Finite Group Databasebeta

← #34021113

Subgroups — #34021113

Order 18688.

1974 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989610C212yesmaximal, complemented
2#22625823C212yesmaximal, complemented
3#22625788C212yesmaximal, complemented
4#22625787C212yesmaximal, complemented
5#22625754C212yesmaximal
6#22625658C212yesmaximal, complemented
7#22625657C212yesmaximal, complemented
8C22×C42×D73C211yesmaximal, characteristic
9#17989610—28no—
10C2×#14556658C2214yescomplemented
11C2×#14556648C2214yes—
12C2×#14556648C2214yes—
13C2×C22⋊#10596833C2214yes—
14C2×#14556646C2214yescomplemented
15#17989453C2214yescomplemented
16#17989453C2214yescomplemented
17C23×C4×D73C411yescharacteristic
18C23×C4×D73C411yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C22×C4×Dic73C411yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23C2×C42×D73—28no—
24C2×C42×D73C411yescharacteristic
25C2×C42×D73C411yescharacteristic
26C2×C42×D73C411yescharacteristic
27C2×C42×D73C411yescharacteristic
28C2×C42×D73C2211yescharacteristic
29C2×C42×D73C2211yescharacteristic
30C2×C42×D73C2211yescharacteristic
31C2×C42×D73C2211yescharacteristic
32C22×C42×C73C411yescharacteristic
33C22×#10596833C2318yes—
34#14556658—28no—
35#14556648—28no—
36#14556648—28no—
37C22⋊#10596833—28no—
38#14556646—28no—
39C24×D73C2×C411yescharacteristic
40C23×Dic73C2×C411yescharacteristic
41C23×Dic73C2×C411yescharacteristic
42C23×Dic73C2311yescharacteristic
43C22×C4×D73—24no—
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—24no—
51C22×C4×D73—24no—
52C22×C4×D73C2×C411yescharacteristic
53C22×C4×D73C2×C411yescharacteristic
54C22×C4×D73C2×C411yescharacteristic
55C22×C4×D73C2×C411yescharacteristic
56C22×C4×D73C2×C411yescharacteristic
57C22×C4×D73C2×C411yescharacteristic
58C22×C4×D73C2×C411yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2×C411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C2×C4×Dic73—24no—
65C2×C4×Dic73—24no—
66C2×C4×Dic73—24no—
67C2×C4×Dic73C2×C411yescharacteristic
68C2×C4×Dic73C2×C411yescharacteristic
69C2×C4×Dic73C2×C411yescharacteristic
70C2×C4×Dic73C2×C411yescharacteristic
71C2×C4×Dic73C2×C411yescharacteristic
72C2×C4×Dic73C2×C411yescharacteristic
73C2×C4×Dic73C2×C411yescharacteristic
74C2×C4×Dic73C2×C411yescharacteristic
75C2×C4×Dic73C2311yescharacteristic
76C2×C4×Dic73C2311yescharacteristic
77C2×C4×Dic73C2311yescharacteristic
78C2×C4×Dic73C2311yescharacteristic
79C42×D73—24no—
80C42×D73—24no—
81C42×D73—24no—
82C42×D73—24no—
83C42×D73—24no—
84C42×D73—24no—
85C42×D73—24no—
86C42×D73D418yes—
87C23×C4×C73C2×C411yescharacteristic
88C23×C4×C73C2×C411yescharacteristic
89C23×C4×C73C2×C411yescharacteristic
90C2×C42×C73—24no—
91C2×C42×C73C2×C411yescharacteristic
92C2×C42×C73C2×C411yescharacteristic
93C2×C42×C73C2×C411yescharacteristic
94C2×C42×C73C2×C411yescharacteristic
95C2×#10596833—28no—
96C2×#10596833—28no—
97C2×#10596833—28no—
98C23×D73—22no—
99C23×D73—22no—
100C23×D73—22no—
101C23×D73—22no—
102C23×D73—22no—
103C23×D73—22no—
104C23×D73M1614yes—
105C23×D73C22×C411yescharacteristic
106C23×D73C22×C411yescharacteristic
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73M1614yes—
115C22×Dic73C22×C411yescharacteristic
116C22×Dic73C22×C411yescharacteristic
117C22×Dic73C22×C411yescharacteristic
118C22×Dic73C22×C411yescharacteristic
119C22×Dic73C22×C411yescharacteristic
120C22×Dic73#4114yes—
121C22×Dic73C2411yescharacteristic
122C2×C4×D73—232no—
123C2×C4×D73—232no—
124C2×C4×D73—232no—
125C2×C4×D73—22no—
126C2×C4×D73—22no—
127C2×C4×D73—22no—
128C2×C4×D73—22no—
129C2×C4×D73—22no—
130C2×C4×D73—22no—
131C2×C4×D73—22no—
132C2×C4×D73—22no—
133C2×C4×D73—22no—
134C2×C4×D73—22no—
135C2×C4×D73—22no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—22no—
153C2×C4×D73—22no—
154C2×C4×D73—22no—
155C2×C4×D73C22⋊C414yes—
156C2×C4×D73C22⋊C414yes—
157C2×C4×D73M1614yes—
158C2×C4×D73M1614yes—
159C2×C4×D73C2×D414yes—
160C2×C4×D73#4114yes—
161C4×Dic73—22no—
162C4×Dic73—22no—
163C4×Dic73—22no—
164C4×Dic73—22no—
165C4×Dic73—22no—
166C4×Dic73—22no—
167C4×Dic73—22no—
168C4×Dic73—22no—
169C4×Dic73—22no—
170C4×Dic73C22⋊C414yes—
171C4×Dic73C2×D414yes—
172C4×Dic73C2×D414yes—
173C24×C73C22×C411yescharacteristic
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C42×C73—22no—
190C42×C73—22no—
191C42×C73—22no—
192C42×C73C22⋊C414yes—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73#11712yes—
198C23×C73C2×M1612yes—
199C23×C73C2×M1612yes—
200C23×C73C23×C411yescharacteristic
201C22×D73—28no—
202C22×D73—28no—
203C22×D73—28no—
204C22×D73—28no—
205C22×D73—21no—
206C22×D73—21no—
207C22×D73—21no—
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—28no—
214C22×D73—28no—
215C22×D73—28no—
216C22×D73C2×C22⋊C412yes—
217C22×D73#11712yes—
218C22×D73C2×M1612yes—
219C22×D73C2×M1612yes—
220C22×D73C2×M1612yes—
221C22×D73C2×M1612yes—
222C2×C4×C73—28no—
223C2×C4×C73—28no—
224C2×C4×C73—28no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73C2×C22⋊C412yes—
238C2×C4×C73C2×C22⋊C412yes—
239C2×C4×C73C2×C22⋊C412yes—
240C2×C4×C73#11712yes—
241C2×C4×C73C2×M1612yes—
242C2×C4×C73C2×M1612yes—
243C2×Dic73—28no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—28no—
253C2×Dic73—28no—
254C2×Dic73C2×C22⋊C412yes—
255C2×Dic73C2×C22⋊C412yes—
256C2×Dic73#11712yes—
257C2×Dic73C2×M1612yes—
258C2×Dic73C2×M1612yes—
259C2×Dic73C2×M1612yes—
260C2×Dic73C2×M1612yes—
261C2×Dic73C22×D412yes—
262C2×Dic73C2×#4112yes—
263C2×Dic73C2×#4112yes—
264C4×D73—28no—
265C4×D73—28no—
266C4×D73—28no—
267C4×D73—28no—
268C4×D73—28no—
269C4×D73—28no—
270C4×D73—28no—
271C4×D73—28no—
272C4×D73—28no—
273C4×D73—28no—
274C4×D73—28no—
275C4×D73—28no—
276#10596833—48no—
277C22×C73—22no—
278C22×C73—22no—
279C22×C73—22no—
280C22×C73—22no—
281C22×C73—22no—
282C22×C73—22no—
283C22×C73#43214yescomplemented
284C22×C73C22×C22⋊C411yescharacteristic
285C22×C73C2×#11711yescharacteristic
286C22×C73C2×#11711yescharacteristic
287C22×C73C22×M1611yescharacteristic
288C22×C73C22×M1611yescharacteristic
289C22×C73C22×M1611yescharacteristic
290C22×C73C22×M1611yescharacteristic
291C2×D73—232no—
292C2×D73—22no—
293C2×D73—22no—
294C2×D73—22no—
295C2×D73—22no—
296C2×D73—22no—
297C2×D73—22no—
298C2×D73—22no—
299C2×D73—22no—
300C2×D73—22no—
301C2×D73—22no—
302C2×D73—22no—
303C2×D73—22no—
304C2×D73#40714yes—
305C2×D73#43214yescomplemented
306C4×C73—22no—
307C4×C73—22no—
308C4×C73—22no—
309C4×C73—22no—
310C4×C73—22no—
311C4×C73—22no—
312Dic73—22no—
313Dic73—22no—
314Dic73—22no—
315Dic73—22no—
316Dic73#40714yes—
317Dic73#52514yes—
318#20715—731nomaximal, Sylow
319C2×C73—24no—
320C2×C73#228011yescharacteristic
321C2×C73C2×#40711yescharacteristic
322C2×C73C2×#40711yescharacteristic
323C2×C73C2×#43211yescharacteristic
324C2×C73C2×#43211yescharacteristic
325C2×C73#292011yescharacteristic
326C2×C73#292011yescharacteristic
327D73—24no—
328D73—24no—
329C23×C42—731no—
330C2×#432—732no—
331#1817—732no—
332#1797—732no—
333#1797—732no—
334#1779—732no—
335#1749—732no—
336#1749—732no—
337C73#2071511yescharacteristic, complemented, Sylow
338C24×C4—731no—
339C24×C4—731no—
340C24×C4—731no—
341C22×C42—731no—
342C22×C42—731no—
343C22×C42—731no—
344C22×C42—731no—
345C22×C42—731no—
346C22×C42—731no—
347C22×C42—731no—
348C22×C42—731no—
349C22×C42—731no—
350C22×C42—731no—
351C22×C42—731no—
352C22×C42—1468no—
353C22×C42#6440811yescharacteristic
354#432—1468no—
355C2×C4⋊C8—734no—
356C2×C22⋊C8—734no—
357C2×C22⋊C8—734no—
358C2×C22⋊C8—734no—
359C2×#97—734no—
360#336—734no—
361#336—734no—
362C25—731no—
363C23×C4—731no—
364C23×C4—731no—
365C23×C4—731no—
366C23×C4—731no—
367C23×C4—731no—
368C23×C4—731no—
369C23×C4—731no—
370C23×C4—731no—
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C23×C4—731no—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4—1464no—
379C23×C4—1464no—
380C23×C4—1464no—
381C23×C4—1464no—
382C23×C4—1464no—
383C23×C4—1464no—
384C23×C4—1464no—
385C23×C4—1464no—
386C23×C4—1464no—
387C23×C4C2×#6440811yescharacteristic
388C23×C4C2×#6440811yescharacteristic
389C23×C4C2×#6440811yescharacteristic
390C22×C8—738no—
391C2×C42—24no—
392C2×C42—731no—
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—738no—
396C2×C42—731no—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—1464no—
406C2×C42—1464no—
407C2×C42—1464no—
408C2×C42—1464no—
409C2×C42—1464no—
410C2×C42—1464no—
411C2×C42—1464no—
412C2×C42—1464no—
413C2×C42—1464no—
414C2×C42—1464no—
415C2×C42C2×#6440811yescharacteristic
416C2×C42C2×#6440811yescharacteristic
417C2×C42C2×#6440811yescharacteristic
418C2×C42C2×#6440811yescharacteristic
419C4⋊C8—1468no—
420C22⋊C8—1468no—
421C22⋊C8—1468no—
422C22⋊C8—1468no—
423#97—1468no—
424C24—731no—
425C24—731no—
426C24—734no—
427C24—1462no—
428C24—1462no—
429C24—1462no—
430C24—1462no—
431C24—1462no—
432C24—1462no—
433C24C22×#6440811yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—734no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—734no—
451C22×C4—734no—
452C22×C4—734no—
453C22×C4—734no—
454C22×C4—734no—
455C22×C4—734no—
456C22×C4—734no—
457C22×C4—1462no—
458C22×C4—1462no—
459C22×C4—1462no—
460C22×C4—1462no—
461C22×C4—1462no—
462C22×C4—1462no—
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—1462no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1462no—
481C22×C4—14632no—
482C22×C4—14632no—
483C22×C4—14632no—
484C22×C4—1462no—
485C22×C4—1462no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4—1462no—
491C22×C4—1462no—
492C22×C4—1462no—
493C22×C4—1462no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4C22×#6440811yescharacteristic
498C22×C4C22×#6440811yescharacteristic
499C22×C4C22×#6440811yescharacteristic
500C22×C4C22×#6440811yescharacteristic
501C22×C4C22×#6440811yescharacteristic
502C22×C4C22×#6440811yescharacteristic
503C2×C8—1468no—
504C2×C8—1468no—
505C2×C8—1468no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—734no—
510C42—734no—
511C42—734no—
512C42—1462no—
513C42—1462no—
514C42—1462no—
515C42—1462no—
516C42—1462no—
517C42—1462no—
518C42—1462no—
519C42—1462no—
520C42—1462no—
521C42C22⋊#6440814yes—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—732no—
527C23—732no—
528C23—732no—
529C23—732no—
530C23—732no—
531C23—732no—
532C23—1468no—
533C23—1468no—
534C23—1468no—
535C23—1468no—
536C23—1468no—
537C23—1468no—
538C23—1461no—
539C23—1461no—
540C23—1461no—
541C23—1461no—
542C23—1461no—
543C23—1461no—
544C23—1461no—
545C23—1461no—
546C23—1468no—
547C23#1455667012yes—
548C23D73⋊M1612yes—
549C23D73⋊M1612yes—
550C23C23×#6440811yescharacteristic
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—28no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—732no—
567C2×C4—732no—
568C2×C4—732no—
569C2×C4—732no—
570C2×C4—732no—
571C2×C4—732no—
572C2×C4—732no—
573C2×C4—732no—
574C2×C4—732no—
575C2×C4—732no—
576C2×C4—1468no—
577C2×C4—1468no—
578C2×C4—1468no—
579C2×C4—1468no—
580C2×C4—1468no—
581C2×C4—1468no—
582C2×C4—1468no—
583C2×C4—1468no—
584C2×C4—1468no—
585C2×C4—1468no—
586C2×C4—1468no—
587C2×C4—1468no—
588C2×C4—1468no—
589C2×C4—1468no—
590C2×C4—1468no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4C2×C22⋊#6440812yes—
600C2×C4C2×C22⋊#6440812yes—
601C2×C4C2×C22⋊#6440812yes—
602C2×C4#1455667012yes—
603C2×C4D73⋊M1612yes—
604C2×C4D73⋊M1612yes—
605C8—2928no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—734no—
613C22—734no—
614C22—14632no—
615C22—1462no—
616C22—1462no—
617C22—1462no—
618C22—1462no—
619C22—1462no—
620C22—1462no—
621C22—1462no—
622C22—1462no—
623C22—1462no—
624C22—1462no—
625C22—1462no—
626C22—1462no—
627C22#1798961014yescomplemented
628C22C22×C22⋊#6440811yescharacteristic
629C22C2×#1455667011yescharacteristic
630C22C2×#1455667011yescharacteristic
631C22C2×D73⋊M1611yescharacteristic
632C22C2×D73⋊M1611yescharacteristic
633C22C2×D73⋊M1611yescharacteristic
634C22C2×D73⋊M1611yescharacteristic
635C4—22no—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—734no—
642C4—734no—
643C4—1462no—
644C4—1462no—
645C4—1462no—
646C4—1462no—
647C2—24no—
648C2—1464no—
649C2—1464no—
650C2#2262637511yescharacteristic
651C2D73⋊#40711yescharacteristic
652C2D73⋊#40711yescharacteristic
653C2D73⋊#43211yescharacteristic
654C2C2×#1798961011yescharacteristic
655C2#2262660911yescharacteristic
656C2#2262661011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC22×C42×C73C4
prime radicalC24×D73C2×C4
cosocleC22×Dic73C24
hypercenterC22×C42#64408
hypocenterC73#20715
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#17989610C2semidirect
2. #22625823C2semidirect
3. #22625788C2semidirect
4. #22625787C2semidirect
6. #22625658C2semidirect
7. #22625657C2semidirect
10. C2×#14556658C22semidirect
14. C2×#14556646C22semidirect
15. #17989453C22semidirect
16. #17989453C22semidirect
283. C22×C73#432semidirect
305. C2×D73#432semidirect
337. C73#20715semidirect
627. C22#17989610semidirect

Maximal subgroups

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

subgroupindex
C2×#179896102
#226258232
#226257882
#226257872
#226257542
#226256582
#226256572
C22×C42×D732
#2071573