Finite Group Databasebeta

← C2×#21458059 #30556852

Subgroups — C2×#21458059 #30556852

Order 15616.

2630 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840475C211yesmaximal, characteristic, complemented
2C2×#16840396C211yesmaximal, characteristic, complemented
3#21458059C2116yesmaximal, direct product factor
4C2×#16840107C211yesmaximal, characteristic, complemented
5C2×#16840089C211yesmaximal, characteristic, complemented
6C2×#16840051C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16839956C211yesmaximal, characteristic, complemented
10C2×#16839898C211yesmaximal, characteristic, complemented
11C2×#16839897C211yesmaximal, characteristic, complemented
12C2×#16839844C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839766C211yesmaximal, characteristic, complemented
15C2×#16839765C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C22×D4×D61—21no—
19C22×D4×D61C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic, complemented
22C22×#11758199C2211yescharacteristic, complemented
23C22×#11758194C2211yescharacteristic, complemented
24C22×#11758189C2211yescharacteristic, complemented
25#16840475—24no—
26#16840475C2218yescomplemented
27#16840396—24no—
28#16840396C2218yescomplemented
29C2×#14519776C2211yescharacteristic, complemented
30C2×#14519773C2211yescharacteristic
31C2×#14519765—21no—
32C2×#14519763—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic, complemented
35C2×#14519751C2211yescharacteristic, complemented
36C2×#14519750—21no—
37C2×#14519750—21no—
38C2×#14519747—21no—
39C2×#14519745—21no—
40C2×#14519739C2211yescharacteristic
41C2×#14519739C2211yescharacteristic, complemented
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×#14519735C2211yescharacteristic, complemented
44C2×#14519734—21no—
45#16840107C2218yescomplemented
46#16840089C2218yescomplemented
47#16840051C2218yescomplemented
48#16840016C2218yescomplemented
49#16840013C2218yescomplemented
50#16839956C2218yescomplemented
51#16839898C2218yescomplemented
52#16839897C2218yescomplemented
53#16839844C2218yescomplemented
54#16839837C2218yescomplemented
55C2×#14519708C2211yescharacteristic, complemented
56C2×#14519706C2211yescharacteristic, complemented
57#16839766C2218yescomplemented
58#16839765C2218yescomplemented
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic, complemented
61C2×#14519698C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65C2×#14519697C2211yescharacteristic, complemented
66C2×#14519697C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic, complemented
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C24×D61—21no—
79C22×Dic122—21no—
80C22×D244—24no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244—22no—
84C22×D244—21no—
85C22×D244—42no—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×D244C2314yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61D411yescharacteristic
95C2×D4×D61—28no—
96C2×D4×D61—24no—
97C2×D4×D61—22no—
98C2×D4×D61—42no—
99C2×D4×D61—48no—
100C2×D4×D61C2314yes—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104C2×D488—24no—
105C2×D488—42no—
106C2×D488C2314yes—
107C2×D488C2314yescomplemented
108C2×#11758199—42no—
109C2×#11758199C2314yescomplemented
110C2×#11758194—42no—
111C2×#11758194C2314yescomplemented
112C2×#11758189—42no—
113C2×#11758189C2314yescomplemented
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116#14519776—22no—
117#14519776C2314yescomplemented
118#14519773—22no—
119#14519773C2314yes—
120#14519765—28no—
121#14519763—28no—
122#14519752—22no—
123#14519752—22no—
124#14519752C2314yes—
125#14519752C2314yescomplemented
126#14519751—22no—
127#14519751C2314yescomplemented
128#14519750—28no—
129#14519750—28no—
130#14519747—28no—
131#14519745—28no—
132#14519739—22no—
133#14519739—22no—
134#14519739C2314yes—
135#14519739C2314yescomplemented
136C4×C22⋊D61D414yes—
137C4×C22⋊D61C2314yes—
138#14519735—22no—
139#14519735C2314yescomplemented
140#14519734—28no—
141C2×C4⋊Dic61C2311yescharacteristic
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C2×C22⋊Dic61D411yescharacteristic
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154#14519708C2314yescomplemented
155#14519706C2314yescomplemented
156#14519699C2314yes—
157#14519699C2314yescomplemented
158#14519698C2314yescomplemented
159#14519697C2314yes—
160#14519697C2314yes—
161#14519697C2314yescomplemented
162#14519697C2314yescomplemented
163#14519697C2314yescomplemented
164#14519689C2314yescomplemented
165C8×Dic61C2314yescomplemented
166C22×D4×C61—21no—
167C22×D4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171#121×C61—22no—
172#121×C61C2314yes—
173#117×C61—22no—
174#117×C61C2314yescomplemented
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181#107×C61C2314yescomplemented
182#106×C61C2314yescomplemented
183#102×C61C2314yescomplemented
184#102×C61C2314yescomplemented
185C22⋊C8×C61C2314yescomplemented
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—24no—
193C23×D61—44no—
194C23×D61—44no—
195C23×D61—44no—
196C23×D61—44no—
197C23×D61—82no—
198C23×D61—82no—
199C23×D61C2×D411yescharacteristic
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—44no—
205C2×D4×C61C2412yes—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61C2×D414yes—
225C22×Dic61—21no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229D4×D61—28no—
230D4×D61—44no—
231D4×D61—48no—
232D4×D61—432no—
233C2×D244—21no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—28no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—24no—
245C2×D244—44no—
246C2×D244—48no—
247C2×D244—44no—
248C2×D244—44no—
249C2×D244—82no—
250C2×D244#4114yes—
251C2×D244C2412yes—
252C2×D244C2412yes—
253C2×D244C2412yes—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2412yes—
262C2×Dic122—24no—
263C2×Dic122—82no—
264C2×C8×C61—22no—
265C2×C8×C61—22no—
266C2×C8×C61C2412yes—
267C2×C8×C61C2412yes—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C2412yes—
272C4⋊C4×C61C2412yes—
273C4⋊C4×C61C2412yes—
274C22⋊C4×C61—24no—
275C22⋊C4×C61—24no—
276C42×C61—24no—
277C22⋊Dic61C2×D414yes—
278#11758199—44no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198C2×D414yes—
286C4⋊Dic61—21no—
287C4⋊Dic61C2412yes—
288#11758196—24no—
289#11758196C2×D414yes—
290C4×Dic61—24no—
291C4×Dic61C2×D412yes—
292C4×Dic61C2412yes—
293#11758194—44no—
294C2×#92418—22no—
295C2×#92418—22no—
296C2×#92418C2412yes—
297C2×#92418C2412yes—
298D488—28no—
299D488—44no—
300#11758189—44no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61C22×D412yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—22no—
311C22×D61—24no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—48no—
318C22×D61—48no—
319C22×D61—48no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—48no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—84no—
330C22×D61—84no—
331C22×D61—816no—
332C22×D61—816no—
333C22×D61C22×D412yes—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—48no—
337D4×C61—42no—
338C2×C4×C61—22no—
339C2×C4×C61—24no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C2×#4112yes—
351C2×C4×C61H(5,𝔽2)12yes—
352C2×C4×C61C2511yescharacteristic
353C22⋊D61—28no—
354C22⋊D61—48no—
355C22⋊D61—48no—
356C22⋊D61—84no—
357C22⋊D61—84no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61AGL(1,ℤ/8)14yes—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365C2×Dic61C22×D412yes—
366D244—24no—
367D244—22no—
368D244—22no—
369D244—22no—
370D244—22no—
371D244—22no—
372D244—48no—
373D244—48no—
374D244—42no—
375D244—42no—
376D244—84no—
377D244C2×#4114yes—
378C4×D61—24no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—48no—
382C4×D61—48no—
383Dic122—84no—
384C8×C61—22no—
385C8×C61—22no—
386#92418—22no—
387#92418—22no—
388C2×#3325—611nomaximal, Sylow
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—44no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—84no—
397C22×C61#54612yes—
398C22×C61C2×AGL(1,ℤ/8)12yes—
399C22×C61#57612yes—
400C22×C61C23×D411yescharacteristic
401C2×D61—22no—
402C2×D61—24no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—42no—
406C2×D61—44no—
407C2×D61—48no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—816no—
416C2×D61—816no—
417C2×D61—84no—
418C2×D61—84no—
419C4×C61—22no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61—42no—
423C4×C61#54612yes—
424C4×C61C22×#4111yescharacteristic
425C4×C61C2×H(5,𝔽2)11yescharacteristic
426Dic61—22no—
427Dic61—22no—
428Dic61—42no—
429Dic61C2×AGL(1,ℤ/8)14yes—
430C2×#555—611no—
431C2×D42—611no—
432#3325—6116no—
433C2×#486—611no—
434C2×#482—611no—
435C2×#482D6111yescharacteristic, complemented
436C2×#476—611no—
437C2×#469—611no—
438C2×#469—611no—
439C2×#459—611no—
440C2×#447—611no—
441C2×#447—611no—
442C2×C4×D8—611no—
443C2×#436—611no—
444C2×#418—611no—
445C2×#418—611no—
446C2×C61—42no—
447C2×C61—82no—
448C2×C61#332514yescomplemented
449C2×C61C2×#54611yescharacteristic
450C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
451C2×C61C2×#57611yescharacteristic
452D61—42no—
453D61—44no—
454D61—82no—
455D61—82no—
456C23×D4—611no—
457C23×D4—611no—
458C23×D4—1221no—
459C22×D8—611no—
460C22×D8—611no—
461C22×D8—611no—
462C22×M16—611no—
463C22×M16—611no—
464#555—618no—
465#555—1224no—
466D42—618no—
467D42—1224no—
468C2×C4⋊Q8—611no—
469C2×#127—611no—
470C2×#124—1221no—
471C2×#124—1221no—
472C2×#121—611no—
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—1221no—
476C2×#121—1221no—
477C2×#121C2×D6111yescharacteristic
478C2×#120—1221no—
479C2×#120—1221no—
480C2×C4×D4—611no—
481C2×C4×D4—611no—
482C2×C4×D4—611no—
483C2×#117—611no—
484C2×#117—1221no—
485C2×#117C2×D6111yescharacteristic, complemented
486#486—618no—
487#482—618no—
488#482C2×D6118yescomplemented
489#476—618no—
490#469—618no—
491#469—618no—
492#459—618no—
493#447—618no—
494#447—618no—
495C4×D8—618no—
496#436—618no—
497C2×#107C2×D6111yescharacteristic, complemented
498C2×#106—611no—
499C2×#106C2×D6111yescharacteristic, complemented
500C2×C4⋊C8—611no—
501#418—618no—
502#418—618no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102C2×D6111yescharacteristic, complemented
512C2×#102C2×D6111yescharacteristic, complemented
513C2×C22⋊C8—611no—
514C2×C22⋊C8C2×D6111yescharacteristic, complemented
515C2×C4×C8—611no—
516C61C2×#332511yescharacteristic, complemented, Sylow
517C25—1221no—
518C25—1221no—
519C22×Q8—1221no—
520C22×D4—21no—
521C22×D4—611no—
522C22×D4—614no—
523C22×D4—611no—
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—614no—
527C22×D4—1224no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1222no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1224no—
535C22×D4—1228no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1222no—
539C22×D4—2442no—
540C22×D4—2442no—
541C22×D4—2448no—
542C22×D4C22×D6111yescharacteristic
543C23×C4—611no—
544C23×C4—1221no—
545C23×C4—1221no—
546C23×C4C22×D6111yescharacteristic
547C2×D8—614no—
548C2×D8—614no—
549C2×D8—614no—
550C2×D8—1224no—
551C2×D8—2442no—
552C2×D8—2442no—
553C2×M16—614no—
554C2×M16—614no—
555C2×M16—2442no—
556C2×M16—2442no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8C22×D6111yescharacteristic
560C22×C8C22×D6111yescharacteristic
561C4⋊Q8—614no—
562C4⋊Q8—1222no—
563#127—614no—
564#127—1222no—
565#124—1228no—
566#124—1228no—
567#121—22no—
568#121—614no—
569#121—614no—
570#121—614no—
571#121—1228no—
572#121—1228no—
573#121—1222no—
574#121—1222no—
575#121—1222no—
576#121C22×D6114yes—
577#120—1228no—
578#120—1228no—
579C4×D4—614no—
580C4×D4—614no—
581C4×D4—614no—
582C4×D4—614no—
583C4×D4—1222no—
584C4×D4—1222no—
585#117—22no—
586#117—614no—
587#117—1228no—
588#117—1222no—
589#117C22×D6114yescomplemented
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C4⋊C4C22×D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C42—21no—
607C2×C42—611no—
608C2×C42—1221no—
609#107C22×D6114yescomplemented
610#106—614no—
611#106C22×D6114yescomplemented
612C4⋊C8—614no—
613#102—614no—
614#102—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618#102—614no—
619#102—614no—
620#102—614no—
621#102C22×D6114yescomplemented
622#102C22×D6114yescomplemented
623C22⋊C8—614no—
624C22⋊C8C22×D6114yescomplemented
625C4×C8—614no—
626C24—21no—
627C24—611no—
628C24—1224no—
629C24—1221no—
630C24—1224no—
631C24—1221no—
632C24—1221no—
633C24—4882no—
634C24—4882no—
635C24—2444no—
636C24—2444no—
637C24—2444no—
638C24—2444no—
639C24D4×D6111yescharacteristic
640C2×Q8—1224no—
641C2×Q8—4882no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—614no—
648C2×D4—614no—
649C2×D4—612no—
650C2×D4—612no—
651C2×D4—612no—
652C2×D4—1228no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1228no—
660C2×D4—1224no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1224no—
664C2×D4—1221no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1222no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4—4882no—
671C2×D4—4882no—
672C2×D4—4882no—
673C2×D4—2444no—
674C2×D4—2448no—
675C2×D4—2444no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2448no—
680C2×D4—2444no—
681C2×D4—24432no—
682C2×D4C23×D6112yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—1224no—
694C22×C4—1224no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1221no—
698C22×C4—2444no—
699C22×C4—2444no—
700C22×C4D4×D6112yes—
701C22×C4D4×D6111yescharacteristic
702C22×C4C23×D6112yes—
703C22×C4C23×D6111yescharacteristic
704D8—1228no—
705D8—2444no—
706D8—2444no—
707M16—2444no—
708M16—2444no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—612no—
712C2×C8—612no—
713C2×C8—1222no—
714C2×C8—1222no—
715C2×C8C23×D6112yes—
716C2×C8C23×D6112yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—614no—
721C4⋊C4—612no—
722C4⋊C4—1224no—
723C4⋊C4—1221no—
724C4⋊C4C23×D6112yes—
725C4⋊C4C23×D6112yes—
726C4⋊C4C23×D6112yes—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—614no—
730C22⋊C4—614no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C42—24no—
738C42—612no—
739C42—612no—
740C42—1224no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—612no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1224no—
754C23—1222no—
755C23—1222no—
756C23—4884no—
757C23—4884no—
758C23—48816no—
759C23—48816no—
760C23—2448no—
761C23—2448no—
762C23—2448no—
763C23—2448no—
764C23—2442no—
765C23—2442no—
766C23—2442no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23C2×D4×D6112yes—
773C23C2×D4×D6111yescharacteristic
774Q8—4884no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—614no—
780D4—1228no—
781D4—1222no—
782D4—1222no—
783D4—1222no—
784D4—1222no—
785D4—1222no—
786D4—1224no—
787D4—4884no—
788D4—4884no—
789D4—4884no—
790D4—2448no—
791D4—2448no—
792D4—2448no—
793D4—2448no—
794D4—2442no—
795D4—2442no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1224no—
815C2×C4—1222no—
816C2×C4—2448no—
817C2×C4—2448no—
818C2×C4—2442no—
819C2×C4C2×D4×D6112yes—
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4#41×D6112yes—
822C2×C4#1451982312yes—
823C2×C4C24×D6111yescharacteristic
824C8—22no—
825C8—22no—
826C8—1222no—
827C8—1222no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—1222no—
837C22—1224no—
838C22—1222no—
839C22—1222no—
840C22—48816no—
841C22—48816no—
842C22—4884no—
843C22—4884no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2444no—
853C22—2448no—
854C22#1684040412yes—
855C22AGL(1,ℤ/8)×D6112yes—
856C22#1684056412yes—
857C22C22×D4×D6111yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—614no—
863C4—1222no—
864C4—1222no—
865C4—2442no—
866C4#1684040412yes—
867C4C2×#41×D6111yescharacteristic
868C4C2×#1451982311yescharacteristic
869C2—42no—
870C2—82no—
871C2—4882no—
872C2—4882no—
873C2—2442no—
874C2—2444no—
875C2#2145805914yesdirect product factor
876C2C2×#1684040411yescharacteristic
877C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
878C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840475C2semidirect
2. C2×#16840396C2semidirect
3. #21458059C2direct (N × H)
4. C2×#16840107C2semidirect
5. C2×#16840089C2semidirect
6. C2×#16840051C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16839956C2semidirect
10. C2×#16839898C2semidirect
11. C2×#16839897C2semidirect
12. C2×#16839844C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839766C2semidirect
15. C2×#16839765C2semidirect
16. C2×C61×#482C2semidirect
21. C22×D488C22semidirect
22. C22×#11758199C22semidirect
23. C22×#11758194C22semidirect
24. C22×#11758189C22semidirect
26. #16840475C22semidirect
28. #16840396C22semidirect
29. C2×#14519776C22semidirect
34. C2×#14519752C22semidirect
35. C2×#14519751C22semidirect
41. C2×#14519739C22semidirect
43. C2×#14519735C22semidirect
45. #16840107C22semidirect
46. #16840089C22semidirect
47. #16840051C22semidirect
48. #16840016C22semidirect
49. #16840013C22semidirect
50. #16839956C22semidirect
51. #16839898C22semidirect
52. #16839897C22semidirect
53. #16839844C22semidirect
54. #16839837C22semidirect
55. C2×#14519708C22semidirect
56. C2×#14519706C22semidirect
57. #16839766C22semidirect
58. #16839765C22semidirect
60. C2×#14519699C22semidirect
61. C2×#14519698C22semidirect
64. C2×#14519697C22semidirect
65. C2×#14519697C22semidirect
66. C2×#14519697C22semidirect
67. C2×#14519689C22semidirect
68. C2×C8×Dic61C22semidirect
70. C2×#117×C61C22semidirect
71. C61×#482C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#102×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
107. C2×D488C23semidirect
109. C2×#11758199C23semidirect
111. C2×#11758194C23semidirect
113. C2×#11758189C23semidirect
117. #14519776C23semidirect
125. #14519752C23semidirect
127. #14519751C23semidirect
135. #14519739C23semidirect
139. #14519735C23semidirect
154. #14519708C23semidirect
155. #14519706C23semidirect
157. #14519699C23semidirect
158. #14519698C23semidirect
161. #14519697C23semidirect
162. #14519697C23semidirect
163. #14519697C23semidirect
164. #14519689C23semidirect
165. C8×Dic61C23semidirect
174. #117×C61C23semidirect
181. #107×C61C23semidirect
182. #106×C61C23semidirect
183. #102×C61C23semidirect
184. #102×C61C23semidirect
185. C22⋊C8×C61C23semidirect
435. C2×#482D61semidirect
448. C2×C61#3325semidirect
485. C2×#117C2×D61semidirect
488. #482C2×D61semidirect
497. C2×#107C2×D61semidirect
499. C2×#106C2×D61semidirect
511. C2×#102C2×D61semidirect
512. C2×#102C2×D61semidirect
514. C2×C22⋊C8C2×D61semidirect
516. C61C2×#3325semidirect
589. #117C22×D61semidirect
609. #107C22×D61semidirect
611. #106C22×D61semidirect
621. #102C22×D61semidirect
622. #102C22×D61semidirect
624. C22⋊C8C22×D61semidirect
875. C2#21458059direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404752
C2×#168403962
#214580592
C2×#168401072
C2×#168400892
C2×#168400512
C2×#168400162
C2×#168400132
C2×#168399562
C2×#168398982
C2×#168398972
C2×#168398442
C2×#168398372
C2×#168397662
C2×#168397652
C2×C61×#4822
C2×#332561