Finite Group Databasebeta

← #33022604

Subgroups — #33022604

Order 18688.

1626 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988515C212yesmaximal
2C2×#17988483C211yesmaximal, characteristic, complemented
3C2×#17988447C211yesmaximal, characteristic
4C2×C4×C22⋊Dic73C211yesmaximal, characteristic
5#22608192C212yesmaximal, complemented
6#22608186C212yesmaximal, complemented
7#22608180C212yesmaximal
8#22608160C211yesmaximal, characteristic, complemented
9#22608160C211yesmaximal, characteristic, complemented
10#22608160C211yesmaximal, characteristic, complemented
11C2×#380×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×#11924007C2212yes—
15C22×C22⋊Dic73C2211yescharacteristic
16C22×C22⋊Dic73C2212yes—
17C22×C22⋊Dic73C2211yescharacteristic
18C22×C4×Dic73C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20#17988515—28no—
21#17988483—24no—
22#17988447—24no—
23C4×C22⋊Dic73—24no—
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C24×C4×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2212yes—
38#380×C73—24no—
39C2×#95×C73C2212yes—
40C23×Dic73C2312yes—
41C23×Dic73C2311yescharacteristic
42C23×Dic73C2312yes—
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C2×C4⋊Dic73—22no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73D414yes—
52C2×#11924007—24no—
53C2×#11924007—24no—
54C2×#11924007—42no—
55C2×C22⋊Dic73—22no—
56C2×C22⋊Dic73—22no—
57C2×C22⋊Dic73—24no—
58C2×C22⋊Dic73—22no—
59C2×C22⋊Dic73—22no—
60C2×C22⋊Dic73—24no—
61C2×C22⋊Dic73—22no—
62C2×C22⋊Dic73—42no—
63C2×C22⋊Dic73D414yes—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—22no—
67C2×C4×Dic73—22no—
68C2×C4×Dic73—22no—
69C2×C4×Dic73—22no—
70#14556498—24no—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—24no—
76#14556498—24no—
77#14556498—22no—
78#14556498—22no—
79#14556498—42no—
80C25×C73C2311yescharacteristic
81C23×C4×C73—22no—
82C23×C4×C73—22no—
83C23×C4×C73—22no—
84C23×C4×C73—22no—
85C23×C4×C73—22no—
86C23×C4×C73—22no—
87C23×C4×C73D414yes—
88C23×C4×C73C2312yes—
89C23×C4×C73C2312yes—
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—22no—
97C2×C4⋊C4×C73—22no—
98C2×C22⋊C4×C73—24no—
99C2×C22⋊C4×C73—24no—
100C2×C22⋊C4×C73—24no—
101#95×C73—24no—
102C22×Dic73—21no—
103C22×Dic73—21no—
104C22×Dic73—21no—
105C22×Dic73—21no—
106C22×Dic73—21no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—22no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—21no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—21no—
123C22×Dic73—22no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—22no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73C2×D412yes—
140C22×Dic73C2×D414yes—
141C22×Dic73C2×D412yes—
142C22×Dic73#4112yes—
143C22×Dic73#4112yes—
144C4⋊Dic73—28no—
145C4⋊Dic73—44no—
146#11924007—48no—
147C22⋊Dic73—28no—
148C22⋊Dic73—28no—
149C22⋊Dic73—48no—
150C4×Dic73—44no—
151C4×Dic73—44no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—21no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—21no—
160C24×C73—21no—
161C24×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73C2×D412yes—
165C24×C73C2×D412yes—
166C24×C73#4112yes—
167C24×C73C2411yescharacteristic
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—28no—
175C22×C4×C73—28no—
176C22×C4×C73—28no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—22no—
188C22×C4×C73—22no—
189C22×C4×C73—22no—
190C22×C4×C73—22no—
191C22×C4×C73—44no—
192C22×C4×C73—44no—
193C22×C4×C73—44no—
194C22×C4×C73—44no—
195C22×C4×C73C2×D412yes—
196C22×C4×C73C2×D412yes—
197C22×C4×C73C2×D412yes—
198C22×C4×C73#4112yes—
199C22×C4×C73#4112yes—
200C22×C4×C73#4112yes—
201C22×C4×C73#4112yes—
202C22×C4×C73#4112yes—
203C4⋊C4×C73—44no—
204C4⋊C4×C73—44no—
205C22⋊C4×C73—48no—
206C23×C73—22no—
207C23×C73—22no—
208C23×C73—22no—
209C23×C73—22no—
210C23×C73—22no—
211C23×C73—22no—
212C23×C73—22no—
213C23×C73—22no—
214C23×C73—22no—
215C23×C73—22no—
216C23×C73—22no—
217C23×C73—22no—
218C23×C73—22no—
219C23×C73—22no—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—22no—
223C23×C73—22no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73#12114yes—
241C23×C73C22×D411yescharacteristic
242C23×C73C22×D411yescharacteristic
243C23×C73C22×D411yescharacteristic
244C23×C73C2×#4111yescharacteristic
245C23×C73C2×#4111yescharacteristic
246C23×C73C2×#4111yescharacteristic
247C23×C73C2×#4111yescharacteristic
248C23×C73C2×#4111yescharacteristic
249C23×C73C2×#4111yescharacteristic
250C23×C73C2×#4111yescharacteristic
251C23×C73C2×#4111yescharacteristic
252C23×C73H(5,𝔽2)11yescharacteristic
253C23×C732−1+411yescharacteristic
254C23×C732−1+411yescharacteristic
255C23×C732−1+411yescharacteristic
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—416no—
264C2×C4×C73—42no—
265C2×C4×C73—42no—
266C2×C4×C73—42no—
267C2×C4×C73—42no—
268C2×C4×C73—42no—
269C2×C4×C73—42no—
270C2×C4×C73—42no—
271C2×C4×C73—42no—
272C2×C4×C73—42no—
273C2×C4×C73—42no—
274C2×C4×C73—42no—
275C2×C4×C73—42no—
276C2×C4×C73—42no—
277C2×C4×C73—42no—
278C2×C4×C73#12114yes—
279C2×C4×C73#12314yes—
280C2×C4×C73#12314yes—
281C2×C4×C73#12314yes—
282C2×C4×C73#12414yes—
283C2×C4×C73#12614yes—
284C2×C4×C73#12614yes—
285C2×Dic73—22no—
286C2×Dic73—22no—
287C2×Dic73—24no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—24no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—24no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—42no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—42no—
316C2×Dic73—41no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C22×C73—24no—
328C22×C73—24no—
329C22×C73—24no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73C2×#12111yescharacteristic
343C22×C73C2×#12111yescharacteristic
344C22×C73C2×#12311yescharacteristic
345C22×C73C2×#12311yescharacteristic
346C22×C73C2×#12311yescharacteristic
347C22×C73#52511yescharacteristic
348C22×C73C2×#12411yescharacteristic
349C22×C73C2×#12611yescharacteristic
350C22×C73C2×#12611yescharacteristic
351C22×C73#52911yescharacteristic
352C22×C73#52911yescharacteristic
353C22×C73#53211yescharacteristic
354C22×C73#53211yescharacteristic
355C22×C73#53611yescharacteristic
356C22×C73#53711yescharacteristic
357C22×C73#54111yescharacteristic
358C22×C73#54111yescharacteristic
359C22×C73#54211yescharacteristic
360C22×C73#54211yescharacteristic
361C22×C73D4211yescharacteristic
362C22×C73#54711yescharacteristic
363C22×C73#54711yescharacteristic
364C22×C73#54711yescharacteristic
365C22×C73#54711yescharacteristic
366C22×C73#54811yescharacteristic
367C22×C73#54811yescharacteristic
368C22×C73#55211yescharacteristic
369C22×C73#55211yescharacteristic
370C22×C73#55211yescharacteristic
371C22×C73#55211yescharacteristic
372C22×C73#55311yescharacteristic
373C22×C73#55311yescharacteristic
374C22×C73#55511yescharacteristic
375C22×C73#55611yescharacteristic
376C22×C73#55611yescharacteristic
377C4×C73—42no—
378C4×C73—82no—
379C4×C73—82no—
380C4×C73#39718yescomplemented
381Dic73—42no—
382Dic73—42no—
383Dic73—44no—
384Dic73—42no—
385Dic73—42no—
386Dic73—82no—
387#15132—731nomaximal, Sylow
388C2×C73—44no—
389C2×C73C2×#39711yescharacteristic
390C2×C73#241511yescharacteristic
391C2×C73#241611yescharacteristic
392C2×C73#242111yescharacteristic
393C2×C73#242211yescharacteristic
394C2×C73#248511yescharacteristic
395C2×C73#248611yescharacteristic
396C2×C73#248911yescharacteristic
397C2×C73#249111yescharacteristic
398C2×C73#249411yescharacteristic
399C2×C73#249511yescharacteristic
400C2×C73#249611yescharacteristic
401C2×C73#249611yescharacteristic
402C2×C73#262511yescharacteristic
403C2×C73#285411yescharacteristic
404C2×#397—732no—
405C2×#389—731no—
406C2×#380—731no—
407C2×#380D7311yescharacteristic
408C2×C4×C22⋊C4—731no—
409#1443—732no—
410#1442—732no—
411#1440—732no—
412C4⋊#95—731no—
413C4⋊#95—731no—
414C4⋊#95—731no—
415C73#1513211yescharacteristic, complemented, Sylow
416C24×C4C2×D7311yescharacteristic
417C22×C4⋊C4—732no—
418C22×C4⋊C4—731no—
419C22×C4⋊C4—731no—
420C22×C4⋊C4C2×D7311yescharacteristic
421C22×C4⋊C4C2×D7311yescharacteristic
422C22×C22⋊C4—732no—
423C22×C22⋊C4—731no—
424C22×C22⋊C4—731no—
425C22×C22⋊C4C2×D7312yes—
426C22×C42—731no—
427C22×C42—731no—
428#397—1468no—
429#389—1464no—
430#380—24no—
431#380—1464no—
432C4×C22⋊C4—1464no—
433C2×#95—732no—
434C2×#95—732no—
435C2×#95—732no—
436C2×#95—732no—
437C2×#95—732no—
438C2×#95—732no—
439C2×#95—732no—
440C2×#95—731no—
441C2×#95—732no—
442C2×#95—731no—
443C2×#95C2×D7312yes—
444C25C22×D7311yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—732no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4—731no—
456C23×C4—732no—
457C23×C4C22⋊D7314yes—
458C23×C4C22×D7312yes—
459C23×C4C22×D7312yes—
460C23×C4C22×D7311yescharacteristic
461C23×C4C22×D7311yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—2922no—
469C2×C4⋊C4—734no—
470C2×C4⋊C4—1464no—
471C2×C4⋊C4—1464no—
472C2×C4⋊C4—1462no—
473C2×C4⋊C4—1462no—
474C2×C4⋊C4—1462no—
475C2×C4⋊C4—1462no—
476C2×C4⋊C4—1462no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—2922no—
481C2×C22⋊C4—734no—
482C2×C22⋊C4—1464no—
483C2×C22⋊C4—1464no—
484C2×C22⋊C4—1462no—
485C2×C22⋊C4—1462no—
486C2×C22⋊C4—1462no—
487C2×C22⋊C4—1462no—
488C2×C22⋊C4—1462no—
489C2×C42—1462no—
490C2×C42—1462no—
491C2×C42—1462no—
492C2×C42—1462no—
493C2×C42—1462no—
494C2×C42—1462no—
495#95—24no—
496#95—2922no—
497#95—1464no—
498#95—1464no—
499#95—1464no—
500#95—1464no—
501#95—1464no—
502#95—1464no—
503#95—1464no—
504#95—1462no—
505#95—1462no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24D4×D7312yes—
519C24C2×C22⋊D7312yes—
520C24#1192402712yes—
521C24C23×D7311yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
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—22no—
544C22×C4—22no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—732no—
550C22×C4—732no—
551C22×C4—734no—
552C22×C4—732no—
553C22×C4—732no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1461no—
562C22×C4—1462no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1462no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1462no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1462no—
581C22×C4—1461no—
582C22×C4—1462no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1462no—
591C22×C4D4×D7312yes—
592C22×C4C2×C22⋊D7312yes—
593C22×C4C2×C22⋊D7312yes—
594C22×C4#1192402712yes—
595C22×C4#1192402712yes—
596C22×C4#1192402712yes—
597C22×C4#1192402812yes—
598C22×C4#1192402812yes—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—2928no—
602C4⋊C4—2924no—
603C4⋊C4—1468no—
604C22⋊C4—48no—
605C22⋊C4—2928no—
606C22⋊C4—1468no—
607C22⋊C4—1468no—
608C42—2924no—
609C42—2924no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#1455656214yes—
645C23C2×D4×D7311yescharacteristic
646C23C2×D4×D7311yescharacteristic
647C23C22×C22⋊D7311yescharacteristic
648C23#41×D7311yescharacteristic
649C23#41×D7311yescharacteristic
650C23C2×#1192402711yescharacteristic
651C23C2×#1192402711yescharacteristic
652C23C2×#1192402711yescharacteristic
653C23C2×#1192402711yescharacteristic
654C23C2×#1192402811yescharacteristic
655C23C2×#1192402811yescharacteristic
656C23#1455663711yescharacteristic
657C23#1455663811yescharacteristic
658C23#1455663911yescharacteristic
659C23#1455663911yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—2922no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—2921no—
687C2×C4—2922no—
688C2×C4—2922no—
689C2×C4—2921no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2922no—
694C2×C4—2921no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—2921no—
699C2×C4—2921no—
700C2×C4—2921no—
701C2×C4—2921no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—2922no—
708C2×C4—2922no—
709C2×C4—1464no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1464no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1464no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4#1455656314yes—
725C2×C4#1455657214yes—
726C2×C4#1455657314yes—
727C2×C4#1455657414yes—
728C2×C4#1455657714yes—
729C2×C4#1455658414yes—
730C2×C4#1455658414yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#1455656211yescharacteristic
747C22C2×#1455656311yescharacteristic
748C22C2×#1455657211yescharacteristic
749C22C2×#1455657311yescharacteristic
750C22C2×#1455657411yescharacteristic
751C22#1798909411yescharacteristic
752C22C2×#1455657711yescharacteristic
753C22C2×#1455658411yescharacteristic
754C22C2×#1455658411yescharacteristic
755C22#1798911811yescharacteristic
756C22#1798911811yescharacteristic
757C22#1798913211yescharacteristic
758C22#1798913211yescharacteristic
759C22#1798916111yescharacteristic
760C22#1798916511yescharacteristic
761C22#1798919711yescharacteristic
762C22#1798919711yescharacteristic
763C22#1798921011yescharacteristic
764C22#1798921011yescharacteristic
765C22#1798922111yescharacteristic
766C22#1798923711yescharacteristic
767C22#1798923811yescharacteristic
768C22#1798923811yescharacteristic
769C22#1798923911yescharacteristic
770C22#1798924311yescharacteristic
771C22#1798924711yescharacteristic
772C22#1798927111yescharacteristic
773C22#1798927211yescharacteristic
774C22#1798927211yescharacteristic
775C22#1798927611yescharacteristic
776C22#1798928111yescharacteristic
777C22#1798928911yescharacteristic
778C22#1798930011yescharacteristic
779C22#1798930511yescharacteristic
780C22#1798930811yescharacteristic
781C4—42no—
782C4—82no—
783C4—82no—
784C4—2922no—
785C4—2922no—
786C4—2924no—
787C4—2922no—
788C4—2922no—
789C4—5842no—
790C4#1798851518yescomplemented
791C2—44no—
792C2C2×#1798851511yescharacteristic
793C2#2261336111yescharacteristic
794C2#2261337211yescharacteristic
795C2#2261343611yescharacteristic
796C2#2261344711yescharacteristic
797C2#2261422211yescharacteristic
798C2#2261423311yescharacteristic
799C2#2261426811yescharacteristic
800C2#2261429011yescharacteristic
801C2#2261432711yescharacteristic
802C2#2261434411yescharacteristic
803C2#2261434911yescharacteristic
804C2#2261435511yescharacteristic
805C2#2261572911yescharacteristic
806C2#2261825711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, cosocleC24×C73C24
FittingC2×#380×C73C2
prime radicalC25×C73C23
hypercenterC2×#380D73
hypocenterC73#15132
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#17988483C2semidirect
5. #22608192C2semidirect
6. #22608186C2semidirect
8. #22608160C2semidirect
9. #22608160C2semidirect
10. #22608160C2semidirect
380. C4×C73#397semidirect
415. C73#15132semidirect
790. C4#17988515semidirect

Maximal subgroups

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

subgroupindex
C2×#179885152
C2×#179884832
C2×#179884472
C2×C4×C22⋊Dic732
#226081922
#226081862
#226081802
#226081602
C2×#380×C732
#1513273