Finite Group Databasebeta

← C2×#21456866 #30551341

Subgroups — C2×#21456866 #30551341

Order 15616.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840363C211yesmaximal, characteristic, complemented
2C2×#16840330C211yesmaximal, characteristic, complemented
3#21456866C2116yesmaximal, direct product factor
4C2×#16840148C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840118C211yesmaximal, characteristic, complemented
8C2×#16839974C211yesmaximal, characteristic, complemented
9C2×#16839958C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic, complemented
13C2×#16839897C211yesmaximal, characteristic, complemented
14C2×#16839894C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758201C2211yescharacteristic, complemented
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic, complemented
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758199C2211yescharacteristic, complemented
25#16840363—24no—
26#16840363C2218yescomplemented
27#16840330—24no—
28#16840330C2218yescomplemented
29C2×#14519774C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31C2×#14519773C2211yescharacteristic, complemented
32C2×#14519768C2211yescharacteristic, complemented
33C2×#14519766C2211yescharacteristic
34C2×#14519760—21no—
35C2×#14519759—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519751—21no—
38C2×#14519750—21no—
39C2×#14519750—21no—
40C2×#14519750—21no—
41C2×#14519748C2211yescharacteristic
42C2×#14519747—21no—
43C2×#14519747—21no—
44C2×C4×D244C2211yescharacteristic, complemented
45C2×#14519734C2211yescharacteristic
46#16840148C2218yescomplemented
47#16840137C2218yescomplemented
48#16840125C2218yescomplemented
49#16840118C2218yescomplemented
50#16839974C2218yescomplemented
51#16839958C2218yescomplemented
52#16839957C2218yescomplemented
53#16839910C2218yescomplemented
54#16839906C2218yescomplemented
55#16839897C2218yescomplemented
56#16839894C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×SD16×C61C2211yescharacteristic, complemented
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic, complemented
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—42no—
80C2×#11758226—42no—
81C2×#11758226C2314yes—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C2×D4×D61—22no—
96C2×D4×D61—42no—
97C2×D4×D61—42no—
98C2×D4×D61C2314yes—
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101C22×C4×D61C2311yescharacteristic
102C2×#11758201—42no—
103C2×#11758201C2314yescomplemented
104C2×D488—42no—
105C2×D488—42no—
106C2×D488C2314yes—
107C2×D488C2314yescomplemented
108C2×#11758199—42no—
109C2×#11758199—42no—
110C2×#11758199—42no—
111C2×#11758199C2314yes—
112C2×#11758199C2314yes—
113C2×#11758199C2314yescomplemented
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116#14519774—22no—
117#14519774C2314yes—
118#14519773—22no—
119#14519773—22no—
120#14519773C2314yes—
121#14519773C2314yescomplemented
122#14519768—22no—
123#14519768C2314yescomplemented
124#14519766—22no—
125#14519766C2314yes—
126#14519760—28no—
127#14519759—28no—
128#14519752—22no—
129#14519752C2314yes—
130#14519751—28no—
131#14519750—28no—
132#14519750—28no—
133#14519750—28no—
134#14519748—22no—
135#14519748C2314yes—
136#14519747—28no—
137#14519747—28no—
138C4×D244—22no—
139C4×D244C2314yescomplemented
140#14519734D414yes—
141#14519734C2314yes—
142C2×C4⋊Dic61—21no—
143C2×C4⋊Dic61C2311yescharacteristic
144C2×#11758196—21no—
145C2×#11758196D411yescharacteristic
146C2×#11758196D411yescharacteristic
147C2×C22⋊Dic61—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198D411yescharacteristic
153C2×#11758198D411yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yescomplemented
156#14519701C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yescomplemented
159#14519698C2314yes—
160#14519697C2314yes—
161#14519697C2314yescomplemented
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yescomplemented
165C8×Dic61C2314yescomplemented
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C2×SD16×C61—42no—
171C2×SD16×C61C2314yescomplemented
172C2×D8×C61—42no—
173C2×D8×C61C2314yes—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176#124×C61—22no—
177#124×C61C2314yes—
178C4×D4×C61—22no—
179C4×D4×C61C2314yescomplemented
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yescomplemented
186#103×C61C2314yescomplemented
187#102×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—24no—
194C23×D61—44no—
195C23×D61—82no—
196C23×D61—82no—
197C23×D61C2×D411yescharacteristic
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61C2412yes—
209C2×D4×C61C2412yes—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—82no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61—82no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61—82no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758226—44no—
234#11758226—44no—
235#11758226—48no—
236D4×D61—44no—
237D4×D61—44no—
238D4×D61—48no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—22no—
244C2×D244—22no—
245C2×D244—24no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—24no—
250C2×D244—24no—
251C2×D244—24no—
252C2×D244—44no—
253C2×D244—82no—
254C2×D244—82no—
255C2×D244—82no—
256C2×D244C2412yes—
257C2×D244C2412yes—
258C2×D244C2412yes—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—24no—
262C2×C4×D61—24no—
263C2×C4×D61—44no—
264C2×C4×D61—82no—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2412yes—
267SD16×C61—44no—
268D8×C61—44no—
269C2×C8×C61—22no—
270C2×C8×C61—22no—
271C2×C8×C61C2412yes—
272C2×C8×C61C2412yes—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—24no—
278C42×C61C2×D412yes—
279C42×C61C2412yes—
280C22⋊Dic61—24no—
281#11758201—44no—
282#11758199—44no—
283#11758199—44no—
284#11758199—44no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289#11758198C2×D414yes—
290#11758198C2×D414yes—
291C4⋊Dic61—21no—
292C4⋊Dic61—24no—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295#11758196C2×D414yes—
296#11758196C2×D414yes—
297C4×Dic61C2×D412yes—
298C4×Dic61C2412yes—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303D488—44no—
304D488—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61C22×D411yescharacteristic
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—48no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—84no—
331C22×D61—84no—
332C22×D61—816no—
333C22×D61C22×D412yes—
334Q8×C61—22no—
335Q8×C61—22no—
336Q8×C61—42no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—42no—
342D4×C61—42no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—84no—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—48no—
357C22⋊D61—84no—
358C22⋊D61—84no—
359C22⋊D61—84no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—42no—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369C2×Dic61C22×D412yes—
370D244—22no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—48no—
377D244—42no—
378D244—42no—
379D244—42no—
380D244—84no—
381D244—84no—
382D244—84no—
383C4×D61—24no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—48no—
387C4×D61—84no—
388C8×C61—22no—
389C8×C61—22no—
390#92418—22no—
391#92418—22no—
392C2×#3220—611nomaximal, Sylow
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—84no—
400C22×C61—84no—
401C22×C61#53512yes—
402C22×C61#57612yes—
403C22×C61#57612yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—44no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—816no—
419C2×D61—84no—
420C2×D61—84no—
421C2×D61—84no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61#53512yes—
427C4×C61C2×H(5,𝔽2)11yescharacteristic
428C4×C61C2×H(5,𝔽2)11yescharacteristic
429Dic61—22no—
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433C2×#540—611no—
434C2×#535—611no—
435#3220—6116no—
436C2×#496—611no—
437C2×#493—611no—
438C2×#490—611no—
439C2×#488—611no—
440C2×#463—611no—
441C2×#463D6111yescharacteristic, complemented
442C2×#459—611no—
443C2×#459—611no—
444C2×#449—611no—
445C2×#449—611no—
446C2×#447—611no—
447C2×#447—611no—
448C2×#433—611no—
449C2×C61—82no—
450C2×C61—82no—
451C2×C61#322014yescomplemented
452C2×C61C2×#53511yescharacteristic
453C2×C61C2×#57611yescharacteristic
454C2×C61C2×#57611yescharacteristic
455D61—42no—
456D61—82no—
457D61—82no—
458D61—82no—
459C22×#41—611no—
460C23×D4—611no—
461C22×SD16—611no—
462C22×SD16C2×D6111yescharacteristic, complemented
463C22×D8—611no—
464C22×D8—611no—
465C22×D8—611no—
466C22×D8—611no—
467C22×D8—611no—
468C22×D8C2×D6111yescharacteristic
469#540—618no—
470#540—1224no—
471#535—618no—
472#535—1224no—
473C2×#127—611no—
474C2×#127—611no—
475C2×#127—611no—
476C2×#125—611no—
477C2×#124—611no—
478C2×#124C2×D6111yescharacteristic
479C2×#123—1221no—
480C2×#123—1221no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—1221no—
484C2×#121—1221no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#120—1221no—
488C2×#120—1221no—
489C2×C4×D4—611no—
490C2×C4×D4C2×D6111yescharacteristic, complemented
491C2×#117—611no—
492#496—618no—
493#493—618no—
494#490—618no—
495#488—618no—
496#463—618no—
497#463C2×D6118yescomplemented
498#459—618no—
499#459—618no—
500#449—618no—
501#449—618no—
502#447—618no—
503#447—618no—
504#433—618no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8C2×D6111yescharacteristic, complemented
507C2×#103—611no—
508C2×#103C2×D6111yescharacteristic, complemented
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102C2×D6111yescharacteristic
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517C2×#97—611no—
518C2×C4×C8—611no—
519C61C2×#322011yescharacteristic, complemented, Sylow
520C25—1221no—
521C2×#41—614no—
522C2×#41—1222no—
523C2×#41—2442no—
524C2×#41—2442no—
525C22×Q8C22×D6111yescharacteristic
526C22×D4—614no—
527C22×D4—611no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1222no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—1221no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—2442no—
542C22×D4—2442no—
543C22×D4C22×D6111yescharacteristic
544C22×D4C22×D6111yescharacteristic
545C23×C4—21no—
546C23×C4—611no—
547C23×C4—1221no—
548C23×C4—1221no—
549C2×SD16—42no—
550C2×SD16—614no—
551C2×SD16—2442no—
552C2×SD16C22×D6114yescomplemented
553C2×D8—42no—
554C2×D8—614no—
555C2×D8—614no—
556C2×D8—614no—
557C2×D8—614no—
558C2×D8—614no—
559C2×D8—2442no—
560C2×D8—2442no—
561C2×D8—2442no—
562C2×D8—2442no—
563C2×D8—2442no—
564C2×D8C22×D6114yes—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8C22×D6111yescharacteristic
568C22×C8C22×D6111yescharacteristic
569#127—614no—
570#127—614no—
571#127—614no—
572#127—1222no—
573#127—1222no—
574#127—1222no—
575#125—614no—
576#125—1222no—
577#124—22no—
578#124—614no—
579#124—1222no—
580#124C22×D6114yes—
581#123—1228no—
582#123—1228no—
583#121—614no—
584#121—614no—
585#121—1228no—
586#121—1228no—
587#121—1228no—
588#121—1228no—
589#121—1222no—
590#121—1222no—
591#120—1228no—
592#120—1228no—
593C4×D4—22no—
594C4×D4—614no—
595C4×D4—1222no—
596C4×D4C22×D6114yescomplemented
597#117—614no—
598#117—614no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C42—611no—
616C2×C42C22×D6111yescharacteristic
617C4⋊C8—614no—
618C4⋊C8C22×D6114yescomplemented
619#103—614no—
620#103C22×D6114yescomplemented
621#102—614no—
622#102—614no—
623#102—614no—
624#102—614no—
625#102—614no—
626#102C22×D6114yes—
627C22⋊C8—614no—
628C22⋊C8—614no—
629#97—614no—
630C4×C8—614no—
631C24—21no—
632C24—21no—
633C24—611no—
634C24—1224no—
635C24—1221no—
636C24—1221no—
637C24—1221no—
638C24—4882no—
639C24—4882no—
640C24—2444no—
641#41—2444no—
642#41—2444no—
643#41—2448no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D6112yes—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—612no—
655C2×D4—612no—
656C2×D4—612no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1224no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1222no—
671C2×D4—1222no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—4882no—
677C2×D4—4882no—
678C2×D4—4882no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2448no—
688C2×D4—2444no—
689C2×D4C23×D6112yes—
690C2×D4C23×D6112yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—82no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—612no—
699C22×C4—612no—
700C22×C4—1224no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1221no—
704C22×C4—1224no—
705C22×C4—4882no—
706C22×C4—2444no—
707C22×C4D4×D6111yescharacteristic
708C22×C4D4×D6111yescharacteristic
709C22×C4C23×D6111yescharacteristic
710SD16—44no—
711SD16—2444no—
712D8—44no—
713D8—2444no—
714D8—2444no—
715D8—2444no—
716D8—2444no—
717D8—2444no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—612no—
721C2×C8—612no—
722C2×C8—1222no—
723C2×C8—1222no—
724C2×C8C23×D6112yes—
725C2×C8C23×D6112yes—
726C4⋊C4—21no—
727C4⋊C4—614no—
728C4⋊C4—614no—
729C4⋊C4—612no—
730C4⋊C4—1224no—
731C4⋊C4—1224no—
732C4⋊C4—1221no—
733C4⋊C4C23×D6112yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—614no—
738C22⋊C4—614no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C22⋊C4—1224no—
742C22⋊C4—1224no—
743C22⋊C4—1224no—
744C42—612no—
745C42—612no—
746C42D4×D6112yes—
747C42C23×D6112yes—
748C23—22no—
749C23—22no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—612no—
757C23—1222no—
758C23—1222no—
759C23—1222no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23—4884no—
764C23—4884no—
765C23—48816no—
766C23—2448no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23—2442no—
776C23C2×D4×D6111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—42no—
785D4—42no—
786D4—1222no—
787D4—1222no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—4884no—
793D4—4884no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—2448no—
801D4—2448no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—612no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—4884no—
823C2×C4—2448no—
824C2×C4—2442no—
825C2×C4C2×D4×D6112yes—
826C2×C4C2×D4×D6112yes—
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#1451982212yes—
829C2×C4#1451982312yes—
830C2×C4C24×D6111yescharacteristic
831C8—22no—
832C8—22no—
833C8—1222no—
834C8—1222no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—84no—
843C22—1222no—
844C22—1222no—
845C22—1222no—
846C22—48816no—
847C22—4884no—
848C22—4884no—
849C22—4884no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2444no—
860C22#1684032812yes—
861C22#1684056412yes—
862C22#1684056612yes—
863C22C22×D4×D6111yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—1222no—
869C4—1222no—
870C4—1222no—
871C4—2442no—
872C4#1684032812yes—
873C4C2×#1451982211yescharacteristic
874C4C2×#1451982311yescharacteristic
875C2—82no—
876C2—82no—
877C2—4882no—
878C2—4882no—
879C2—4882no—
880C2—2442no—
881C2#2145686614yesdirect product factor
882C2C2×#1684032811yescharacteristic
883C2C2×#1684056411yescharacteristic
884C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
hypercenterC2×#463D61
hypocenterC61C2×#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840363C2semidirect
2. C2×#16840330C2semidirect
3. #21456866C2direct (N × H)
4. C2×#16840148C2semidirect
5. C2×#16840137C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840118C2semidirect
8. C2×#16839974C2semidirect
9. C2×#16839958C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839906C2semidirect
13. C2×#16839897C2semidirect
14. C2×#16839894C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#463C2semidirect
19. C22×#11758201C22semidirect
21. C22×D488C22semidirect
24. C22×#11758199C22semidirect
26. #16840363C22semidirect
28. #16840330C22semidirect
31. C2×#14519773C22semidirect
32. C2×#14519768C22semidirect
44. C2×C4×D244C22semidirect
46. #16840148C22semidirect
47. #16840137C22semidirect
48. #16840125C22semidirect
49. #16840118C22semidirect
50. #16839974C22semidirect
51. #16839958C22semidirect
52. #16839957C22semidirect
53. #16839910C22semidirect
54. #16839906C22semidirect
55. #16839897C22semidirect
56. #16839894C22semidirect
57. #16839822C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
64. C2×#14519697C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
69. C22×SD16×C61C22semidirect
72. C2×C4×D4×C61C22semidirect
73. C61×#463C22semidirect
74. C2×C4⋊C8×C61C22semidirect
75. C2×#103×C61C22semidirect
103. C2×#11758201C23semidirect
107. C2×D488C23semidirect
113. C2×#11758199C23semidirect
121. #14519773C23semidirect
123. #14519768C23semidirect
139. C4×D244C23semidirect
155. C4⋊#92418C23semidirect
156. #14519701C23semidirect
158. #14519699C23semidirect
161. #14519697C23semidirect
164. #14519687C23semidirect
165. C8×Dic61C23semidirect
171. C2×SD16×C61C23semidirect
179. C4×D4×C61C23semidirect
185. C4⋊C8×C61C23semidirect
186. #103×C61C23semidirect
441. C2×#463D61semidirect
451. C2×C61#3220semidirect
462. C22×SD16C2×D61semidirect
490. C2×C4×D4C2×D61semidirect
497. #463C2×D61semidirect
506. C2×C4⋊C8C2×D61semidirect
508. C2×#103C2×D61semidirect
519. C61C2×#3220semidirect
552. C2×SD16C22×D61semidirect
596. C4×D4C22×D61semidirect
618. C4⋊C8C22×D61semidirect
620. #103C22×D61semidirect
881. C2#21456866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403632
C2×#168403302
#214568662
C2×#168401482
C2×#168401372
C2×#168401252
C2×#168401182
C2×#168399742
C2×#168399582
C2×#168399572
C2×#168399102
C2×#168399062
C2×#168398972
C2×#168398942
C2×#168398222
C2×C61×#4632
C2×#322061