Finite Group Databasebeta

← #33090343

Subgroups — #33090343

Order 18688.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988697C211yesmaximal, characteristic
2#22612575C211yesmaximal, characteristic, complemented
3#22610806C211yesmaximal, characteristic
4#22610796C211yesmaximal, characteristic
5#22610671C211yesmaximal, characteristic, complemented
6#22610656C211yesmaximal, characteristic, complemented
7#22610631C211yesmaximal, characteristic, complemented
8#22610627C211yesmaximal, characteristic, complemented
9#22610617C211yesmaximal, characteristic, complemented
10#22610613C211yesmaximal, characteristic, complemented
11#22609829C211yesmaximal, characteristic, complemented
12C4×#14556511C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14#22609618C211yesmaximal, characteristic, complemented
15C73×#2319C211yesmaximal, characteristic, complemented
16C22×#11924013C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18#17988697C418yescomplemented
19C2×#14556524C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×#14556512C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34#17988489C2211yescharacteristic
35#17988489C2211yescharacteristic
36#17988485C2211yescharacteristic
37#17988485C2211yescharacteristic
38#17988476—21no—
39#17988476—21no—
40#17988449—21no—
41#17988446—21no—
42C4×C4⋊Dic73C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C2×C4×D4×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#388×C73—21no—
55#388×C73—21no—
56#381×C73—21no—
57#380×C73—21no—
58C4×C4⋊C4×C73C2211yescharacteristic
59#376×C73C2211yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C2×#11924013—22no—
63C2×#11924013—22no—
64C2×#11924013C2×C414yes—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C4×D292—22no—
70C4×D292C2×C414yes—
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×C4×Dic73—21no—
82#14556524—22no—
83#14556522—22no—
84#14556522C2×C414yes—
85#14556512—22no—
86#14556512—22no—
87#14556512C2×C414yes—
88#14556511—22no—
89#14556511—22no—
90#14556511C2×C414yes—
91#14556502—22no—
92#14556502—22no—
93#14556502C2×C414yes—
94C4×#10596831—22no—
95C4×#10596831—22no—
96C4×#10596831—22no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100C22×D4×C73C2311yescharacteristic
101C23×C4×C73—21no—
102C4×D4×C73—22no—
103C4×D4×C73C2×C414yes—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
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×D292—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292C22×C412yes—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C2×C4×D73—24no—
136C2×C4×D73—81no—
137C2×C4×D73—81no—
138#11924013—28no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831C22×C412yes—
146C2×#10596831C22×C412yes—
147C2×#10596831#4112yes—
148C2×#10596831#4112yes—
149C2×#10596831#4112yes—
150C2×#10596831#4112yes—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73C22×C412yes—
157#11924007—81no—
158#11924007—81no—
159#11924005—24no—
160#11924005—81no—
161#11924005—81no—
162#11924005—81no—
163#11924005—81no—
164C4×Dic73—81no—
165C24×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73C22×C412yes—
172C22×C4×C73—21no—
173C22×C4×C73—24no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—81no—
177C22×C4×C73—81no—
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2411yescharacteristic
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—
193C22⋊C4×C73—24no—
194C22⋊C4×C73—81no—
195C22⋊C4×C73—81no—
196C22⋊C4×C73—81no—
197C22⋊C4×C73—81no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—81no—
203C42×C73C22×C412yes—
204C42×C73#4112yes—
205C23×C73—22no—
206C23×C73—41no—
207C23×C73—41no—
208C23×C73—41no—
209C23×C73—41no—
210C23×C73—41no—
211C23×C73—41no—
212C23×C73C22×D411yescharacteristic
213C22×D73—22no—
214C22×D73—41no—
215C22×D73—41no—
216C22×D73—41no—
217C22×D73—41no—
218C22×D73—41no—
219C22×D73—41no—
220D4×C73—22no—
221D4×C73—22no—
222D4×C73—41no—
223D4×C73—41no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—22no—
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—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—84no—
250C2×C4×C73C4×D412yes—
251C2×C4×C73C4×D412yes—
252C2×C4×C73C23×C411yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73C2×#4111yescharacteristic
258C2×Dic73—22no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267D292—22no—
268D292—22no—
269D292—41no—
270D292—41no—
271C4×D73—84no—
272#10596831—22no—
273#10596831—22no—
274#10596831—22no—
275#10596831#11714yes—
276C22×C73—42no—
277C22×C73—42no—
278C22×C73—42no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—81no—
282C22×C73—81no—
283C22×C73C2×C4×D411yescharacteristic
284C22×C73#53211yescharacteristic
285C22×C73#53211yescharacteristic
286C22×C73#57611yescharacteristic
287C22×C73#57611yescharacteristic
288C22×C73#57711yescharacteristic
289C22×C73#57711yescharacteristic
290C2×D73—42no—
291C2×D73—42no—
292C2×D73—42no—
293C2×D73—81no—
294C2×D73—81no—
295C2×D73—81no—
296C2×D73—81no—
297C4×C73—22no—
298C4×C73—22no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73—41no—
303C4×C73—42no—
304C4×C73—81no—
305C4×C73—81no—
306C4×C73C2×#11711yescharacteristic
307C4×C73C4×#4111yescharacteristic
308C4×C73#52911yescharacteristic
309C4×C73#52911yescharacteristic
310Dic73—42no—
311Dic73—81no—
312Dic73—81no—
313#21290—731nomaximal, Sylow
314C2×C73—82no—
315C2×C73#229311yescharacteristic
316C2×C73#294611yescharacteristic
317C2×C73#294611yescharacteristic
318C2×C73#317311yescharacteristic
319C2×C73#317611yescharacteristic
320C2×C73#317911yescharacteristic
321C2×C73#317911yescharacteristic
322D73—82no—
323C2×#442—731no—
324#2319—731no—
325#2319D7311yescharacteristic, complemented
326#1972—731no—
327#1970—731no—
328#1944—731no—
329#1941—731no—
330#1936—731no—
331#1936—731no—
332#1934—731no—
333#1934—731no—
334#1776—731no—
335C4×#102—731no—
336C4×#102—731no—
337#1726—731no—
338C73#2129011yescharacteristic, complemented, Sylow
339C22×D8—731no—
340C2×C4×D4—731no—
341C2×C4×D4C2×D7311yescharacteristic
342#442—738no—
343C2×#107—731no—
344C2×#106—731no—
345C2×#106—731no—
346C2×#102—731no—
347C2×#102—731no—
348C2×#102—731no—
349C2×#102—731no—
350C2×#102—731no—
351C2×#102—731no—
352C2×#97—731no—
353C2×#97—731no—
354C2×#97—731no—
355C2×C4×C8—731no—
356C2×C4×C8—731no—
357C2×C4×C8—731no—
358#390—731no—
359#390—731no—
360#390C2×D7311yescharacteristic
361#390C2×D7311yescharacteristic
362#389—731no—
363#389—731no—
364#389C2×D7311yescharacteristic
365#389C2×D7311yescharacteristic
366#388—21no—
367#388—21no—
368#388—1461no—
369#388—1461no—
370#381—21no—
371#381—1461no—
372#380—21no—
373#380—1461no—
374C4×C4⋊C4—731no—
375C4×C4⋊C4C2×D7311yescharacteristic
376#376C2×D7311yescharacteristic
377#340—731no—
378#340—731no—
379#340—731no—
380#340—731no—
381#340—731no—
382#340—731no—
383C22×D4—731no—
384C22×D4C22×D7311yescharacteristic
385C23×C4—21no—
386C23×C4—1461no—
387C2×D8—734no—
388C2×D8—1462no—
389C2×D8—1462no—
390C22×C8—731no—
391C22×C8—731no—
392C22×C8—731no—
393C22×C8—731no—
394C4×D4—22no—
395C4×D4—734no—
396C4×D4—1462no—
397C4×D4C4×D7314yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—1461no—
404C2×C4⋊C4—1461no—
405C2×C4⋊C4C22×D7311yescharacteristic
406C2×C4⋊C4C22×D7311yescharacteristic
407C2×C4⋊C4C22×D7311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—1461no—
414C2×C22⋊C4—1461no—
415C2×C22⋊C4—1461no—
416C2×C22⋊C4—1461no—
417C2×C22⋊C4—1461no—
418C2×C42—21no—
419C2×C42—1461no—
420C2×C42C22×D7311yescharacteristic
421C2×C42C22×D7311yescharacteristic
422C2×C42C22×D7311yescharacteristic
423#107—1462no—
424#106—734no—
425#106—1462no—
426#102—734no—
427#102—734no—
428#102—1462no—
429#102—1462no—
430#102—1462no—
431#102—1462no—
432#97—734no—
433#97—1462no—
434#97—1462no—
435C4×C8—1462no—
436C4×C8—1462no—
437C4×C8—1462no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444#95C22⋊D7311yescharacteristic
445#95C22⋊D7311yescharacteristic
446#95C22⋊D7311yescharacteristic
447#95C22⋊D7311yescharacteristic
448C24—21no—
449C24—1461no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—732no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4—1461no—
460C2×D4—1461no—
461C2×D4C2×C4×D7312yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—5841no—
469C22×C4—5841no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1464no—
474C22×C4C2×C22⋊D7311yescharacteristic
475C22×C4C2×C22⋊D7311yescharacteristic
476C22×C4C2×C22⋊D7311yescharacteristic
477C22×C4C2×C22⋊D7311yescharacteristic
478C22×C4C2×C22⋊D7311yescharacteristic
479C22×C4C2×C22⋊D7311yescharacteristic
480C22×C4C23×D7311yescharacteristic
481D8—1468no—
482C2×C8—732no—
483C2×C8—732no—
484C2×C8—732no—
485C2×C8—732no—
486C2×C8—732no—
487C2×C8—732no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—5841no—
502C4⋊C4—5841no—
503C4⋊C4—732no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4C2×C4×D7312yes—
510C22⋊C4—24no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—5841no—
516C22⋊C4—5841no—
517C22⋊C4—5841no—
518C22⋊C4—5841no—
519C22⋊C4—1464no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—81no—
525C42—5841no—
526C42C2×C4×D7312yes—
527C42#1192402812yes—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—2921no—
536C23—2921no—
537C23—2921no—
538C23—2921no—
539C23—2921no—
540C23—2921no—
541C23—1462no—
542C23C22×C22⋊D7311yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—2921no—
548D4—2921no—
549D4—1462no—
550D4—1462no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
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—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—5844no—
586C2×C4—1462no—
587C2×C4C4×C22⋊D7312yes—
588C2×C4C4×C22⋊D7312yes—
589C2×C4C22×C4×D7311yescharacteristic
590C2×C4#41×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4#41×D7311yescharacteristic
594C2×C4C2×#1192402811yescharacteristic
595C8—734no—
596C8—1462no—
597C8—1462no—
598C8—1462no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—2922no—
607C22—2922no—
608C22—2922no—
609C22—5841no—
610C22—5841no—
611C22—5841no—
612C22—5841no—
613C22C2×C4×C22⋊D7311yescharacteristic
614C22#1798913311yescharacteristic
615C22#1798913311yescharacteristic
616C22#1798939011yescharacteristic
617C22#1798939011yescharacteristic
618C22#1798939511yescharacteristic
619C22#1798939811yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—2922no—
630C4—5841no—
631C4—5841no—
632C4#117×D7311yescharacteristic
633C4#1798905511yescharacteristic
634C4#1798911511yescharacteristic
635C4#1798911511yescharacteristic
636C2—82no—
637C2—5842no—
638C2#2261239011yescharacteristic
639C2#2261875911yescharacteristic
640C2#2261876311yescharacteristic
641C2#2262054211yescharacteristic
642C2#2262057511yescharacteristic
643C2#2262060811yescharacteristic
644C2#2262061611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2319C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
cosocleC22×C4×C73C24
hypercenter#2319D73
hypocenterC73#21290
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #22612575C2semidirect
5. #22610671C2semidirect
6. #22610656C2semidirect
7. #22610631C2semidirect
8. #22610627C2semidirect
9. #22610617C2semidirect
10. #22610613C2semidirect
11. #22609829C2semidirect
12. C4×#14556511C2semidirect
13. C4×#14556512C2semidirect
14. #22609618C2semidirect
15. C73×#2319C2semidirect
18. #17988697C4semidirect
325. #2319D73semidirect
338. C73#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#179886972
#226125752
#226108062
#226107962
#226106712
#226106562
#226106312
#226106272
#226106172
#226106132
#226098292
C4×#145565112
C4×#145565122
#226096182
C73×#23192
#2129073