Finite Group Databasebeta

← C2×#21456660 #30550643

Subgroups — C2×#21456660 #30550643

Order 15616.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic, complemented
2C2×#16840269C211yesmaximal, characteristic, complemented
3#21456660C2116yesmaximal, direct product factor
4C2×#16840102C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840085C211yesmaximal, characteristic, complemented
8C2×#16840017C211yesmaximal, characteristic, complemented
9C2×#16840014C211yesmaximal, characteristic, complemented
10C2×#16840011C211yesmaximal, characteristic, complemented
11C2×#16840005C211yesmaximal, characteristic, complemented
12C2×#16839923C211yesmaximal, characteristic, complemented
13C2×#16839907C211yesmaximal, characteristic, complemented
14C2×#16839906C211yesmaximal, characteristic, complemented
15C2×#16839724C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×#11758201C2211yescharacteristic, complemented
20C22×#11758199C2211yescharacteristic, complemented
21C22×#11758189C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23#16840275—24no—
24#16840275C2218yescomplemented
25#16840269—24no—
26#16840269C2218yescomplemented
27C2×#14519762—21no—
28C2×#14519758—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×#14519747—21no—
37C2×#14519745—21no—
38C2×#14519739—21no—
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61—21no—
41C2×#14519737—21no—
42C2×#14519736C2211yescharacteristic
43C2×#14519735C2211yescharacteristic
44#16840102C2218yescomplemented
45#16840100C2218yescomplemented
46#16840087C2218yescomplemented
47#16840085C2218yescomplemented
48#16840017C2218yescomplemented
49#16840014C2218yescomplemented
50#16840011C2218yescomplemented
51#16840005C2218yescomplemented
52#16839923C2218yescomplemented
53#16839907C2218yescomplemented
54#16839906C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic, complemented
64C2×#14519698C2211yescharacteristic, complemented
65#16839724C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic, complemented
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yescomplemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C24×D61D411yescharacteristic
78C2×#11758226—22no—
79C2×#11758226—42no—
80C2×#11758226—42no—
81C2×#11758226C2314yes—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61D411yescharacteristic
89C22×C4×D61—21no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D414yes—
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C22×C4×D61C2314yes—
98C2×#11758201—42no—
99C2×#11758201C2314yescomplemented
100C2×#11758199—42no—
101C2×#11758199C2314yescomplemented
102C2×#11758189—42no—
103C2×#11758189—42no—
104C2×#11758189C2314yes—
105C2×#11758189C2314yes—
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108#14519762—28no—
109#14519758—28no—
110#14519753—22no—
111#14519753—22no—
112#14519753—22no—
113#14519753C2314yes—
114#14519753C2314yes—
115#14519753C2314yes—
116#14519752—22no—
117#14519752C2314yes—
118#14519751—22no—
119#14519751C2314yes—
120#14519748—22no—
121#14519748—22no—
122#14519748C2314yes—
123#14519748C2314yes—
124#14519747—28no—
125#14519745—28no—
126#14519739—28no—
127C4×C22⋊D61—28no—
128C4×C22⋊D61—28no—
129#14519737—28no—
130#14519736—22no—
131#14519736C2314yes—
132#14519735—22no—
133#14519735C2314yes—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519710C2314yescomplemented
153#14519709C2314yescomplemented
154#14519708C2314yescomplemented
155#14519701C2314yescomplemented
156#14519701C2314yescomplemented
157#14519701C2314yescomplemented
158#14519699C2314yescomplemented
159#14519699C2314yescomplemented
160#14519698C2314yescomplemented
161C22⋊#92418C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×Q8×C61C2311yescharacteristic
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C23×C4×C61—21no—
173C23×C4×C61C2311yescharacteristic
174C2×Q16×C61—42no—
175C2×Q16×C61C2314yescomplemented
176C2×SD16×C61—42no—
177C2×SD16×C61C2314yescomplemented
178C22×C8×C61C2311yescharacteristic
179C22×C8×C61C2311yescharacteristic
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61C2314yes—
182C2×C4⋊C4×C61—21no—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61—42no—
192C23×D61—42no—
193C23×D61—42no—
194C23×D61C2×D411yescharacteristic
195C23×D61C2×D411yescharacteristic
196C23×D61C2×D414yes—
197#41×C61—44no—
198#41×C61—44no—
199#41×C61—48no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61C2412yes—
207C2×Q8×C61C2412yes—
208C2×D4×C61—24no—
209C2×D4×C61—21no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—44no—
213C2×D4×C61C2412yes—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—24no—
220C22×C4×C61—44no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—42no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D414yes—
238#11758226—44no—
239#11758226—44no—
240#11758226—48no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—24no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—44no—
247C2×D244—44no—
248C2×D244C2412yes—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—24no—
254C2×C4×D61—48no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61—42no—
258C2×C4×D61—42no—
259C2×C4×D61—44no—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2×D414yes—
263C2×C4×D61C2×D414yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266Q16×C61—44no—
267SD16×C61—44no—
268C2×C8×C61—22no—
269C2×C8×C61—22no—
270C2×C8×C61C2412yes—
271C2×C8×C61C2412yes—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278C22⋊Dic61—24no—
279#11758201—44no—
280#11758199—44no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61C2412yes—
291C4⋊Dic61C2412yes—
292C4⋊Dic61C2412yes—
293#11758196—24no—
294#11758196—24no—
295#11758196—24no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C2×#92418—22no—
299C2×#92418—22no—
300C2×#92418C2412yes—
301C2×#92418C2412yes—
302#11758189—44no—
303#11758189—44no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61C22×D412yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—44no—
321C22×D61—44no—
322C22×D61—44no—
323C22×D61—416no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61C22×D412yes—
328C22×D61C22×D412yes—
329Q8×C61—22no—
330Q8×C61—22no—
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—42no—
334Q8×C61—42no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—48no—
338D4×C61—42no—
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—48no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61H(5,𝔽2)12yes—
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61C2511yescharacteristic
355C22⋊D61—48no—
356C22⋊D61—48no—
357C22⋊D61—48no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—44no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369D244—22no—
370D244—22no—
371D244—48no—
372D244—48no—
373D244—42no—
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—44no—
381C4×D61—44no—
382C4×D61—48no—
383C8×C61—22no—
384C8×C61—22no—
385#92418—22no—
386#92418—22no—
387C2×#3197—611nomaximal, Sylow
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—44no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—84no—
396C22×C61#53412yes—
397C22×C61#57512yes—
398C22×C61#57512yes—
399C22×C61C23×D411yescharacteristic
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—416no—
407C2×D61—44no—
408C2×D61—44no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—84no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61#53412yes—
418C4×C61C2×H(5,𝔽2)11yescharacteristic
419C4×C61C2×H(5,𝔽2)11yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425C2×#525—611no—
426C2×#525—611no—
427#3197—6116no—
428C2×#485—611no—
429C2×#485—611no—
430C2×#482—611no—
431C2×#482—611no—
432C2×#470—611no—
433C2×#469—611no—
434C2×#468—611no—
435C2×#468—611no—
436C2×#452—611no—
437C2×#452D6111yescharacteristic, complemented
438C2×#449—611no—
439C2×#449—611no—
440C2×#407—611no—
441C2×C61—42no—
442C2×C61—82no—
443C2×C61#319714yescomplemented
444C2×C61C2×#53411yescharacteristic
445C2×C61C2×#57511yescharacteristic
446C2×C61C2×#57511yescharacteristic
447D61—42no—
448D61—42no—
449D61—82no—
450C22×#41—611no—
451C22×#41C2×D6111yescharacteristic
452C24×C4—611no—
453C22×Q16C2×D6111yescharacteristic, complemented
454C22×SD16—611no—
455C22×SD16C2×D6111yescharacteristic, complemented
456C22×D8—611no—
457C22×M16—611no—
458C22×M16—611no—
459#525—618no—
460#525—618no—
461#525—1224no—
462#525—1224no—
463C2×#123—1221no—
464C2×#123—1221no—
465C2×C22⋊Q8—611no—
466C2×C22⋊Q8—611no—
467C2×C22⋊Q8—611no—
468C2×C22⋊Q8C2×D6111yescharacteristic
469C2×#121—611no—
470C2×#121—611no—
471C2×#121—611no—
472C2×#121—611no—
473C2×#120—1221no—
474C2×#120—1221no—
475C2×C4×D4—1221no—
476C2×C4×D4—1221no—
477C2×C4×D4—1221no—
478C2×C4×D4—1221no—
479C2×#117—611no—
480C2×#117—611no—
481#485—618no—
482#485—618no—
483#482—618no—
484#482—618no—
485#470—618no—
486#469—618no—
487#468—618no—
488#468—618no—
489#452—618no—
490#452C2×D6118yescomplemented
491#449—618no—
492#449—618no—
493C2×#107—611no—
494C2×#107—611no—
495C2×#106—611no—
496C2×#106—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103C2×D6111yescharacteristic, complemented
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102C2×D6111yescharacteristic, complemented
505#407—618no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508C2×C22⋊C8—611no—
509C2×C22⋊C8C2×D6111yescharacteristic
510C61C2×#319711yescharacteristic, complemented, Sylow
511C25—611no—
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—614no—
516C2×#41—1222no—
517C2×#41—2442no—
518C2×#41—2442no—
519C2×#41C22×D6114yes—
520C22×Q8C22×D6111yescharacteristic
521C22×Q8C22×D6111yescharacteristic
522C22×D4—21no—
523C22×D4—611no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—21no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—614no—
537C23×C4—614no—
538C23×C4—1221no—
539C23×C4—2442no—
540C23×C4—2442no—
541C23×C4C22×D6111yescharacteristic
542C2×Q16—42no—
543C2×Q16C22×D6114yescomplemented
544C2×SD16—42no—
545C2×SD16—614no—
546C2×SD16—2442no—
547C2×SD16C22×D6114yescomplemented
548C2×D8—614no—
549C2×D8—2442no—
550C2×M16—614no—
551C2×M16—614no—
552C2×M16—2442no—
553C2×M16—2442no—
554C22×C8—611no—
555C22×C8—611no—
556C22×C8C22×D6111yescharacteristic
557C22×C8C22×D6111yescharacteristic
558#123—1228no—
559#123—1228no—
560C22⋊Q8—22no—
561C22⋊Q8—614no—
562C22⋊Q8—614no—
563C22⋊Q8—614no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1222no—
567C22⋊Q8C22×D6114yes—
568#121—614no—
569#121—614no—
570#121—614no—
571#121—614no—
572#121—1222no—
573#121—1222no—
574#121—1222no—
575#121—1222no—
576#120—1228no—
577#120—1228no—
578C4×D4—1228no—
579C4×D4—1228no—
580C4×D4—1228no—
581C4×D4—1228no—
582#117—614no—
583#117—614no—
584#117—1222no—
585#117—1222no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C42—1221no—
605C2×C42—1221no—
606#107—614no—
607#107—614no—
608#106—614no—
609#106—614no—
610#103—614no—
611#103—614no—
612#103—614no—
613#103C22×D6114yescomplemented
614#102—614no—
615#102—614no—
616#102—614no—
617#102C22×D6114yescomplemented
618C22⋊C8—614no—
619C22⋊C8—614no—
620C22⋊C8—614no—
621C22⋊C8C22×D6114yes—
622C24—21no—
623C24—611no—
624C24—611no—
625C24—614no—
626C24—1221no—
627C24—2442no—
628C24—2442no—
629C24—2442no—
630C24D4×D6111yescharacteristic
631#41—44no—
632#41—44no—
633#41—48no—
634#41—2444no—
635#41—2444no—
636#41—2448no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8C23×D6112yes—
644C2×Q8C23×D6112yes—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—612no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1221no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—2444no—
660C2×D4—2444no—
661C2×D4—2444no—
662C2×D4—2444no—
663C2×D4—2444no—
664C2×D4C23×D6112yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—24no—
671C22×C4—44no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—614no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—614no—
680C22×C4—614no—
681C22×C4—1224no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2448no—
690C22×C4—2444no—
691C22×C4—2444no—
692C22×C4—2442no—
693C22×C4—2442no—
694C22×C4—2444no—
695C22×C4—2442no—
696C22×C4D4×D6112yes—
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6112yes—
699C22×C4C23×D6111yescharacteristic
700Q16—44no—
701SD16—44no—
702SD16—2444no—
703D8—2444no—
704M16—2444no—
705M16—2444no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—612no—
709C2×C8—612no—
710C2×C8—1222no—
711C2×C8—1222no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—612no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1224no—
720C4⋊C4—1224no—
721C4⋊C4—1224no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4C23×D6112yes—
726C22⋊C4—24no—
727C22⋊C4—1224no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C42—1224no—
737C42—1224no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—612no—
746C23—612no—
747C23—1222no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1222no—
754C23—2444no—
755C23—2444no—
756C23—2444no—
757C23—24416no—
758C23—2442no—
759C23—2442no—
760C23—2442no—
761C23C2×D4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—1222no—
774D4—1222no—
775D4—2448no—
776D4—2448no—
777D4—2448no—
778D4—2448no—
779D4—2448no—
780D4—2442no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1224no—
797C2×C4—1224no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—2444no—
806C2×C4—2444no—
807C2×C4—2448no—
808C2×C4—2444no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4C2×D4×D6112yes—
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4#1451982212yes—
815C2×C4#1451982212yes—
816C2×C4C24×D6111yescharacteristic
817C8—22no—
818C8—22no—
819C8—1222no—
820C8—1222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—1222no—
830C22—1222no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—1222no—
835C22—4884no—
836C22—24416no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2444no—
841C22—2444no—
842C22#1684032212yes—
843C22#1684055912yes—
844C22#1684056112yes—
845C22C22×D4×D6111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—1222no—
851C4—1222no—
852C4—2442no—
853C4—2442no—
854C4—2442no—
855C4#1684032212yes—
856C4C2×#1451982211yescharacteristic
857C4C2×#1451982211yescharacteristic
858C2—42no—
859C2—82no—
860C2—4882no—
861C2—2442no—
862C2—2442no—
863C2#2145666014yesdirect product factor
864C2C2×#1684032211yescharacteristic
865C2C2×#1684055911yescharacteristic
866C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
hypercenterC2×#452D61
hypocenterC61C2×#3197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840275C2semidirect
2. C2×#16840269C2semidirect
3. #21456660C2direct (N × H)
4. C2×#16840102C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840085C2semidirect
8. C2×#16840017C2semidirect
9. C2×#16840014C2semidirect
10. C2×#16840011C2semidirect
11. C2×#16840005C2semidirect
12. C2×#16839923C2semidirect
13. C2×#16839907C2semidirect
14. C2×#16839906C2semidirect
15. C2×#16839724C2semidirect
16. C2×C61×#452C2semidirect
19. C22×#11758201C22semidirect
20. C22×#11758199C22semidirect
24. #16840275C22semidirect
26. #16840269C22semidirect
44. #16840102C22semidirect
45. #16840100C22semidirect
46. #16840087C22semidirect
47. #16840085C22semidirect
48. #16840017C22semidirect
49. #16840014C22semidirect
50. #16840011C22semidirect
51. #16840005C22semidirect
52. #16839923C22semidirect
53. #16839907C22semidirect
54. #16839906C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519701C22semidirect
60. C2×#14519701C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519699C22semidirect
63. C2×#14519699C22semidirect
64. C2×#14519698C22semidirect
65. #16839724C22semidirect
70. C22×Q16×C61C22semidirect
71. C22×SD16×C61C22semidirect
73. C61×#452C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#102×C61C22semidirect
99. C2×#11758201C23semidirect
101. C2×#11758199C23semidirect
151. #14519711C23semidirect
152. #14519710C23semidirect
153. #14519709C23semidirect
154. #14519708C23semidirect
155. #14519701C23semidirect
156. #14519701C23semidirect
157. #14519701C23semidirect
158. #14519699C23semidirect
159. #14519699C23semidirect
160. #14519698C23semidirect
175. C2×Q16×C61C23semidirect
177. C2×SD16×C61C23semidirect
185. #103×C61C23semidirect
186. #102×C61C23semidirect
437. C2×#452D61semidirect
443. C2×C61#3197semidirect
453. C22×Q16C2×D61semidirect
455. C22×SD16C2×D61semidirect
490. #452C2×D61semidirect
500. C2×#103C2×D61semidirect
504. C2×#102C2×D61semidirect
510. C61C2×#3197semidirect
543. C2×Q16C22×D61semidirect
547. C2×SD16C22×D61semidirect
613. #103C22×D61semidirect
617. #102C22×D61semidirect
863. C2#21456660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×#168402692
#214566602
C2×#168401022
C2×#168401002
C2×#168400872
C2×#168400852
C2×#168400172
C2×#168400142
C2×#168400112
C2×#168400052
C2×#168399232
C2×#168399072
C2×#168399062
C2×#168397242
C2×C61×#4522
C2×#319761