Finite Group Databasebeta

← #33094105

Subgroups — #33094105

Order 18688.

826 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988949C211yesmaximal, characteristic
2#22612642C211yesmaximal, characteristic
3#22610893C211yesmaximal, characteristic, complemented
4#22610740C211yesmaximal, characteristic
5#22610627C211yesmaximal, characteristic
6#22610620C211yesmaximal, characteristic, complemented
7#22610613C211yesmaximal, characteristic
8#22610606C211yesmaximal, characteristic, complemented
9#22610064C211yesmaximal, characteristic, complemented
10#22609764C211yesmaximal, characteristic, complemented
11#22609759C211yesmaximal, characteristic
12C4×#14556514C211yesmaximal, characteristic, complemented
13C4×#14556511C211yesmaximal, characteristic
14#22609618C211yesmaximal, characteristic, complemented
15C73×#2331C211yesmaximal, characteristic, complemented
16C2×#14556579C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19#17988949C418yescomplemented
20C2×#14556514C2211yescharacteristic
21C2×#14556514C2211yescharacteristic
22C2×#14556514C2211yescharacteristic
23C2×#14556514C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988493C2211yescharacteristic
35#17988489C2211yescharacteristic
36#17988479—21no—
37#17988479—21no—
38#17988461—21no—
39#17988461—21no—
40#17988457C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C2×C4⋊Q8×C73C2211yescharacteristic
50#391×C73—21no—
51#391×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#387×C73—21no—
55#387×C73—21no—
56#382×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#376×C73C2211yescharacteristic
60C22×Dic146C2311yescharacteristic
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556579—22no—
68#14556579C2×C414yes—
69C4×Dic146—22no—
70C4×Dic146—22no—
71C4×D292—22no—
72C4×D292—22no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73—21no—
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×#11924007—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×C4×Dic73—21no—
84#14556514—22no—
85#14556514—22no—
86#14556514C2×C414yescomplemented
87#14556514C2×C414yescomplemented
88#14556511—22no—
89#14556511—22no—
90#14556511C2×C414yes—
91#14556511C2×C414yes—
92#14556502—22no—
93#14556502—22no—
94#14556502C2×C414yescomplemented
95C4×#10596831—22no—
96C4×#10596831—22no—
97C4×#10596831—22no—
98#14556498—21no—
99#14556498—21no—
100C22×Q8×C73—21no—
101C4⋊Q8×C73—22no—
102C4⋊Q8×C73C2×C414yescomplemented
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73D411yescharacteristic
122#95×C73D411yescharacteristic
123#95×C73D411yescharacteristic
124#95×C73D411yescharacteristic
125C23×D73—21no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146—21no—
130C2×Dic146—21no—
131C2×Dic146C22×C412yes—
132C2×D292—21no—
133C2×D292—21no—
134C2×D292—21no—
135C2×D292—21no—
136C2×D292—21no—
137C2×D292C22×C412yes—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C2×C4×D73—42no—
142C2×C4×D73—81no—
143C2×C4×D73—81no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831C22×C412yes—
153C2×#10596831C22×C412yes—
154C2×#10596831#4112yes—
155C2×#10596831#4112yes—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—81no—
161C4⋊Dic73—81no—
162#11924007—42no—
163#11924005—24no—
164#11924005—24no—
165#11924005—42no—
166#11924005—81no—
167#11924005—81no—
168C4×Dic73—42no—
169C2×Q8×C73—24no—
170C2×Q8×C73—81no—
171C2×Q8×C73—81no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2411yescharacteristic
183C4⋊C4×C73—24no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—81no—
191C4⋊C4×C73—81no—
192C4⋊C4×C73C22×C412yes—
193C4⋊C4×C73C22×C412yes—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—81no—
197C42×C73—81no—
198C42×C73C22×C412yes—
199C42×C73#4112yes—
200C42×C73#4112yes—
201C42×C73#4112yes—
202C23×C73C22×D411yescharacteristic
203C22×D73—22no—
204C22×D73—41no—
205C22×D73—41no—
206C22×D73—41no—
207C22×D73—41no—
208C22×D73—41no—
209C22×D73—41no—
210Q8×C73—84no—
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—22no—
220C2×C4×C73—22no—
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—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73C4×D412yes—
238C2×C4×C73C4×D412yes—
239C2×C4×C73#12412yes—
240C2×C4×C73#12412yes—
241C2×C4×C73C23×C411yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×Dic73—22no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256D292—22no—
257D292—22no—
258D292—41no—
259D292—41no—
260C4×D73—84no—
261Dic146—22no—
262Dic146—22no—
263Dic146—41no—
264Dic146—41no—
265#10596831—22no—
266#10596831—22no—
267#10596831—22no—
268#10596831—22no—
269C22×C73C2×C4×D411yescharacteristic
270C22×C73C2×#12411yescharacteristic
271C22×C73#53211yescharacteristic
272C22×C73#57611yescharacteristic
273C22×C73#57711yescharacteristic
274C22×C73#57711yescharacteristic
275C22×C73#57811yescharacteristic
276C2×D73—42no—
277C2×D73—42no—
278C2×D73—42no—
279C2×D73—81no—
280C2×D73—81no—
281C2×D73—81no—
282C2×D73—81no—
283C4×C73—22no—
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—42no—
290C4×C73—42no—
291C4×C73—81no—
292C4×C73—81no—
293C4×C73C4×#4111yescharacteristic
294C4×C73C4×#4111yescharacteristic
295C4×C73#52911yescharacteristic
296C4×C73#52911yescharacteristic
297Dic73—42no—
298Dic73—81no—
299Dic73—81no—
300#21654—731nomaximal, Sylow
301C2×C73C4×#12411yescharacteristic
302C2×C73#294611yescharacteristic
303C2×C73#294711yescharacteristic
304C2×C73#313611yescharacteristic
305C2×C73#313711yescharacteristic
306C2×C73#317311yescharacteristic
307C2×C73#317511yescharacteristic
308D73—82no—
309C2×#489—731no—
310#2331D7311yescharacteristic, complemented
311#2326—731no—
312#1990—731no—
313#1958—731no—
314#1936—731no—
315#1935—731no—
316#1934—731no—
317#1933—731no—
318#1836—731no—
319#1763—731no—
320#1762—731no—
321C4×#103—731no—
322C4×#102—731no—
323#1726—731no—
324C73#2165411yescharacteristic, complemented, Sylow
325C2×C4⋊Q8C2×D7311yescharacteristic
326C2×#124—731no—
327C2×C4×Q8—731no—
328C2×C4×D4—731no—
329#489—738no—
330C2×#103—731no—
331C2×#103—731no—
332C2×#103—731no—
333C2×#103—731no—
334C2×#102—731no—
335C2×#102—731no—
336C2×#102—731no—
337C2×#102—731no—
338C2×#97—731no—
339C2×#97—731no—
340C2×#97—731no—
341C2×C4×C8—731no—
342C2×C4×C8—731no—
343C2×C4×C8—731no—
344#391—21no—
345#391—21no—
346#391—731no—
347#390—731no—
348#389C2×D7311yescharacteristic
349#389C2×D7311yescharacteristic
350#388—1461no—
351#388—1461no—
352#387—21no—
353#387—21no—
354#385—1461no—
355#385—1461no—
356#384—731no—
357#382C2×D7311yescharacteristic
358C4×C4⋊C4C2×D7311yescharacteristic
359C4×C4⋊C4C2×D7311yescharacteristic
360#376C2×D7311yescharacteristic
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368#340—731no—
369C22×Q8—21no—
370C22×Q8—731no—
371C22×D4—731no—
372C23×C4—1461no—
373C22×C8—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C4⋊Q8—22no—
378C4⋊Q8C4×D7314yescomplemented
379#124—734no—
380#124—1462no—
381C4×Q8—1462no—
382C4×Q8—1462no—
383C4×D4—1462no—
384C4×D4—1462no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4C22×D7311yescharacteristic
394C2×C4⋊C4C22×D7311yescharacteristic
395C2×C4⋊C4C22×D7311yescharacteristic
396C2×C4⋊C4C22×D7311yescharacteristic
397C2×C22⋊C4—1461no—
398C2×C22⋊C4—1461no—
399C2×C22⋊C4—1461no—
400C2×C22⋊C4—1461no—
401C2×C22⋊C4—1461no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—1461no—
405C2×C42C22×D7311yescharacteristic
406C2×C42C22×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408#103—734no—
409#103—734no—
410#103—1462no—
411#103—1462no—
412#102—734no—
413#102—734no—
414#102—1462no—
415#102—1462no—
416#97—734no—
417#97—1462no—
418#97—1462no—
419C4×C8—1462no—
420C4×C8—1462no—
421C4×C8—1462no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—1461no—
429#95—1461no—
430#95C22⋊D7311yescharacteristic
431#95C22⋊D7311yescharacteristic
432#95C22⋊D7311yescharacteristic
433#95C22⋊D7311yescharacteristic
434C24—1461no—
435C2×Q8—24no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—732no—
439C2×Q8—1461no—
440C2×Q8—1461no—
441C2×Q8—1461no—
442C2×Q8—1461no—
443C2×Q8—1461no—
444C2×D4—732no—
445C2×D4—1461no—
446C2×D4—1461no—
447C2×D4—1461no—
448C2×D4—1461no—
449C2×D4—1461no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—2922no—
455C22×C4—5841no—
456C22×C4—5841no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4C2×C22⋊D7311yescharacteristic
461C22×C4C2×C22⋊D7311yescharacteristic
462C22×C4C2×C22⋊D7311yescharacteristic
463C22×C4C2×C22⋊D7311yescharacteristic
464C22×C4C2×C22⋊D7311yescharacteristic
465C22×C4C2×C22⋊D7311yescharacteristic
466C22×C4C23×D7311yescharacteristic
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—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—2922no—
489C4⋊C4—5841no—
490C4⋊C4—5841no—
491C4⋊C4—1461no—
492C4⋊C4—1461no—
493C4⋊C4—1461no—
494C4⋊C4—1461no—
495C4⋊C4C2×C4×D7312yes—
496C4⋊C4C2×C4×D7312yes—
497C22⋊C4—2922no—
498C22⋊C4—5841no—
499C22⋊C4—5841no—
500C22⋊C4—1464no—
501C22⋊C4—1464no—
502C42—21no—
503C42—21no—
504C42—81no—
505C42—81no—
506C42—2922no—
507C42C2×C4×D7312yes—
508C42#1192402812yes—
509C42#1192402912yes—
510C42#1192402912yes—
511C23—2921no—
512C23—2921no—
513C23—2921no—
514C23—2921no—
515C23—2921no—
516C23—2921no—
517C23—1462no—
518C23C22×C22⋊D7311yescharacteristic
519Q8—84no—
520Q8—2921no—
521Q8—2921no—
522Q8—1462no—
523Q8—1462no—
524D4—2921no—
525D4—2921no—
526D4—1462no—
527D4—1462no—
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—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—5844no—
563C2×C4—1462no—
564C2×C4C4×C22⋊D7312yes—
565C2×C4C4×C22⋊D7312yes—
566C2×C4#1455658012yes—
567C2×C4#1455658012yes—
568C2×C4C22×C4×D7311yescharacteristic
569C2×C4#41×D7311yescharacteristic
570C2×C4#41×D7311yescharacteristic
571C2×C4C2×#1192402811yescharacteristic
572C2×C4C2×#1192402911yescharacteristic
573C2×C4C2×#1192402911yescharacteristic
574C8—1462no—
575C8—1462no—
576C8—1462no—
577C8—1462no—
578C22—2922no—
579C22—2922no—
580C22—2922no—
581C22—5841no—
582C22—5841no—
583C22—5841no—
584C22—5841no—
585C22C2×C4×C22⋊D7311yescharacteristic
586C22C2×#1455658011yescharacteristic
587C22#1798913311yescharacteristic
588C22#1798939011yescharacteristic
589C22#1798939511yescharacteristic
590C22#1798939811yescharacteristic
591C22#1798940211yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—42no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—2922no—
603C4—5841no—
604C4—5841no—
605C4C4×#1192402911yescharacteristic
606C4C4×#1192402911yescharacteristic
607C4#1798912411yescharacteristic
608C4#1798912411yescharacteristic
609C2—5842no—
610C2C4×#1455658011yescharacteristic
611C2#2261876311yescharacteristic
612C2#2261877411yescharacteristic
613C2#2262029011yescharacteristic
614C2#2262030111yescharacteristic
615C2#2262054211yescharacteristic
616C2#2262056411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2331C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenter#2331D73
hypocenterC73#21654
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #22610893C2semidirect
6. #22610620C2semidirect
8. #22610606C2semidirect
9. #22610064C2semidirect
10. #22609764C2semidirect
12. C4×#14556514C2semidirect
14. #22609618C2semidirect
15. C73×#2331C2semidirect
19. #17988949C4semidirect
86. #14556514C2×C4semidirect
87. #14556514C2×C4semidirect
94. #14556502C2×C4semidirect
102. C4⋊Q8×C73C2×C4semidirect
310. #2331D73semidirect
324. C73#21654semidirect
378. C4⋊Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179889492
#226126422
#226108932
#226107402
#226106272
#226106202
#226106132
#226106062
#226100642
#226097642
#226097592
C4×#145565142
C4×#145565112
#226096182
C73×#23312
#2165473