Finite Group Databasebeta

← #33007967

Subgroups — #33007967

Order 18688.

2510 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11924007C211yesmaximal, characteristic
2C2×#17988462C211yesmaximal, characteristic
3C2×#17988460C211yesmaximal, characteristic
4C2×#17988459C211yesmaximal, characteristic
5C2×#17988456C212yesmaximal, complemented
6C2×#17988445C211yesmaximal, characteristic
7C2×C22⋊C4×Dic73C211yesmaximal, characteristic
8#22608195C212yesmaximal, complemented
9#22608194C212yesmaximal, complemented
10#22608159C212yesmaximal, complemented
11C2×#385×C73C211yesmaximal, characteristic
12C24×Dic73C2211yescharacteristic
13C24×Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2212yes—
15C22×#11924007—24no—
16C22×#11924007—28no—
17C22×#11924007C2211yescharacteristic
18C22×#11924007C2212yes—
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2212yes—
21C22×#11924007C2212yes—
22C22×#11924007C2212yes—
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C4×Dic73C2212yes—
26#17988462—24no—
27#17988460—24no—
28#17988459—24no—
29#17988456—28no—
30#17988445—24no—
31C22⋊C4×Dic73C418yescomplemented
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2212yes—
38C24×C4×C73C2211yescharacteristic
39C22×C4⋊C4×C73C2212yes—
40C22×C22⋊C4×C73C2211yescharacteristic
41C22×C22⋊C4×C73C2211yescharacteristic
42#385×C73—24no—
43C2×#95×C73C2212yes—
44C23×Dic73—24no—
45C23×Dic73—24no—
46C23×Dic73—24no—
47C23×Dic73—22no—
48C23×Dic73—22no—
49C23×Dic73—22no—
50C23×Dic73—42no—
51C23×Dic73C2×C414yes—
52C23×Dic73D414yes—
53C23×Dic73Q814yes—
54C23×Dic73C2311yescharacteristic
55C23×Dic73C2311yescharacteristic
56C23×Dic73C2312yes—
57C23×Dic73C2311yescharacteristic
58C23×Dic73C2312yes—
59C23×Dic73C2311yescharacteristic
60C2×C4⋊Dic73—24no—
61C2×C4⋊Dic73—24no—
62C2×C4⋊Dic73—42no—
63C2×#11924007—232no—
64C2×#11924007—24no—
65C2×#11924007—24no—
66C2×#11924007—24no—
67C2×#11924007—24no—
68C2×#11924007—22no—
69C2×#11924007—22no—
70C2×#11924007—24no—
71C2×#11924007—24no—
72C2×#11924007—24no—
73C2×#11924007—24no—
74C2×#11924007—24no—
75C2×#11924007—24no—
76C2×#11924007—24no—
77C2×#11924007—42no—
78C2×#11924007—42no—
79C2×#11924007D418yes—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73C2×C414yes—
84C2×C22⋊Dic73D414yes—
85C2×C22⋊Dic73Q814yes—
86C2×C4×Dic73—24no—
87C2×C4×Dic73—24no—
88C2×C4×Dic73C2×C418yescomplemented
89#14556498—22no—
90#14556498—22no—
91#14556498—24no—
92#14556498—24no—
93#14556498—24no—
94#14556498C2×C418yescomplemented
95C25×C73C2311yescharacteristic
96C23×C4×C73—22no—
97C23×C4×C73—24no—
98C23×C4×C73—22no—
99C23×C4×C73—22no—
100C23×C4×C73—42no—
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2311yescharacteristic
103C23×C4×C73C2312yes—
104C23×C4×C73C2312yes—
105C2×C4⋊C4×C73—24no—
106C2×C4⋊C4×C73—24no—
107C2×C4⋊C4×C73—42no—
108C2×C22⋊C4×C73—22no—
109C2×C22⋊C4×C73—22no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73C2×C414yes—
112C2×C22⋊C4×C73D414yes—
113C2×C22⋊C4×C73Q814yes—
114#95×C73—24no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—216no—
122C22×Dic73—28no—
123C22×Dic73—216no—
124C22×Dic73—28no—
125C22×Dic73—28no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—48no—
143C22×Dic73—48no—
144C22×Dic73—44no—
145C22×Dic73—44no—
146C22×Dic73C4⋊C4116yescomplemented
147C22×Dic73C22×C412yes—
148C22×Dic73C22×C414yes—
149C22×Dic73C22×C412yes—
150C22×Dic73C2×D414yes—
151C22×Dic73C2×D412yes—
152C22×Dic73C2×D414yes—
153C22×Dic73C2×D412yes—
154C22×Dic73C2×D414yes—
155C22×Dic73C2×Q812yes—
156C22×Dic73C2×Q814yes—
157C22×Dic73C2×Q812yes—
158C22×Dic73#4114yes—
159C4⋊Dic73—48no—
160#11924007—216no—
161#11924007—216no—
162#11924007—48no—
163#11924007—48no—
164#11924007—44no—
165#11924007—44no—
166C22⋊Dic73—44no—
167C22⋊Dic73C4⋊C4116yescomplemented
168C4×Dic73—216no—
169C24×C73—22no—
170C24×C73—22no—
171C24×C73—22no—
172C24×C73—22no—
173C24×C73C22×C412yes—
174C24×C73C2×D412yes—
175C24×C73C2×D412yes—
176C24×C73C2×D412yes—
177C24×C73C2×Q812yes—
178C24×C73C2×Q812yes—
179C24×C73C2×Q812yes—
180C24×C73C2411yescharacteristic
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—28no—
186C22×C4×C73—22no—
187C22×C4×C73—22no—
188C22×C4×C73—22no—
189C22×C4×C73—22no—
190C22×C4×C73—22no—
191C22×C4×C73—22no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—48no—
203C22×C4×C73—48no—
204C22×C4×C73—44no—
205C22×C4×C73—44no—
206C22×C4×C73C22×C414yes—
207C22×C4×C73C2×D414yes—
208C22×C4×C73C2×D414yes—
209C22×C4×C73C2×Q814yes—
210C4⋊C4×C73—48no—
211C22⋊C4×C73—44no—
212C22⋊C4×C73C4⋊C4116yescomplemented
213C23×C73—24no—
214C23×C73—24no—
215C23×C73—22no—
216C23×C73—24no—
217C23×C73—22no—
218C23×C73—22no—
219C23×C73—22no—
220C23×C73—24no—
221C23×C73—24no—
222C23×C73—24no—
223C23×C73—24no—
224C23×C73—24no—
225C23×C73—24no—
226C23×C73—24no—
227C23×C73—24no—
228C23×C73—24no—
229C23×C73C2×C4⋊C414yes—
230C23×C73C2×C4⋊C414yes—
231C23×C73C2×C4⋊C414yes—
232C23×C73#12714yes—
233C23×C73C4⋊Q814yes—
234C23×C73C4⋊Q814yes—
235C23×C73C4⋊Q814yes—
236C23×C73C23×C411yescharacteristic
237C23×C73C22×D411yescharacteristic
238C23×C73C22×D411yescharacteristic
239C23×C73C22×D412yes—
240C23×C73C22×D411yescharacteristic
241C23×C73C22×Q811yescharacteristic
242C23×C73C22×Q811yescharacteristic
243C23×C73C22×Q811yescharacteristic
244C23×C73C2×#4112yes—
245C23×C73H(5,𝔽2)12yes—
246C23×C732−1+412yes—
247C2×C4×C73—24no—
248C2×C4×C73—24no—
249C2×C4×C73—24no—
250C2×C4×C73—24no—
251C2×C4×C73—24no—
252C2×C4×C73—24no—
253C2×C4×C73—24no—
254C2×C4×C73—24no—
255C2×C4×C73—24no—
256C2×C4×C73—416no—
257C2×C4×C73—42no—
258C2×C4×C73—42no—
259C2×C4×C73—42no—
260C2×C4×C73—42no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—42no—
268C2×C4×C73—42no—
269C2×C4×C73—42no—
270C2×C4×C73—42no—
271C2×C4×C73C2×C4⋊C418yescomplemented
272C2×Dic73—24no—
273C2×Dic73—24no—
274C2×Dic73—24no—
275C2×Dic73—22no—
276C2×Dic73—24no—
277C2×Dic73—22no—
278C2×Dic73—24no—
279C2×Dic73—24no—
280C2×Dic73—24no—
281C2×Dic73—24no—
282C2×Dic73—232no—
283C2×Dic73—24no—
284C2×Dic73—24no—
285C2×Dic73—24no—
286C2×Dic73—416no—
287C2×Dic73—42no—
288C2×Dic73—42no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—42no—
298C2×Dic73—42no—
299C2×Dic73—42no—
300C2×Dic73—42no—
301C2×Dic73C2×C4⋊C414yes—
302C2×Dic73C2×C4⋊C414yes—
303C2×Dic73C2×C4⋊C418yescomplemented
304C2×Dic73C4×D418yes—
305C2×Dic73#12014yes—
306C2×Dic73C22⋊Q818yes—
307C2×Dic73#12314yes—
308C22×C73—24no—
309C22×C73—28no—
310C22×C73—28no—
311C22×C73—24no—
312C22×C73—24no—
313C22×C73—28no—
314C22×C73—28no—
315C22×C73—24no—
316C22×C73—24no—
317C22×C73—24no—
318C22×C73#38418yescomplemented
319C22×C73C22×C4⋊C411yescharacteristic
320C22×C73C22×C4⋊C411yescharacteristic
321C22×C73C22×C4⋊C411yescharacteristic
322C22×C73C2×C4×D412yes—
323C22×C73#52012yes—
324C22×C73C2×#12011yescharacteristic
325C22×C73C2×C22⋊Q812yes—
326C22×C73C2×#12311yescharacteristic
327C22×C73C2×#12711yescharacteristic
328C22×C73C2×C4⋊Q811yescharacteristic
329C22×C73C2×C4⋊Q811yescharacteristic
330C22×C73C2×C4⋊Q811yescharacteristic
331C22×C73#53511yescharacteristic
332C22×C73#53611yescharacteristic
333C22×C73#54412yes—
334C22×C73D4212yes—
335C22×C73D4212yes—
336C22×C73#54712yes—
337C22×C73#54712yes—
338C22×C73D4×Q812yes—
339C22×C73D4×Q812yes—
340C22×C73#55412yes—
341C22×C73#55412yes—
342C4×C73—28no—
343C4×C73—44no—
344C4×C73—81no—
345C4×C73—81no—
346Dic73—28no—
347Dic73—24no—
348Dic73—44no—
349Dic73—81no—
350Dic73—81no—
351Dic73#38518yescomplemented
352#13880—731nomaximal, Sylow
353C2×C73—28no—
354C2×C73C2×#38411yescharacteristic
355C2×C73C2×#38511yescharacteristic
356C2×C73#231711yescharacteristic
357C2×C73D4×C4⋊C412yes—
358C2×C73D4×C4⋊C412yes—
359C2×C73#243311yescharacteristic
360C2×C73#243411yescharacteristic
361C2×C73#244012yes—
362C2×C73#244012yes—
363C2×C73#250111yescharacteristic
364C2×C73#250211yescharacteristic
365C23×C4⋊C4—731no—
366C2×#385—731no—
367C2×#385—731no—
368C2×#385—731no—
369C2×#385D7311yescharacteristic
370C2×#384—732no—
371C2×#380—731no—
372C2×C4×C22⋊C4—731no—
373#1444—732no—
374#1444—732no—
375C4⋊#95—732no—
376C73#1388011yescharacteristic, complemented, Sylow
377C24×C4—731no—
378C24×C4—731no—
379C24×C4C2×D7311yescharacteristic
380C22×C4⋊C4—732no—
381C22×C4⋊C4—732no—
382C22×C4⋊C4—732no—
383C22×C4⋊C4—732no—
384C22×C4⋊C4—732no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4—731no—
387C22×C4⋊C4—1468no—
388C22×C4⋊C4—1464no—
389C22×C4⋊C4C2×D7312yes—
390C22×C22⋊C4—731no—
391C22×C22⋊C4—731no—
392C22×C22⋊C4C2×D7311yescharacteristic
393C22×C22⋊C4C2×D7311yescharacteristic
394C22×C42—732no—
395#385—24no—
396#385—1464no—
397#385—1464no—
398#385—1464no—
399#384—1468no—
400#380—1464no—
401C4×C22⋊C4—738no—
402C2×#95—732no—
403C2×#95—732no—
404C2×#95—732no—
405C2×#95—732no—
406C2×#95—731no—
407C2×#95—731no—
408C2×#95C2×D7312yes—
409C25C22×D7311yescharacteristic
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—2922no—
416C23×C4—731no—
417C23×C4—734no—
418C23×C4—734no—
419C23×C4—734no—
420C23×C4—732no—
421C23×C4—731no—
422C23×C4—732no—
423C23×C4—731no—
424C23×C4—731no—
425C23×C4—1462no—
426C23×C4—1462no—
427C23×C4—1464no—
428C23×C4—1462no—
429C23×C4—1464no—
430C23×C4—1464no—
431C23×C4C22×D7311yescharacteristic
432C23×C4C22×D7311yescharacteristic
433C23×C4C22×D7312yes—
434C23×C4C22×D7312yes—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—2922no—
439C2×C4⋊C4—2922no—
440C2×C4⋊C4—2922no—
441C2×C4⋊C4—738no—
442C2×C4⋊C4—1462no—
443C2×C4⋊C4—1462no—
444C2×C4⋊C4—1464no—
445C2×C4⋊C4—1464no—
446C2×C4⋊C4—1464no—
447C2×C4⋊C4—1464no—
448C2×C4⋊C4—1464no—
449C2×C4⋊C4—1464no—
450C2×C4⋊C4—1464no—
451C2×C4⋊C4—1464no—
452C2×C4⋊C4—1464no—
453C2×C4⋊C4—1464no—
454C2×C4⋊C4—1464no—
455C2×C4⋊C4—1464no—
456C2×C4⋊C4—14632no—
457C2×C4⋊C4—1464no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—734no—
462C2×C22⋊C4—734no—
463C2×C22⋊C4—734no—
464C2×C22⋊C4—1462no—
465C2×C22⋊C4—1462no—
466C2×C22⋊C4—1462no—
467C2×C22⋊C4Dic14614yes—
468C2×C22⋊C4C4×D7314yes—
469C2×C22⋊C4C22⋊D7314yes—
470C2×C42—738no—
471C2×C42—1464no—
472C2×C42—1464no—
473#95—24no—
474#95—738no—
475#95—1462no—
476#95—1462no—
477#95—1464no—
478#95—1464no—
479#95—1464no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×C4×D7312yes—
485C24D4×D7312yes—
486C24D4×D7312yes—
487C24C2×C22⋊D7312yes—
488C24Q8×D7312yes—
489C24Q8×D7312yes—
490C24C2×Dic14612yes—
491C24C23×D7311yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—2924no—
518C22×C4—2924no—
519C22×C4—2928no—
520C22×C4—2928no—
521C22×C4—732no—
522C22×C4—734no—
523C22×C4—732no—
524C22×C4—732no—
525C22×C4—734no—
526C22×C4—7316no—
527C22×C4—732no—
528C22×C4—734no—
529C22×C4—734no—
530C22×C4—732no—
531C22×C4—734no—
532C22×C4—732no—
533C22×C4—734no—
534C22×C4—1461no—
535C22×C4—1461no—
536C22×C4—1461no—
537C22×C4—1461no—
538C22×C4—1462no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1462no—
542C22×C4—1462no—
543C22×C4—1462no—
544C22×C4—1468no—
545C22×C4—1462no—
546C22×C4—1462no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—1462no—
550C22×C4—1462no—
551C22×C4—1468no—
552C22×C4—14616no—
553C22×C4—14616no—
554C22×C4—1468no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4C2×C4×D7314yes—
562C22×C4D4×D7314yes—
563C22×C4C2×C22⋊D7314yes—
564C22×C4C2×Dic14614yes—
565C4⋊C4—48no—
566C4⋊C4—2928no—
567C4⋊C4—2928no—
568C4⋊C4—2924no—
569C4⋊C4—2924no—
570C4⋊C4—2928no—
571C4⋊C4—14616no—
572C4⋊C4—14616no—
573C22⋊C4—44no—
574C22⋊C4—2924no—
575C22⋊C4—7316no—
576C22⋊C4#11924007116yescomplemented
577C42—14616no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23C4⋊C4×D7314yes—
595C23C4⋊C4×D7314yes—
596C23C2×#1192400714yes—
597C23#1455658714yes—
598C23#1455658914yes—
599C23#1455659014yes—
600C23#1455659014yes—
601C23C22×C4×D7311yescharacteristic
602C23C2×D4×D7311yescharacteristic
603C23C2×D4×D7311yescharacteristic
604C23C2×D4×D7312yes—
605C23C22×C22⋊D7311yescharacteristic
606C23C2×Q8×D7311yescharacteristic
607C23C2×Q8×D7311yescharacteristic
608C23C22×Dic14611yescharacteristic
609C23#41×D7312yes—
610C23#1455663612yes—
611C23#1455663812yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—416no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—29216no—
637C2×C4—2922no—
638C2×C4—2922no—
639C2×C4—2922no—
640C2×C4—2922no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2922no—
646C2×C4—2922no—
647C2×C4—2922no—
648C2×C4—2922no—
649C2×C4—2921no—
650C2×C4—2921no—
651C2×C4—734no—
652C2×C4—738no—
653C2×C4—734no—
654C2×C4—738no—
655C2×C4—734no—
656C2×C4—738no—
657C2×C4—734no—
658C2×C4—1464no—
659C2×C4—1464no—
660C2×C4—1464no—
661C2×C4—14632no—
662C2×C4—1464no—
663C2×C4—1464no—
664C2×C4—1464no—
665C2×C4—1464no—
666C2×C4—1464no—
667C2×C4—1464no—
668C2×C4—1464no—
669C2×C4—1462no—
670C2×C4—1464no—
671C2×C4—1462no—
672C2×C4C2×#1192400718yescomplemented
673C22—24no—
674C22—24no—
675C22—24no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—28no—
680C22—28no—
681C22—24no—
682C22—24no—
683C22#1798845618yescomplemented
684C22C2×C4⋊C4×D7311yescharacteristic
685C22C2×C4⋊C4×D7311yescharacteristic
686C22C22×#1192400711yescharacteristic
687C22C4×D4×D7312yes—
688C22#1798906612yes—
689C22#120×D7311yescharacteristic
690C22C22⋊Q8×D7312yes—
691C22#123×D7311yescharacteristic
692C22C2×#1455658711yescharacteristic
693C22C2×#1455658911yescharacteristic
694C22C2×#1455659011yescharacteristic
695C22C2×#1455659011yescharacteristic
696C22#1798915211yescharacteristic
697C22#1798915911yescharacteristic
698C22#1798921612yes—
699C22#1798921912yes—
700C22D4×C22⋊D7312yes—
701C22#1798923512yes—
702C22#1798923612yes—
703C22#1798925012yes—
704C22D4×Dic14612yes—
705C22#1798929112yes—
706C22#1798929612yes—
707C4—28no—
708C4—44no—
709C4—81no—
710C4—81no—
711C4—2924no—
712C4—5841no—
713C4—5841no—
714C4—738no—
715C4—1468no—
716C4—1464no—
717C2—28no—
718C2C2×#1798845611yescharacteristic
719C2#385×D7311yescharacteristic
720C2#2261255011yescharacteristic
721C2D4×#1192400712yes—
722C2#2261282912yes—
723C2#2261356611yescharacteristic
724C2#2261357311yescharacteristic
725C2#2261363012yes—
726C2#2261363212yes—
727C2#2261440011yescharacteristic
728C2#2261440711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#385×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73#13880
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#17988456C2semidirect
8. #22608195C2semidirect
9. #22608194C2semidirect
10. #22608159C2semidirect
31. C22⋊C4×Dic73C4semidirect
88. C2×C4×Dic73C2×C4semidirect
94. #14556498C2×C4semidirect
146. C22×Dic73C4⋊C4semidirect
167. C22⋊Dic73C4⋊C4semidirect
212. C22⋊C4×C73C4⋊C4semidirect
271. C2×C4×C73C2×C4⋊C4semidirect
303. C2×Dic73C2×C4⋊C4semidirect
318. C22×C73#384semidirect
351. Dic73#385semidirect
376. C73#13880semidirect
576. C22⋊C4#11924007semidirect
672. C2×C4C2×#11924007semidirect
683. C22#17988456semidirect

Maximal subgroups

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

subgroupindex
C23×#119240072
C2×#179884622
C2×#179884602
C2×#179884592
C2×#179884562
C2×#179884452
C2×C22⋊C4×Dic732
#226081952
#226081942
#226081592
C2×#385×C732
#1388073