Finite Group Databasebeta

← #33094071

Subgroups — #33094071

Order 18688.

882 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988950C211yesmaximal, characteristic
2#22612668C211yesmaximal, characteristic, complemented
3#22612653C211yesmaximal, characteristic
4#22610894C211yesmaximal, characteristic, complemented
5#22610735C211yesmaximal, characteristic
6#22610629C211yesmaximal, characteristic, complemented
7#22610625C211yesmaximal, characteristic, complemented
8#22610616C211yesmaximal, characteristic, complemented
9#22610612C211yesmaximal, characteristic, complemented
10#22610063C211yesmaximal, characteristic, complemented
11#22609757C211yesmaximal, characteristic, complemented
12C4×#14556511C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14#22609619C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C2×#14556587C2211yescharacteristic
17C2×#14556582C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19#17988950C418yescomplemented
20C2×#14556513C2211yescharacteristic
21C2×#14556513C2211yescharacteristic
22C2×#14556512C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556501C2211yescharacteristic
27C2×#14556501C2211yescharacteristic
28C2×C4×#10596831C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31#17988490C2211yescharacteristic
32#17988488C2211yescharacteristic
33#17988486C2211yescharacteristic
34#17988485—21no—
35#17988484—21no—
36#17988483C2211yescharacteristic
37#17988471—21no—
38#17988470—21no—
39#17988466—21no—
40#17988466—21no—
41#17988463—21no—
42#17988463—21no—
43#17988456C2211yescharacteristic
44#17988452C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46#17988433C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×#102×C73C2211yescharacteristic
55C2×#102×C73C2211yescharacteristic
56C2×#97×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C22⋊D73—21no—
62C22×C22⋊D73—21no—
63C22×C4×D73—21no—
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556587—22no—
67#14556587C2×C414yes—
68#14556582—22no—
69#14556582C2×C414yescomplemented
70C4×D292—22no—
71C4×D292—22no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924007—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89#14556513—22no—
90#14556513C2×C414yescomplemented
91#14556512—22no—
92#14556512C2×C414yescomplemented
93#14556511—22no—
94#14556511C2×C414yescomplemented
95#14556501—22no—
96#14556501C2×C414yescomplemented
97C4×#10596831—22no—
98C8×Dic73—22no—
99C8×Dic73—22no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498D411yescharacteristic
106#14556498D411yescharacteristic
107#14556498D411yescharacteristic
108#14556498D411yescharacteristic
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C4×D4×C73—22no—
114C4×D4×C73—22no—
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C22⋊C4×C73—21no—
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#102×C73—22no—
122#102×C73C2×C414yescomplemented
123#97×C73—22no—
124#95×C73—21no—
125C23×D73—21no—
126C2×D292—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292C22×C412yes—
132C2×C22⋊D73—24no—
133C2×C22⋊D73—24no—
134C2×C22⋊D73—81no—
135C2×C22⋊D73—81no—
136C2×C22⋊D73—81no—
137C2×C22⋊D73—81no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73C2×D411yescharacteristic
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×D411yescharacteristic
144C22×Dic73C2×D411yescharacteristic
145C2×C4×D73—42no—
146C2×C4×D73—81no—
147C2×C4×D73—81no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831C22×C412yes—
153C2×#10596831#4112yes—
154C4⋊Dic73—21no—
155C4⋊Dic73—24no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—81no—
161C4⋊Dic73C22×C412yes—
162#11924007—24no—
163#11924007—81no—
164#11924007—81no—
165#11924007—81no—
166C22⋊Dic73—81no—
167C22⋊Dic73—81no—
168#11924005—42no—
169#11924005—81no—
170#11924005—81no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—81no—
174C4×Dic73C22×C412yes—
175C4×Dic73#4112yes—
176C24×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73C22×C412yes—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—42no—
187C22×C4×C73—81no—
188C22×C4×C73—81no—
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2411yescharacteristic
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C22×C412yes—
197C2×C8×C73#4112yes—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C412yes—
204C22⋊C4×C73—42no—
205C42×C73—81no—
206C42×C73#4112yes—
207C42×C73#4112yes—
208C23×C73—22no—
209C23×C73—41no—
210C23×C73—41no—
211C23×C73—41no—
212C23×C73—41no—
213C23×C73—41no—
214C23×C73—41no—
215C23×C73C22×D411yescharacteristic
216C22×D73—22no—
217C22×D73—41no—
218C22×D73—41no—
219C22×D73—41no—
220C22×D73—41no—
221C22×D73—41no—
222C22×D73—41no—
223D4×C73—22no—
224D4×C73—22no—
225D4×C73—41no—
226D4×C73—41no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—22no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—84no—
241C2×C4×C73#12412yes—
242C2×C4×C73#12412yes—
243C2×C4×C73C23×C411yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C22⋊D73—84no—
250C22⋊D73—84no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—22no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—41no—
270C2×Dic73C4×D412yes—
271C2×Dic73C4×D412yes—
272D292—22no—
273D292—22no—
274D292—41no—
275D292—41no—
276C4×D73—84no—
277C8×C73—22no—
278C8×C73—22no—
279#10596831—22no—
280#10596831—22no—
281C22×C73—42no—
282C22×C73—42no—
283C22×C73—42no—
284C22×C73—81no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73—81no—
288C22×C73C2×C4×D411yescharacteristic
289C22×C73C2×#12411yescharacteristic
290C22×C73#53211yescharacteristic
291C22×C73#57611yescharacteristic
292C22×C73#57611yescharacteristic
293C22×C73#57711yescharacteristic
294C22×C73#57711yescharacteristic
295C2×D73—42no—
296C2×D73—42no—
297C2×D73—42no—
298C2×D73—81no—
299C2×D73—81no—
300C2×D73—81no—
301C2×D73—81no—
302C4×C73—22no—
303C4×C73—22no—
304C4×C73—42no—
305C4×C73—81no—
306C4×C73—81no—
307C4×C73C4×#4111yescharacteristic
308C4×C73C4×#4111yescharacteristic
309C4×C73#52911yescharacteristic
310C4×C73#52911yescharacteristic
311Dic73—22no—
312Dic73—22no—
313Dic73—41no—
314Dic73—41no—
315Dic73—42no—
316Dic73—81no—
317Dic73—81no—
318#21652—731nomaximal, Sylow
319C2×C73—82no—
320C2×C73C4×#12411yescharacteristic
321C2×C73#294611yescharacteristic
322C2×C73#294611yescharacteristic
323C2×C73#313611yescharacteristic
324C2×C73#313611yescharacteristic
325C2×C73#317411yescharacteristic
326C2×C73#317611yescharacteristic
327D73—82no—
328C2×#490—731no—
329#2330—731no—
330#2328—731no—
331#1991—731no—
332#1957—731no—
333#1936—731no—
334#1936—731no—
335#1934—731no—
336#1934—731no—
337#1836—731no—
338#1762—731no—
339#1762D7311yescharacteristic, complemented
340C4×#102—731no—
341C4×#102—731no—
342#1726—731no—
343C73#2165211yescharacteristic, complemented, Sylow
344C2×#127—731no—
345C2×#125—731no—
346C2×C4×D4—731no—
347C2×C4×D4C2×D7311yescharacteristic
348#490—738no—
349C2×#102—731no—
350C2×#102—731no—
351C2×#102—731no—
352C2×#102—731no—
353C2×#102—731no—
354C2×#102—731no—
355C2×#102C2×D7311yescharacteristic
356C2×#102C2×D7311yescharacteristic
357C2×#97—731no—
358C2×#97—731no—
359C2×#97C2×D7311yescharacteristic
360C2×C4×C8—731no—
361C2×C4×C8—731no—
362C2×C4×C8—731no—
363#390—731no—
364#390—731no—
365#389—731no—
366#389—731no—
367#389—1461no—
368#389—1461no—
369#387—1461no—
370#387—1461no—
371#386—1461no—
372#386—1461no—
373#386—1461no—
374#386—1461no—
375#384—731no—
376#382—731no—
377C4×C4⋊C4—731no—
378C4×C4⋊C4C2×D7311yescharacteristic
379#376—731no—
380#340—731no—
381#340—731no—
382#340—731no—
383#340—731no—
384#340—731no—
385#340—731no—
386#340C2×D7311yescharacteristic
387#340C2×D7311yescharacteristic
388C22×D4—731no—
389C22×D4—1461no—
390C22×D4—1461no—
391C22×D4C22×D7311yescharacteristic
392C23×C4—21no—
393C23×C4—1461no—
394C22×C8—731no—
395C22×C8—731no—
396C22×C8C22×D7311yescharacteristic
397C22×C8C22×D7311yescharacteristic
398#127—734no—
399#127—1462no—
400#125—734no—
401#125—1462no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—1462no—
405C4×D4—1462no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—1461no—
410C2×C4⋊C4—1461no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4C22×D7311yescharacteristic
416C2×C4⋊C4C22×D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1461no—
420C2×C22⋊C4—1461no—
421C2×C22⋊C4—1461no—
422C2×C22⋊C4—1461no—
423C2×C22⋊C4—1461no—
424C2×C42—21no—
425C2×C42—731no—
426C2×C42—731no—
427C2×C42—1461no—
428C2×C42C22×D7311yescharacteristic
429#102—22no—
430#102—734no—
431#102—734no—
432#102—734no—
433#102—1462no—
434#102—1462no—
435#102—1462no—
436#102C4×D7314yescomplemented
437#97—22no—
438#97—734no—
439#97—1462no—
440C4×C8—1462no—
441C4×C8—1462no—
442C4×C8—1462no—
443#95—21no—
444#95—731no—
445#95—731no—
446#95—731no—
447#95—731no—
448#95—1461no—
449#95—1461no—
450#95—1461no—
451#95—1461no—
452#95—1461no—
453C24—21no—
454C24—1461no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—5841no—
461C2×D4—5841no—
462C2×D4—5841no—
463C2×D4—5841no—
464C2×D4—732no—
465C2×D4—1464no—
466C2×D4—1464no—
467C2×D4—1461no—
468C2×D4—1461no—
469C2×D4—1461no—
470C2×D4—1461no—
471C2×D4—1461no—
472C2×D4C2×C4×D7312yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—2922no—
480C22×C4—5841no—
481C22×C4—5841no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—731no—
485C22×C4—731no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4D4×D7311yescharacteristic
490C22×C4D4×D7311yescharacteristic
491C22×C4C23×D7311yescharacteristic
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—732no—
497C2×C8—732no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8C2×C4×D7312yes—
503C2×C8#1192402812yes—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—5841no—
510C4⋊C4—5841no—
511C4⋊C4—5841no—
512C4⋊C4—5841no—
513C4⋊C4—732no—
514C4⋊C4—1464no—
515C4⋊C4—1464no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C4⋊C4—1461no—
521C4⋊C4C2×C4×D7312yes—
522C22⋊C4—42no—
523C22⋊C4—2922no—
524C22⋊C4—5841no—
525C22⋊C4—5841no—
526C22⋊C4—5841no—
527C22⋊C4—5841no—
528C42—81no—
529C42—5841no—
530C42—732no—
531C42—732no—
532C42—1461no—
533C42—1461no—
534C42#1192402712yes—
535C42#1192402812yes—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—2921no—
544C23—2921no—
545C23—2921no—
546C23—2921no—
547C23—2921no—
548C23—2921no—
549C23—1462no—
550C23C2×D4×D7311yescharacteristic
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—2921no—
556D4—2921no—
557D4—5844no—
558D4—5844no—
559D4—1462no—
560D4—1462no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—84no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—5844no—
584C2×C4—732no—
585C2×C4—732no—
586C2×C4—1461no—
587C2×C4—1461no—
588C2×C4—1461no—
589C2×C4—1461no—
590C2×C4—1461no—
591C2×C4—1461no—
592C2×C4—1462no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4#1455657712yes—
598C2×C4#1455657712yes—
599C2×C4C22×C4×D7311yescharacteristic
600C2×C4#41×D7311yescharacteristic
601C2×C4#41×D7311yescharacteristic
602C2×C4C2×#1192402711yescharacteristic
603C2×C4C2×#1192402811yescharacteristic
604C2×C4C2×#1192402811yescharacteristic
605C8—22no—
606C8—22no—
607C8—1462no—
608C8—1462no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—2922no—
617C22—2922no—
618C22—2922no—
619C22—5841no—
620C22—5841no—
621C22—5841no—
622C22—5841no—
623C22C4×D4×D7311yescharacteristic
624C22C2×#1455657711yescharacteristic
625C22#1798913411yescharacteristic
626C22#1798939111yescharacteristic
627C22#1798939111yescharacteristic
628C22#1798939611yescharacteristic
629C22#1798939711yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—2922no—
636C4—2921no—
637C4—2921no—
638C4—5841no—
639C4—5841no—
640C4—1462no—
641C4—1462no—
642C4C4×#1192402711yescharacteristic
643C4C4×#1192402811yescharacteristic
644C4#1798911511yescharacteristic
645C4#1798911711yescharacteristic
646C2—82no—
647C2—5842no—
648C2C4×#1455657711yescharacteristic
649C2#2261876011yescharacteristic
650C2#2261876211yescharacteristic
651C2#2262028111yescharacteristic
652C2#2262028811yescharacteristic
653C2#2262055711yescharacteristic
654C2#2262057911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1762C2
socleC23×C73C22×D4
prime radicalC2×#14556587C22
cosocleC22×C4×C73C24
hypercenter#1762D73
hypocenterC73#21652
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #22612668C2semidirect
4. #22610894C2semidirect
6. #22610629C2semidirect
7. #22610625C2semidirect
8. #22610616C2semidirect
9. #22610612C2semidirect
10. #22610063C2semidirect
11. #22609757C2semidirect
12. C4×#14556511C2semidirect
13. C4×#14556512C2semidirect
14. #22609619C2semidirect
15. C73×#1762C2semidirect
19. #17988950C4semidirect
69. #14556582C2×C4semidirect
90. #14556513C2×C4semidirect
92. #14556512C2×C4semidirect
94. #14556511C2×C4semidirect
96. #14556501C2×C4semidirect
122. #102×C73C2×C4semidirect
339. #1762D73semidirect
343. C73#21652semidirect
436. #102C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179889502
#226126682
#226126532
#226108942
#226107352
#226106292
#226106252
#226106162
#226106122
#226100632
#226097572
C4×#145565112
C4×#145565122
#226096192
C73×#17622
#2165273