Finite Group Databasebeta

← #33022630

Subgroups — #33022630

Order 18688.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988523C212yesmaximal
2C2×#17988486C211yesmaximal, characteristic, complemented
3C2×#17988483C211yesmaximal, characteristic, complemented
4C2×#17988456C211yesmaximal, characteristic, complemented
5C2×#17988447C211yesmaximal, characteristic
6C2×C4×C22⋊Dic73C211yesmaximal, characteristic
7#22608197C212yesmaximal, complemented
8#22608195C212yesmaximal, complemented
9#22608174C212yesmaximal
10#22608160C211yesmaximal, characteristic, complemented
11C2×#380×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2212yes—
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924007C2212yes—
18C22×C22⋊Dic73C2212yes—
19C22×C22⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23#17988523—28no—
24#17988486—24no—
25#17988483—24no—
26#17988456—24no—
27#17988447—24no—
28C4×C22⋊Dic73—24no—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C24×C4×C73C2211yescharacteristic
37C22×C4⋊C4×C73C2211yescharacteristic
38C22×C4⋊C4×C73C2211yescharacteristic
39C22×C22⋊C4×C73C2212yes—
40#380×C73—24no—
41C2×#95×C73C2212yes—
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C23×Dic73C2311yescharacteristic
48C2×C4⋊Dic73—24no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—24no—
52C2×C4⋊Dic73—22no—
53C2×C4⋊Dic73—22no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—42no—
56C2×C4⋊Dic73D414yes—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—24no—
60C2×#11924007—24no—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—42no—
64C2×#11924007—42no—
65C2×#11924007—42no—
66C2×C22⋊Dic73—22no—
67C2×C22⋊Dic73—22no—
68C2×C22⋊Dic73—22no—
69C2×C22⋊Dic73—22no—
70C2×C22⋊Dic73—24no—
71C2×C22⋊Dic73—24no—
72C2×C22⋊Dic73—42no—
73C2×C22⋊Dic73D414yes—
74C2×C22⋊Dic73Q814yes—
75C2×C4×Dic73—22no—
76C2×C4×Dic73—22no—
77C2×C4×Dic73—22no—
78C2×C4×Dic73—22no—
79C2×C4×Dic73—22no—
80C2×C4×Dic73D414yes—
81#14556498—22no—
82#14556498—22no—
83#14556498—24no—
84#14556498—24no—
85#14556498—24no—
86#14556498—24no—
87#14556498—24no—
88C25×C73C2311yescharacteristic
89C23×C4×C73—22no—
90C23×C4×C73—22no—
91C23×C4×C73—22no—
92C23×C4×C73—22no—
93C23×C4×C73—22no—
94C23×C4×C73—22no—
95C23×C4×C73Q814yes—
96C23×C4×C73C2312yes—
97C23×C4×C73C2312yes—
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—22no—
102C2×C4⋊C4×C73—22no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73—22no—
105C2×C4⋊C4×C73D414yes—
106C2×C22⋊C4×C73—24no—
107C2×C22⋊C4×C73—24no—
108C2×C22⋊C4×C73—42no—
109#95×C73—24no—
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—21no—
121C22×Dic73—21no—
122C22×Dic73—22no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—22no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—22no—
135C22×Dic73—21no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73C2×D414yes—
144C22×Dic73C2×D412yes—
145C22×Dic73C2×D412yes—
146C22×Dic73C2×D412yes—
147C22×Dic73C2×D412yes—
148C22×Dic73C2×Q812yes—
149C22×Dic73C2×Q812yes—
150C22×Dic73#4112yes—
151C22×Dic73#4112yes—
152C4⋊Dic73—28no—
153C4⋊Dic73—48no—
154C4⋊Dic73—44no—
155#11924007—48no—
156#11924007—48no—
157#11924007—48no—
158C22⋊Dic73—28no—
159C22⋊Dic73—28no—
160C22⋊Dic73—48no—
161C4×Dic73—28no—
162C4×Dic73—44no—
163C24×C73—21no—
164C24×C73—21no—
165C24×C73—21no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73—21no—
169C24×C73—21no—
170C24×C73—21no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—21no—
175C24×C73C2×D412yes—
176C24×C73C2×Q812yes—
177C24×C73C2×Q812yes—
178C24×C73C2411yescharacteristic
179C22×C4×C73—21no—
180C22×C4×C73—22no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—22no—
189C22×C4×C73—22no—
190C22×C4×C73—22no—
191C22×C4×C73—28no—
192C22×C4×C73—28no—
193C22×C4×C73—28no—
194C22×C4×C73—22no—
195C22×C4×C73—22no—
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—44no—
202C22×C4×C73—44no—
203C22×C4×C73—44no—
204C22×C4×C73—44no—
205C22×C4×C73C2×D412yes—
206C22×C4×C73C2×D412yes—
207C22×C4×C73C2×D414yes—
208C22×C4×C73C2×D412yes—
209C22×C4×C73C2×Q812yes—
210C22×C4×C73C2×Q812yes—
211C22×C4×C73#4112yes—
212C22×C4×C73#4112yes—
213C22×C4×C73#4112yes—
214C4⋊C4×C73—28no—
215C4⋊C4×C73—44no—
216C22⋊C4×C73—48no—
217C23×C73—22no—
218C23×C73—22no—
219C23×C73—22no—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—22no—
223C23×C73—22no—
224C23×C73—22no—
225C23×C73—22no—
226C23×C73—22no—
227C23×C73—22no—
228C23×C73—22no—
229C23×C73—22no—
230C23×C73—22no—
231C23×C73—22no—
232C23×C73—22no—
233C23×C73—22no—
234C23×C73—22no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73C4⋊Q814yes—
252C23×C73C22×D411yescharacteristic
253C23×C73C22×D411yescharacteristic
254C23×C73C22×D411yescharacteristic
255C23×C73C22×D411yescharacteristic
256C23×C73C22×Q811yescharacteristic
257C23×C73C22×Q811yescharacteristic
258C23×C73C2×#4111yescharacteristic
259C23×C73C2×#4111yescharacteristic
260C23×C73C2×#4111yescharacteristic
261C23×C73C2×#4111yescharacteristic
262C23×C73C2×#4111yescharacteristic
263C23×C73H(5,𝔽2)11yescharacteristic
264C23×C73H(5,𝔽2)11yescharacteristic
265C23×C732−1+411yescharacteristic
266C23×C732−1+411yescharacteristic
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—24no—
271C2×C4×C73—24no—
272C2×C4×C73—24no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—42no—
278C2×C4×C73—42no—
279C2×C4×C73—42no—
280C2×C4×C73—42no—
281C2×C4×C73—416no—
282C2×C4×C73—42no—
283C2×C4×C73—42no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73C22⋊Q814yes—
290C2×C4×C73C22⋊Q814yes—
291C2×C4×C73C22⋊Q814yes—
292C2×C4×C73#12314yes—
293C2×C4×C73#12314yes—
294C2×C4×C73#12314yes—
295C2×C4×C73#12714yes—
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—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—24no—
311C2×Dic73—24no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—24no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—42no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—42no—
323C2×Dic73—41no—
324C2×Dic73—42no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334C2×Dic73—42no—
335C2×Dic73—42no—
336C2×Dic73#12114yes—
337C2×Dic73C22⋊Q814yes—
338C22×C73—24no—
339C22×C73—24no—
340C22×C73—24no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73—42no—
353C22×C73C2×#12111yescharacteristic
354C22×C73C2×C22⋊Q811yescharacteristic
355C22×C73C2×C22⋊Q811yescharacteristic
356C22×C73C2×C22⋊Q811yescharacteristic
357C22×C73C2×C22⋊Q811yescharacteristic
358C22×C73C2×#12311yescharacteristic
359C22×C73C2×#12311yescharacteristic
360C22×C73C2×#12311yescharacteristic
361C22×C73C2×#12711yescharacteristic
362C22×C73C2×C4⋊Q811yescharacteristic
363C22×C73#53211yescharacteristic
364C22×C73#53311yescharacteristic
365C22×C73#53311yescharacteristic
366C22×C73#53511yescharacteristic
367C22×C73#53611yescharacteristic
368C22×C73#54211yescharacteristic
369C22×C73#54211yescharacteristic
370C22×C73#54411yescharacteristic
371C22×C73#54411yescharacteristic
372C22×C73D4211yescharacteristic
373C22×C73D4211yescharacteristic
374C22×C73#54711yescharacteristic
375C22×C73#54711yescharacteristic
376C22×C73#54711yescharacteristic
377C22×C73#54711yescharacteristic
378C22×C73D4×Q811yescharacteristic
379C22×C73D4×Q811yescharacteristic
380C22×C73#55011yescharacteristic
381C22×C73#55011yescharacteristic
382C22×C73#55211yescharacteristic
383C22×C73#55211yescharacteristic
384C22×C73#55311yescharacteristic
385C22×C73#55311yescharacteristic
386C22×C73#55411yescharacteristic
387C22×C73#55411yescharacteristic
388C4×C73—42no—
389C4×C73—44no—
390C4×C73—82no—
391C4×C73#39918yescomplemented
392Dic73—24no—
393Dic73—24no—
394Dic73—44no—
395Dic73—42no—
396Dic73—42no—
397Dic73—82no—
398#15135—731nomaximal, Sylow
399C2×C73—44no—
400C2×C73C2×#39911yescharacteristic
401C2×C73#242211yescharacteristic
402C2×C73#242211yescharacteristic
403C2×C73#242311yescharacteristic
404C2×C73#242311yescharacteristic
405C2×C73#244011yescharacteristic
406C2×C73#244011yescharacteristic
407C2×C73#244111yescharacteristic
408C2×C73#244111yescharacteristic
409C2×C73#248611yescharacteristic
410C2×C73#248711yescharacteristic
411C2×C73#254111yescharacteristic
412C2×C73#254211yescharacteristic
413C2×C73#262811yescharacteristic
414C2×C73#285711yescharacteristic
415C2×#399—732no—
416C2×#389—731no—
417C2×#389—731no—
418C2×#384—731no—
419C2×#380—731no—
420C2×#380D7311yescharacteristic
421C2×C4×C22⋊C4—731no—
422#1445—732no—
423#1444—732no—
424#1439—732no—
425C4⋊#95—731no—
426C73#1513511yescharacteristic, complemented, Sylow
427C24×C4C2×D7311yescharacteristic
428C22×C4⋊C4—732no—
429C22×C4⋊C4—732no—
430C22×C4⋊C4—732no—
431C22×C4⋊C4—731no—
432C22×C4⋊C4—732no—
433C22×C4⋊C4—731no—
434C22×C4⋊C4C2×D7311yescharacteristic
435C22×C4⋊C4C2×D7311yescharacteristic
436C22×C22⋊C4—732no—
437C22×C22⋊C4—731no—
438C22×C22⋊C4—731no—
439C22×C22⋊C4C2×D7312yes—
440C22×C42—731no—
441C22×C42—731no—
442#399—1468no—
443#389—1464no—
444#389—1464no—
445#384—1464no—
446#380—24no—
447#380—1464no—
448C4×C22⋊C4—1464no—
449C2×#95—732no—
450C2×#95—732no—
451C2×#95—732no—
452C2×#95—732no—
453C2×#95—731no—
454C2×#95—732no—
455C2×#95—731no—
456C2×#95C2×D7312yes—
457C25C22×D7311yescharacteristic
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—731no—
465C23×C4—731no—
466C23×C4—731no—
467C23×C4—732no—
468C23×C4—731no—
469C23×C4—732no—
470C23×C4Dic14614yes—
471C23×C4C22×D7312yes—
472C23×C4C22×D7312yes—
473C23×C4C22×D7311yescharacteristic
474C23×C4C22×D7311yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—2922no—
481C2×C4⋊C4—2922no—
482C2×C4⋊C4—2922no—
483C2×C4⋊C4—2922no—
484C2×C4⋊C4—734no—
485C2×C4⋊C4—1464no—
486C2×C4⋊C4—1464no—
487C2×C4⋊C4—1464no—
488C2×C4⋊C4—1464no—
489C2×C4⋊C4—1464no—
490C2×C4⋊C4—1464no—
491C2×C4⋊C4—1464no—
492C2×C4⋊C4—1462no—
493C2×C4⋊C4—1462no—
494C2×C4⋊C4—1464no—
495C2×C4⋊C4—1462no—
496C2×C4⋊C4—1462no—
497C2×C4⋊C4—1462no—
498C2×C4⋊C4C22⋊D7314yes—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—2922no—
503C2×C22⋊C4—734no—
504C2×C22⋊C4—734no—
505C2×C22⋊C4—1464no—
506C2×C22⋊C4—1464no—
507C2×C22⋊C4—1462no—
508C2×C22⋊C4—1462no—
509C2×C22⋊C4—1462no—
510C2×C22⋊C4—1462no—
511C2×C42—734no—
512C2×C42—1462no—
513C2×C42—1462no—
514C2×C42—1462no—
515C2×C42—1462no—
516C2×C42—1462no—
517#95—24no—
518#95—1464no—
519#95—1462no—
520#95—1462no—
521#95—1464no—
522#95—1464no—
523#95—1464no—
524#95—1464no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24D4×D7312yes—
538C24Q8×D7312yes—
539C24C2×Dic14612yes—
540C24C23×D7311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—732no—
573C22×C4—734no—
574C22×C4—732no—
575C22×C4—732no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1462no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1462no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4—1461no—
596C22×C4—1462no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1462no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4D4×D7312yes—
610C22×C4D4×D7312yes—
611C22×C4C2×C22⋊D7314yes—
612C22×C4C2×C22⋊D7312yes—
613C22×C4C2×Dic14612yes—
614C22×C4C2×Dic14612yes—
615C22×C4#1192402712yes—
616C22×C4#1192402712yes—
617C22×C4#1192402812yes—
618C4⋊C4—28no—
619C4⋊C4—44no—
620C4⋊C4—2928no—
621C4⋊C4—2928no—
622C4⋊C4—2928no—
623C4⋊C4—2928no—
624C4⋊C4—2924no—
625C4⋊C4—1468no—
626C22⋊C4—48no—
627C22⋊C4—2928no—
628C22⋊C4—1468no—
629C22⋊C4—1468no—
630C42—2924no—
631C42—1468no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1455659014yes—
667C23C2×D4×D7311yescharacteristic
668C23C2×D4×D7311yescharacteristic
669C23C2×D4×D7311yescharacteristic
670C23C22×C22⋊D7311yescharacteristic
671C23C2×Q8×D7311yescharacteristic
672C23C22×Dic14611yescharacteristic
673C23#41×D7311yescharacteristic
674C23#41×D7311yescharacteristic
675C23C2×#1192402711yescharacteristic
676C23C2×#1192402711yescharacteristic
677C23C2×#1192402811yescharacteristic
678C23#1455663611yescharacteristic
679C23#1455663711yescharacteristic
680C23#1455663811yescharacteristic
681C23#1455663911yescharacteristic
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2922no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2922no—
710C2×C4—2921no—
711C2×C4—2922no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2922no—
716C2×C4—2922no—
717C2×C4—2922no—
718C2×C4—2922no—
719C2×C4—2922no—
720C2×C4—2922no—
721C2×C4—2922no—
722C2×C4—2922no—
723C2×C4—734no—
724C2×C4—734no—
725C2×C4—1462no—
726C2×C4—1464no—
727C2×C4—1462no—
728C2×C4—1464no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1464no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4#1455656814yes—
747C2×C4#1455656814yes—
748C2×C4#1455657014yes—
749C2×C4#1455657214yes—
750C2×C4#1455657314yes—
751C2×C4#1455657314yes—
752C2×C4#1455658714yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22#121×D7311yescharacteristic
769C22C22⋊Q8×D7311yescharacteristic
770C22C2×#1455656811yescharacteristic
771C22C2×#1455656811yescharacteristic
772C22C2×#1455657011yescharacteristic
773C22C2×#1455657211yescharacteristic
774C22C2×#1455657311yescharacteristic
775C22C2×#1455657311yescharacteristic
776C22C2×#1455658711yescharacteristic
777C22C2×#1455659011yescharacteristic
778C22#1798913211yescharacteristic
779C22#1798913911yescharacteristic
780C22#1798914011yescharacteristic
781C22#1798915311yescharacteristic
782C22#1798916011yescharacteristic
783C22#1798920411yescharacteristic
784C22#1798921011yescharacteristic
785C22#1798921511yescharacteristic
786C22#1798921811yescharacteristic
787C22D4×C22⋊D7311yescharacteristic
788C22#1798922111yescharacteristic
789C22#1798923611yescharacteristic
790C22#1798923711yescharacteristic
791C22#1798923811yescharacteristic
792C22#1798923911yescharacteristic
793C22#1798925011yescharacteristic
794C22Q8×C22⋊D7311yescharacteristic
795C22#1798925511yescharacteristic
796C22#1798925611yescharacteristic
797C22#1798927111yescharacteristic
798C22#1798927611yescharacteristic
799C22#1798928111yescharacteristic
800C22#1798928411yescharacteristic
801C22#1798929211yescharacteristic
802C22#1798929511yescharacteristic
803C4—42no—
804C4—44no—
805C4—82no—
806C4—2922no—
807C4—2922no—
808C4—2924no—
809C4—5842no—
810C4—1464no—
811C4—1464no—
812C4#1798852318yescomplemented
813C2—44no—
814C2C2×#1798852311yescharacteristic
815C2#2261344111yescharacteristic
816C2#2261344711yescharacteristic
817C2#2261345211yescharacteristic
818C2#2261345811yescharacteristic
819C2#2261362711yescharacteristic
820C2#2261363411yescharacteristic
821C2#2261363811yescharacteristic
822C2#2261364511yescharacteristic
823C2#2261423511yescharacteristic
824C2#2261424411yescharacteristic
825C2#2261487411yescharacteristic
826C2#2261488111yescharacteristic
827C2#2261575611yescharacteristic
828C2#2261828111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, cosocleC24×C73C24
FittingC2×#380×C73C2
prime radicalC25×C73C23
hypercenterC2×#380D73
hypocenterC73#15135
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#17988486C2semidirect
3. C2×#17988483C2semidirect
4. C2×#17988456C2semidirect
7. #22608197C2semidirect
8. #22608195C2semidirect
10. #22608160C2semidirect
391. C4×C73#399semidirect
426. C73#15135semidirect
812. C4#17988523semidirect

Maximal subgroups

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

subgroupindex
C2×#179885232
C2×#179884862
C2×#179884832
C2×#179884562
C2×#179884472
C2×C4×C22⋊Dic732
#226081972
#226081952
#226081742
#226081602
C2×#380×C732
#1513573