Finite Group Databasebeta

← #33102418

Subgroups — #33102418

Order 18688.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988665C211yesmaximal, characteristic, complemented
2#22612860C211yesmaximal, characteristic, complemented
3#22610897C211yesmaximal, characteristic, complemented
4#22610889C211yesmaximal, characteristic, complemented
5#22610370C211yesmaximal, characteristic, complemented
6#22610370C211yesmaximal, characteristic, complemented
7#22610254C211yesmaximal, characteristic, complemented
8#22610249C211yesmaximal, characteristic, complemented
9#22610026C211yesmaximal, characteristic, complemented
10#22610017C211yesmaximal, characteristic, complemented
11#22609941C211yesmaximal, characteristic, complemented
12C4×#14556512C211yesmaximal, characteristic, complemented
13#22609652C211yesmaximal, characteristic, complemented
14#22609650C211yesmaximal, characteristic, complemented
15C2×#553×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20#17988665—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556512C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C4×#10596831C2211yescharacteristic
29#17988480—21no—
30#17988473—21no—
31#17988467—21no—
32#17988453C2211yescharacteristic
33#17988447C2211yescharacteristic
34#17988447C2211yescharacteristic
35C4×C4⋊Dic73C2211yescharacteristic
36C22⋊C4×Dic73—21no—
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#553×C73—24no—
50#553×C73C418yescomplemented
51C2×#126×C73—21no—
52C2×#125×C73C2211yescharacteristic
53C2×#123×C73—21no—
54C2×#121×C73—21no—
55C2×#121×C73C2211yescharacteristic
56C2×#121×C73C2211yescharacteristic
57C2×C4×D4×C73—21no—
58C2×C4×D4×C73C2211yescharacteristic
59C2×C4×D4×C73C2211yescharacteristic
60C2×#117×C73C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C23×Dic73—21no—
63C2×#11924012—22no—
64C2×#11924012—22no—
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—41no—
68C2×#11924012—41no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556550—22no—
74#14556550—41no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—41no—
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C4⋊#10596831—22no—
88#14556512—22no—
89#14556512—22no—
90#14556512—41no—
91#14556512—41no—
92C22⋊#10596831—22no—
93C22⋊#10596831—22no—
94C4×#10596831—22no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100C22×D4×C73—21no—
101C22×D4×C73—21no—
102C22×D4×C73D411yescharacteristic
103C22×D4×C73C2311yescharacteristic
104C23×C4×C73—21no—
105C23×C4×C73—21no—
106C23×C4×C73C2311yescharacteristic
107C23×C4×C73C2311yescharacteristic
108#126×C73—28no—
109#125×C73—22no—
110#125×C73C2×C414yescomplemented
111#123×C73—28no—
112#121×C73—28no—
113#121×C73—22no—
114#121×C73—22no—
115#121×C73C2×C414yes—
116#121×C73C2×C414yescomplemented
117C4×D4×C73—28no—
118C4×D4×C73—22no—
119C4×D4×C73C2×C414yes—
120C4×D4×C73C2×C414yescomplemented
121C4×D4×C73D414yes—
122#117×C73—22no—
123#117×C73C2×C414yes—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73C2×C414yescomplemented
129C2×C4⋊C4×C73D411yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—21no—
137C2×C22⋊C4×C73D411yescharacteristic
138C2×C22⋊C4×C73D411yescharacteristic
139C2×C42×C73—21no—
140C2×C42×C73C2311yescharacteristic
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—81no—
148#11924012—44no—
149#11924012—44no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831#4112yes—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—42no—
170C4⋊Dic73#4112yes—
171C22⋊Dic73—42no—
172C22⋊Dic73—42no—
173C22⋊Dic73—81no—
174C4×Dic73—42no—
175C4×Dic73—81no—
176C24×C73—21no—
177C24×C73C2×D411yescharacteristic
178C24×C73C2×D411yescharacteristic
179C2×D4×C73—24no—
180C2×D4×C73—24no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—41no—
187C2×D4×C73—41no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—81no—
191C2×D4×C73—81no—
192C2×D4×C73C22⋊C414yes—
193C2×D4×C73C22×C412yes—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—24no—
206C22×C4×C73—24no—
207C22×C4×C73—81no—
208C22×C4×C73—81no—
209C22×C4×C73—81no—
210C22×C4×C73—81no—
211C22×C4×C73C22×C412yes—
212C22×C4×C73C22×C412yes—
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D412yes—
218C22×C4×C73C2×D412yes—
219C22×C4×C73C2411yescharacteristic
220C4⋊C4×C73—24no—
221C4⋊C4×C73—24no—
222C4⋊C4×C73—24no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73C22⋊C414yes—
227C4⋊C4×C73C22×C412yes—
228C4⋊C4×C73C22×C412yes—
229C4⋊C4×C73C22×C412yes—
230C22⋊C4×C73—24no—
231C22⋊C4×C73—24no—
232C22⋊C4×C73—24no—
233C22⋊C4×C73—24no—
234C22⋊C4×C73C22⋊C414yes—
235C22⋊C4×C73C22⋊C414yes—
236C42×C73—24no—
237C42×C73C22×C412yes—
238C42×C73C2×D412yes—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—22no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73C2×C22⋊C412yes—
259C23×C73C2×C22⋊C412yes—
260C23×C73C22×D411yescharacteristic
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—44no—
264D4×C73—48no—
265D4×C73—41no—
266D4×C73—41no—
267D4×C73—84no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—84no—
294C2×C4×C73—84no—
295C2×C4×C73C2×C22⋊C412yes—
296C2×C4×C73C2×C22⋊C412yes—
297C2×C4×C73C2×C22⋊C412yes—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C23×C411yescharacteristic
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C2×C4×C732−1+411yescharacteristic
305C2×Dic73—22no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—84no—
318#10596831—22no—
319#10596831—41no—
320#10596831—41no—
321#10596831—41no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73C22×C22⋊C411yescharacteristic
344C22×C73#54611yescharacteristic
345C22×C73#54711yescharacteristic
346C22×C73#57511yescharacteristic
347C22×C73#57511yescharacteristic
348C22×C73#57611yescharacteristic
349C22×C73#57711yescharacteristic
350C4×C73—22no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73C4×#4111yescharacteristic
358C4×C73#52011yescharacteristic
359C4×C73#54611yescharacteristic
360C4×C73#54711yescharacteristic
361Dic73—42no—
362Dic73—81no—
363Dic73—81no—
364Dic73—81no—
365#22501—731nomaximal, Sylow
366C2×C73—42no—
367C2×C73—42no—
368C2×C73—82no—
369C2×C73#233911yescharacteristic
370C2×C73#289611yescharacteristic
371C2×C73#289711yescharacteristic
372C2×C73#332211yescharacteristic
373C2×C73#332611yescharacteristic
374C2×C73#335111yescharacteristic
375C2×C73#335511yescharacteristic
376C2×#553D7311yescharacteristic
377C2×#436—731no—
378#2352—731no—
379#1991—731no—
380#1989—731no—
381#1895—731no—
382#1895—731no—
383#1875—731no—
384#1874—731no—
385#1825—731no—
386#1823—731no—
387#1804—731no—
388C4×#102—731no—
389#1736—731no—
390#1736—731no—
391C73#2250111yescharacteristic, complemented, Sylow
392C22×M16—731no—
393C22×M16—731no—
394#553—24no—
395#553Dic7318yescomplemented
396C2×#126—21no—
397C2×#125C2×D7311yescharacteristic
398C2×#123—21no—
399C2×#121—21no—
400C2×#121C2×D7311yescharacteristic
401C2×#121C2×D7311yescharacteristic
402C2×C4×D4—21no—
403C2×C4×D4C2×D7311yescharacteristic
404C2×C4×D4C2×D7311yescharacteristic
405C2×#117—731no—
406C2×#117C2×D7311yescharacteristic
407C22×C4⋊C4—731no—
408C22×C4⋊C4C2×D7311yescharacteristic
409#436—1464no—
410C2×C4⋊C8—731no—
411C2×#102—731no—
412C2×#102—731no—
413C2×#102—731no—
414C2×#102—731no—
415C2×C22⋊C8—731no—
416C2×C22⋊C8—731no—
417C2×C4×C8—731no—
418#388—1461no—
419#387—1461no—
420#386—1461no—
421#382—731no—
422#380—731no—
423#380—731no—
424C4×C4⋊C4—731no—
425C4×C22⋊C4—1461no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#340—731no—
431#340—731no—
432#340—731no—
433#340—731no—
434#340—731no—
435#340—731no—
436#340—731no—
437#340—731no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C22⋊D7311yescharacteristic
441C22×D4C22×D7311yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—1461no—
445C23×C4C22×D7311yescharacteristic
446C23×C4C22×D7311yescharacteristic
447C2×M16—2921no—
448C2×M16—2921no—
449C2×M16—1462no—
450C2×M16—1462no—
451C2×M16—1462no—
452C2×M16—1462no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456C22×C8—731no—
457#126—28no—
458#125—22no—
459#125C2×Dic7314yescomplemented
460#123—28no—
461#121—28no—
462#121—22no—
463#121—22no—
464#121C2×Dic7314yes—
465#121C2×Dic7314yescomplemented
466C4×D4—28no—
467C4×D4—22no—
468C4×D4C2×Dic7314yes—
469C4×D4C2×Dic7314yescomplemented
470C4×D4C22⋊D7314yes—
471#117—22no—
472#117—2921no—
473#117—1462no—
474#117C2×Dic7314yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—2921no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—731no—
484C2×C4⋊C4—1461no—
485C2×C4⋊C4—1462no—
486C2×C4⋊C4C2×Dic7314yescomplemented
487C2×C4⋊C4C22⋊D7311yescharacteristic
488C2×C4⋊C4C22×D7311yescharacteristic
489C2×C4⋊C4C22×D7311yescharacteristic
490C2×C4⋊C4C22×D7311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—1461no—
496C2×C22⋊C4—1461no—
497C2×C22⋊C4—1461no—
498C2×C22⋊C4C22⋊D7311yescharacteristic
499C2×C22⋊C4C22⋊D7311yescharacteristic
500C2×C42—21no—
501C2×C42—1461no—
502C2×C42—1461no—
503C2×C42C22×D7311yescharacteristic
504C4⋊C8—1462no—
505#102—2921no—
506#102—2921no—
507#102—1462no—
508#102—1462no—
509C22⋊C8—1462no—
510C22⋊C8—1462no—
511C4×C8—1462no—
512#95—1461no—
513#95—1461no—
514#95—1461no—
515#95—1461no—
516#95—1461no—
517C24—21no—
518C24C2×C22⋊D7311yescharacteristic
519C24C2×C22⋊D7311yescharacteristic
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4C22⋊Dic7314yes—
534C2×D4C22×Dic7312yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—2922no—
553C22×C4—2922no—
554C22×C4—5841no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4—1461no—
559C22×C4C22×Dic7312yes—
560C22×C4C22×Dic7312yes—
561C22×C4C2×C22⋊D7311yescharacteristic
562C22×C4C2×C22⋊D7311yescharacteristic
563C22×C4C2×C22⋊D7311yescharacteristic
564C22×C4C2×C22⋊D7311yescharacteristic
565C22×C4C2×C22⋊D7312yes—
566C22×C4C2×C22⋊D7312yes—
567C22×C4C23×D7311yescharacteristic
568M16—2924no—
569M16—2924no—
570C2×C8—732no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—2922no—
589C4⋊C4—732no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C4⋊C4—1461no—
596C4⋊C4—1461no—
597C4⋊C4C22⋊Dic7314yes—
598C4⋊C4C22×Dic7312yes—
599C4⋊C4C22×Dic7312yes—
600C4⋊C4C22×Dic7312yes—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—2922no—
606C22⋊C4—2922no—
607C22⋊C4—5841no—
608C22⋊C4C22⋊Dic7314yes—
609C22⋊C4C22⋊Dic7314yes—
610C42—24no—
611C42—2922no—
612C42—5841no—
613C42C22×Dic7312yes—
614C42C2×C22⋊D7312yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C2×C22⋊Dic7312yes—
635C23C2×C22⋊Dic7312yes—
636C23C22×C22⋊D7311yescharacteristic
637D4—22no—
638D4—22no—
639D4—44no—
640D4—48no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—5844no—
683C2×C4—1462no—
684C2×C4C2×C22⋊Dic7312yes—
685C2×C4C2×C22⋊Dic7312yes—
686C2×C4C2×C22⋊Dic7312yes—
687C2×C4C2×C22⋊Dic7312yes—
688C2×C4C23×Dic7311yescharacteristic
689C2×C4C22×C22⋊D7311yescharacteristic
690C2×C4#41×D7311yescharacteristic
691C2×C4#41×D7311yescharacteristic
692C2×C4#1455663711yescharacteristic
693C2×C4#1455663811yescharacteristic
694C8—2921no—
695C8—2921no—
696C8—2921no—
697C8—1462no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C22×C22⋊Dic7311yescharacteristic
720C22#1798922511yescharacteristic
721C22#1798923611yescharacteristic
722C22#1798938511yescharacteristic
723C22#1798938511yescharacteristic
724C22#1798939011yescharacteristic
725C22#1798939811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—2922no—
734C4—5841no—
735C4—5841no—
736C4—5841no—
737C4#41×Dic7311yescharacteristic
738C4#1798907011yescharacteristic
739C4#1798922511yescharacteristic
740C4#1798923611yescharacteristic
741C2—42no—
742C2—42no—
743C2—82no—
744C2#2261276111yescharacteristic
745C2#2261845011yescharacteristic
746C2#2261845711yescharacteristic
747C2#2262212611yescharacteristic
748C2#2262217811yescharacteristic
749C2#2262248511yescharacteristic
750C2#2262253111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#553×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#553D73
hypocenterC73#22501
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17988665C2semidirect
2. #22612860C2semidirect
3. #22610897C2semidirect
4. #22610889C2semidirect
5. #22610370C2semidirect
6. #22610370C2semidirect
7. #22610254C2semidirect
8. #22610249C2semidirect
9. #22610026C2semidirect
10. #22610017C2semidirect
11. #22609941C2semidirect
12. C4×#14556512C2semidirect
13. #22609652C2semidirect
14. #22609650C2semidirect
50. #553×C73C4semidirect
110. #125×C73C2×C4semidirect
116. #121×C73C2×C4semidirect
120. C4×D4×C73C2×C4semidirect
128. C2×C4⋊C4×C73C2×C4semidirect
391. C73#22501semidirect
395. #553Dic73semidirect
459. #125C2×Dic73semidirect
465. #121C2×Dic73semidirect
469. C4×D4C2×Dic73semidirect
486. C2×C4⋊C4C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886652
#226128602
#226108972
#226108892
#226103702
#226102542
#226102492
#226100262
#226100172
#226099412
C4×#145565122
#226096522
#226096502
C2×#553×C732
#2250173