Finite Group Databasebeta

← #33096179

Subgroups — #33096179

Order 18688.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610546C211yesmaximal, characteristic
2#22610546C211yesmaximal, characteristic
3#22610539C211yesmaximal, characteristic
4#22610539C211yesmaximal, characteristic
5#22610497C211yesmaximal, characteristic, complemented
6#22610497C211yesmaximal, characteristic, complemented
7#22610490C211yesmaximal, characteristic, complemented
8#22610490C211yesmaximal, characteristic, complemented
9#22610085C211yesmaximal, characteristic, complemented
10#22610051C211yesmaximal, characteristic, complemented
11#22609911C211yesmaximal, characteristic
12#22609911C211yesmaximal, characteristic
13#22609788C211yesmaximal, characteristic, complemented
14#22609788C211yesmaximal, characteristic, complemented
15C73×#2283C211yesmaximal, characteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×C4⋊#10596831C2211yescharacteristic
18C2×C4⋊#10596831C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32#17988342C2211yescharacteristic
33#17988342C2211yescharacteristic
34#17988342C2211yescharacteristic
35#17988342C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44C22×C42×C73C2211yescharacteristic
45#383×C73C411yescharacteristic
46#383×C73C411yescharacteristic
47#382×C73C411yescharacteristic
48#382×C73C411yescharacteristic
49#381×C73C411yescharacteristic
50#381×C73C411yescharacteristic
51#380×C73C411yescharacteristic
52#380×C73C411yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55C4×C22⋊C4×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#376×C73C2211yescharacteristic
58#376×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C4⋊#10596831—22no—
68C4⋊#10596831—22no—
69C4⋊#10596831—22no—
70C4⋊#10596831—22no—
71C4⋊#10596831—41no—
72C4⋊#10596831—41no—
73C4⋊#10596831—41no—
74C4⋊#10596831—41no—
75C22⋊#10596831—41no—
76C22⋊#10596831—41no—
77C22⋊#10596831—41no—
78C22⋊#10596831—41no—
79#14556502—41no—
80#14556502—41no—
81C4×#10596831—41no—
82C4×#10596831—41no—
83C23×C4×C73C2×C411yescharacteristic
84C23×C4×C73C2×C411yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73C2×C411yescharacteristic
87C2×C4⋊C4×C73C2×C411yescharacteristic
88C2×C4⋊C4×C73C2×C411yescharacteristic
89C2×C4⋊C4×C73C2×C411yescharacteristic
90C2×C22⋊C4×C73C2×C411yescharacteristic
91C2×C22⋊C4×C73C2×C411yescharacteristic
92C2×C22⋊C4×C73C2×C411yescharacteristic
93C2×C22⋊C4×C73C2×C411yescharacteristic
94C2×C42×C73—22no—
95C2×C42×C73—22no—
96C2×C42×C73C2×C411yescharacteristic
97C2×C42×C73C2×C411yescharacteristic
98C2×C42×C73C2311yescharacteristic
99C2×C42×C73C2311yescharacteristic
100C2×C42×C73C2311yescharacteristic
101C2×C42×C73C2311yescharacteristic
102C2×C42×C73C2311yescharacteristic
103C2×C42×C73C2311yescharacteristic
104#95×C73C2×C411yescharacteristic
105#95×C73C2×C411yescharacteristic
106#95×C73C2×C411yescharacteristic
107#95×C73C2×C411yescharacteristic
108#95×C73C2×C411yescharacteristic
109#95×C73C2×C411yescharacteristic
110#95×C73C2×C411yescharacteristic
111#95×C73C2×C411yescharacteristic
112#95×C73C2×C411yescharacteristic
113#95×C73C2×C411yescharacteristic
114#95×C73C2×C411yescharacteristic
115#95×C73C2×C411yescharacteristic
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C2×#10596831—21no—
121C2×#10596831—21no—
122C2×#10596831—21no—
123C2×#10596831—21no—
124C2×#10596831—21no—
125C2×#10596831—21no—
126C2×#10596831—21no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C24×C73C22×C411yescharacteristic
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—41no—
156C22×C4×C73—41no—
157C22×C4×C73C22×C411yescharacteristic
158C22×C4×C73C22×C411yescharacteristic
159C22×C4×C73C22×C411yescharacteristic
160C22×C4×C73C22×C411yescharacteristic
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C2411yescharacteristic
171C4⋊C4×C73—22no—
172C4⋊C4×C73—22no—
173C4⋊C4×C73—41no—
174C4⋊C4×C73—41no—
175C22⋊C4×C73—22no—
176C22⋊C4×C73—22no—
177C22⋊C4×C73—41no—
178C22⋊C4×C73—41no—
179C42×C73—22no—
180C42×C73—22no—
181C42×C73—21no—
182C42×C73—21no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73#4112yes—
192C42×C73#4112yes—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73#13112yes—
200C23×C73C23×C411yescharacteristic
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
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×C73—44no—
238C2×C4×C73—44no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73#11712yes—
244C2×C4×C73#11712yes—
245C2×C4×C73#13112yes—
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73H(5,𝔽2)11yescharacteristic
249C2×C4×C73H(5,𝔽2)11yescharacteristic
250C2×C4×C732−1+411yescharacteristic
251C2×C4×C732−1+411yescharacteristic
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—22no—
261C22×C73—22no—
262C22×C73—22no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73C2×#11711yescharacteristic
268C22×C73#52011yescharacteristic
269C22×C73#52011yescharacteristic
270C22×C73C2×#13111yescharacteristic
271C22×C73C2×#13111yescharacteristic
272C22×C73#56811yescharacteristic
273C22×C73#56811yescharacteristic
274C4×C73—22no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73—41no—
287C4×C73#54011yescharacteristic
288C4×C73#54111yescharacteristic
289C4×C73#54211yescharacteristic
290C4×C73#54211yescharacteristic
291#21928—731nomaximal, Sylow
292C2×C73—42no—
293C2×C73#231411yescharacteristic
294C2×C73#292411yescharacteristic
295C2×C73#292411yescharacteristic
296C2×C73#299211yescharacteristic
297C2×C73#299311yescharacteristic
298C2×C73#299411yescharacteristic
299C2×C73#299511yescharacteristic
300#2283D7311yescharacteristic
301#1924—731no—
302#1924—731no—
303#1923—731no—
304#1923—731no—
305#1917—731no—
306#1917—731no—
307#1916—731no—
308#1916—731no—
309#1843—731no—
310#1832—731no—
311#1797—731no—
312#1797—731no—
313#1768—731no—
314#1768—731no—
315C73#2192811yescharacteristic, complemented, Sylow
316C22×C42C2×D7311yescharacteristic
317C2×C4⋊C8—731no—
318C2×C4⋊C8—731no—
319C2×C4⋊C8—731no—
320C2×C4⋊C8—731no—
321C2×C4⋊C8—731no—
322C2×C4⋊C8—731no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C22⋊C8—731no—
326C2×C22⋊C8—731no—
327C2×C22⋊C8—731no—
328C2×C22⋊C8—731no—
329C2×#97—731no—
330C2×#97—731no—
331C2×C4×C8—731no—
332C2×C4×C8—731no—
333#383Dic7311yescharacteristic
334#383Dic7311yescharacteristic
335#382Dic7311yescharacteristic
336#382Dic7311yescharacteristic
337#381Dic7311yescharacteristic
338#381Dic7311yescharacteristic
339#380Dic7311yescharacteristic
340#380Dic7311yescharacteristic
341C4×C4⋊C4C2×D7311yescharacteristic
342C4×C4⋊C4C2×D7311yescharacteristic
343C4×C22⋊C4C2×D7311yescharacteristic
344C4×C22⋊C4C2×D7311yescharacteristic
345#376C2×D7311yescharacteristic
346#376C2×D7311yescharacteristic
347#336—731no—
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353#336—731no—
354#336—731no—
355#336—731no—
356#336—731no—
357#336—731no—
358#336—731no—
359C23×C4C2×Dic7311yescharacteristic
360C23×C4C2×Dic7311yescharacteristic
361C23×C4C22×D7311yescharacteristic
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—731no—
370C2×C4⋊C4C2×Dic7311yescharacteristic
371C2×C4⋊C4C2×Dic7311yescharacteristic
372C2×C4⋊C4C2×Dic7311yescharacteristic
373C2×C4⋊C4C2×Dic7311yescharacteristic
374C2×C22⋊C4C2×Dic7311yescharacteristic
375C2×C22⋊C4C2×Dic7311yescharacteristic
376C2×C22⋊C4C2×Dic7311yescharacteristic
377C2×C22⋊C4C2×Dic7311yescharacteristic
378C2×C42—22no—
379C2×C42—22no—
380C2×C42C2×Dic7311yescharacteristic
381C2×C42C2×Dic7311yescharacteristic
382C2×C42C22×D7311yescharacteristic
383C2×C42C22×D7311yescharacteristic
384C2×C42C22×D7311yescharacteristic
385C2×C42C22×D7311yescharacteristic
386C2×C42C22×D7311yescharacteristic
387C2×C42C22×D7311yescharacteristic
388C4⋊C8—2921no—
389C4⋊C8—2921no—
390C4⋊C8—2921no—
391C4⋊C8—2921no—
392C4⋊C8—1462no—
393C4⋊C8—1462no—
394C4⋊C8—1462no—
395C4⋊C8—1462no—
396C22⋊C8—2921no—
397C22⋊C8—2921no—
398C22⋊C8—2921no—
399C22⋊C8—2921no—
400#97—2921no—
401#97—2921no—
402C4×C8—2921no—
403C4×C8—2921no—
404#95C2×Dic7311yescharacteristic
405#95C2×Dic7311yescharacteristic
406#95C2×Dic7311yescharacteristic
407#95C2×Dic7311yescharacteristic
408#95C2×Dic7311yescharacteristic
409#95C2×Dic7311yescharacteristic
410#95C2×Dic7311yescharacteristic
411#95C2×Dic7311yescharacteristic
412#95C2×Dic7311yescharacteristic
413#95C2×Dic7311yescharacteristic
414#95C2×Dic7311yescharacteristic
415#95C2×Dic7311yescharacteristic
416#95C2×Dic7311yescharacteristic
417#95C2×Dic7311yescharacteristic
418#95C2×Dic7311yescharacteristic
419#95C2×Dic7311yescharacteristic
420C24C22×Dic7311yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4C22×Dic7311yescharacteristic
434C22×C4C22×Dic7311yescharacteristic
435C22×C4C22×Dic7311yescharacteristic
436C22×C4C22×Dic7311yescharacteristic
437C22×C4C22×Dic7311yescharacteristic
438C22×C4C22×Dic7311yescharacteristic
439C22×C4C22×Dic7311yescharacteristic
440C22×C4C22×Dic7311yescharacteristic
441C22×C4C22×Dic7311yescharacteristic
442C22×C4C22×Dic7311yescharacteristic
443C22×C4C22×Dic7311yescharacteristic
444C22×C4C22×Dic7311yescharacteristic
445C22×C4C22×Dic7311yescharacteristic
446C22×C4C23×D7311yescharacteristic
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—22no—
480C42—22no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42#1192402812yes—
492C42#1192402812yes—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#1455659812yes—
500C23C23×Dic7311yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4#1455655012yes—
544C2×C4#1455655012yes—
545C2×C4#1455659812yes—
546C2×C4C2×#1192402811yescharacteristic
547C2×C4C2×#1192402811yescharacteristic
548C2×C4#1455663711yescharacteristic
549C2×C4#1455663711yescharacteristic
550C2×C4#1455663811yescharacteristic
551C2×C4#1455663811yescharacteristic
552C8—2921no—
553C8—2921no—
554C8—2921no—
555C8—2921no—
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#1455655011yescharacteristic
568C22#1798907011yescharacteristic
569C22#1798907011yescharacteristic
570C22C2×#1455659811yescharacteristic
571C22C2×#1455659811yescharacteristic
572C22#1798935411yescharacteristic
573C22#1798935411yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4#1798919211yescharacteristic
588C4#1798919911yescharacteristic
589C4#1798920811yescharacteristic
590C4#1798920811yescharacteristic
591C2—42no—
592C2#2261254011yescharacteristic
593C2#2261858911yescharacteristic
594C2#2261858911yescharacteristic
595C2#2261907011yescharacteristic
596C2#2261908011yescharacteristic
597C2#2261909111yescharacteristic
598C2#2261910111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2283C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#2283D73
hypocenterC73#21928
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2283

Complements

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

NH ≅ G/Ntype
5. #22610497C2semidirect
6. #22610497C2semidirect
7. #22610490C2semidirect
8. #22610490C2semidirect
9. #22610085C2semidirect
10. #22610051C2semidirect
13. #22609788C2semidirect
14. #22609788C2semidirect
315. C73#21928semidirect

Maximal subgroups

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

subgroupindex
#226105462
#226105392
#226104972
#226104902
#226100852
#226100512
#226099112
#226097882
C73×#22832
#2192873