Finite Group Databasebeta

← #34021966

Subgroups — #34021966

Order 18688.

948 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989612C211yesmaximal, characteristic, complemented
2C2×C4×#11924036C211yesmaximal, characteristic, complemented
3#22626003C211yesmaximal, characteristic, complemented
4#22626002C211yesmaximal, characteristic, complemented
5#22625986C211yesmaximal, characteristic, complemented
6#22625985C211yesmaximal, characteristic, complemented
7#22625907C211yesmaximal, characteristic
8#22625907C211yesmaximal, characteristic
9#22625876C211yesmaximal, characteristic, complemented
10#22625876C211yesmaximal, characteristic, complemented
11#22625719C211yesmaximal, characteristic, complemented
12#22625660C211yesmaximal, characteristic, complemented
13#22625658C211yesmaximal, characteristic, complemented
14#22625650C211yesmaximal, characteristic, complemented
15#22612369C211yesmaximal, characteristic
16C22×#11924036C2211yescharacteristic
17C22×#11924036C2211yescharacteristic
18#17989612—24no—
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×#14556648C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C4×#11924036—24no—
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556553C2211yescharacteristic
47C2×#14556549C2211yescharacteristic
48C2×C42×D73C2211yescharacteristic
49#17988478C411yescharacteristic
50#17988476C411yescharacteristic
51#17988473C411yescharacteristic
52#17988465C411yescharacteristic
53#17988465C411yescharacteristic
54#17988461C411yescharacteristic
55#17988458C411yescharacteristic
56#17988438C2211yescharacteristic
57#17988434C2211yescharacteristic
58#17988434C2211yescharacteristic
59#17988432C2211yescharacteristic
60#387×C73C411yescharacteristic
61C2×#11924036—22no—
62C2×#11924036—22no—
63C2×#11924036—22no—
64C2×#11924036—22no—
65C2×#11924036—22no—
66C2×#11924036—22no—
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75#14556658—22no—
76#14556658—22no—
77C4⋊#10596833—22no—
78C4⋊#10596833—22no—
79#14556648—22no—
80#14556648—22no—
81#14556648—22no—
82#14556648—22no—
83#14556648—22no—
84#14556648—22no—
85#14556646—22no—
86#14556646—22no—
87C4×#10596833—22no—
88C4×#10596833—22no—
89C4×#10596833—22no—
90C4×#10596833D414yescomplemented
91C22×D292C2×C411yescharacteristic
92C22×C4×D73C2×C411yescharacteristic
93C22×C4×D73C2×C411yescharacteristic
94C22×C4×D73C2311yescharacteristic
95C22×C4×D73C2311yescharacteristic
96#14556553—22no—
97#14556553—22no—
98#14556549—22no—
99#14556549—22no—
100C2×C4⋊Dic73C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×#11924005C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×C4×Dic73C2×C411yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117C42×D73—22no—
118C42×D73—22no—
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C4⋊C4×C73C2×C411yescharacteristic
127C2×C42×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#11924036—28no—
133#11924036—28no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833C2×D412yes—
155C2×#10596833C2×D412yes—
156C2×#10596833#4112yes—
157C2×#10596833#4112yes—
158C23×D73C22×C411yescharacteristic
159C23×D73C22×C411yescharacteristic
160C2×D292—22no—
161C2×D292—22no—
162C2×D292—22no—
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C2411yescharacteristic
169C2×C4×D73—22no—
170C2×C4×D73—22no—
171C2×C4×D73—22no—
172C2×C4×D73—22no—
173C2×C4×D73—22no—
174C2×C4×D73—22no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—21no—
184C2×C4×D73—21no—
185C2×C4×D73#4112yes—
186C2×C4×D73#4112yes—
187C4⋊Dic73—22no—
188#11924007—22no—
189#11924007—22no—
190#11924005—22no—
191#11924005—22no—
192#11924005—22no—
193#11924005—22no—
194#11924005—22no—
195#11924005—22no—
196#11924005—22no—
197#11924005—22no—
198C4×Dic73—22no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—21no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73C2×D412yes—
208C4×Dic73#4112yes—
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C22×C411yescharacteristic
214C22×C4×C73C22×C411yescharacteristic
215C22×C4×C73C22×C411yescharacteristic
216C4⋊C4×C73—22no—
217C4⋊C4×C73—22no—
218C42×C73—22no—
219C23×C73C23×C411yescharacteristic
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—21no—
223C22×D73—21no—
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—21no—
230C22×D73—21no—
231C22×D73#11712yes—
232C22×D73#13112yes—
233C22×D73#13112yes—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73#11712yes—
253C2×C4×C73C4×D412yes—
254C2×C4×C73#13112yes—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73C4×D412yes—
269C2×Dic73#13112yes—
270C2×Dic73C22×D411yescharacteristic
271C2×Dic73C2×#4111yescharacteristic
272C2×Dic73C2×#4111yescharacteristic
273C2×Dic73C2×#4111yescharacteristic
274C2×Dic73C2×#4111yescharacteristic
275C2×Dic73C2×#4111yescharacteristic
276D292—44no—
277C4×D73—28no—
278C4×D73—28no—
279C4×D73—22no—
280C4×D73—22no—
281C4×D73—22no—
282C4×D73—22no—
283C4×D73—41no—
284C4×D73—41no—
285C4×D73—41no—
286C4×D73—41no—
287#10596833—22no—
288#10596833—22no—
289#10596833—22no—
290#10596833—22no—
291#10596833—41no—
292#10596833—41no—
293#10596833—41no—
294#10596833—41no—
295C22×C73C2×#11711yescharacteristic
296C22×C73C2×C4×D411yescharacteristic
297C22×C73C4×#4111yescharacteristic
298C22×C73C2×#13111yescharacteristic
299C22×C73C2×#13111yescharacteristic
300C22×C73C2×#13111yescharacteristic
301C22×C73C2×#13111yescharacteristic
302C2×D73—22no—
303C2×D73—22no—
304C2×D73—22no—
305C2×D73—22no—
306C2×D73—22no—
307C2×D73—22no—
308C2×D73—41no—
309C2×D73—41no—
310C2×D73—41no—
311C2×D73—41no—
312C2×D73—41no—
313C2×D73—41no—
314C2×D73—41no—
315C2×D73#43314yescomplemented
316C4×C73—22no—
317C4×C73—22no—
318C4×C73—22no—
319C4×C73—41no—
320C4×C73—41no—
321C4×C73—41no—
322C4×C73—41no—
323Dic73—22no—
324Dic73—22no—
325Dic73—41no—
326Dic73—41no—
327Dic73—41no—
328Dic73#52511yescharacteristic
329Dic73#52511yescharacteristic
330Dic73#52911yescharacteristic
331Dic73#52911yescharacteristic
332#21103—731nomaximal, Sylow
333C2×C73#229011yescharacteristic
334C2×C73C2×#43311yescharacteristic
335C2×C73#292211yescharacteristic
336C2×C73#292911yescharacteristic
337C2×C73#292911yescharacteristic
338C2×C73#296611yescharacteristic
339C2×C73#296611yescharacteristic
340D73—24no—
341D73—81no—
342C2×#433—731no—
343C22×C4×C8—731no—
344#2290—731no—
345#1923—731no—
346#1923—731no—
347#1916—731no—
348#1916—731no—
349#1869—731no—
350#1869—731no—
351#1850—731no—
352#1850—731no—
353#1768—731no—
354#1750—731no—
355#1749—731no—
356#1746—731no—
357C73#2110311yescharacteristic, complemented, Sylow
358C23×C8—731no—
359C23×C8—731no—
360C2×C4×D4—731no—
361C2×#117—731no—
362C22×C42—731no—
363#433—1464no—
364C2×C4⋊C8—731no—
365C2×C4⋊C8—731no—
366C2×C4⋊C8—731no—
367C2×C4⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C22⋊C8—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C22⋊C8—731no—
374C2×#97—731no—
375C2×#97—731no—
376C2×C4×C8—731no—
377C2×C4×C8—731no—
378C2×C4×C8—731no—
379C2×C4×C8—731no—
380C2×C4×C8—1464no—
381#388—731no—
382#388—731no—
383#387—731no—
384#387#6440811yescharacteristic
385#386—731no—
386#386—731no—
387#385—731no—
388#385—731no—
389C4×C4⋊C4—731no—
390C4×C22⋊C4—731no—
391C4×C22⋊C4—731no—
392#376—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403C22×D4—731no—
404C23×C4—731no—
405C23×C4—731no—
406C23×C4—731no—
407C23×C4—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—731no—
414C22×C8—731no—
415C22×C8—731no—
416C22×C8—1462no—
417C22×C8—1462no—
418C22×C8—1462no—
419C22×C8—1462no—
420C22×C8—1462no—
421C22×C8—1462no—
422C4×D4—1462no—
423C4×D4—1462no—
424#117—1462no—
425#117—1462no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—731no—
429C2×C4⋊C4C2×#6440811yescharacteristic
430C2×C4⋊C4C2×#6440811yescharacteristic
431C2×C22⋊C4—731no—
432C2×C22⋊C4—731no—
433C2×C22⋊C4—731no—
434C2×C22⋊C4—731no—
435C2×C22⋊C4—731no—
436C2×C22⋊C4—731no—
437C2×C22⋊C4—731no—
438C2×C22⋊C4—731no—
439C2×C42—731no—
440C2×C42—731no—
441C2×C42—731no—
442C2×C42—731no—
443C2×C42—731no—
444C2×C42—731no—
445C2×C42—1462no—
446C2×C42—1462no—
447C2×C42C2×#6440811yescharacteristic
448C4⋊C8—1462no—
449C4⋊C8—1462no—
450C4⋊C8—1462no—
451C4⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454C22⋊C8—1462no—
455C22⋊C8—1462no—
456C22⋊C8—1462no—
457C22⋊C8—1462no—
458#97—1462no—
459#97—1462no—
460C4×C8—734no—
461C4×C8—1462no—
462C4×C8—1462no—
463C4×C8—1462no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95—731no—
468#95—731no—
469#95—731no—
470#95C2×#6440811yescharacteristic
471#95C2×#6440811yescharacteristic
472#95C2×#6440811yescharacteristic
473#95C2×#6440811yescharacteristic
474C24—731no—
475C24—731no—
476C2×D4—1462no—
477C2×D4—1462no—
478C2×D4—1462no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—732no—
483C22×C4—732no—
484C22×C4—731no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1461no—
495C22×C4—1462no—
496C22×C4—1461no—
497C22×C4—1461no—
498C22×C4—1462no—
499C22×C4—1462no—
500C22×C4—1462no—
501C22×C4—1462no—
502C22×C4—1462no—
503C22×C4C22×#6440811yescharacteristic
504C22×C4C22×#6440811yescharacteristic
505C22×C4C22×#6440811yescharacteristic
506C22×C4C22×#6440811yescharacteristic
507C22×C4C22×#6440811yescharacteristic
508C22×C4C22×#6440811yescharacteristic
509C22×C4C22×#6440811yescharacteristic
510C2×C8—732no—
511C2×C8—732no—
512C2×C8—732no—
513C2×C8—732no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C2×C8—1461no—
528C2×C8—1461no—
529C2×C8—1461no—
530C2×C8—1461no—
531C2×C8—1461no—
532C2×C8—1461no—
533C2×C8—1461no—
534C2×C8—1468no—
535C2×C8—1468no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—1462no—
539C4⋊C4—1462no—
540C4⋊C4—1462no—
541C22⋊C4—1462no—
542C22⋊C4—1462no—
543C22⋊C4—1462no—
544C22⋊C4—1462no—
545C22⋊C4—1462no—
546C22⋊C4—1462no—
547C22⋊C4—1462no—
548C22⋊C4—1462no—
549C42—22no—
550C42—732no—
551C42—732no—
552C42—1461no—
553C42—1461no—
554C42—1461no—
555C42—1461no—
556C42—1461no—
557C42—1462no—
558C42—1461no—
559C42—1461no—
560C42—1461no—
561C23—732no—
562C23—732no—
563C23—732no—
564C23—1461no—
565C23—1461no—
566C23—1461no—
567C23—1461no—
568C23—1461no—
569C23—1461no—
570C23—1461no—
571C23—1461no—
572C23—1461no—
573C23—1461no—
574C23—1461no—
575C23C23×#6440811yescharacteristic
576D4—2924no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—2921no—
596C2×C4—2921no—
597C2×C4—2921no—
598C2×C4—2921no—
599C2×C4—731no—
600C2×C4—731no—
601C2×C4—731no—
602C2×C4—731no—
603C2×C4—731no—
604C2×C4—731no—
605C2×C4—732no—
606C2×C4—732no—
607C2×C4—1462no—
608C2×C4—1462no—
609C2×C4—1462no—
610C2×C4—1462no—
611C2×C4—1468no—
612C2×C4—1468no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4#1455667012yes—
627C2×C4D4×#6440812yes—
628C2×C4#1455667912yes—
629C8—2921no—
630C8—2921no—
631C8—2921no—
632C8—2921no—
633C8—1462no—
634C8—1462no—
635C8—1462no—
636C8—1462no—
637C22—2921no—
638C22—2921no—
639C22—2921no—
640C22—2921no—
641C22—2921no—
642C22—2921no—
643C22—2921no—
644C22—734no—
645C22—1462no—
646C22—1462no—
647C22—1462no—
648C22—1462no—
649C22—1462no—
650C22—1462no—
651C22C2×#1455667011yescharacteristic
652C22C2×D4×#6440811yescharacteristic
653C22#41×#6440811yescharacteristic
654C22D73⋊#13111yescharacteristic
655C22D73⋊#13111yescharacteristic
656C22D73⋊#13111yescharacteristic
657C22C2×#1455667911yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—2921no—
666C4—2921no—
667C4—2921no—
668C4—731no—
669C4—731no—
670C4—731no—
671C4—731no—
672C4—1462no—
673C4—1462no—
674C2—5841no—
675C2—1464no—
676C2#2262638511yescharacteristic
677C2D73⋊#43311yescharacteristic
678C2#2262661611yescharacteristic
679C2#2262664711yescharacteristic
680C2#2262664811yescharacteristic
681C2#2262674811yescharacteristic
682C2#2262674911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#387×C73C4
prime radicalC22×D292C2×C4
cosocleC22×Dic73C24
hypercenter#387#64408
hypocenterC73#21103
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#17989612C2semidirect
2. C2×C4×#11924036C2semidirect
3. #22626003C2semidirect
4. #22626002C2semidirect
5. #22625986C2semidirect
6. #22625985C2semidirect
9. #22625876C2semidirect
10. #22625876C2semidirect
11. #22625719C2semidirect
12. #22625660C2semidirect
13. #22625658C2semidirect
14. #22625650C2semidirect
90. C4×#10596833D4semidirect
315. C2×D73#433semidirect
357. C73#21103semidirect

Maximal subgroups

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

subgroupindex
C2×#179896122
C2×C4×#119240362
#226260032
#226260022
#226259862
#226259852
#226259072
#226258762
#226257192
#226256602
#226256582
#226256502
#226123692
#2110373