Finite Group Databasebeta

← C2×#21456598 #30550563

Subgroups — C2×#21456598 #30550563

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2C2×C22⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21456598C2116yesmaximal, direct product factor
4C2×#16840104C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840091C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840002C211yesmaximal, characteristic, complemented
9C2×#16840000C211yesmaximal, characteristic, complemented
10C2×#16839990C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic, complemented
13C2×#16839916C211yesmaximal, characteristic, complemented
14C2×#16839899C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758200C2211yescharacteristic, complemented
21C22×C8×D61C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840269—24no—
24#16840269C2218yes—
25C2×#14519758—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519755—21no—
29C2×#14519754—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519753C2211yescharacteristic
33C22⋊Q8×D61—24no—
34C22⋊Q8×D61C2218yescomplemented
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×#14519745—21no—
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61—21no—
40C2×#14519736C2211yescharacteristic
41C2×C4⋊C4×D61—21no—
42C2×C4⋊C4×D61C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840104C2218yescomplemented
45#16840100C2218yescomplemented
46#16840091C2218yescomplemented
47#16840074C2218yescomplemented
48#16840002C2218yescomplemented
49#16840000C2218yescomplemented
50#16839990C2218yescomplemented
51#16839988C2218yescomplemented
52#16839924C2218yescomplemented
53#16839916C2218yescomplemented
54#16839899C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519701C2211yescharacteristic, complemented
64C2×#14519698C2211yescharacteristic, complemented
65C2×C22⋊#92418C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C22⋊C8×D61C2218yescomplemented
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
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—22no—
81C2×Q8×D61—42no—
82C2×Q8×D61—42no—
83C2×Q8×D61C2314yes—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61D411yescharacteristic
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—42no—
90C22×C4×D61—42no—
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D414yes—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2314yes—
97C2×#11758202—42no—
98C2×#11758202C2314yescomplemented
99C2×#11758200—42no—
100C2×#11758200C2314yescomplemented
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—42no—
104C2×C8×D61—42no—
105C2×C8×D61C2314yes—
106C2×C8×D61C2314yes—
107#14519758—28no—
108#14519757—22no—
109#14519757C2314yes—
110#14519756—22no—
111#14519756C2314yes—
112#14519755—28no—
113#14519754—28no—
114#14519753—22no—
115#14519753—22no—
116#14519753—22no—
117#14519753C2314yes—
118#14519753C2314yes—
119#14519753C2314yes—
120#14519748—22no—
121#14519748—22no—
122#14519748C2314yes—
123#14519748C2314yes—
124#14519745—28no—
125C4×C22⋊D61—28no—
126C4×C22⋊D61—28no—
127#14519736—22no—
128#14519736C2314yes—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C4⋊C4×D61—28no—
139C4⋊C4×D61—22no—
140C4⋊C4×D61C2314yes—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C22⋊C4×D61—28no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519710C2314yescomplemented
153#14519709C2314yescomplemented
154#14519708C2314yescomplemented
155#14519702C2314yescomplemented
156#14519702C2314yescomplemented
157#14519701C2314yescomplemented
158#14519701C2314yescomplemented
159#14519701C2314yescomplemented
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—24no—
191C23×D61—24no—
192C23×D61—42no—
193C23×D61C2×D414yes—
194C23×D61C2×D411yescharacteristic
195C23×D61C2×D411yescharacteristic
196#41×C61—44no—
197#41×C61—44no—
198#41×C61—48no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—22no—
205C2×Q8×C61C2412yes—
206C2×Q8×C61C2412yes—
207C2×D4×C61—24no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—44no—
212C2×D4×C61C2412yes—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—44no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—44no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—42no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D414yes—
236Q8×D61—44no—
237Q8×D61—44no—
238Q8×D61—48no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—48no—
246C2×C4×D61—44no—
247C2×C4×D61—44no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—44no—
251C2×C4×D61—44no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D412yes—
254C2×C4×D61C2×D414yes—
255C2×C4×D61C2×D414yes—
256C2×C4×D61C2412yes—
257C2×C4×D61C2412yes—
258C2×Dic122—22no—
259C2×Dic122—22no—
260C2×Dic122—21no—
261C2×Dic122—24no—
262C2×Dic122—44no—
263C2×Dic122C2412yes—
264Q16×C61—44no—
265SD16×C61—44no—
266C2×C8×C61—22no—
267C2×C8×C61—22no—
268C2×C8×C61C2412yes—
269C2×C8×C61C2412yes—
270C4⋊C4×C61—24no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C2412yes—
273C22⋊C4×C61—24no—
274C22⋊Dic61—24no—
275C22⋊Dic61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278#11758202—44no—
279#11758200—44no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—24no—
288C4⋊Dic61C2412yes—
289C4⋊Dic61C2412yes—
290C4⋊Dic61C2412yes—
291#11758196—24no—
292#11758196—24no—
293#11758196—24no—
294#11758196—24no—
295#11758196—24no—
296C4×Dic61—24no—
297C2×#92418—22no—
298C2×#92418—22no—
299C2×#92418C2412yes—
300C2×#92418C2412yes—
301C8×D61—44no—
302C8×D61—44no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61C22×D412yes—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—28no—
317C22×D61—28no—
318C22×D61—44no—
319C22×D61—416no—
320C22×D61#13514yes—
321C22×D61#13714yes—
322C22×D61C22×D412yes—
323C22×D61C22×D412yes—
324Q8×C61—22no—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—42no—
329Q8×C61—42no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—48no—
333D4×C61—42no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—48no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61C22×D412yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61H(5,𝔽2)12yes—
348C2×C4×C61H(5,𝔽2)12yes—
349C2×C4×C61C2511yescharacteristic
350C22⋊D61—48no—
351C22⋊D61—48no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—44no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365C4×D61—24no—
366C4×D61—24no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—44no—
372C4×D61—44no—
373C4×D61—48no—
374C4×D61—48no—
375Dic122—22no—
376Dic122—22no—
377Dic122—48no—
378Dic122—42no—
379C8×C61—22no—
380C8×C61—22no—
381#92418—22no—
382#92418—22no—
383C2×#3190—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—44no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—84no—
392C22×C61#53412yes—
393C22×C61C2×#13512yes—
394C22×C61C2×#13712yes—
395C22×C61C23×D411yescharacteristic
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—28no—
399C2×D61—28no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—416no—
403C2×D61C2×#13514yes—
404C2×D61C2×#13714yes—
405C4×C61—22no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61#53412yes—
410C4×C61C2×H(5,𝔽2)11yescharacteristic
411C4×C61C2×H(5,𝔽2)11yescharacteristic
412Dic61—22no—
413Dic61—22no—
414Dic61—42no—
415Dic61—42no—
416Dic61—42no—
417Dic61—42no—
418C2×#525—611no—
419C22×C22⋊Q8—611no—
420#3190—6116no—
421C2×#485—611no—
422C2×#485—611no—
423C2×#483—611no—
424C2×#480—611no—
425C2×#467—611no—
426C2×#467—611no—
427C2×#465—611no—
428C2×#465—611no—
429C2×#452—611no—
430C2×#452D6111yescharacteristic, complemented
431C2×#451—611no—
432C2×#448—611no—
433C22×C22⋊C8—611no—
434C2×C61—42no—
435C2×C61—82no—
436C2×C61#319014yescomplemented
437C2×C61C2×#53411yescharacteristic
438C2×C61C22×#13511yescharacteristic
439C2×C61C22×#13711yescharacteristic
440D61—24no—
441D61—24no—
442C22×#41C2×D6111yescharacteristic
443C23×Q8—611no—
444C24×C4—611no—
445C22×Q16—611no—
446C22×Q16C2×D6111yescharacteristic, complemented
447C22×SD16—611no—
448C22×SD16C2×D6111yescharacteristic, complemented
449C23×C8—611no—
450C23×C8—611no—
451#525—618no—
452#525—1224no—
453C2×#123—1221no—
454C2×C22⋊Q8—611no—
455C2×C22⋊Q8—611no—
456C2×C22⋊Q8—611no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—618no—
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—1221no—
461C2×C22⋊Q8—1221no—
462C2×C22⋊Q8—1224no—
463C2×C22⋊Q8C2×D6111yescharacteristic
464C2×#121—611no—
465C2×#121—611no—
466C2×#120—1221no—
467C2×C4×D4—1221no—
468C2×C4×D4—1221no—
469C2×#117—611no—
470C22×C4⋊C4—611no—
471C22×C4⋊C4—1221no—
472C22×C22⋊C4—1221no—
473#485—618no—
474#485—618no—
475#483—618no—
476#480—618no—
477#467—618no—
478#467—618no—
479#465—618no—
480#465—618no—
481#452—618no—
482#452C2×D6118yescomplemented
483#451—618no—
484#448—618no—
485C2×#107—611no—
486C2×#107—611no—
487C2×#106—611no—
488C2×#106—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#103—611no—
493C2×#103—611no—
494C2×#103C2×D6111yescharacteristic, complemented
495C2×#102—611no—
496C2×#102C2×D6111yescharacteristic, complemented
497C2×C22⋊C8—611no—
498C2×C22⋊C8—611no—
499C2×C22⋊C8—611no—
500C2×C22⋊C8—618no—
501C2×C22⋊C8C2×D6111yescharacteristic
502C61C2×#319011yescharacteristic, complemented, Sylow
503C25—611no—
504C2×#41—22no—
505C2×#41—42no—
506C2×#41—42no—
507C2×#41C22×D6114yes—
508C22×Q8—614no—
509C22×Q8—611no—
510C22×Q8—1221no—
511C22×Q8—1222no—
512C22×Q8—2442no—
513C22×Q8—2442no—
514C22×Q8C22×D6111yescharacteristic
515C22×Q8C22×D6111yescharacteristic
516C22×D4—21no—
517C22×D4—1221no—
518C22×D4—1221no—
519C22×D4C22×D6111yescharacteristic
520C23×C4—21no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—614no—
527C23×C4—614no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—2442no—
531C23×C4—2442no—
532C23×C4C22×D6111yescharacteristic
533C2×Q16—42no—
534C2×Q16—614no—
535C2×Q16—2442no—
536C2×Q16C22×D6114yescomplemented
537C2×SD16—42no—
538C2×SD16—614no—
539C2×SD16—2442no—
540C2×SD16C22×D6114yescomplemented
541C22×C8—611no—
542C22×C8—611no—
543C22×C8—614no—
544C22×C8—614no—
545C22×C8—2442no—
546C22×C8—2442no—
547C22×C8C22×D6111yescharacteristic
548C22×C8C22×D6111yescharacteristic
549#123—1228no—
550C22⋊Q8—22no—
551C22⋊Q8—614no—
552C22⋊Q8—614no—
553C22⋊Q8—614no—
554C22⋊Q8—614no—
555C22⋊Q8—614no—
556C22⋊Q8—1228no—
557C22⋊Q8—1228no—
558C22⋊Q8—1222no—
559C22⋊Q8—1222no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8C22×D6114yes—
564#121—614no—
565#121—614no—
566#121—1222no—
567#121—1222no—
568#120—1228no—
569C4×D4—1228no—
570C4×D4—1228no—
571#117—614no—
572#117—1222no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1228no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4C22×D6111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—1228no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
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×C42—1221no—
598#107—614no—
599#107—614no—
600#106—614no—
601#106—614no—
602#103—614no—
603#103—614no—
604#103—614no—
605#103—614no—
606#103—614no—
607#103C22×D6114yescomplemented
608#102—614no—
609#102C22×D6114yescomplemented
610C22⋊C8—614no—
611C22⋊C8—614no—
612C22⋊C8—614no—
613C22⋊C8C22×D6114yes—
614C24—21no—
615C24—611no—
616C24—611no—
617C24—614no—
618C24—1224no—
619C24—1224no—
620C24—2442no—
621C24D4×D6111yescharacteristic
622#41—44no—
623#41—44no—
624#41—48no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—612no—
632C2×Q8—1224no—
633C2×Q8—1221no—
634C2×Q8—1222no—
635C2×Q8—1222no—
636C2×Q8—2444no—
637C2×Q8—2444no—
638C2×Q8—2444no—
639C2×Q8—2448no—
640C2×Q8C23×D6112yes—
641C2×Q8C23×D6112yes—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—2444no—
650C2×D4—2444no—
651C2×D4C23×D6112yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—614no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—614no—
667C22×C4—614no—
668C22×C4—1224no—
669C22×C4—1224no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—2448no—
679C22×C4—2444no—
680C22×C4—2444no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4—2444no—
684C22×C4—2444no—
685C22×C4—2442no—
686C22×C4D4×D6112yes—
687C22×C4D4×D6111yescharacteristic
688C22×C4C23×D6112yes—
689C22×C4C23×D6111yescharacteristic
690Q16—44no—
691Q16—2444no—
692SD16—44no—
693SD16—2444no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—612no—
697C2×C8—612no—
698C2×C8—1222no—
699C2×C8—1222no—
700C2×C8—2444no—
701C2×C8—2444no—
702C2×C8C23×D6112yes—
703C2×C8C23×D6112yes—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—612no—
707C4⋊C4—612no—
708C4⋊C4—612no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—1224no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1224no—
718C4⋊C4C23×D6112yes—
719C22⋊C4—24no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C22⋊C4—1224no—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C42—1224no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—614no—
737C23—614no—
738C23—612no—
739C23—612no—
740C23—1228no—
741C23—1228no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—2444no—
747C23—24416no—
748C23C2×D4×D6112yes—
749C23C2×D4×D6111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—1222no—
757Q8—1222no—
758Q8—2448no—
759Q8—2442no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—42no—
764D4—2448no—
765D4—2448no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—612no—
778C2×C4—612no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1224no—
782C2×C4—1224no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—2444no—
792C2×C4—2444no—
793C2×C4—2448no—
794C2×C4—2448no—
795C2×C4—2444no—
796C2×C4—2442no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4C2×D4×D6112yes—
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4#1451982212yes—
803C2×C4#1451982212yes—
804C2×C4C24×D6111yescharacteristic
805C8—22no—
806C8—22no—
807C8—1222no—
808C8—1222no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—84no—
817C22—614no—
818C22—614no—
819C22—1222no—
820C22—1222no—
821C22—1222no—
822C22—1222no—
823C22—1228no—
824C22—1228no—
825C22—24416no—
826C22#1684032212yes—
827C22#135×D6112yes—
828C22#137×D6112yes—
829C22C22×D4×D6111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—1222no—
835C4—1222no—
836C4—2442no—
837C4—2442no—
838C4—2442no—
839C4—2442no—
840C4#1684032212yes—
841C4C2×#1451982211yescharacteristic
842C4C2×#1451982211yescharacteristic
843C2—42no—
844C2—82no—
845C2—1224no—
846C2—1224no—
847C2#2145659814yesdirect product factor
848C2C2×#1684032211yescharacteristic
849C2C2×#135×D6111yescharacteristic
850C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC2×#16840269C2
hypercenterC2×#452D61
hypocenterC61C2×#3190
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
2. C2×C22⋊Q8×D61C2semidirect
3. #21456598C2direct (N × H)
4. C2×#16840104C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840091C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840002C2semidirect
9. C2×#16840000C2semidirect
10. C2×#16839990C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839924C2semidirect
13. C2×#16839916C2semidirect
14. C2×#16839899C2semidirect
15. C2×C22⋊C8×D61C2semidirect
16. C2×C61×#452C2semidirect
19. C22×#11758202C22semidirect
20. C22×#11758200C22semidirect
34. C22⋊Q8×D61C22semidirect
44. #16840104C22semidirect
45. #16840100C22semidirect
46. #16840091C22semidirect
47. #16840074C22semidirect
48. #16840002C22semidirect
49. #16840000C22semidirect
50. #16839990C22semidirect
51. #16839988C22semidirect
52. #16839924C22semidirect
53. #16839916C22semidirect
54. #16839899C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519701C22semidirect
63. C2×#14519701C22semidirect
64. C2×#14519698C22semidirect
68. C22⋊C8×D61C22semidirect
70. C22×Q16×C61C22semidirect
71. C22×SD16×C61C22semidirect
73. C61×#452C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#102×C61C22semidirect
98. C2×#11758202C23semidirect
100. C2×#11758200C23semidirect
151. #14519711C23semidirect
152. #14519710C23semidirect
153. #14519709C23semidirect
154. #14519708C23semidirect
155. #14519702C23semidirect
156. #14519702C23semidirect
157. #14519701C23semidirect
158. #14519701C23semidirect
159. #14519701C23semidirect
160. #14519698C23semidirect
175. C2×Q16×C61C23semidirect
177. C2×SD16×C61C23semidirect
185. #103×C61C23semidirect
186. #102×C61C23semidirect
430. C2×#452D61semidirect
436. C2×C61#3190semidirect
446. C22×Q16C2×D61semidirect
448. C22×SD16C2×D61semidirect
482. #452C2×D61semidirect
494. C2×#103C2×D61semidirect
496. C2×#102C2×D61semidirect
502. C61C2×#3190semidirect
536. C2×Q16C22×D61semidirect
540. C2×SD16C22×D61semidirect
607. #103C22×D61semidirect
609. #102C22×D61semidirect
847. C2#21456598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402692
C2×C22⋊Q8×D612
#214565982
C2×#168401042
C2×#168401002
C2×#168400912
C2×#168400742
C2×#168400022
C2×#168400002
C2×#168399902
C2×#168399882
C2×#168399242
C2×#168399162
C2×#168398992
C2×C22⋊C8×D612
C2×C61×#4522
C2×#319061