Finite Group Databasebeta

← #33085497

Subgroups — #33085497

Order 18688.

1386 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989063C211yesmaximal, characteristic
2C2×#17988612C211yesmaximal, characteristic
3C2×#17988594C211yesmaximal, characteristic
4C2×#103×D73C211yesmaximal, characteristic
5#22612552C211yesmaximal, characteristic
6#22609947C211yesmaximal, characteristic, complemented
7#22609946C211yesmaximal, characteristic, complemented
8#22609945C211yesmaximal, characteristic, complemented
9#22609944C211yesmaximal, characteristic, complemented
10#22609935C211yesmaximal, characteristic, complemented
11#22609934C211yesmaximal, characteristic, complemented
12#22609933C211yesmaximal, characteristic, complemented
13#22609649C211yesmaximal, characteristic
14#22609646C211yesmaximal, characteristic
15C73×#1803C211yesmaximal, characteristic, complemented
16C22×Q8×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#17989063—24no—
20#17989063C418yescomplemented
21C2×Q8×Dic73C2211yescharacteristic
22C2×C4×Dic146—21no—
23C2×C4×Dic146C2211yescharacteristic
24C2×#14556556—21no—
25C2×#14556556C2211yescharacteristic
26C2×#14556549—21no—
27C2×#14556549C2211yescharacteristic
28C2×#14556549C2211yescharacteristic
29C2×#14556548—21no—
30C2×#14556548C2211yescharacteristic
31C2×C4⋊C4×D73C2211yescharacteristic
32#17988612—24no—
33C2×C4⋊#10596831C2211yescharacteristic
34C2×#14556520C2211yescharacteristic
35C2×#14556520C2211yescharacteristic
36#17988594—24no—
37C2×#14556516C2211yescharacteristic
38C2×#14556516C2211yescharacteristic
39C2×#14556515C2211yescharacteristic
40C2×#14556515C2211yescharacteristic
41C2×#14556514C2211yescharacteristic
42C2×#14556514C2211yescharacteristic
43#103×D73—24no—
44#17988482—21no—
45#17988482—21no—
46#17988458—21no—
47#17988458—21no—
48#17988456C2211yescharacteristic
49#17988453C2211yescharacteristic
50#17988452C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55#17988349C2211yescharacteristic
56#17988349C2211yescharacteristic
57C2×C4×Q8×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×#103×C73C2211yescharacteristic
60C2×#103×C73C2211yescharacteristic
61#384×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63#340×C73C2211yescharacteristic
64C22×Dic146—21no—
65C22×Dic146C2311yescharacteristic
66C2×Q8×D73—22no—
67C2×Q8×D73—22no—
68C2×Q8×D73—22no—
69C2×Q8×D73C2×C414yes—
70C2×Q8×D73D414yes—
71C2×Q8×D73Q814yes—
72C22×C4×D73—21no—
73C22×C4×D73—21no—
74C22×C4×D73C2311yescharacteristic
75C2×#11924011—22no—
76C2×#11924011—22no—
77C2×#11924011—22no—
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C2×C8×D73—22no—
81C2×C8×D73—22no—
82C2×C8×D73—22no—
83Q8×Dic73—22no—
84Q8×Dic73C2×C414yescomplemented
85C4×Dic146—28no—
86C4×Dic146—22no—
87C4×Dic146C2×C414yescomplemented
88#14556556—28no—
89#14556556—22no—
90#14556556C2×C414yescomplemented
91#14556549—22no—
92#14556549—28no—
93#14556549—22no—
94#14556549—22no—
95#14556549C2×C414yes—
96#14556548—28no—
97#14556548C2×C414yes—
98#14556548D414yes—
99C2×C4⋊Dic73—21no—
100C2×C4⋊Dic73C2311yescharacteristic
101C2×C4⋊Dic73C2311yescharacteristic
102C2×C4⋊Dic73C2311yescharacteristic
103C2×#11924007—21no—
104C2×#11924007—21no—
105C2×#11924007—21no—
106C2×#11924007—21no—
107C2×#11924007—21no—
108C2×#11924007D411yescharacteristic
109C2×#11924007D411yescharacteristic
110C4⋊C4×D73—22no—
111C4⋊C4×D73—22no—
112C2×#11924005—21no—
113C2×#11924005—21no—
114C2×#11924005D411yescharacteristic
115C2×#11924005D411yescharacteristic
116C2×C4×Dic73—21no—
117C2×C4×Dic73—21no—
118C2×C4×Dic73—21no—
119C2×C4×Dic73—21no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122C4⋊#10596831—22no—
123#14556520—22no—
124#14556520—22no—
125#14556516—22no—
126#14556516—22no—
127#14556515—22no—
128#14556515—22no—
129#14556514—22no—
130#14556514—22no—
131#14556498—21no—
132#14556498—21no—
133#14556498—21no—
134#14556498—21no—
135C22×Q8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C4×Q8×C73—22no—
139C4×Q8×C73C2×C414yescomplemented
140C2×C4⋊C4×C73—21no—
141C2×C4⋊C4×C73—21no—
142C2×C4⋊C4×C73—21no—
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C42×C73—21no—
147C2×C42×C73C2311yescharacteristic
148C4⋊C8×C73—22no—
149#103×C73—22no—
150#103×C73—22no—
151C23×D73C2×D411yescharacteristic
152C2×Dic146—21no—
153C2×Dic146—21no—
154C2×Dic146—21no—
155C2×Dic146—24no—
156C2×Dic146—24no—
157C2×Dic146—24no—
158C2×Dic146C22×C412yes—
159C2×Dic146C2×D412yes—
160C2×Dic146C2×Q812yes—
161Q8×D73—28no—
162Q8×D73—28no—
163Q8×D73—28no—
164Q8×D73C4⋊C4116yescomplemented
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73C2×D411yescharacteristic
170C22×Dic73C2×D411yescharacteristic
171C22×Dic73C2×D411yescharacteristic
172C2×C4×D73—24no—
173C2×C4×D73—24no—
174C2×C4×D73—24no—
175C2×C4×D73—42no—
176C2×C4×D73—81no—
177C2×C4×D73—81no—
178C2×C4×D73C22×C412yes—
179C2×C4×D73C2×D412yes—
180C2×C4×D73C2×D412yes—
181C2×C4×D73C2×Q812yes—
182C2×C4×D73#4112yes—
183C2×C4×D73#4112yes—
184#11924011—44no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C8×D73—44no—
192C4⋊Dic73—21no—
193C4⋊Dic73—24no—
194C4⋊Dic73—21no—
195C4⋊Dic73—21no—
196C4⋊Dic73—21no—
197C4⋊Dic73—21no—
198C4⋊Dic73C22×C412yes—
199#11924007—24no—
200#11924007—24no—
201#11924007—42no—
202#11924007—81no—
203#11924007—81no—
204#11924007C22⋊C414yes—
205#11924007C22⋊C414yes—
206#11924005—24no—
207#11924005—42no—
208#11924005C22⋊C414yes—
209#11924005C22⋊C414yes—
210C4×Dic73—24no—
211C4×Dic73—24no—
212C4×Dic73—24no—
213C4×Dic73—24no—
214C4×Dic73—42no—
215C4×Dic73C22×C412yes—
216C4×Dic73C2×D412yes—
217C2×Q8×C73—21no—
218C2×Q8×C73—21no—
219C2×Q8×C73—21no—
220C2×Q8×C73C22×C412yes—
221C2×Q8×C73C2×D412yes—
222C2×Q8×C73C2×Q812yes—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2411yescharacteristic
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—81no—
243C4⋊C4×C73—81no—
244C4⋊C4×C73C22×C412yes—
245C42×C73—24no—
246C42×C73C22×C412yes—
247C42×C73C2×D412yes—
248C23×C73C22×D411yescharacteristic
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73C2×C22⋊C412yes—
254C22×D73#12112yes—
255C22×D73C22⋊Q812yes—
256Q8×C73—22no—
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73C2×C4⋊C414yes—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73C2×C22⋊C412yes—
277C2×C4×C73C2×C22⋊C412yes—
278C2×C4×C73C23×C411yescharacteristic
279C2×C4×C73C22×D411yescharacteristic
280C2×C4×C73C22×D411yescharacteristic
281C2×C4×C73C22×Q811yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×Dic73—22no—
285C2×Dic73—22no—
286C2×Dic73—22no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—22no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73C2×C22⋊C412yes—
301C2×Dic73C2×C22⋊C412yes—
302C2×Dic73C2×C22⋊C412yes—
303C2×Dic73#12112yes—
304C2×Dic73C22⋊Q812yes—
305C4×D73—216no—
306C4×D73—84no—
307C4×D73C2×C4⋊C414yes—
308C4×D73#11714yes—
309C4×D73#12114yes—
310C4×D73C22⋊Q814yes—
311Dic146—22no—
312Dic146—22no—
313Dic146—22no—
314Dic146—216no—
315Dic146C2×C4⋊C414yes—
316C8×C73—41no—
317C8×C73—41no—
318#10596831—41no—
319#10596831—41no—
320C22×C73C22×C22⋊C411yescharacteristic
321C22×C73C2×#12111yescharacteristic
322C22×C73C2×C22⋊Q811yescharacteristic
323C22×C73#57711yescharacteristic
324C22×C73#57711yescharacteristic
325C22×C73#57811yescharacteristic
326C22×C73#57811yescharacteristic
327C2×D73—22no—
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—22no—
333C2×D73#38014yes—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—24no—
337C4×C73—42no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73C22×C4⋊C411yescharacteristic
341C4×C73C2×#11711yescharacteristic
342C4×C73C2×#12111yescharacteristic
343C4×C73C2×C22⋊Q811yescharacteristic
344Dic73—22no—
345Dic73—22no—
346Dic73—24no—
347Dic73—42no—
348Dic73—81no—
349Dic73—81no—
350Dic73#38014yes—
351#20651—731nomaximal, Sylow
352C2×C73C2×#38011yescharacteristic
353C2×C73#289811yescharacteristic
354C2×C73#289811yescharacteristic
355C2×C73#304311yescharacteristic
356C2×C73#304411yescharacteristic
357C2×C73#308211yescharacteristic
358C2×C73#308211yescharacteristic
359D73—24no—
360C2×#519—731no—
361C2×#424—731no—
362C2×#419—731no—
363C22×#103—731no—
364#2317—731no—
365#1805—731no—
366#1805—731no—
367#1805—731no—
368#1805—731no—
369#1803—731no—
370#1803—731no—
371#1803—731no—
372#1803D7311yescharacteristic, complemented
373#1736—731no—
374#1735—731no—
375C73#2065111yescharacteristic, complemented, Sylow
376C23×Q8—731no—
377C22×M16—731no—
378C23×C8—731no—
379#519—738no—
380#519—1464no—
381C2×C4×Q8—731no—
382C2×C4×Q8—731no—
383C2×C4×Q8—731no—
384C2×C4×Q8—1461no—
385C2×C4×Q8—1461no—
386C2×C4×Q8C2×D7311yescharacteristic
387C2×#117—731no—
388C2×#117—731no—
389C2×#117—731no—
390C2×#117—1461no—
391C2×#117—1461no—
392C22×C4⋊C4—731no—
393#424—1464no—
394C2×C4⋊C8—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8C2×D7311yescharacteristic
398#419—1464no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#103—731no—
405C2×#103—1464no—
406C2×#103C2×D7311yescharacteristic
407C2×#103C2×D7311yescharacteristic
408#389—1461no—
409#389—1461no—
410#385—1461no—
411#385—1461no—
412#384—731no—
413#384C2×D7311yescharacteristic
414#382—731no—
415#382—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#340—731no—
420#340—731no—
421#340—731no—
422#340C2×D7311yescharacteristic
423#340C2×D7311yescharacteristic
424C22×Q8—734no—
425C22×Q8—734no—
426C22×Q8—734no—
427C22×Q8—731no—
428C22×Q8—1461no—
429C22×Q8—1462no—
430C22×Q8—1462no—
431C22×Q8—1462no—
432C22×Q8C22×D7311yescharacteristic
433C23×C4—731no—
434C23×C4—1461no—
435C23×C4—1461no—
436C2×M16—1462no—
437C2×M16—1462no—
438C2×M16—1462no—
439C22×C8—731no—
440C22×C8—731no—
441C22×C8—1462no—
442C22×C8—1462no—
443C22×C8—1462no—
444C22×C8C22×D7311yescharacteristic
445C22×C8C22×D7311yescharacteristic
446C4×Q8—22no—
447C4×Q8—734no—
448C4×Q8—734no—
449C4×Q8—734no—
450C4×Q8—1468no—
451C4×Q8—1462no—
452C4×Q8—1462no—
453C4×Q8—1468no—
454C4×Q8—1462no—
455C4×Q8C4×D7314yescomplemented
456#117—734no—
457#117—734no—
458#117—734no—
459#117—1468no—
460#117—1462no—
461#117—1462no—
462#117—1468no—
463#117—1462no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—1462no—
473C2×C4⋊C4—1462no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4—1461no—
478C2×C4⋊C4—1461no—
479C2×C4⋊C4—1461no—
480C2×C4⋊C4C22×D7311yescharacteristic
481C2×C4⋊C4C22×D7311yescharacteristic
482C2×C4⋊C4C22×D7311yescharacteristic
483C2×C22⋊C4—731no—
484C2×C22⋊C4—731no—
485C2×C22⋊C4—1461no—
486C2×C22⋊C4—1461no—
487C2×C42—21no—
488C2×C42—731no—
489C2×C42—1461no—
490C2×C42—1461no—
491C2×C42—1461no—
492C2×C42—1461no—
493C2×C42—1461no—
494C2×C42C22×D7311yescharacteristic
495C4⋊C8—22no—
496C4⋊C8—1462no—
497C4⋊C8—1462no—
498C4⋊C8—1462no—
499#103—22no—
500#103—22no—
501#103—1462no—
502#103—1462no—
503#103—1462no—
504#103—1462no—
505#103—1462no—
506#103—1462no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511C24—731no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—7316no—
516C2×Q8—732no—
517C2×Q8—732no—
518C2×Q8—732no—
519C2×Q8—1464no—
520C2×Q8—1464no—
521C2×Q8—1464no—
522C2×Q8—1468no—
523C2×Q8—1468no—
524C2×Q8—1468no—
525C2×Q8—1461no—
526C2×Q8—1461no—
527C2×Q8—1461no—
528C2×Q8C2×C4×D7312yes—
529C2×Q8D4×D7312yes—
530C2×Q8Q8×D7312yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—2922no—
536C22×C4—5841no—
537C22×C4—5841no—
538C22×C4—731no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—732no—
543C22×C4—732no—
544C22×C4—732no—
545C22×C4—731no—
546C22×C4—731no—
547C22×C4—1464no—
548C22×C4—1464no—
549C22×C4—1464no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4D4×D7311yescharacteristic
555C22×C4D4×D7311yescharacteristic
556C22×C4C23×D7311yescharacteristic
557M16—2924no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—2924no—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—2922no—
580C4⋊C4—5841no—
581C4⋊C4—5841no—
582C4⋊C4—734no—
583C4⋊C4—734no—
584C4⋊C4—732no—
585C4⋊C4—1464no—
586C4⋊C4—1464no—
587C4⋊C4—1461no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1464no—
592C4⋊C4—1461no—
593C4⋊C4C2×C4×D7312yes—
594C22⋊C4—2922no—
595C22⋊C4—734no—
596C22⋊C4—734no—
597C22⋊C4—1464no—
598C42—24no—
599C42—2922no—
600C42—732no—
601C42—732no—
602C42—1464no—
603C42—1464no—
604C42—1464no—
605C42—1464no—
606C42C2×C4×D7312yes—
607C42D4×D7312yes—
608C23—732no—
609C23—732no—
610C23—732no—
611C23—1461no—
612C23—1461no—
613C23—1461no—
614C23—1461no—
615C23C2×D4×D7311yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—734no—
620Q8—14616no—
621Q8—1462no—
622Q8—1462no—
623Q8—1462no—
624Q8C4⋊C4×D7314yes—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2921no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—5844no—
650C2×C4—732no—
651C2×C4—732no—
652C2×C4—732no—
653C2×C4—734no—
654C2×C4—734no—
655C2×C4—734no—
656C2×C4—734no—
657C2×C4—732no—
658C2×C4—732no—
659C2×C4—14616no—
660C2×C4—1462no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4C22⋊C4×D7312yes—
669C2×C4C22⋊C4×D7312yes—
670C2×C4C22×C4×D7311yescharacteristic
671C2×C4C2×D4×D7311yescharacteristic
672C2×C4C2×D4×D7311yescharacteristic
673C2×C4C2×Q8×D7311yescharacteristic
674C2×C4#41×D7311yescharacteristic
675C2×C4#41×D7311yescharacteristic
676C8—41no—
677C8—41no—
678C8—2921no—
679C8—2921no—
680C22—734no—
681C22—1462no—
682C22—1462no—
683C22—1462no—
684C22—1462no—
685C22—1462no—
686C22—1462no—
687C22C2×C22⋊C4×D7311yescharacteristic
688C22#121×D7311yescharacteristic
689C22C22⋊Q8×D7311yescharacteristic
690C22#1798939311yescharacteristic
691C22#1798939711yescharacteristic
692C22#1798940011yescharacteristic
693C22#1798940311yescharacteristic
694C4—24no—
695C4—22no—
696C4—22no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—2922no—
701C4—5841no—
702C4—5841no—
703C4—734no—
704C4—1464no—
705C4—1462no—
706C4—1462no—
707C4C2×C4⋊C4×D7311yescharacteristic
708C4#117×D7311yescharacteristic
709C4#121×D7311yescharacteristic
710C4C22⋊Q8×D7311yescharacteristic
711C2—1464no—
712C2#380×D7311yescharacteristic
713C2#2261845911yescharacteristic
714C2#2261846211yescharacteristic
715C2#2261944711yescharacteristic
716C2#2261945611yescharacteristic
717C2#2261976611yescharacteristic
718C2#2261976811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1803C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1803D73
hypocenterC73#20651
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
6. #22609947C2semidirect
7. #22609946C2semidirect
8. #22609945C2semidirect
9. #22609944C2semidirect
10. #22609935C2semidirect
11. #22609934C2semidirect
12. #22609933C2semidirect
15. C73×#1803C2semidirect
20. #17989063C4semidirect
84. Q8×Dic73C2×C4semidirect
87. C4×Dic146C2×C4semidirect
90. #14556556C2×C4semidirect
139. C4×Q8×C73C2×C4semidirect
164. Q8×D73C4⋊C4semidirect
372. #1803D73semidirect
375. C73#20651semidirect
455. C4×Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890632
C2×#179886122
C2×#179885942
C2×#103×D732
#226125522
#226099472
#226099462
#226099452
#226099442
#226099352
#226099342
#226099332
#226096492
#226096462
C73×#18032
#2065173