Finite Group Databasebeta

← #33008192

Subgroups — #33008192

Order 18688.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988454C211yesmaximal, characteristic, complemented
2C2×C4×#11924005C211yesmaximal, characteristic
3C2×#95×D73C211yesmaximal, characteristic
4#22608191C212yesmaximal, complemented
5#22608191C212yesmaximal, complemented
6#22608158C211yesmaximal, characteristic, complemented
7#22608155C211yesmaximal, characteristic, complemented
8#22608152C212yesmaximal
9#22608152C212yesmaximal
10#22608152C211yesmaximal, characteristic
11C73×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D73C2212yes—
13C23×C4×D73C2211yescharacteristic
14C22×#11924005C2212yes—
15C22×#11924005C2211yescharacteristic
16C22×#11924005C2211yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18#17988454—24no—
19C4×#11924005C418yescomplemented
20C2×#14556498C2212yes—
21C2×#14556498C2212yes—
22C2×#14556498C2211yescharacteristic
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2211yescharacteristic
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32#95×D73—24no—
33C22×C42×C73C2211yescharacteristic
34C2×#95×C73C2211yescharacteristic
35C2×#95×C73C2212yes—
36C2×#95×C73C2212yes—
37C2×#95×C73C2211yescharacteristic
38C24×D73C2311yescharacteristic
39C23×Dic73C2312yes—
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2311yescharacteristic
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2312yes—
44C22×C4×D73—24no—
45C22×C4×D73—24no—
46C22×C4×D73—24no—
47C22×C4×D73—24no—
48C22×C4×D73—24no—
49C22×C4×D73—24no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73—42no—
53C22×C4×D73—42no—
54C22×C4×D73—42no—
55C22×C4×D73C2×C414yes—
56C2×#11924005—22no—
57C2×#11924005—24no—
58C2×#11924005—22no—
59C2×#11924005—24no—
60C2×#11924005—24no—
61C2×#11924005—24no—
62C2×#11924005C2×C414yes—
63C2×#11924005C2×C414yes—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73C2×C414yescomplemented
67#14556498—24no—
68#14556498—24no—
69#14556498—24no—
70#14556498—22no—
71#14556498—24no—
72#14556498—24no—
73#14556498—22no—
74#14556498—42no—
75#14556498—42no—
76#14556498—42no—
77#14556498C2×C414yescomplemented
78#14556498C2×C414yescomplemented
79C23×C4×C73C2312yes—
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2312yes—
83C23×C4×C73C2311yescharacteristic
84C2×C42×C73—42no—
85C2×C42×C73C2×C414yescomplemented
86#95×C73—22no—
87#95×C73—42no—
88#95×C73—42no—
89#95×C73D414yes—
90C23×D73—21no—
91C23×D73—22no—
92C23×D73—21no—
93C23×D73—22no—
94C23×D73—21no—
95C23×D73—21no—
96C23×D73C22×C412yes—
97C23×D73#4112yes—
98C23×D73#4114yes—
99C23×D73#4112yes—
100C23×D73#4114yes—
101C22×Dic73—21no—
102C22×Dic73—21no—
103C22×Dic73—21no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—21no—
107C22×Dic73—21no—
108C22×Dic73—22no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—21no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73C22×C412yes—
129C22×Dic73C22×C412yes—
130C22×Dic73C22×C412yes—
131C22×Dic73#4114yes—
132C2×C4×D73—216no—
133C2×C4×D73—28no—
134C2×C4×D73—28no—
135C2×C4×D73—44no—
136C2×C4×D73—48no—
137C2×C4×D73—48no—
138C2×C4×D73—48no—
139C2×C4×D73—48no—
140C2×C4×D73—48no—
141C2×C4×D73—48no—
142C2×C4×D73—48no—
143C2×C4×D73—48no—
144#11924005—28no—
145#11924005—28no—
146#11924005—48no—
147C4×Dic73—28no—
148C24×C73C2411yescharacteristic
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—22no—
152C22×C4×C73—22no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—21no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—21no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73C22×C412yes—
173C22×C4×C73C22×C412yes—
174C22×C4×C73C22×C412yes—
175C22×C4×C73C2×D414yes—
176C22×C4×C73C2×D412yes—
177C22×C4×C73#4112yes—
178C42×C73—44no—
179C23×C73C23×C411yescharacteristic
180C23×C73C22×D411yescharacteristic
181C23×C73C2×#4112yes—
182C23×C73C2×#4111yescharacteristic
183C23×C73C2×#4112yes—
184C23×C73C2×#4111yescharacteristic
185C23×C73C2×#4112yes—
186C23×C73C2×#4111yescharacteristic
187C23×C73H(5,𝔽2)12yes—
188C23×C73H(5,𝔽2)11yescharacteristic
189C23×C732−1+411yescharacteristic
190C22×D73—22no—
191C22×D73—22no—
192C22×D73—22no—
193C22×D73—22no—
194C22×D73—24no—
195C22×D73—24no—
196C22×D73—24no—
197C22×D73—24no—
198C22×D73—24no—
199C22×D73—22no—
200C22×D73—22no—
201C22×D73—24no—
202C22×D73—24no—
203C22×D73—24no—
204C22×D73—24no—
205C22×D73—22no—
206C22×D73—24no—
207C22×D73—22no—
208C22×D73#11714yes—
209C22×D73#11714yes—
210C22×D73#11714yes—
211C22×D73#12618yes—
212C22×D73#12618yes—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—24no—
224C2×C4×C73—24no—
225C2×C4×C73—24no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—42no—
231C2×C4×C73—42no—
232C2×C4×C73—42no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—42no—
237C2×C4×C73—42no—
238C2×C4×C73—42no—
239C2×C4×C73—42no—
240C2×C4×C73—42no—
241C2×C4×C73C4×D414yes—
242C2×Dic73—22no—
243C2×Dic73—22no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—22no—
251C2×Dic73—24no—
252C2×Dic73—24no—
253C2×Dic73—24no—
254C2×Dic73—42no—
255C2×Dic73—42no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C2×Dic73—42no—
259C2×Dic73—42no—
260C2×Dic73—42no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—42no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C2×Dic73—42no—
270C2×Dic73—42no—
271C2×Dic73—42no—
272C2×Dic73—42no—
273C4×D73—416no—
274C4×D73—432no—
275C22×C73C2×#11711yescharacteristic
276C22×C73C2×#11711yescharacteristic
277C22×C73C2×#11711yescharacteristic
278C22×C73C2×C4×D411yescharacteristic
279C22×C73C4×#4111yescharacteristic
280C22×C73#51811yescharacteristic
281C22×C73#52011yescharacteristic
282C22×C73#52512yes—
283C22×C73C2×#12612yes—
284C22×C73C2×#12612yes—
285C22×C73#52912yes—
286C22×C73#53812yes—
287C22×C73#53912yes—
288C22×C73#54612yes—
289C22×C73#54611yescharacteristic
290C22×C73#54811yescharacteristic
291C22×C73#55112yes—
292C22×C73#55112yes—
293C22×C73#55112yes—
294C22×C73#55212yes—
295C22×C73#55211yescharacteristic
296C22×C73#55312yes—
297C22×C73#55311yescharacteristic
298C2×D73—24no—
299C2×D73—24no—
300C2×D73—24no—
301C2×D73—24no—
302C2×D73—24no—
303C2×D73—28no—
304C2×D73—28no—
305C2×D73—28no—
306C2×D73—28no—
307C2×D73—24no—
308C2×D73#38318yescomplemented
309C4×C73—24no—
310C4×C73—42no—
311C4×C73—42no—
312C4×C73—44no—
313C4×C73—82no—
314Dic73—42no—
315Dic73—42no—
316Dic73—44no—
317Dic73—42no—
318Dic73—82no—
319#13901—731nomaximal, Sylow
320C2×C73C2×#38311yescharacteristic
321C2×C73#229011yescharacteristic
322C2×C73#231811yescharacteristic
323C2×C73#234211yescharacteristic
324C2×C73#234311yescharacteristic
325C2×C73#235211yescharacteristic
326C2×C73#235311yescharacteristic
327C2×C73#248012yes—
328C2×C73#248112yes—
329C2×C73#249312yes—
330C2×C73#251012yes—
331D73—28no—
332C2×#383—731no—
333C2×C4×C22⋊C4—731no—
334C22×#95—731no—
335#1443—732no—
336#1443—732no—
337#1434—731no—
338#1434—731no—
339#1434D7311yescharacteristic, complemented
340C22⋊#95—732no—
341C22⋊#95—732no—
342C22⋊#95—731no—
343C73#1390111yescharacteristic, complemented, Sylow
344C24×C4—731no—
345C24×C4—732no—
346C22×C22⋊C4—731no—
347C22×C22⋊C4—731no—
348C22×C22⋊C4—732no—
349C22×C42—731no—
350C22×C42C2×D7311yescharacteristic
351#383—1464no—
352C4×C22⋊C4—738no—
353C2×#95—732no—
354C2×#95—732no—
355C2×#95—732no—
356C2×#95—731no—
357C2×#95—731no—
358C2×#95—732no—
359C2×#95—732no—
360C2×#95—731no—
361C2×#95—732no—
362C2×#95—732no—
363C2×#95—731no—
364C2×#95—732no—
365C2×#95—1464no—
366C2×#95C2×D7311yescharacteristic
367C2×#95C2×D7312yes—
368C2×#95C2×D7312yes—
369C2×#95C2×D7311yescharacteristic
370C25—731no—
371C23×C4—2922no—
372C23×C4—2922no—
373C23×C4—2922no—
374C23×C4—734no—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4—732no—
379C23×C4—732no—
380C23×C4—1464no—
381C23×C4—1464no—
382C23×C4—1464no—
383C23×C4—1464no—
384C23×C4—1464no—
385C23×C4—1464no—
386C23×C4—1462no—
387C23×C4—1462no—
388C23×C4C22×D7312yes—
389C23×C4C22×D7311yescharacteristic
390C23×C4C22×D7311yescharacteristic
391C23×C4C22×D7312yes—
392C23×C4C22×D7311yescharacteristic
393C2×C22⋊C4—734no—
394C2×C22⋊C4—734no—
395C2×C22⋊C4—1464no—
396C2×C22⋊C4—1464no—
397C2×C22⋊C4—1464no—
398C2×C22⋊C4—1462no—
399C2×C22⋊C4—1464no—
400C2×C22⋊C4—1462no—
401C2×C42—42no—
402C2×C42—734no—
403C2×C42—1462no—
404C2×C42—1462no—
405C2×C42C4×D7314yescomplemented
406#95—22no—
407#95—42no—
408#95—42no—
409#95—2922no—
410#95—2922no—
411#95—2922no—
412#95—734no—
413#95—734no—
414#95—1464no—
415#95—1464no—
416#95—1464no—
417#95—1462no—
418#95—1462no—
419#95—1464no—
420#95—1464no—
421#95D29214yes—
422C24—732no—
423C24—732no—
424C24—734no—
425C24—732no—
426C24—734no—
427C24—1461no—
428C24—1462no—
429C24—1461no—
430C24—1461no—
431C24—1462no—
432C24—1461no—
433C24C23×D7311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—2928no—
458C22×C4—2928no—
459C22×C4—2928no—
460C22×C4—2928no—
461C22×C4—2924no—
462C22×C4—2928no—
463C22×C4—2928no—
464C22×C4—2928no—
465C22×C4—2928no—
466C22×C4—732no—
467C22×C4—732no—
468C22×C4—732no—
469C22×C4—734no—
470C22×C4—1468no—
471C22×C4—14616no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1462no—
483C22×C4—1462no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4—1462no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1461no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1462no—
498C22×C4—1461no—
499C22×C4—1468no—
500C22×C4C2×C4×D7312yes—
501C22×C4C2×C4×D7312yes—
502C22×C4C2×C4×D7312yes—
503C22×C4C2×D29214yes—
504C22×C4C2×D29212yes—
505C22×C4#1192402812yes—
506C22⋊C4—2928no—
507C22⋊C4—1468no—
508C22⋊C4—1468no—
509C42—44no—
510C42—1468no—
511C23—734no—
512C23—734no—
513C23—734no—
514C23—738no—
515C23—738no—
516C23—1464no—
517C23—1464no—
518C23—1464no—
519C23—1462no—
520C23—1462no—
521C23—1464no—
522C23—1464no—
523C23—1464no—
524C23—1464no—
525C23—1462no—
526C23—1464no—
527C23—1462no—
528C23—1462no—
529C23—1462no—
530C23—1462no—
531C23—1462no—
532C23—1464no—
533C23—1464no—
534C23C22×C4×D7311yescharacteristic
535C23C22×D29211yescharacteristic
536C23#41×D7312yes—
537C23#41×D7311yescharacteristic
538C23#41×D7312yes—
539C23#41×D7311yescharacteristic
540C23#41×D7312yes—
541C23C2×#1192402811yescharacteristic
542C23#1455663611yescharacteristic
543C23#1455663612yes—
544C23#1455663911yescharacteristic
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—29216no—
574C2×C4—29232no—
575C2×C4—2922no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—2922no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2922no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2922no—
585C2×C4—2922no—
586C2×C4—2922no—
587C2×C4—2922no—
588C2×C4—2922no—
589C2×C4—2922no—
590C2×C4—2922no—
591C2×C4—2922no—
592C2×C4—2922no—
593C2×C4—2922no—
594C2×C4—1464no—
595C2×C4—1464no—
596C2×C4—1462no—
597C2×C4—1462no—
598C2×C4—1462no—
599C2×C4—1462no—
600C2×C4—1462no—
601C2×C4—1462no—
602C2×C4—1462no—
603C2×C4—1462no—
604C2×C4—1462no—
605C2×C4—1464no—
606C2×C4C4×D29214yes—
607C22—738no—
608C22—1464no—
609C22—1464no—
610C22—1468no—
611C22—1464no—
612C22—1464no—
613C22—1464no—
614C22—1464no—
615C22—1468no—
616C22—1468no—
617C22—1468no—
618C22#117×D7311yescharacteristic
619C22#117×D7311yescharacteristic
620C22#117×D7311yescharacteristic
621C22C2×C4×D29211yescharacteristic
622C22#1798905511yescharacteristic
623C22#1798906011yescharacteristic
624C22#1798906811yescharacteristic
625C22#1798909912yes—
626C22#126×D7312yes—
627C22#126×D7312yes—
628C22#1798911512yes—
629C22#1798916912yes—
630C22#1798918312yes—
631C22#1798923212yes—
632C22#1798923211yescharacteristic
633C22#1798924911yescharacteristic
634C22#1798926512yes—
635C22#1798926612yes—
636C22#1798926712yes—
637C22#1798926912yes—
638C22#1798927811yescharacteristic
639C22#1798928212yes—
640C22#1798928711yescharacteristic
641C4—24no—
642C4—42no—
643C4—42no—
644C4—44no—
645C4—82no—
646C4—2922no—
647C4—2922no—
648C4—2922no—
649C4—2924no—
650C4—5842no—
651C2—1468no—
652C2#383×D7311yescharacteristic
653C2#2261237511yescharacteristic
654C2#2261256611yescharacteristic
655C2#2261278311yescharacteristic
656C2#2261278411yescharacteristic
657C2#2261286311yescharacteristic
658C2#2261286811yescharacteristic
659C2#2261417512yes—
660C2#2261419012yes—
661C2#2261432112yes—
662C2#2261449012yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1434C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenter#1434D73
hypocenterC73#13901
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#17988454C2semidirect
4. #22608191C2semidirect
5. #22608191C2semidirect
6. #22608158C2semidirect
7. #22608155C2semidirect
11. C73×#1434C2semidirect
19. C4×#11924005C4semidirect
66. C2×C4×Dic73C2×C4semidirect
77. #14556498C2×C4semidirect
78. #14556498C2×C4semidirect
85. C2×C42×C73C2×C4semidirect
308. C2×D73#383semidirect
339. #1434D73semidirect
343. C73#13901semidirect
405. C2×C42C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884542
C2×C4×#119240052
C2×#95×D732
#226081912
#226081582
#226081552
#226081522
C73×#14342
#1390173