Finite Group Databasebeta

← #33008129

Subgroups — #33008129

Order 18688.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988449C211yesmaximal, characteristic
2C2×C4×#11924005C211yesmaximal, characteristic
3C2×#17988433C211yesmaximal, characteristic, complemented
4#22608191C212yesmaximal, complemented
5#22608175C212yesmaximal
6#22608167C212yesmaximal
7#22608162C212yesmaximal, complemented
8#22608159C211yesmaximal, characteristic, complemented
9#22608156C211yesmaximal, characteristic, complemented
10#22608152C211yesmaximal, characteristic
11C73×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×#11924007C2212yes—
14C22×#11924005C2212yes—
15C22×#11924005C2212yes—
16C22×#11924005C2211yescharacteristic
17C22×#11924005C2211yescharacteristic
18C22×C4×Dic73C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20#17988449—24no—
21C4×#11924005C418yescomplemented
22#17988433—24no—
23C2×#14556498C2211yescharacteristic
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C22×C42×C73C2211yescharacteristic
34C2×#95×C73C2211yescharacteristic
35C2×#95×C73C2211yescharacteristic
36C2×#95×C73C2212yes—
37C2×#95×C73C2212yes—
38C24×D73C2311yescharacteristic
39C23×Dic73C2311yescharacteristic
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C23×Dic73C2311yescharacteristic
44C22×C4×D73—24no—
45C22×C4×D73—22no—
46C22×C4×D73—22no—
47C22×C4×D73—42no—
48C22×C4×D73C2×C414yes—
49C2×#11924007—24no—
50C2×#11924007—24no—
51C2×#11924007—42no—
52C2×#11924005—22no—
53C2×#11924005—22no—
54C2×#11924005—24no—
55C2×#11924005—24no—
56C2×#11924005—24no—
57C2×#11924005—24no—
58C2×#11924005—24no—
59C2×#11924005—42no—
60C2×#11924005—42no—
61C2×#11924005C2×C414yes—
62C2×#11924005C2×C414yes—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—24no—
65C2×C4×Dic73—24no—
66C2×C4×Dic73—42no—
67C2×C4×Dic73C2×C414yes—
68#14556498—24no—
69#14556498—24no—
70#14556498—24no—
71#14556498—22no—
72#14556498—42no—
73#14556498—42no—
74#14556498—42no—
75#14556498C2×C414yes—
76#14556498C2×C414yes—
77#14556498D414yes—
78C23×C4×C73C2312yes—
79C23×C4×C73C2312yes—
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C2×C42×C73—22no—
84C2×C42×C73—22no—
85C2×C42×C73C2×C414yes—
86#95×C73—22no—
87#95×C73—22no—
88#95×C73—24no—
89#95×C73—42no—
90C23×D73—21no—
91C23×D73—21no—
92C23×D73—21no—
93C23×D73—22no—
94C23×D73—22no—
95C23×D73—21no—
96C23×D73—21no—
97C23×D73—22no—
98C23×D73—21no—
99C23×D73C22×C412yes—
100C23×D73#4114yes—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—21no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—21no—
122C22×Dic73—22no—
123C22×Dic73C22×C412yes—
124C22×Dic73C22×C412yes—
125C22×Dic73C22×C412yes—
126C22×Dic73C2×D414yes—
127C22×Dic73#4114yes—
128C22×Dic73#4112yes—
129C22×Dic73#4112yes—
130C2×C4×D73—28no—
131C2×C4×D73—28no—
132C2×C4×D73—44no—
133C2×C4×D73—48no—
134C2×C4×D73—48no—
135#11924007—48no—
136#11924005—28no—
137#11924005—28no—
138#11924005—48no—
139#11924005—48no—
140C4×Dic73—216no—
141C4×Dic73—44no—
142C24×C73C2411yescharacteristic
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—22no—
168C22×C4×C73C22×C412yes—
169C22×C4×C73C22×C412yes—
170C22×C4×C73C22×C412yes—
171C22×C4×C73C2×D412yes—
172C22×C4×C73#4112yes—
173C22×C4×C73#4114yes—
174C42×C73—28no—
175C23×C73C23×C411yescharacteristic
176C23×C73C22×D411yescharacteristic
177C23×C73C2×#4112yes—
178C23×C73C2×#4111yescharacteristic
179C23×C73C2×#4111yescharacteristic
180C23×C73C2×#4112yes—
181C23×C73C2×#4111yescharacteristic
182C23×C73C2×#4112yes—
183C23×C73H(5,𝔽2)11yescharacteristic
184C23×C73H(5,𝔽2)12yes—
185C23×C732−1+411yescharacteristic
186C22×D73—22no—
187C22×D73—22no—
188C22×D73—22no—
189C22×D73—22no—
190C22×D73—22no—
191C22×D73—22no—
192C22×D73—24no—
193C22×D73—24no—
194C22×D73—24no—
195C22×D73—24no—
196C22×D73—24no—
197C22×D73—24no—
198C22×D73—42no—
199C22×D73—42no—
200C22×D73—42no—
201C22×D73—42no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—42no—
205C22×D73—42no—
206C22×D73—41no—
207C22×D73—41no—
208C22×D73#11714yes—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—24no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
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#11714yes—
239C2×C4×C73C4×D414yes—
240C2×Dic73—22no—
241C2×Dic73—22no—
242C2×Dic73—24no—
243C2×Dic73—24no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—24no—
251C2×Dic73—24no—
252C2×Dic73—24no—
253C2×Dic73—24no—
254C2×Dic73—24no—
255C2×Dic73—24no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C2×Dic73—42no—
259C2×Dic73—42no—
260C2×Dic73—42no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73#11714yes—
269C4×D73—416no—
270C22×C73C2×#11711yescharacteristic
271C22×C73C2×#11711yescharacteristic
272C22×C73C2×#11711yescharacteristic
273C22×C73C2×C4×D411yescharacteristic
274C22×C73C4×#4111yescharacteristic
275C22×C73#51811yescharacteristic
276C22×C73#52011yescharacteristic
277C22×C73#52512yes—
278C22×C73#52912yes—
279C22×C73#52912yes—
280C22×C73#52912yes—
281C22×C73#54012yes—
282C22×C73#54212yes—
283C22×C73#54612yes—
284C22×C73#54711yescharacteristic
285C22×C73#55011yescharacteristic
286C22×C73#55112yes—
287C22×C73#55112yes—
288C22×C73#55112yes—
289C22×C73#55212yes—
290C22×C73#55312yes—
291C22×C73#55511yescharacteristic
292C22×C73#55611yescharacteristic
293C2×D73—24no—
294C2×D73—24no—
295C2×D73—24no—
296C2×D73—42no—
297C2×D73—42no—
298C2×D73—42no—
299C2×D73—44no—
300C2×D73—44no—
301C2×D73—44no—
302C2×D73—44no—
303C2×D73—42no—
304C4×C73—24no—
305C4×C73—24no—
306C4×C73—42no—
307C4×C73—82no—
308C4×C73—82no—
309Dic73—24no—
310Dic73—42no—
311Dic73—42no—
312Dic73—44no—
313Dic73—44no—
314#13895—731nomaximal, Sylow
315C2×C73#228311yescharacteristic
316C2×C73#229011yescharacteristic
317C2×C73#231911yescharacteristic
318C2×C73#234211yescharacteristic
319C2×C73#234311yescharacteristic
320C2×C73#235311yescharacteristic
321C2×C73#235411yescharacteristic
322C2×C73#247012yes—
323C2×C73#247112yes—
324C2×C73#252612yes—
325C2×C73#252712yes—
326D73—44no—
327C2×#381—731no—
328C2×C4×C22⋊C4—731no—
329C2×#376—731no—
330#1443—732no—
331#1439—732no—
332#1437—732no—
333#1436—732no—
334C4⋊#95—731no—
335#1434—731no—
336#1434D7311yescharacteristic, complemented
337C22⋊#95—731no—
338C73#1389511yescharacteristic, complemented, Sylow
339C24×C4—731no—
340C22×C4⋊C4—732no—
341C22×C22⋊C4—732no—
342C22×C22⋊C4—732no—
343C22×C22⋊C4—731no—
344C22×C22⋊C4—731no—
345C22×C42—731no—
346C22×C42—732no—
347C22×C42C2×D7311yescharacteristic
348#381—1464no—
349C4×C22⋊C4—738no—
350#376—1464no—
351C2×#95—732no—
352C2×#95—732no—
353C2×#95—732no—
354C2×#95—731no—
355C2×#95—731no—
356C2×#95—731no—
357C2×#95—731no—
358C2×#95—732no—
359C2×#95—732no—
360C2×#95—732no—
361C2×#95C2×D7311yescharacteristic
362C2×#95C2×D7311yescharacteristic
363C2×#95C2×D7312yes—
364C2×#95C2×D7312yes—
365C25—731no—
366C23×C4—2922no—
367C23×C4—734no—
368C23×C4—731no—
369C23×C4—732no—
370C23×C4—731no—
371C23×C4—732no—
372C23×C4—731no—
373C23×C4—1464no—
374C23×C4—1462no—
375C23×C4—1462no—
376C23×C4C22×D7312yes—
377C23×C4C22×D7312yes—
378C23×C4C22×D7311yescharacteristic
379C23×C4C22×D7311yescharacteristic
380C23×C4C22×D7311yescharacteristic
381C2×C4⋊C4—2922no—
382C2×C4⋊C4—1464no—
383C2×C4⋊C4—1464no—
384C2×C22⋊C4—2922no—
385C2×C22⋊C4—2922no—
386C2×C22⋊C4—734no—
387C2×C22⋊C4—734no—
388C2×C22⋊C4—1464no—
389C2×C22⋊C4—1464no—
390C2×C22⋊C4—1464no—
391C2×C22⋊C4—1464no—
392C2×C22⋊C4—1462no—
393C2×C22⋊C4—1462no—
394C2×C22⋊C4—1464no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—2922no—
398C2×C42—734no—
399C2×C42—1464no—
400C2×C42—1464no—
401C2×C42—1464no—
402C2×C42C4×D7314yes—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—42no—
407#95—2922no—
408#95—2922no—
409#95—2922no—
410#95—734no—
411#95—734no—
412#95—734no—
413#95—1464no—
414#95—1464no—
415#95—1464no—
416#95—1462no—
417C24—732no—
418C24—734no—
419C24—1461no—
420C24—1461no—
421C24—1461no—
422C24—1462no—
423C24—1461no—
424C24—1462no—
425C24—1461no—
426C24—1462no—
427C24—1461no—
428C24C23×D7311yescharacteristic
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—2928no—
455C22×C4—2928no—
456C22×C4—2924no—
457C22×C4—732no—
458C22×C4—732no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—732no—
462C22×C4—734no—
463C22×C4—734no—
464C22×C4—1468no—
465C22×C4—1462no—
466C22×C4—1461no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4—1461no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1461no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1462no—
481C22×C4—1462no—
482C22×C4—1462no—
483C22×C4—1461no—
484C22×C4—1462no—
485C22×C4—1468no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4C2×C4×D7312yes—
489C22×C4C2×C4×D7312yes—
490C22×C4C2×C4×D7312yes—
491C22×C4D4×D7312yes—
492C22×C4#1192402712yes—
493C22×C4#1192402814yes—
494C4⋊C4—2928no—
495C22⋊C4—2928no—
496C22⋊C4—2928no—
497C22⋊C4—1468no—
498C22⋊C4—1468no—
499C42—28no—
500C42—2924no—
501C42—14616no—
502C23—2922no—
503C23—2922no—
504C23—2921no—
505C23—2921no—
506C23—2922no—
507C23—2922no—
508C23—2921no—
509C23—2921no—
510C23—2922no—
511C23—2922no—
512C23—734no—
513C23—1464no—
514C23—1464no—
515C23—1464no—
516C23—1464no—
517C23—1462no—
518C23—1462no—
519C23—1462no—
520C23—1462no—
521C23—1462no—
522C23—1462no—
523C23—1464no—
524C23—1464no—
525C23C22×C4×D7311yescharacteristic
526C23C2×D4×D7311yescharacteristic
527C23#41×D7312yes—
528C23#41×D7311yescharacteristic
529C23#41×D7311yescharacteristic
530C23#41×D7312yes—
531C23C2×#1192402711yescharacteristic
532C23C2×#1192402812yes—
533C23#1455663611yescharacteristic
534C23#1455663712yes—
535C23#1455663911yescharacteristic
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—29216no—
566C2×C4—2922no—
567C2×C4—2922no—
568C2×C4—2922no—
569C2×C4—2922no—
570C2×C4—2922no—
571C2×C4—2922no—
572C2×C4—2922no—
573C2×C4—2922no—
574C2×C4—2922no—
575C2×C4—2922no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—734no—
579C2×C4—1464no—
580C2×C4—1464no—
581C2×C4—1464no—
582C2×C4—1464no—
583C2×C4—1462no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1462no—
587C2×C4—1462no—
588C2×C4—1462no—
589C2×C4—1464no—
590C2×C4—1464no—
591C2×C4—1464no—
592C2×C4—1464no—
593C2×C4—1462no—
594C2×C4—1462no—
595C2×C4#1455654814yes—
596C2×C4#1455655114yes—
597C22—2924no—
598C22—2924no—
599C22—2922no—
600C22—2922no—
601C22—2922no—
602C22—2922no—
603C22—2924no—
604C22—2924no—
605C22—1464no—
606C22—1464no—
607C22—1464no—
608C22#117×D7311yescharacteristic
609C22#117×D7311yescharacteristic
610C22C2×#1455654811yescharacteristic
611C22C2×#1455655111yescharacteristic
612C22#1798905511yescharacteristic
613C22#1798906111yescharacteristic
614C22#1798906811yescharacteristic
615C22#1798909612yes—
616C22#1798911512yes—
617C22#1798911512yes—
618C22#1798911712yes—
619C22#1798918812yes—
620C22#1798920912yes—
621C22#1798922912yes—
622C22#1798923911yescharacteristic
623C22#1798925511yescharacteristic
624C22#1798926012yes—
625C22#1798926212yes—
626C22#1798926712yes—
627C22#1798926912yes—
628C22#1798928812yes—
629C22#1798930111yescharacteristic
630C22#1798930811yescharacteristic
631C4—24no—
632C4—24no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—2924no—
637C4—2924no—
638C4—2922no—
639C4—2922no—
640C4—1464no—
641C2—2924no—
642C2#2261232311yescharacteristic
643C2#2261237011yescharacteristic
644C2#2261256911yescharacteristic
645C2#2261277311yescharacteristic
646C2#2261278411yescharacteristic
647C2#2261286411yescharacteristic
648C2#2261287511yescharacteristic
649C2#2261402912yes—
650C2#2261404412yes—
651C2#2261470512yes—
652C2#2261472012yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1434C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenter#1434D73
hypocenterC73#13895
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#17988433C2semidirect
4. #22608191C2semidirect
7. #22608162C2semidirect
8. #22608159C2semidirect
9. #22608156C2semidirect
11. C73×#1434C2semidirect
21. C4×#11924005C4semidirect
336. #1434D73semidirect
338. C73#13895semidirect

Maximal subgroups

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

subgroupindex
C2×#179884492
C2×C4×#119240052
C2×#179884332
#226081912
#226081752
#226081672
#226081622
#226081592
#226081562
#226081522
C73×#14342
#1389573