C2412yes—
266C2×C8×C61C2412yes—
267C2×C8×C61C2412yes—
268C2×C8×C61C2412yes—
269C4⋊C4×C61C2×D414yes—
270C4⋊C4×C61C2×D414yes—
271C22⋊C4×C61C2×D414yes—
272C22⋊C4×C61C2×D414yes—
273C42×C61C2×D412yes—
274C42×C61C2×D412yes—
275C42×C61C2412yes—
276C42×C61C2412yes—
277C22⋊Dic61—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286C4⋊Dic61—24no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C2412yes—
290C4⋊Dic61C2412yes—
291#11758196—24no—
292#11758196—24no—
293C4×Dic61—24no—
294Dic244—44no—
295D488—44no—
296D488—44no—
297D488—44no—
298#11758190—44no—
299#11758190—44no—
300#11758190—44no—
301#11758190—44no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—48no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
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—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—24no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D412yes—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61H(5,𝔽2)12yes—
342C2×C4×C61H(5,𝔽2)12yes—
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—48no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354D244—22no—
355D244—22no—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—22no—
362D244—48no—
363D244—42no—
364D244—42no—
365D244—42no—
366D244—42no—
367D244—84no—
368D244—84no—
369D244—84no—
370D244—84no—
371C4×D61—48no—
372C4×D61—84no—
373Dic122—22no—
374Dic122—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—42no—
378Dic122—42no—
379Dic122—84no—
380C8×C61—22no—
381C8×C61—22no—
382C8×C61—22no—
383C8×C61—22no—
384C2×#3224—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—44no—
389C22×C61#53512yes—
390C22×C61#57612yes—
391C22×C61#57712yes—
392C22×C61C23×D411yescharacteristic
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
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—816no—
406C2×D61—84no—
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#53512yes—
416C4×C61C2×H(5,𝔽2)11yescharacteristic
417C4×C61C2×H(5,𝔽2)11yescharacteristic
418Dic61—42no—
419Dic61—42no—
420Dic61—42no—
421Dic61—42no—
422C2×#542—611no—
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×#433D6111yescharacteristic, complemented
438C2×C61—42no—
439C2×C61#322414yescomplemented
440C2×C61C2×#53511yescharacteristic
441C2×C61C2×#57611yescharacteristic
442C2×C61C2×#57711yescharacteristic
443D61—82no—
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—618no—
458#542—1224no—
459#535—618no—
460#535—1224no—
461C2×C4⋊Q8—611no—
462C2×#127—611no—
463C2×#127—611no—
464C2×#126—1221no—
465C2×#124—611no—
466C2×#124—611no—
467C2×#124—611no—
468C2×#124—1221no—
469C2×#123—1221no—
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—1221no—
472C2×#121—611no—
473C2×#121—1221no—
474C2×#121—1221no—
475C2×#120—1221no—
476C2×#120—1221no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
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#433C2×D6118yescomplemented
493C2×C4⋊C8C2×D6111yescharacteristic, complemented
494C2×C4⋊C8C2×D6111yescharacteristic, complemented
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⋊C8C2×D6111yescharacteristic
504C2×C22⋊C8C2×D6111yescharacteristic
505C2×#97C2×D6111yescharacteristic, complemented
506C2×C4×C8C2×D6111yescharacteristic, complemented
507C61C2×#322411yescharacteristic, complemented, Sylow
508C25—1221no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—2442no—
512C2×#41—2442no—
513C22×Q8—611no—
514C22×Q8—611no—
515C22×Q8—1221no—
516C22×D4—611no—
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—1221no—
528C22×D4—1222no—
529C22×D4—2442no—
530C22×D4—2442no—
531C23×C4—1221no—
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×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552C22×C8C22×D6111yescharacteristic
553C22×C8C22×D6111yescharacteristic
554C4⋊Q8—614no—
555C4⋊Q8—1222no—
556#127—614no—
557#127—614no—
558#127—1222no—
559#127—1222no—
560#126—1228no—
561#124—614no—
562#124—614no—
563#124—614no—
564#124—1228no—
565#124—1222no—
566#124—1222no—
567#124—1222no—
568#123—1228no—
569C22⋊Q8—614no—
570C22⋊Q8—1222no—
571C22⋊Q8—1228no—
572#121—614no—
573#121—1222no—
574#121—1228no—
575#121—1228no—
576#120—1228no—
577#120—1228no—
578C4×Q8—614no—
579C4×Q8—1222no—
580C4×D4—614no—
581C4×D4—1222no—
582#117D24414yes—
583#117C22×D6114yes—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—1221no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4D24411yescharacteristic
590C2×C4⋊C4D24411yescharacteristic
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4D24411yescharacteristic
601C2×C22⋊C4D24411yescharacteristic
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C4⋊C8C22×D6114yescomplemented
606C4⋊C8C22×D6114yescomplemented
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⋊C8C22×D6114yes—
616C22⋊C8C22×D6114yes—
617#97C22×D6114yescomplemented
618C4×C8C22×D6114yescomplemented
619C24—1224no—
620C24—1221no—
621C24—1221no—
622C24—1221no—
623C24—1221no—
624C24—4882no—
625C24—4882no—
626C24—2444no—
627C24C2×D24411yescharacteristic
628#41—2444no—
629#41—2444no—
630#41—2448no—
631C2×Q8—612no—
632C2×Q8—612no—
633C2×Q8—1224no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1222no—
637C2×Q8—1222no—
638C2×Q8—1222no—
639C2×Q8—1222no—
640C2×Q8—4882no—
641C2×D4—612no—
642C2×D4—612no—
643C2×D4—612no—
644C2×D4—612no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—1224no—
650C2×D4—1224no—
651C2×D4—1221no—
652C2×D4—1224no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1222no—
657C2×D4—1222no—
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—4882no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4—2448no—
673C2×D4—2444no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1224no—
681C22×C4—1224no—
682C22×C4—4882no—
683C22×C4—2444no—
684C22×C4C2×D24412yes—
685C22×C4C2×D24411yescharacteristic
686C22×C4C2×D24411yescharacteristic
687C22×C4C2×D24411yescharacteristic
688C22×C4C2×D24411yescharacteristic
689C22×C4C2×D24411yescharacteristic
690C22×C4C23×D6112yes—
691C22×C4C23×D6111yescharacteristic
692Q16—2444no—
693SD16—2444no—
694SD16—2444no—
695SD16—2444no—
696SD16—2444no—
697D8—2444no—
698D8—2444no—
699D8—2444no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8C23×D6112yes—
705C2×C8C23×D6112yes—
706C2×C8C23×D6112yes—
707C2×C8C23×D6112yes—
708C4⋊C4—612no—
709C4⋊C4—612no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4C2×D24414yes—
716C4⋊C4C2×D24414yes—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4C2×D24414yes—
727C22⋊C4C2×D24414yes—
728C42—1224no—
729C42C2×D24412yes—
730C42C2×D24412yes—
731C42C23×D6112yes—
732C42C23×D6112yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—1222no—
737C23—1222no—
738C23—1222no—
739C23—1222no—
740C23—4884no—
741C23—4884no—
742C23—48816no—
743C23—2448no—
744C23—2442no—
745C23—2442no—
746C23—2442no—
747C23—2442no—
748C23—2442no—
749C23—2442no—
750C23—2442no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23—2442no—
755C23—2442no—
756C23C22×D24412yes—
757C23C22×D24411yescharacteristic
758Q8—1222no—
759Q8—1222no—
760Q8—1222no—
761Q8—1222no—
762Q8—4884no—
763Q8—2442no—
764Q8—2442no—
765D4—1222no—
766D4—1222no—
767D4—1222no—
768D4—1222no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—4884no—
774D4—4884no—
775D4—4884no—
776D4—4884no—
777D4—4884no—
778D4—2448no—
779D4—2448no—
780D4—2442no—
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—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—4884no—
797C2×C4—2448no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2442no—
802C2×C4C22×D24412yes—
803C2×C4C22×D24412yes—
804C2×C4C22×D24412yes—
805C2×C4C22×D24412yes—
806C2×C4C22×D24412yes—
807C2×C4C22×D24411yescharacteristic
808C2×C4#1451982312yes—
809C2×C4#1451982312yes—
810C2×C4C24×D6111yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—48816no—
820C22—4884no—
821C22—4884no—
822C22—4884no—
823C22—4884no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22—2442no—
828C22—2442no—
829C22—2442no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22#1684033112yes—
837C22#1684056712yes—
838C22#1684057412yes—
839C22C23×D24411yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—2442no—
846C4—2442no—
847C4—2442no—
848C4—2442no—
849C4#1684033112yes—
850C4C2×#1451982311yescharacteristic
851C4C2×#1451982311yescharacteristic
852C2—42no—
853C2—4882no—
854C2—4882no—
855C2—4882no—
856C2—4882no—
857C2#2145691514yesdirect product factor
858C2C2×#1684033111yescharacteristic
859C2C2×#1684056711yescharacteristic
860C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
hypercenterC2×#433D61
hypocenterC61C2×#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. C2×#16840331C2semidirect
3. #21456915C2direct (N × H)
4. C2×#16840151C2semidirect
5. C2×#16840146C2semidirect
6. C2×#16840122C2semidirect
7. C2×#16840109C2semidirect
8. C2×#16839985C2semidirect
9. C2×#16839963C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839958C2semidirect
12. C2×#16839926C2semidirect
13. C2×#16839909C2semidirect
14. C2×#16839915C2semidirect
15. C2×#16839898C2semidirect
16. C2×C61×#433C2semidirect
19. C22×Dic244C22semidirect
22. C22×#11758190C22semidirect
23. C22×#11758190C22semidirect
26. C22×D488C22semidirect
28. #16840383C22semidirect
30. #16840331C22semidirect
31. C2×#14519777C22semidirect
37. C2×#14519765C22semidirect
47. C2×C4×Dic122C22semidirect
48. C2×C4×D244C22semidirect
49. #16840151C22semidirect
50. #16840146C22semidirect
51. #16840122C22semidirect
52. #16840109C22semidirect
53. #16839985C22semidirect
54. #16839978C22semidirect
55. #16839963C22semidirect
56. #16839958C22semidirect
57. #16839926C22semidirect
58. #16839915C22semidirect
59. #16839909C22semidirect
60. #16839898C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519702C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519699C22semidirect
70. C61×#433C22semidirect
71. C2×C4⋊C8×C61C22semidirect
72. C2×C4⋊C8×C61C22semidirect
75. C2×#97×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
103. C2×Dic244C23semidirect
110. C2×#11758190C23semidirect
111. C2×#11758190C23semidirect
117. C2×D488C23semidirect
119. #14519777C23semidirect
130. #14519765C23semidirect
143. C4×Dic122C23semidirect
145. C4×D244C23semidirect
161. #14519702C23semidirect
162. #14519702C23semidirect
167. #14519699C23semidirect
168. #14519699C23semidirect
182. C4⋊C8×C61C23semidirect
183. C4⋊C8×C61C23semidirect
186. #97×C61C23semidirect
187. C4×C8×C61C23semidirect
437. C2×#433D61semidirect
439. C2×C61#3224semidirect
492. #433C2×D61semidirect
493. C2×C4⋊C8C2×D61semidirect
494. C2×C4⋊C8C2×D61semidirect
505. C2×#97C2×D61semidirect
506. C2×C4×C8C2×D61semidirect
507. C61C2×#3224semidirect
605. C4⋊C8C22×D61semidirect
606. C4⋊C8C22×D61semidirect
617. #97C22×D61semidirect
618. C4×C8C22×D61semidirect
857. C2#21456915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
C2×#168403312
#214569152
C2×#168401512
C2×#168401462
C2×#168401222
C2×#168401092
C2×#168399852
C2×#168399632
C2×#168399782
C2×#168399582
C2×#168399262
C2×#168399092
C2×#168399152
C2×#168398982
C2×C61×#4332
C2×#322461