Finite Group Databasebeta

← #33013010

Subgroups — #33013010

Order 18688.

1454 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988499C211yesmaximal, characteristic
2C2×#17988492C211yesmaximal, characteristic, complemented
3C2×#17988480C211yesmaximal, characteristic
4#22608201C211yesmaximal, characteristic, complemented
5#22608192C212yesmaximal, complemented
6#22608190C211yesmaximal, characteristic, complemented
7#22608178C212yesmaximal
8#22608168C212yesmaximal
9#22608165C212yesmaximal, complemented
10#95×Dic73C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic
12C23×Dic146C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C22⋊Dic73C2211yescharacteristic
15C22×C22⋊Dic73C2211yescharacteristic
16C22×C22⋊Dic73C2212yes—
17C22×C4×Dic73C2212yes—
18C22×C4×Dic73C2211yescharacteristic
19#17988499C418yescomplemented
20#17988492—24no—
21#17988480—24no—
22C2×#14556498C2212yes—
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2211yescharacteristic
26C2×#14556498C2211yescharacteristic
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2212yes—
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C22⋊C4×C73C2211yescharacteristic
35C22×C22⋊C4×C73C2212yes—
36C2×#95×C73C2211yescharacteristic
37C2×#95×C73C2212yes—
38C22×Dic146—22no—
39C22×Dic146—22no—
40C22×Dic146—42no—
41C22×Dic146—42no—
42C22×Dic146C2×C414yes—
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2312yes—
46C23×Dic73C2312yes—
47C23×Dic73C2311yescharacteristic
48C23×Dic73C2311yescharacteristic
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—24no—
51C2×C22⋊Dic73—22no—
52C2×C22⋊Dic73—22no—
53C2×C22⋊Dic73—24no—
54C2×C22⋊Dic73—42no—
55C2×C22⋊Dic73—42no—
56C2×C22⋊Dic73—42no—
57C2×C22⋊Dic73C2×C418yes—
58C2×C4×Dic73—24no—
59C2×C4×Dic73—42no—
60C2×C4×Dic73—42no—
61C2×C4×Dic73—42no—
62C2×C4×Dic73D414yes—
63#14556498—22no—
64#14556498—24no—
65#14556498—24no—
66#14556498—22no—
67#14556498—24no—
68#14556498—42no—
69#14556498—42no—
70#14556498—42no—
71#14556498—42no—
72#14556498C2×C418yes—
73#14556498C2×C414yes—
74C25×C73C2311yescharacteristic
75C23×C4×C73C2312yes—
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2312yes—
78C23×C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—42no—
81C2×C22⋊C4×C73—22no—
82C2×C22⋊C4×C73—22no—
83C2×C22⋊C4×C73—24no—
84C2×C22⋊C4×C73—42no—
85C2×C22⋊C4×C73—42no—
86C2×C22⋊C4×C73C2×C414yes—
87#95×C73—22no—
88#95×C73—24no—
89C2×Dic146—28no—
90C2×Dic146—48no—
91C2×Dic146—44no—
92C2×Dic146—44no—
93C2×Dic146—48no—
94C22×Dic73—21no—
95C22×Dic73—22no—
96C22×Dic73—21no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—21no—
111C22×Dic73—22no—
112C22×Dic73—21no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—21no—
119C22×Dic73—22no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73C22×C414yes—
124C22×Dic73C22×C414yes—
125C22×Dic73C2×D412yes—
126C22×Dic73C2×D412yes—
127C22×Dic73#4114yes—
128C4⋊Dic73—44no—
129C22⋊Dic73—48no—
130C22⋊Dic73—44no—
131C22⋊Dic73—44no—
132C4×Dic73—44no—
133C4×Dic73—48no—
134C24×C73—21no—
135C24×C73—21no—
136C24×C73—22no—
137C24×C73—22no—
138C24×C73—21no—
139C24×C73—22no—
140C24×C73—22no—
141C24×C73—21no—
142C24×C73—21no—
143C24×C73—21no—
144C24×C73C22×C412yes—
145C24×C73C2411yescharacteristic
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—21no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—21no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
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×C73C22×C412yes—
166C22×C4×C73C22×C412yes—
167C22×C4×C73C2×D412yes—
168C22×C4×C73#4114yes—
169C22×C4×C73#4112yes—
170C4⋊C4×C73—44no—
171C22⋊C4×C73—28no—
172C22⋊C4×C73—48no—
173C23×C73—22no—
174C23×C73—24no—
175C23×C73—24no—
176C23×C73—22no—
177C23×C73—22no—
178C23×C73—41no—
179C23×C73—42no—
180C23×C73—41no—
181C23×C73—41no—
182C23×C73—41no—
183C23×C73—41no—
184C23×C73—41no—
185C23×C73—42no—
186C23×C73—42no—
187C23×C73—42no—
188C23×C73—42no—
189C23×C73—42no—
190C23×C73—41no—
191C23×C73—42no—
192C23×C73—41no—
193C23×C73—42no—
194C23×C73—42no—
195C23×C73—42no—
196C23×C73C23×C411yescharacteristic
197C23×C73C22×D411yescharacteristic
198C23×C73C2×#4112yes—
199C23×C73C2×#4111yescharacteristic
200C23×C73C2×#4112yes—
201C23×C73H(5,𝔽2)12yes—
202C23×C73H(5,𝔽2)11yescharacteristic
203C23×C73H(5,𝔽2)12yes—
204C23×C732−1+411yescharacteristic
205C23×C732−1+411yescharacteristic
206C23×C732−1+411yescharacteristic
207C2×C4×C73—24no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—24no—
211C2×C4×C73—22no—
212C2×C4×C73—24no—
213C2×C4×C73—24no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—41no—
217C2×C4×C73—42no—
218C2×C4×C73—41no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
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×C73C4×D414yes—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—24no—
234C2×Dic73—24no—
235C2×Dic73—24no—
236C2×Dic73—24no—
237C2×Dic73—24no—
238C2×Dic73—24no—
239C2×Dic73—24no—
240C2×Dic73—24no—
241C2×Dic73—22no—
242C2×Dic73—22no—
243C2×Dic73—22no—
244C2×Dic73—42no—
245C2×Dic73—42no—
246C2×Dic73—42no—
247C2×Dic73—42no—
248C2×Dic73—42no—
249C2×Dic73—42no—
250C2×Dic73—42no—
251C2×Dic73—42no—
252C2×Dic73—42no—
253C2×Dic73—42no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—42no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73#12414yes—
265Dic146—416no—
266C22×C73—42no—
267C22×C73—42no—
268C22×C73—44no—
269C22×C73—44no—
270C22×C73—42no—
271C22×C73—81no—
272C22×C73—81no—
273C22×C73—82no—
274C22×C73—82no—
275C22×C73—81no—
276C22×C73—81no—
277C22×C73C2×C4×D411yescharacteristic
278C22×C73C4×#4112yes—
279C22×C73#51812yes—
280C22×C73#51911yescharacteristic
281C22×C73#52011yescharacteristic
282C22×C73C2×#12411yescharacteristic
283C22×C73#52912yes—
284C22×C73#53211yescharacteristic
285C22×C73#53411yescharacteristic
286C22×C73#53511yescharacteristic
287C22×C73#53611yescharacteristic
288C22×C73#53711yescharacteristic
289C22×C73#53812yes—
290C22×C73#53812yes—
291C22×C73#53812yes—
292C22×C73#53912yes—
293C22×C73#53912yes—
294C22×C73#54111yescharacteristic
295C22×C73#54212yes—
296C22×C73#54211yescharacteristic
297C22×C73#54212yes—
298C22×C73#54212yes—
299C22×C73#54212yes—
300C4×C73—24no—
301C4×C73—44no—
302C4×C73—42no—
303C4×C73—82no—
304Dic73—24no—
305Dic73—44no—
306Dic73—44no—
307Dic73—42no—
308Dic73—81no—
309Dic73—81no—
310#14323—731nomaximal, Sylow
311C2×C73—82no—
312C2×C73C4×#12411yescharacteristic
313C2×C73#232111yescharacteristic
314C2×C73#232311yescharacteristic
315C2×C73#233212yes—
316C2×C73#233712yes—
317C2×C73#263911yescharacteristic
318C2×C73#264011yescharacteristic
319C2×C73#265012yes—
320C2×C73#265312yes—
321C2×C73#266211yescharacteristic
322C2×C73#266311yescharacteristic
323C2×#393—731no—
324C2×#391—731no—
325C2×#388—731no—
326#1446—731no—
327#1443—732no—
328#1442—731no—
329#1440—732no—
330#1439D7311yescharacteristic
331#1437—732no—
332#1436—732no—
333C4×#95—731no—
334C73#1432311yescharacteristic, complemented, Sylow
335C23×Q8—731no—
336C22×C4⋊C4—731no—
337C22×C4⋊C4C2×D7311yescharacteristic
338C22×C22⋊C4—732no—
339C22×C22⋊C4—731no—
340C22×C22⋊C4—731no—
341C22×C22⋊C4C2×D7311yescharacteristic
342C22×C22⋊C4C2×D7312yes—
343C22×C42—731no—
344C22×C42—732no—
345#393—738no—
346#391—1464no—
347#388—1464no—
348C2×#95—732no—
349C2×#95—732no—
350C2×#95—732no—
351C2×#95—732no—
352C2×#95—731no—
353C2×#95—732no—
354C2×#95—732no—
355C2×#95—732no—
356C2×#95—732no—
357C2×#95—731no—
358C2×#95—731no—
359C2×#95C2×D7311yescharacteristic
360C2×#95C2×D7312yes—
361C25C22×D7311yescharacteristic
362C22×Q8—2922no—
363C22×Q8—2922no—
364C22×Q8—734no—
365C22×Q8—1462no—
366C22×Q8—1462no—
367C23×C4—731no—
368C23×C4—732no—
369C23×C4—732no—
370C23×C4—731no—
371C23×C4—731no—
372C23×C4—731no—
373C23×C4C22×D7312yes—
374C23×C4C22×D7311yescharacteristic
375C23×C4C22×D7312yes—
376C23×C4C22×D7311yescharacteristic
377C2×C4⋊C4—22no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—1464no—
380C2×C4⋊C4—1462no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—2922no—
387C2×C22⋊C4—2922no—
388C2×C22⋊C4—2922no—
389C2×C22⋊C4—738no—
390C2×C22⋊C4—1464no—
391C2×C22⋊C4—1462no—
392C2×C22⋊C4—1462no—
393C2×C22⋊C4C4×D7314yes—
394C2×C42—2922no—
395C2×C42—2922no—
396C2×C42—2922no—
397C2×C42—734no—
398C2×C42—1464no—
399#95—22no—
400#95—24no—
401#95—2922no—
402#95—2922no—
403#95—2922no—
404#95—2922no—
405#95—734no—
406#95—738no—
407#95—1462no—
408#95—1464no—
409#95—1464no—
410#95—1462no—
411#95—1464no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—22no—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24C2×C4×D7312yes—
423C24C23×D7311yescharacteristic
424C2×Q8—2924no—
425C2×Q8—2924no—
426C2×Q8—2928no—
427C2×Q8—2928no—
428C2×Q8—1468no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
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—732no—
449C22×C4—734no—
450C22×C4—734no—
451C22×C4—734no—
452C22×C4—732no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4—1461no—
459C22×C4—1462no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1461no—
477C22×C4—1462no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1462no—
481C22×C4—1461no—
482C22×C4C2×C4×D7312yes—
483C22×C4C2×C4×D7312yes—
484C22×C4D4×D7312yes—
485C22×C4#1192402714yes—
486C22×C4#1192402712yes—
487C4⋊C4—44no—
488C4⋊C4—2924no—
489C22⋊C4—28no—
490C22⋊C4—48no—
491C22⋊C4—2924no—
492C22⋊C4—2924no—
493C22⋊C4—2928no—
494C42—2924no—
495C42—2928no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—22no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23C22×C4×D7311yescharacteristic
520C23C2×D4×D7311yescharacteristic
521C23#41×D7312yes—
522C23C2×#1192402712yes—
523C23C2×#1192402711yescharacteristic
524C23#1455663612yes—
525C23#1455663611yescharacteristic
526C23#1455663712yes—
527C23#1455663811yescharacteristic
528C23#1455663811yescharacteristic
529C23#1455663911yescharacteristic
530Q8—29216no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—2922no—
555C2×C4—2922no—
556C2×C4—2922no—
557C2×C4—2922no—
558C2×C4—2922no—
559C2×C4—2922no—
560C2×C4—2922no—
561C2×C4—2922no—
562C2×C4—2922no—
563C2×C4—2922no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—2922no—
569C2×C4—2922no—
570C2×C4—2922no—
571C2×C4—2922no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—734no—
575C2×C4—1462no—
576C2×C4—1462no—
577C2×C4—1462no—
578C2×C4—1464no—
579C2×C4—1464no—
580C2×C4—1464no—
581C2×C4—1464no—
582C2×C4—1464no—
583C2×C4—1464no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1464no—
587C2×C4—1464no—
588C2×C4#1455655114yes—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—44no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22C2×#1455655111yescharacteristic
601C22C4×#1192402712yes—
602C22#1798905912yes—
603C22#1798906411yescharacteristic
604C22#1798906811yescharacteristic
605C22#124×D7311yescharacteristic
606C22#1798911812yes—
607C22#1798913511yescharacteristic
608C22#1798914811yescharacteristic
609C22#1798915211yescharacteristic
610C22#1798916011yescharacteristic
611C22#1798916611yescharacteristic
612C22#1798917212yes—
613C22#1798917312yes—
614C22#1798917412yes—
615C22#1798917812yes—
616C22#1798918112yes—
617C22#1798919711yescharacteristic
618C22#1798920112yes—
619C22#1798920412yes—
620C22#1798920411yescharacteristic
621C22#1798920712yes—
622C22#1798921012yes—
623C4—24no—
624C4—44no—
625C4—42no—
626C4—82no—
627C4—2924no—
628C4—2922no—
629C4—2924no—
630C4—5841no—
631C4—5841no—
632C4—1464no—
633C2—82no—
634C2#2261247811yescharacteristic
635C2#2261259411yescharacteristic
636C2#2261260911yescharacteristic
637C2#2261268812yes—
638C2#2261274512yes—
639C2#2261585811yescharacteristic
640C2#2261586911yescharacteristic
641C2#2261595012yes—
642C2#2261599512yes—
643C2#2261607311yescharacteristic
644C2#2261608411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1439C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenter#1439D73
hypocenterC73#14323
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#17988492C2semidirect
4. #22608201C2semidirect
5. #22608192C2semidirect
6. #22608190C2semidirect
9. #22608165C2semidirect
10. #95×Dic73C2semidirect
19. #17988499C4semidirect
334. C73#14323semidirect

Maximal subgroups

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

subgroupindex
C2×#179884992
C2×#179884922
C2×#179884802
#226082012
#226081922
#226081902
#226081782
#226081682
#226081652
#95×Dic732
C73×#14392
#1432373