Finite Group Databasebeta

← C2×#22614267 #33255312

Subgroups — C2×#22614267 #33255312

Order 18688.

2638 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556581C211yesmaximal, characteristic, complemented
2C22×#14556569C211yesmaximal, characteristic
3#22614267C2116yesmaximal, direct product factor
4C2×#17988528C211yesmaximal, characteristic, complemented
5C2×#17988516C211yesmaximal, characteristic
6C2×#17988514C211yesmaximal, characteristic
7C2×#17988491C211yesmaximal, characteristic, complemented
8C2×#17988491C211yesmaximal, characteristic, complemented
9C2×#17988477C211yesmaximal, characteristic
10C2×#17988476C211yesmaximal, characteristic
11C2×#17988452C211yesmaximal, characteristic, complemented
12C2×#17988451C211yesmaximal, characteristic, complemented
13C2×#17988446C211yesmaximal, characteristic
14C2×#17988438C211yesmaximal, characteristic, complemented
15C2×#17988434C211yesmaximal, characteristic
16C2×#400×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C2×#14556581—28no—
20C2×#14556581C2218yescomplemented
21C2×#14556569—28no—
22C2×#14556569C2218yes—
23C22×C4⋊Dic73C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×#11924005C2211yescharacteristic
34C22×#11924005C2211yescharacteristic
35C22×#11924005C2211yescharacteristic
36C22×C4×Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39C22×C4×Dic73C2211yescharacteristic
40#17988528C2218yescomplemented
41#17988516C2218yes—
42#17988514C2218yes—
43#17988491C2218yescomplemented
44#17988491C2218yescomplemented
45#17988477C2218yes—
46#17988476C2218yes—
47#17988452C2218yescomplemented
48#17988451C2218yescomplemented
49#17988446C2218yes—
50#17988438C2218yescomplemented
51#17988434C2218yes—
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63#400×C73C2218yescomplemented
64C2×#95×C73C2211yescharacteristic
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C24×D73C2311yescharacteristic
70C22×Dic146—24no—
71C22×Dic146—24no—
72C22×Dic146—24no—
73C22×Dic146C2314yes—
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C22×C4×D73—24no—
82C22×C4×D73—24no—
83C22×C4×D73—24no—
84C22×C4×D73C2314yes—
85#14556581—232no—
86#14556569—232no—
87C2×C4⋊Dic73—24no—
88C2×C4⋊Dic73C2314yes—
89C2×#11924007—24no—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007D418yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×#11924005—24no—
102C2×#11924005—24no—
103C2×#11924005—24no—
104C2×#11924005—24no—
105C2×#11924005—24no—
106C2×#11924005—24no—
107C2×#11924005C2314yes—
108C2×#11924005C2314yes—
109C2×#11924005C2314yes—
110C2×#11924005C2314yes—
111C2×#11924005C2314yes—
112C2×#11924005C2314yes—
113C2×C4×Dic73—24no—
114C2×C4×Dic73—24no—
115C2×C4×Dic73—24no—
116C2×C4×Dic73—24no—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119C2×C4×Dic73C2314yes—
120C2×C4×Dic73C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73—24no—
138C2×C4⋊C4×C73—24no—
139C2×C4⋊C4×C73C2314yes—
140C2×C4⋊C4×C73C2314yes—
141#95×C73C2314yes—
142#95×C73C2314yes—
143#95×C73C2314yes—
144#95×C73C2314yes—
145#95×C73C2314yes—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73—22no—
149C23×D73—22no—
150C23×D73—22no—
151C23×D73—22no—
152C23×D73#4114yes—
153C23×D73C2412yes—
154C2×Dic146—28no—
155C2×Dic146—28no—
156C2×Dic146—28no—
157C2×Dic146—416no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73C2×D414yes—
175C22×Dic73C2×D414yes—
176C22×Dic73#4114yes—
177C22×Dic73#4114yes—
178C22×Dic73#4114yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C2×C4×D73—28no—
187C2×C4×D73—28no—
188C2×C4×D73—28no—
189C2×C4×D73—416no—
190C4⋊Dic73—28no—
191#11924007—28no—
192#11924007—28no—
193#11924007—28no—
194#11924007—28no—
195#11924007—28no—
196#11924007C2×D4116yes—
197#11924005—28no—
198#11924005—28no—
199#11924005—28no—
200#11924005—28no—
201#11924005—28no—
202#11924005—28no—
203C4×Dic73—28no—
204C4×Dic73—28no—
205C4×Dic73—28no—
206C4×Dic73—28no—
207C24×C73C2411yescharacteristic
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73C2×D414yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C22×C4×C73C2412yes—
232C22×C4×C73C2412yes—
233C22×C4×C73C2412yes—
234C22×C4×C73C2412yes—
235C22×C4×C73C2412yes—
236C4⋊C4×C73—28no—
237C4⋊C4×C73—28no—
238C23×C73C22×D412yes—
239C23×C73C2×#4112yes—
240C23×C73C2×#4112yes—
241C23×C73C2×#4112yes—
242C23×C73C2×#4112yes—
243C23×C732−1+412yes—
244C23×C732−1+412yes—
245C23×C73C2511yescharacteristic
246C22×D73—28no—
247C22×D73—28no—
248C22×D73—28no—
249C22×D73—22no—
250C22×D73—22no—
251C22×D73—22no—
252C22×D73—22no—
253C22×D73—22no—
254C22×D73—22no—
255C22×D73—44no—
256C22×D73—44no—
257C22×D73—44no—
258C22×D73—44no—
259C22×D73C2×#4114yes—
260C2×C4×C73—28no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—44no—
282C2×C4×C73—44no—
283C2×C4×C73—44no—
284C2×C4×C73—44no—
285C2×C4×C73—44no—
286C2×C4×C73—44no—
287C2×C4×C73C22×D414yes—
288C2×Dic73—28no—
289C2×Dic73—28no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—44no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73#124116yes—
311C2×Dic73C22×D414yes—
312C2×Dic73C22×D414yes—
313C2×Dic73C2×#4114yes—
314C2×Dic73C2×#4114yes—
315C2×Dic73C2×#4114yes—
316C4×D73—416no—
317Dic146—416no—
318C22×C73C2×#12414yes—
319C22×C73#52914yes—
320C22×C73#54114yes—
321C22×C73#54714yes—
322C22×C73#54814yes—
323C22×C73#55214yes—
324C22×C73#55214yes—
325C22×C73C23×D411yescharacteristic
326C22×C73C22×#4111yescharacteristic
327C22×C73C22×#4111yescharacteristic
328C22×C73C22×#4111yescharacteristic
329C22×C73C22×#4111yescharacteristic
330C22×C73C2×2−1+411yescharacteristic
331C22×C73C2×2−1+411yescharacteristic
332C2×D73—24no—
333C2×D73—24no—
334C2×D73—24no—
335C2×D73—42no—
336C2×D73—42no—
337C2×D73—42no—
338C2×D73—42no—
339C2×D73—416no—
340C4×C73—24no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73—42no—
347Dic73—24no—
348Dic73—24no—
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352Dic73—42no—
353Dic73C2×#12418yes—
354C2×#2489—731nomaximal, Sylow
355C2×C73#248918yescomplemented
356C2×C73C22×#12411yescharacteristic
357C2×C73C2×#52911yescharacteristic
358C2×C73C2×#54111yescharacteristic
359C2×C73C2×#54711yescharacteristic
360C2×C73C2×#54811yescharacteristic
361C2×C73C2×#55211yescharacteristic
362C2×C73C2×#55211yescharacteristic
363D73—44no—
364C22×#125—731no—
365C22×C22⋊Q8—731no—
366#2489—7316no—
367C2×#400—731no—
368C2×#400D7311yescharacteristic, complemented
369C2×#397—731no—
370C2×#397—731no—
371C2×#391—731no—
372C2×#391—731no—
373C2×#388—731no—
374C2×#388—731no—
375C2×#382—731no—
376C2×#382—731no—
377C2×#380—731no—
378C2×C4×C4⋊C4—731no—
379C2×C4×C22⋊C4—731no—
380C73C2×#248911yescharacteristic, complemented, Sylow
381C23×Q8—731no—
382C24×C4—731no—
383C2×#125—738no—
384C2×#125—1468no—
385C2×C22⋊Q8—738no—
386C2×C22⋊Q8—1468no—
387C22×C4⋊C4—731no—
388C22×C4⋊C4—731no—
389C22×C4⋊C4—731no—
390C22×C4⋊C4—731no—
391C22×C4⋊C4—731no—
392C22×C4⋊C4—731no—
393C22×C4⋊C4—731no—
394C22×C4⋊C4C2×D7311yescharacteristic
395C22×C4⋊C4C2×D7311yescharacteristic
396C22×C22⋊C4—731no—
397C22×C22⋊C4—731no—
398C22×C22⋊C4—731no—
399C22×C22⋊C4—731no—
400C22×C22⋊C4—731no—
401C22×C22⋊C4—731no—
402C22×C42—731no—
403C22×C42—731no—
404C22×C42—731no—
405C22×C42—731no—
406#400—738no—
407#400C2×D7318yescomplemented
408#397—738no—
409#397—738no—
410#391—738no—
411#391—738no—
412#388—738no—
413#388—738no—
414#382—738no—
415#382—738no—
416#380—738no—
417C4×C4⋊C4—738no—
418C4×C22⋊C4—738no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95—731no—
424C2×#95—731no—
425C2×#95—731no—
426C2×#95—731no—
427C2×#95—731no—
428C2×#95C2×D7311yescharacteristic
429C2×#95C2×D7311yescharacteristic
430C2×#95C2×D7311yescharacteristic
431C2×#95C2×D7311yescharacteristic
432C2×#95C2×D7311yescharacteristic
433C25—731no—
434C22×Q8—734no—
435C22×Q8—1464no—
436C22×Q8—1464no—
437C22×Q8—1464no—
438C23×C4—731no—
439C23×C4—731no—
440C23×C4—731no—
441C23×C4—731no—
442C23×C4—731no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—734no—
446C23×C4—1464no—
447C23×C4—1464no—
448C23×C4—1464no—
449C23×C4C22×D7311yescharacteristic
450C23×C4C22×D7311yescharacteristic
451C23×C4C22×D7311yescharacteristic
452C23×C4C22×D7311yescharacteristic
453C23×C4C22×D7311yescharacteristic
454C23×C4C22×D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456#125—14632no—
457C22⋊Q8—14632no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—738no—
461C2×C4⋊C4—734no—
462C2×C4⋊C4—734no—
463C2×C4⋊C4—734no—
464C2×C4⋊C4—734no—
465C2×C4⋊C4—734no—
466C2×C4⋊C4—734no—
467C2×C4⋊C4—734no—
468C2×C4⋊C4—1464no—
469C2×C4⋊C4—1464no—
470C2×C4⋊C4—1464no—
471C2×C4⋊C4—1464no—
472C2×C4⋊C4—1464no—
473C2×C4⋊C4—1464no—
474C2×C4⋊C4C22×D7314yes—
475C2×C4⋊C4C22×D7314yes—
476C2×C22⋊C4—734no—
477C2×C22⋊C4—734no—
478C2×C22⋊C4—734no—
479C2×C22⋊C4—734no—
480C2×C22⋊C4—734no—
481C2×C22⋊C4—734no—
482C2×C22⋊C4—1464no—
483C2×C22⋊C4—1464no—
484C2×C22⋊C4—1464no—
485C2×C22⋊C4—1464no—
486C2×C22⋊C4—1464no—
487C2×C22⋊C4—1464no—
488C2×C42—734no—
489C2×C42—734no—
490C2×C42—734no—
491C2×C42—734no—
492C2×C42—1464no—
493C2×C42—1464no—
494C2×C42—1464no—
495C2×C42—1464no—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95—734no—
501#95—734no—
502#95—734no—
503#95—734no—
504#95—734no—
505#95C22×D7314yes—
506#95C22×D7314yes—
507#95C22×D7314yes—
508#95C22×D7314yes—
509#95C22×D7314yes—
510C24—734no—
511C24—732no—
512C24—1462no—
513C24—1462no—
514C24—1462no—
515C24—1462no—
516C24—1462no—
517C24—1462no—
518C24C23×D7311yescharacteristic
519C2×Q8—29216no—
520C2×Q8—1468no—
521C2×Q8—1468no—
522C2×Q8—1468no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—29216no—
544C22×C4—734no—
545C22×C4—734no—
546C22×C4—734no—
547C22×C4—732no—
548C22×C4—734no—
549C22×C4—734no—
550C22×C4—732no—
551C22×C4—732no—
552C22×C4—732no—
553C22×C4—732no—
554C22×C4—732no—
555C22×C4—732no—
556C22×C4—1468no—
557C22×C4—1468no—
558C22×C4—1468no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4D4×D7314yes—
576C22×C4C23×D7312yes—
577C22×C4C23×D7312yes—
578C22×C4C23×D7312yes—
579C22×C4C23×D7312yes—
580C22×C4C23×D7312yes—
581C22×C4C23×D7312yes—
582C22×C4C23×D7312yes—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—7316no—
586C4⋊C4—1468no—
587C4⋊C4—1468no—
588C4⋊C4—1468no—
589C4⋊C4—1468no—
590C4⋊C4—1468no—
591C4⋊C4—1468no—
592C22⋊C4—1468no—
593C22⋊C4—1468no—
594C22⋊C4—1468no—
595C22⋊C4—1468no—
596C22⋊C4—1468no—
597C22⋊C4—1468no—
598C42—1468no—
599C42—1468no—
600C42—1468no—
601C42—1468no—
602C23—2924no—
603C23—2924no—
604C23—2924no—
605C23—2924no—
606C23—734no—
607C23—1468no—
608C23—1462no—
609C23—1462no—
610C23—1462no—
611C23—1462no—
612C23—1462no—
613C23—1462no—
614C23—1468no—
615C23—1468no—
616C23C2×D4×D7312yes—
617C23#41×D7312yes—
618C23#41×D7312yes—
619C23#41×D7312yes—
620C23#41×D7312yes—
621C23#1455663812yes—
622C23#1455663912yes—
623C23C24×D7311yescharacteristic
624Q8—29216no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—29216no—
653C2×C4—2924no—
654C2×C4—2924no—
655C2×C4—2924no—
656C2×C4—2924no—
657C2×C4—734no—
658C2×C4—734no—
659C2×C4—734no—
660C2×C4—7316no—
661C2×C4—734no—
662C2×C4—734no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1468no—
680C2×C4—1468no—
681C2×C4C2×D4×D7314yes—
682C22—2922no—
683C22—2922no—
684C22—2922no—
685C22—2922no—
686C22—29216no—
687C22—1464no—
688C22—1464no—
689C22—1464no—
690C22#124×D7314yes—
691C22#1798912014yes—
692C22#1798919614yes—
693C22#1798923514yes—
694C22#1798924714yes—
695C22#1798926914yes—
696C22#1798927314yes—
697C22C22×D4×D7311yescharacteristic
698C22C2×#41×D7311yescharacteristic
699C22C2×#41×D7311yescharacteristic
700C22C2×#41×D7311yescharacteristic
701C22C2×#41×D7311yescharacteristic
702C22C2×#1455663811yescharacteristic
703C22C2×#1455663911yescharacteristic
704C4—24no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2922no—
712C4—2922no—
713C4—2922no—
714C4—2922no—
715C4—738no—
716C4—1464no—
717C4—1464no—
718C2—2924no—
719C2#2261426718yesdirect product factor
720C2C2×#124×D7311yescharacteristic
721C2C2×#1798912011yescharacteristic
722C2C2×#1798919611yescharacteristic
723C2C2×#1798923511yescharacteristic
724C2C2×#1798924711yescharacteristic
725C2C2×#1798926911yescharacteristic
726C2C2×#1798927311yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#400×C73C2
socleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#400D73
hypocenterC73C2×#2489
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#14556581C2semidirect
3. #22614267C2direct (N × H)
4. C2×#17988528C2semidirect
7. C2×#17988491C2semidirect
8. C2×#17988491C2semidirect
11. C2×#17988452C2semidirect
12. C2×#17988451C2semidirect
14. C2×#17988438C2semidirect
16. C2×#400×C73C2semidirect
20. C2×#14556581C22semidirect
40. #17988528C22semidirect
43. #17988491C22semidirect
44. #17988491C22semidirect
47. #17988452C22semidirect
48. #17988451C22semidirect
50. #17988438C22semidirect
63. #400×C73C22semidirect
355. C2×C73#2489semidirect
368. C2×#400D73semidirect
380. C73C2×#2489semidirect
407. #400C2×D73semidirect
719. C2#22614267direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565812
C22×#145565692
#226142672
C2×#179885282
C2×#179885162
C2×#179885142
C2×#179884912
C2×#179884772
C2×#179884762
C2×#179884522
C2×#179884512
C2×#179884462
C2×#179884382
C2×#179884342
C2×#400×C732
C2×#248973