Finite Group Databasebeta

← #33013228

Subgroups — #33013228

Order 18688.

1422 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11924005C211yesmaximal, characteristic
2#22608191C212yesmaximal, complemented
3#22608190C212yesmaximal, complemented
4#22608179C212yesmaximal
5#22608173C212yesmaximal
6#22608158C211yesmaximal, characteristic, complemented
7#22608156C211yesmaximal, characteristic, complemented
8#22608156C211yesmaximal, characteristic, complemented
9#22608152C211yesmaximal, characteristic
10#22608152C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×#11924005C2211yescharacteristic
14C22×#11924005C2211yescharacteristic
15C22×#11924005C2212yes—
16C22×#11924005C2212yes—
17C22×C4×Dic73C2211yescharacteristic
18C4×#11924005C418yescomplemented
19C2×#14556498C2211yescharacteristic
20C2×#14556498C2211yescharacteristic
21C2×#14556498C2212yes—
22C2×#14556498C2212yes—
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2211yescharacteristic
31C22×C4⋊C4×C73C2212yes—
32C22×C42×C73C2211yescharacteristic
33C2×#95×C73C2211yescharacteristic
34C2×#95×C73C2211yescharacteristic
35C2×#95×C73C2212yes—
36C24×D73C2311yescharacteristic
37C23×Dic73C2312yes—
38C23×Dic73C2312yes—
39C23×Dic73C2311yescharacteristic
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2311yescharacteristic
42C22×C4×D73—22no—
43C22×C4×D73—22no—
44C22×C4×D73—42no—
45C22×C4×D73—42no—
46C22×C4×D73C2×C414yes—
47C2×#11924005—24no—
48C2×#11924005—24no—
49C2×#11924005—24no—
50C2×#11924005—24no—
51C2×#11924005—42no—
52C2×#11924005—42no—
53C2×#11924005—42no—
54C2×#11924005—42no—
55C2×#11924005C2×C414yes—
56C2×#11924005C2×C414yes—
57C2×C4×Dic73—42no—
58C2×C4×Dic73C2×C414yes—
59#14556498—24no—
60#14556498—22no—
61#14556498—22no—
62#14556498—42no—
63#14556498—42no—
64#14556498—42no—
65#14556498—42no—
66#14556498—42no—
67#14556498—42no—
68#14556498—42no—
69#14556498C2×C414yes—
70#14556498C2×C414yes—
71C23×C4×C73C2312yes—
72C23×C4×C73C2312yes—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C2×C4⋊C4×C73—24no—
77C2×C4⋊C4×C73—42no—
78C2×C4⋊C4×C73—42no—
79C2×C42×C73—42no—
80C2×C42×C73C2×C414yes—
81#95×C73—22no—
82#95×C73—22no—
83#95×C73—42no—
84C23×D73—22no—
85C23×D73—21no—
86C23×D73—21no—
87C23×D73—21no—
88C23×D73—21no—
89C23×D73—22no—
90C23×D73—22no—
91C23×D73—21no—
92C23×D73—21no—
93C23×D73C22×C412yes—
94C23×D73#4114yes—
95C22×Dic73—22no—
96C22×Dic73—22no—
97C22×Dic73—21no—
98C22×Dic73—21no—
99C22×Dic73—21no—
100C22×Dic73—21no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—21no—
106C22×Dic73—21no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73C22×C412yes—
122C22×Dic73C22×C412yes—
123C22×Dic73C22×C412yes—
124C2×C4×D73—28no—
125C2×C4×D73—44no—
126C2×C4×D73—44no—
127C2×C4×D73—48no—
128C2×C4×D73—48no—
129#11924005—28no—
130#11924005—28no—
131#11924005—48no—
132#11924005—48no—
133C4×Dic73—44no—
134C24×C73C2411yescharacteristic
135C22×C4×C73—22no—
136C22×C4×C73—22no—
137C22×C4×C73—21no—
138C22×C4×C73—22no—
139C22×C4×C73—21no—
140C22×C4×C73—22no—
141C22×C4×C73—21no—
142C22×C4×C73—22no—
143C22×C4×C73—21no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—22no—
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×C73C22×C412yes—
159C22×C4×C73C22×C412yes—
160C22×C4×C73C22×C412yes—
161C22×C4×C73#4112yes—
162C22×C4×C73#4114yes—
163C22×C4×C73#4112yes—
164C4⋊C4×C73—48no—
165C42×C73—44no—
166C23×C73C23×C411yescharacteristic
167C23×C73C2×#4112yes—
168C23×C73C2×#4111yescharacteristic
169C23×C73C2×#4112yes—
170C23×C73C2×#4111yescharacteristic
171C23×C73H(5,𝔽2)12yes—
172C23×C73H(5,𝔽2)11yescharacteristic
173C23×C73H(5,𝔽2)11yescharacteristic
174C23×C73H(5,𝔽2)12yes—
175C23×C732−1+411yescharacteristic
176C23×C732−1+411yescharacteristic
177C22×D73—22no—
178C22×D73—22no—
179C22×D73—22no—
180C22×D73—22no—
181C22×D73—22no—
182C22×D73—22no—
183C22×D73—24no—
184C22×D73—24no—
185C22×D73—24no—
186C22×D73—24no—
187C22×D73—24no—
188C22×D73—24no—
189C22×D73—42no—
190C22×D73—42no—
191C22×D73—42no—
192C22×D73—42no—
193C22×D73—42no—
194C22×D73—41no—
195C22×D73—41no—
196C22×D73—42no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73#11714yes—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—24no—
205C2×C4×C73—24no—
206C2×C4×C73—24no—
207C2×C4×C73—24no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
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#11714yes—
228C2×C4×C73#11714yes—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73—42no—
241C2×Dic73—42no—
242C2×Dic73—42no—
243C2×Dic73—42no—
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—42no—
255C2×Dic73—42no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C4×D73—416no—
259C22×C73C2×#11711yescharacteristic
260C22×C73C2×#11711yescharacteristic
261C22×C73C2×#11711yescharacteristic
262C22×C73#51811yescharacteristic
263C22×C73#51811yescharacteristic
264C22×C73#52011yescharacteristic
265C22×C73#52011yescharacteristic
266C22×C73#52912yes—
267C22×C73#52912yes—
268C22×C73#53812yes—
269C22×C73#53812yes—
270C22×C73#53812yes—
271C22×C73#53812yes—
272C22×C73#53812yes—
273C22×C73#53912yes—
274C22×C73#53912yes—
275C22×C73#53912yes—
276C22×C73#54012yes—
277C22×C73#54011yescharacteristic
278C22×C73#54111yescharacteristic
279C22×C73#54212yes—
280C22×C73#54211yescharacteristic
281C22×C73#54211yescharacteristic
282C2×D73—24no—
283C2×D73—24no—
284C2×D73—24no—
285C2×D73—42no—
286C2×D73—42no—
287C2×D73—42no—
288C2×D73—42no—
289C2×D73—44no—
290C2×D73—44no—
291C2×D73—44no—
292C2×D73—44no—
293C4×C73—24no—
294C4×C73—24no—
295C4×C73—42no—
296C4×C73—82no—
297C4×C73—82no—
298Dic73—42no—
299Dic73—42no—
300Dic73—42no—
301Dic73—82no—
302Dic73—82no—
303#14351—731nomaximal, Sylow
304C2×C73#228311yescharacteristic
305C2×C73#231211yescharacteristic
306C2×C73#231411yescharacteristic
307C2×C73#231811yescharacteristic
308C2×C73#231811yescharacteristic
309C2×C73#231811yescharacteristic
310C2×C73#231911yescharacteristic
311C2×C73#264812yes—
312C2×C73#264912yes—
313C2×C73#265212yes—
314C2×C73#265312yes—
315D73—44no—
316C2×C4×C22⋊C4—731no—
317#1443—732no—
318#1442—732no—
319#1440—732no—
320#1439—732no—
321C4⋊#95D7311yescharacteristic, complemented
322#1434—731no—
323#1434—731no—
324#1434—731no—
325C22⋊#95—731no—
326C22⋊#95—731no—
327C73#1435111yescharacteristic, complemented, Sylow
328C24×C4—731no—
329C22×C4⋊C4C2×D7312yes—
330C22×C22⋊C4—732no—
331C22×C22⋊C4—732no—
332C22×C22⋊C4—731no—
333C22×C22⋊C4—731no—
334C22×C42—731no—
335C22×C42C2×D7311yescharacteristic
336C4×C22⋊C4—738no—
337C2×#95—732no—
338C2×#95—732no—
339C2×#95—732no—
340C2×#95—732no—
341C2×#95—732no—
342C2×#95—732no—
343C2×#95—732no—
344C2×#95—731no—
345C2×#95—731no—
346C2×#95—731no—
347C2×#95—731no—
348C2×#95—732no—
349C2×#95C2×D7311yescharacteristic
350C2×#95C2×D7311yescharacteristic
351C2×#95C2×D7312yes—
352C25—731no—
353C23×C4—2922no—
354C23×C4—2922no—
355C23×C4—734no—
356C23×C4—731no—
357C23×C4—731no—
358C23×C4—731no—
359C23×C4—732no—
360C23×C4—732no—
361C23×C4—1462no—
362C23×C4—1462no—
363C23×C4C22×D7312yes—
364C23×C4C22×D7312yes—
365C23×C4C22×D7311yescharacteristic
366C23×C4C22×D7311yescharacteristic
367C23×C4C22×D7311yescharacteristic
368C2×C4⋊C4—24no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C22⋊C4—2922no—
372C2×C22⋊C4—2922no—
373C2×C22⋊C4—2922no—
374C2×C22⋊C4—2922no—
375C2×C22⋊C4—734no—
376C2×C22⋊C4—734no—
377C2×C22⋊C4—1464no—
378C2×C22⋊C4—1464no—
379C2×C22⋊C4—1464no—
380C2×C22⋊C4—1464no—
381C2×C42—42no—
382C2×C42—2922no—
383C2×C42—734no—
384C2×C42C4×D7314yes—
385#95—22no—
386#95—22no—
387#95—42no—
388#95—2922no—
389#95—2922no—
390#95—2922no—
391#95—2922no—
392#95—2922no—
393#95—2922no—
394#95—2922no—
395#95—734no—
396#95—734no—
397#95—1464no—
398#95—1462no—
399#95—1462no—
400C24—732no—
401C24—734no—
402C24—1461no—
403C24—1462no—
404C24—1461no—
405C24—1461no—
406C24—1461no—
407C24—1462no—
408C24—1462no—
409C24—1461no—
410C24—1461no—
411C24C23×D7311yescharacteristic
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—2928no—
436C22×C4—2928no—
437C22×C4—2924no—
438C22×C4—2924no—
439C22×C4—732no—
440C22×C4—732no—
441C22×C4—732no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1461no—
458C22×C4—1462no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1468no—
469C22×C4C2×C4×D7312yes—
470C22×C4C2×C4×D7312yes—
471C22×C4C2×C4×D7312yes—
472C22×C4#1192402712yes—
473C22×C4#1192402814yes—
474C22×C4#1192402912yes—
475C4⋊C4—48no—
476C22⋊C4—2928no—
477C22⋊C4—2928no—
478C22⋊C4—1468no—
479C22⋊C4—1468no—
480C42—44no—
481C42—2924no—
482C23—2922no—
483C23—2922no—
484C23—2922no—
485C23—2922no—
486C23—2922no—
487C23—2921no—
488C23—2921no—
489C23—2922no—
490C23—2921no—
491C23—2921no—
492C23—734no—
493C23—1464no—
494C23—1464no—
495C23—1464no—
496C23—1464no—
497C23—1464no—
498C23—1462no—
499C23—1462no—
500C23—1462no—
501C23—1462no—
502C23—1462no—
503C23—1462no—
504C23—1464no—
505C23C22×C4×D7311yescharacteristic
506C23#41×D7312yes—
507C23C2×#1192402711yescharacteristic
508C23C2×#1192402812yes—
509C23C2×#1192402911yescharacteristic
510C23#1455663611yescharacteristic
511C23#1455663612yes—
512C23#1455663611yescharacteristic
513C23#1455663712yes—
514C23#1455663911yescharacteristic
515C23#1455663911yescharacteristic
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—29216no—
544C2×C4—2922no—
545C2×C4—2922no—
546C2×C4—2922no—
547C2×C4—2922no—
548C2×C4—2922no—
549C2×C4—2922no—
550C2×C4—2922no—
551C2×C4—2922no—
552C2×C4—2922no—
553C2×C4—2922no—
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—1462no—
565C2×C4—1462no—
566C2×C4—1462no—
567C2×C4—1462no—
568C2×C4—1462no—
569C2×C4—1462no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1462no—
573C2×C4#1455654814yes—
574C2×C4#1455654914yes—
575C22—2922no—
576C22—2922no—
577C22—2922no—
578C22—2922no—
579C22—2924no—
580C22—2924no—
581C22—2924no—
582C22—2924no—
583C22—1464no—
584C22—1464no—
585C22—1464no—
586C22#117×D7311yescharacteristic
587C22C2×#1455654811yescharacteristic
588C22C2×#1455654911yescharacteristic
589C22#1798906011yescharacteristic
590C22#1798906111yescharacteristic
591C22#1798906811yescharacteristic
592C22#1798906811yescharacteristic
593C22#1798911912yes—
594C22#1798912412yes—
595C22#1798916912yes—
596C22#1798917112yes—
597C22#1798917412yes—
598C22#1798917512yes—
599C22#1798917712yes—
600C22#1798918312yes—
601C22#1798918412yes—
602C22#1798918512yes—
603C22#1798918812yes—
604C22#1798919111yescharacteristic
605C22#1798919811yescharacteristic
606C22#1798920912yes—
607C22#1798921111yescharacteristic
608C22#1798921111yescharacteristic
609C4—24no—
610C4—24no—
611C4—42no—
612C4—82no—
613C4—82no—
614C4—2922no—
615C4—2922no—
616C4—2922no—
617C4—5842no—
618C4—5842no—
619C2—2924no—
620C2#2261232711yescharacteristic
621C2#2261252811yescharacteristic
622C2#2261253911yescharacteristic
623C2#2261256511yescharacteristic
624C2#2261256611yescharacteristic
625C2#2261256711yescharacteristic
626C2#2261256911yescharacteristic
627C2#2261592312yes—
628C2#2261594012yes—
629C2#2261598312yes—
630C2#2261600012yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×C4⋊#95C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC4⋊#95D73
hypocenterC73#14351
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. #22608191C2semidirect
3. #22608190C2semidirect
6. #22608158C2semidirect
7. #22608156C2semidirect
8. #22608156C2semidirect
11. C73×C4⋊#95C2semidirect
18. C4×#11924005C4semidirect
321. C4⋊#95D73semidirect
327. C73#14351semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#119240052
#226081912
#226081902
#226081792
#226081732
#226081582
#226081562
#226081522
C73×C4⋊#952
#1435173