Finite Group Databasebeta

← #34020697

Subgroups — #34020697

Order 18688.

850 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989612C211yesmaximal, characteristic
2C2×#17989594C211yesmaximal, characteristic
3#22625731C211yesmaximal, characteristic, complemented
4#22625730C211yesmaximal, characteristic, complemented
5#22625727C211yesmaximal, characteristic, complemented
6#22625726C211yesmaximal, characteristic, complemented
7#22625719C211yesmaximal, characteristic, complemented
8#22625719C211yesmaximal, characteristic, complemented
9#22625717C211yesmaximal, characteristic, complemented
10#22625716C211yesmaximal, characteristic, complemented
11#22625672C211yesmaximal, characteristic
12#22625672C211yesmaximal, characteristic
13#22625669C211yesmaximal, characteristic
14#22625669C211yesmaximal, characteristic
15#22612423C211yesmaximal, characteristic
16C22×#11924038C2211yescharacteristic
17C22×#11924036C2211yescharacteristic
18#17989612C418yescomplemented
19#17989594C418yescomplemented
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×#14556658C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25C2×C4⋊#10596833C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×#14556646C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×#14556646C2211yescharacteristic
34C2×#14556646C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556549C2211yescharacteristic
47#17988479C411yescharacteristic
48#17988478C411yescharacteristic
49#17988477C411yescharacteristic
50#17988476C411yescharacteristic
51#17988473C411yescharacteristic
52#17988472C411yescharacteristic
53#17988470C411yescharacteristic
54C4⋊C4×Dic73C2211yescharacteristic
55#17988438C2211yescharacteristic
56#17988434C2211yescharacteristic
57#17988434C2211yescharacteristic
58#17988432C2211yescharacteristic
59C42×Dic73C2211yescharacteristic
60#387×C73C411yescharacteristic
61C2×#11924038—41no—
62C2×#11924038—41no—
63C2×#11924038C2×C414yes—
64C2×#11924036—41no—
65C2×#11924036—41no—
66C2×#11924036C2×C414yes—
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75#14556658C2×C414yes—
76#14556658C2×C414yes—
77#14556658C2×C414yes—
78C4⋊#10596833C2×C414yes—
79C4⋊#10596833C2×C414yes—
80C4⋊#10596833C2×C414yes—
81#14556648C2×C414yes—
82#14556648C2×C414yes—
83#14556646—41no—
84#14556646—41no—
85#14556646—41no—
86#14556646—41no—
87#14556646—41no—
88#14556646—41no—
89#14556646C2×C414yes—
90C4×#10596833—41no—
91C4×#10596833—41no—
92C4×#10596833C2×C414yes—
93C22×C4×D73C2311yescharacteristic
94#14556549C2×C414yes—
95#14556549C2×C414yes—
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×C4⋊Dic73C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×C4×Dic73C2×C411yescharacteristic
107C2×C4×Dic73C2×C411yescharacteristic
108C2×C4×Dic73C2×C411yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C42×C73C2×C411yescharacteristic
126#95×C73C2×C411yescharacteristic
127#95×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#11924038—44no—
131#11924036—44no—
132C2×#10596833—21no—
133C2×#10596833—21no—
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×#10596833C22×C412yes—
149C2×#10596833C22×C412yes—
150C2×#10596833C22×C412yes—
151C2×#10596833C22×C412yes—
152C2×#10596833C22×C412yes—
153C2×#10596833C22×C412yes—
154C2×#10596833C22×C412yes—
155C2×#10596833C22×C412yes—
156C23×D73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C22×C411yescharacteristic
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C2411yescharacteristic
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73C22×C412yes—
169C2×C4×D73C22×C412yes—
170C4⋊Dic73—41no—
171C4⋊Dic73C4214yes—
172#11924007—41no—
173#11924007—41no—
174#11924005—41no—
175#11924005—41no—
176#11924005—41no—
177#11924005—41no—
178#11924005C4214yes—
179#11924005C4214yes—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—41no—
189C4×Dic73—41no—
190C4×Dic73—41no—
191C4×Dic73C22×C412yes—
192C4×Dic73C22×C412yes—
193C4×Dic73C22×C412yes—
194C4×Dic73C22×C412yes—
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C4⋊C4×C73—41no—
203C4⋊C4×C73C4214yes—
204C42×C73—41no—
205C23×C73C23×C411yescharacteristic
206C22×D73—21no—
207C22×D73—21no—
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73C2×C4212yes—
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×C73C2×C4212yes—
232C2×C4×C73C2×C4212yes—
233C2×C4×C73C2×C4212yes—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73C2×C4212yes—
251C2×Dic73C2×C4212yes—
252C2×Dic73C23×C411yescharacteristic
253C2×Dic73C23×C411yescharacteristic
254C2×Dic73H(5,𝔽2)11yescharacteristic
255C2×Dic73H(5,𝔽2)11yescharacteristic
256C2×Dic732−1+411yescharacteristic
257C2×Dic732−1+411yescharacteristic
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—22no—
262#10596833—22no—
263#10596833—22no—
264#10596833—22no—
265#10596833—22no—
266#10596833—22no—
267#10596833—22no—
268#10596833—22no—
269#10596833—22no—
270C22×C73C22×C4211yescharacteristic
271C22×C73#52011yescharacteristic
272C22×C73#52011yescharacteristic
273C22×C73#56811yescharacteristic
274C22×C73#56811yescharacteristic
275C22×C73#56811yescharacteristic
276C22×C73#56811yescharacteristic
277C2×D73—22no—
278C2×D73—22no—
279C2×D73—22no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C2×D73—41no—
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291Dic73—22no—
292Dic73—22no—
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296Dic73—41no—
297Dic73#51811yescharacteristic
298Dic73#51911yescharacteristic
299Dic73#52011yescharacteristic
300Dic73#52011yescharacteristic
301#20554—731nomaximal, Sylow
302C2×C73#227411yescharacteristic
303C2×C73#287511yescharacteristic
304C2×C73#287511yescharacteristic
305C2×C73#299511yescharacteristic
306C2×C73#299511yescharacteristic
307C2×C73#299511yescharacteristic
308C2×C73#299511yescharacteristic
309D73—42no—
310C2×#433—731no—
311C2×#424—731no—
312#2298—731no—
313#1771—731no—
314#1771—731no—
315#1770—731no—
316#1770—731no—
317#1768—731no—
318#1768—731no—
319#1767—731no—
320#1767—731no—
321#1753—731no—
322#1753—731no—
323#1752—731no—
324#1752—731no—
325C73#2055411yescharacteristic, complemented, Sylow
326C22×M16—731no—
327C23×C8—731no—
328C2×#117—731no—
329#433—738no—
330#424—738no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C22⋊C8—731no—
338C2×C22⋊C8—731no—
339C2×#97—731no—
340C2×#97—731no—
341C2×#97—731no—
342C2×#97—731no—
343C2×#97—731no—
344C2×#97—731no—
345C2×#97—731no—
346C2×C4×C8—731no—
347C2×C4×C8—731no—
348C2×C4×C8—731no—
349#388—731no—
350#388—731no—
351#388—731no—
352#388—731no—
353#387—731no—
354#387—731no—
355#387—731no—
356#387#6440811yescharacteristic
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359C4×C22⋊C4—731no—
360C4×C22⋊C4—731no—
361#376—731no—
362C43—731no—
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371C23×C4—731no—
372C2×M16—2921no—
373C2×M16—2921no—
374C2×M16—734no—
375C22×C8—2921no—
376C22×C8—2921no—
377C22×C8—734no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—731no—
386#117—734no—
387#117—734no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4C2×#6440811yescharacteristic
393C2×C4⋊C4C2×#6440811yescharacteristic
394C2×C22⋊C4—731no—
395C2×C22⋊C4—731no—
396C2×C22⋊C4—731no—
397C2×C22⋊C4—731no—
398C2×C22⋊C4—731no—
399C2×C22⋊C4—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—731no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42C2×#6440811yescharacteristic
410C4⋊C8—734no—
411C4⋊C8—734no—
412C4⋊C8—734no—
413C4⋊C8—734no—
414C4⋊C8—734no—
415C4⋊C8—734no—
416C22⋊C8—734no—
417C22⋊C8—734no—
418#97—2921no—
419#97—2921no—
420#97—2921no—
421#97—2921no—
422#97—2921no—
423#97—2921no—
424#97—734no—
425C4×C8—2921no—
426C4×C8—2921no—
427C4×C8—734no—
428#95—731no—
429#95—731no—
430#95—731no—
431#95—731no—
432#95—731no—
433#95—731no—
434#95—731no—
435#95—731no—
436#95C2×#6440811yescharacteristic
437#95C2×#6440811yescharacteristic
438#95C2×#6440811yescharacteristic
439#95C2×#6440811yescharacteristic
440C24—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—732no—
445C22×C4—732no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4C22×#6440811yescharacteristic
455C22×C4C22×#6440811yescharacteristic
456C22×C4C22×#6440811yescharacteristic
457C22×C4C22×#6440811yescharacteristic
458C22×C4C22×#6440811yescharacteristic
459C22×C4C22×#6440811yescharacteristic
460C22×C4C22×#6440811yescharacteristic
461M16—2924no—
462C2×C8—2924no—
463C2×C8—732no—
464C2×C8—732no—
465C2×C8—732no—
466C2×C8—732no—
467C2×C8—732no—
468C2×C8—732no—
469C2×C8—732no—
470C2×C8—732no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C4⋊C4—41no—
488C4⋊C4—2921no—
489C4⋊C4—2921no—
490C4⋊C4—2921no—
491C4⋊C4—734no—
492C4⋊C4C4×#6440814yes—
493C22⋊C4—2921no—
494C22⋊C4—2921no—
495C22⋊C4—2921no—
496C22⋊C4—2921no—
497C22⋊C4—734no—
498C22⋊C4—734no—
499C42—41no—
500C42—2921no—
501C42—2921no—
502C42—2921no—
503C42—732no—
504C42—732no—
505C42—732no—
506C42—732no—
507C42—1461no—
508C42—1461no—
509C42—1461no—
510C42—1461no—
511C42—1461no—
512C42—1461no—
513C42—1461no—
514C42—1461no—
515C23—732no—
516C23—1461no—
517C23—1461no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23—1461no—
522C23C23×#6440811yescharacteristic
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—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—731no—
542C2×C4—731no—
543C2×C4—731no—
544C2×C4—731no—
545C2×C4—731no—
546C2×C4—731no—
547C2×C4—732no—
548C2×C4—732no—
549C2×C4—1462no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4—1462no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4C2×C4×#6440812yes—
570C2×C4C2×C4×#6440812yes—
571C2×C4C2×C4×#6440812yes—
572C8—1462no—
573C8—1462no—
574C8—1462no—
575C8—1462no—
576C8—1462no—
577C8—1462no—
578C8—1462no—
579C8—1462no—
580C22—2921no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22—1462no—
585C22—1462no—
586C22—1462no—
587C22C22×C4×#6440811yescharacteristic
588C22#1798965611yescharacteristic
589C22#1798965611yescharacteristic
590C22#1798966511yescharacteristic
591C22#1798966611yescharacteristic
592C22#1798966611yescharacteristic
593C22#1798966711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—2921no—
602C4—2921no—
603C4—2921no—
604C4—2921no—
605C4—731no—
606C4—731no—
607C4—731no—
608C4—731no—
609C4—1462no—
610C4—1462no—
611C2—2922no—
612C2#2262636811yescharacteristic
613C2#2262650211yescharacteristic
614C2#2262650311yescharacteristic
615C2#2262688511yescharacteristic
616C2#2262688611yescharacteristic
617C2#2262688811yescharacteristic
618C2#2262688911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
Fitting#387×C73C4
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#387#64408
hypocenterC73#20554
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #22625731C2semidirect
4. #22625730C2semidirect
5. #22625727C2semidirect
6. #22625726C2semidirect
7. #22625719C2semidirect
8. #22625719C2semidirect
9. #22625717C2semidirect
10. #22625716C2semidirect
18. #17989612C4semidirect
19. #17989594C4semidirect
325. C73#20554semidirect

Maximal subgroups

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

subgroupindex
C2×#179896122
C2×#179895942
#226257312
#226257302
#226257272
#226257262
#226257192
#226257172
#226257162
#226256722
#226256692
#226124232
#2055473