Finite Group Databasebeta

← #33084581

Subgroups — #33084581

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988702C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic
3#22618699C211yesmaximal, characteristic
4#22618358C211yesmaximal, characteristic, complemented
5#22618357C211yesmaximal, characteristic, complemented
6#22609832C211yesmaximal, characteristic, complemented
7#22609811C211yesmaximal, characteristic, complemented
8#22609809C211yesmaximal, characteristic, complemented
9#22609778C211yesmaximal, characteristic, complemented
10#22609775C211yesmaximal, characteristic, complemented
11#22609774C211yesmaximal, characteristic, complemented
12#22609743C211yesmaximal, characteristic, complemented
13#22609740C211yesmaximal, characteristic, complemented
14#22609619C211yesmaximal, characteristic, complemented
15C73×#1765C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556599C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20#41×Dic73C2211yescharacteristic
21#17989055C2211yescharacteristic
22#17988702C418yescomplemented
23#17988701C418yescomplemented
24#17988679C412yescomplemented
25#17988678C412yescomplemented
26#17988672C412yescomplemented
27#17988667C412yescomplemented
28C2×#14556526C2211yescharacteristic
29C2×#14556526C2211yescharacteristic
30#17988623C2211yescharacteristic
31C2×#14556519C2211yescharacteristic
32C2×#14556518C2211yescharacteristic
33C2×#14556517C2211yescharacteristic
34#17988584C2211yescharacteristic
35#17988545—21no—
36#17988545C2211yescharacteristic
37#17988544—21no—
38#17988543C2211yescharacteristic
39#17988542—21no—
40#17988542C2211yescharacteristic
41#17988541—21no—
42M16×Dic73—21no—
43M16×Dic73C2211yescharacteristic
44M16×Dic73C2211yescharacteristic
45C4×#11924011—21no—
46C2×#14556501—21no—
47C2×#14556501C2211yescharacteristic
48C2×#14556501C2211yescharacteristic
49#97×D73—21no—
50C2×C4×#10596831C2211yescharacteristic
51C2×C8×Dic73C2211yescharacteristic
52C2×C8×Dic73C2211yescharacteristic
53#17988433C2211yescharacteristic
54#17988352C2211yescharacteristic
55#17988348C2211yescharacteristic
56#17988347C2211yescharacteristic
57#17988346C2211yescharacteristic
58C2×#131×C73C2211yescharacteristic
59C2×#104×C73C2211yescharacteristic
60#416×C73C2211yescharacteristic
61#405×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63#341×C73C2211yescharacteristic
64#339×C73C2211yescharacteristic
65C2×#11924028C2311yescharacteristic
66#14556611C2×C414yes—
67#14556611C2×C414yes—
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72#14556599—22no—
73#14556599C2×C414yescomplemented
74#14556598—22no—
75#14556598C2×C414yescomplemented
76#14556597—22no—
77#14556597C2×C414yescomplemented
78C2×#11924012—21no—
79C2×#11924012C2311yescharacteristic
80C2×#11924012C2311yescharacteristic
81C2×#11924011—21no—
82C2×#11924011—21no—
83C22×#10596831—21no—
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C2×C8×D73—21no—
87C2×C8×D73—21no—
88Q8×Dic73C2×C412yes—
89#14556556C2×C412yes—
90D4×Dic73—22no—
91D4×Dic73C2×C412yes—
92#14556553C2×C412yes—
93#14556551—22no—
94#14556550—21no—
95#14556550C2311yescharacteristic
96#14556548—21no—
97C2×C4×Dic73—21no—
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C42×D73—21no—
101#14556526C2×C414yescomplemented
102#14556526C2×C414yescomplemented
103#14556524C2×C412yes—
104#14556522C2×C412yes—
105#14556519C2×C414yescomplemented
106#14556518C2×C414yescomplemented
107#14556517C2×C414yescomplemented
108#14556516C2×C412yes—
109#14556513C2×C412yes—
110#14556502—21no—
111#14556501—21no—
112#14556501—22no—
113#14556501—21no—
114#14556501—21no—
115#14556501—21no—
116#14556501D411yescharacteristic
117#14556501D411yescharacteristic
118#14556501D411yescharacteristic
119#14556501D411yescharacteristic
120C4×#10596831—21no—
121C4×#10596831C2×C414yescomplemented
122C8×Dic73—21no—
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73C2×C412yes—
127C8×Dic73C2×C412yes—
128C8×Dic73C2×C414yescomplemented
129#14556498—22no—
130C2×#41×C73C2311yescharacteristic
131#131×C73—22no—
132#131×C73C2×C414yescomplemented
133C2×M16×C73—21no—
134C2×M16×C73C2311yescharacteristic
135C2×M16×C73C2311yescharacteristic
136C22×C8×C73—21no—
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139#117×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141#104×C73C2×C414yescomplemented
142#103×C73C2×C412yes—
143#102×C73C2×C412yes—
144#97×C73—21no—
145#97×C73—22no—
146C4×C8×C73—21no—
147#11924028—21no—
148#11924028—21no—
149#11924028C22×C412yes—
150#11924028C22×C412yes—
151C2×Dic146C22×C411yescharacteristic
152C2×D292C22×C411yescharacteristic
153C2×C22⋊D73—21no—
154C22×Dic73—21no—
155C22×Dic73—22no—
156C22×Dic73#4112yes—
157C2×C4×D73—21no—
158C2×C4×D73—22no—
159#11924018C4214yes—
160#11924016C4214yes—
161#11924015C4214yes—
162#11924013C4214yes—
163#11924012—21no—
164#11924012—21no—
165#11924012—24no—
166#11924012C22×C412yes—
167#11924012C22×C412yes—
168#11924011—24no—
169#11924011—24no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—24no—
173C2×#10596831C22×C411yescharacteristic
174C2×#10596831C22×C411yescharacteristic
175C2×#10596831C22×C412yes—
176C2×#10596831C22×C412yes—
177C2×#10596831C22×C412yes—
178C2×#10596831C2×D411yescharacteristic
179C2×#10596831C2×D411yescharacteristic
180C2×#10596831#4112yes—
181C8×D73—24no—
182C8×D73—24no—
183C4⋊Dic73—22no—
184C4⋊Dic73C22×C412yes—
185#11924007—22no—
186C22⋊Dic73—21no—
187C22⋊Dic73—22no—
188#11924005—22no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—22no—
192C4×Dic73—22no—
193C4×Dic73C22×C412yes—
194C4×Dic73C22×C412yes—
195C4×Dic73C2×D411yescharacteristic
196C4×Dic73C2×D411yescharacteristic
197#41×C73—21no—
198#41×C73—21no—
199#41×C73C22×C412yes—
200#41×C73C22×C412yes—
201C2×Q8×C73C22×C411yescharacteristic
202C2×D4×C73—21no—
203C2×D4×C73C22×C411yescharacteristic
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73C2411yescharacteristic
207M16×C73—21no—
208M16×C73—21no—
209M16×C73—24no—
210M16×C73C22×C412yes—
211M16×C73C22×C412yes—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—24no—
217C2×C8×C73C22×C412yes—
218C2×C8×C73C22×C412yes—
219C2×C8×C73C2×D411yescharacteristic
220C2×C8×C73C2×D411yescharacteristic
221C2×C8×C73#4112yes—
222C4⋊C4×C73C22×C412yes—
223C22⋊C4×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73C22×C412yes—
227C23×C73—21no—
228C23×C73C2×#4111yescharacteristic
229C22×D73—21no—
230Q8×C73—21no—
231Q8×C73C2×C4212yes—
232D4×C73—22no—
233D4×C73—22no—
234D4×C73—21no—
235D4×C73C2×C4212yes—
236C2×C4×C73—21no—
237C2×C4×C73—22no—
238C2×C4×C73—22no—
239C2×C4×C73—22no—
240C2×C4×C73—22no—
241C2×C4×C73—42no—
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C23×C411yescharacteristic
244C2×C4×C73C23×C411yescharacteristic
245C2×C4×C73C22×D411yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C22⋊D73—22no—
249C22⋊D73—22no—
250C2×Dic73—21no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—42no—
254C2×Dic73—42no—
255C2×Dic73—82no—
256C2×Dic73C4×D412yes—
257C2×Dic73C4×D412yes—
258D292—21no—
259D292C2×C4212yes—
260C4×D73—22no—
261C4×D73—22no—
262C4×D73—82no—
263Dic146—21no—
264Dic146C2×C4212yes—
265C8×C73—22no—
266C8×C73—22no—
267C8×C73—22no—
268C8×C73C4×D412yes—
269C8×C73C4×D412yes—
270#10596831—22no—
271#10596831—22no—
272#10596831C2×C4212yes—
273#10596831C2×C4212yes—
274#10596831C4×D412yes—
275#10596831C4×D412yes—
276C22×C73—22no—
277C22×C73—22no—
278C22×C73—42no—
279C22×C73C2×C4×D411yescharacteristic
280C22×C73C4×#4111yescharacteristic
281C22×C73C4×#4111yescharacteristic
282C2×D73—22no—
283C2×D73—42no—
284C4×C73—22no—
285C4×C73—42no—
286C4×C73—42no—
287C4×C73C22×C4211yescharacteristic
288C4×C73C2×C4×D411yescharacteristic
289C4×C73C2×C4×D411yescharacteristic
290C4×C73C4×#4111yescharacteristic
291Dic73—22no—
292Dic73—22no—
293Dic73—22no—
294Dic73—42no—
295Dic73—42no—
296#20514—731nomaximal, Sylow
297C2×C73—21no—
298C2×C73—21no—
299C2×C73—42no—
300C2×C73C42×D411yescharacteristic
301C2×C73#295712yes—
302D73—42no—
303C2×#443—731no—
304C2×#443—731no—
305C4×#135—731no—
306#2875—731no—
307#2875—731no—
308C4×#108—731no—
309#1772—731no—
310#1772—731no—
311#1765—731no—
312#1765—731no—
313#1765—731no—
314#1765D7311yescharacteristic, complemented
315#1759—731no—
316#1759—731no—
317#1726—731no—
318C73#2051411yescharacteristic, complemented, Sylow
319C2×#135—731no—
320C2×#131—731no—
321C2×#131—731no—
322C2×#131—731no—
323C2×#131C2×D7311yescharacteristic
324C4×#41—731no—
325C4×#41—731no—
326#443—738no—
327#443—738no—
328C4×Q16—732no—
329C4×SD16—732no—
330C4×SD16—732no—
331C4×D8—732no—
332C2×#108—731no—
333C2×#108—731no—
334#427—731no—
335C2×#104—731no—
336C2×#104—731no—
337C2×#104—731no—
338C2×#104C2×D7311yescharacteristic
339#416—731no—
340#416C2×D7311yescharacteristic
341#405—731no—
342#405—731no—
343#405—731no—
344#405—1461no—
345#405—1461no—
346#405—1461no—
347#405—1461no—
348#405C2×D7311yescharacteristic
349C4×M16—731no—
350C4×M16—731no—
351C4×M16—1461no—
352C4×M16—1461no—
353C2×#97—731no—
354C2×#97—731no—
355C2×#97—1461no—
356C2×#97—1461no—
357C2×#97C2×D7311yescharacteristic
358C2×C4×C8—731no—
359C2×C4×C8—731no—
360C2×C4×C8—731no—
361#376—731no—
362#341—731no—
363#341C2×D7311yescharacteristic
364#339—731no—
365#339—731no—
366#339—731no—
367#339C2×D7311yescharacteristic
368C2×#41—731no—
369C2×#41C22×D7311yescharacteristic
370#135—734no—
371#135—734no—
372C2×Q16—731no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×D8—731no—
376#131—22no—
377#131—734no—
378#131—734no—
379#131—734no—
380#131—1462no—
381#131—1462no—
382#131—1462no—
383#131C4×D7314yescomplemented
384C2×M16—21no—
385C2×M16—731no—
386C2×M16—731no—
387C2×M16—1461no—
388C2×M16—1461no—
389C2×M16—1461no—
390C2×M16C22×D7311yescharacteristic
391C2×M16C22×D7311yescharacteristic
392C22×C8—21no—
393C22×C8—731no—
394C22×C8—731no—
395C22×C8—1461no—
396C22×C8—1461no—
397C22×C8—1461no—
398C22×C8C22×D7311yescharacteristic
399C22×C8C22×D7311yescharacteristic
400C4×Q8—732no—
401C4×Q8—732no—
402C4×D4—732no—
403C4×D4—732no—
404C4×D4—1462no—
405C4×D4—1462no—
406#117—731no—
407#117—1461no—
408#117—1461no—
409#117C22×D7311yescharacteristic
410C2×C42—731no—
411C2×C42—731no—
412C2×C42—1461no—
413C2×C42—1461no—
414C2×C42C22×D7311yescharacteristic
415#108—734no—
416#108—734no—
417#107—732no—
418#106—732no—
419#104—734no—
420#104—734no—
421#104—734no—
422#104C4×D7314yescomplemented
423#103—732no—
424#103C4×D7312yes—
425#102—732no—
426#102C4×D7312yes—
427#97—21no—
428#97—22no—
429#97—731no—
430#97—731no—
431#97—731no—
432#97—731no—
433#97—1461no—
434#97—1461no—
435#97—1461no—
436#97—1462no—
437#97—1461no—
438#97—1461no—
439C4×C8—21no—
440C4×C8—732no—
441C4×C8—732no—
442C4×C8—734no—
443C4×C8—734no—
444C4×C8—1461no—
445C4×C8—1461no—
446C4×C8—1461no—
447C4×C8—1461no—
448C4×C8—1461no—
449#95—1462no—
450#41—21no—
451#41—21no—
452#41—732no—
453#41—732no—
454#41—1461no—
455#41—1461no—
456#41C2×C4×D7312yes—
457#41C2×C4×D7312yes—
458C2×Q8—731no—
459C2×Q8C2×C4×D7311yescharacteristic
460C2×D4—21no—
461C2×D4—731no—
462C2×D4—1461no—
463C2×D4C2×C4×D7311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—732no—
467C22×C4—1462no—
468C22×C4—1461no—
469C22×C4—1462no—
470C22×C4—1461no—
471C22×C4C23×D7311yescharacteristic
472Q16—734no—
473SD16—734no—
474SD16—734no—
475D8—734no—
476M16—21no—
477M16—21no—
478M16—24no—
479M16—732no—
480M16—732no—
481M16—1464no—
482M16—1464no—
483M16—1461no—
484M16—1461no—
485M16—1464no—
486M16C2×C4×D7312yes—
487M16C2×C4×D7312yes—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—24no—
493C2×C8—731no—
494C2×C8—731no—
495C2×C8—732no—
496C2×C8—732no—
497C2×C8—732no—
498C2×C8—731no—
499C2×C8—731no—
500C2×C8—732no—
501C2×C8—1464no—
502C2×C8—1464no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1464no—
506C2×C8C2×C4×D7312yes—
507C2×C8C2×C4×D7312yes—
508C2×C8D4×D7311yescharacteristic
509C2×C8D4×D7311yescharacteristic
510C2×C8#1192402712yes—
511C4⋊C4—732no—
512C4⋊C4—1462no—
513C4⋊C4—1462no—
514C4⋊C4C2×C4×D7312yes—
515C22⋊C4—21no—
516C22⋊C4—1462no—
517C22⋊C4—1462no—
518C22⋊C4—1461no—
519C42—21no—
520C42—21no—
521C42—732no—
522C42—731no—
523C42—731no—
524C42—732no—
525C42—1462no—
526C42—1462no—
527C42—1461no—
528C42—1461no—
529C42C2×C4×D7312yes—
530C23—21no—
531C23—1461no—
532C23#41×D7311yescharacteristic
533Q8—21no—
534Q8—732no—
535Q8—1461no—
536Q8C42×D7312yes—
537D4—22no—
538D4—22no—
539D4—21no—
540D4—732no—
541D4—1462no—
542D4—1462no—
543D4—1461no—
544D4C42×D7312yes—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—42no—
551C2×C4—2922no—
552C2×C4—2922no—
553C2×C4—5842no—
554C2×C4—5842no—
555C2×C4—732no—
556C2×C4—732no—
557C2×C4—1462no—
558C2×C4—1462no—
559C2×C4—1461no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4C22×C4×D7311yescharacteristic
563C2×C4C22×C4×D7311yescharacteristic
564C2×C4C22×C4×D7311yescharacteristic
565C2×C4C2×D4×D7311yescharacteristic
566C2×C4#41×D7311yescharacteristic
567C2×C4C2×#1192402711yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—732no—
572C8—732no—
573C8—732no—
574C8—732no—
575C8—1462no—
576C8—1462no—
577C8#1455655112yes—
578C8#1455655112yes—
579C22—22no—
580C22—22no—
581C22—42no—
582C22—2922no—
583C22—1462no—
584C22C4×D4×D7311yescharacteristic
585C22C4×#1192402711yescharacteristic
586C22#1798905511yescharacteristic
587C4—22no—
588C4—42no—
589C4—42no—
590C4—2922no—
591C4—2922no—
592C4—1462no—
593C4—1462no—
594C4—1462no—
595C4C2×C42×D7311yescharacteristic
596C4C4×D4×D7311yescharacteristic
597C4C2×#1455655111yescharacteristic
598C4C4×#1192402711yescharacteristic
599C2—21no—
600C2—21no—
601C2—42no—
602C2—2922no—
603C2C4×#1455655111yescharacteristic
604C2#2261884512yes—
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC4×C73C22×C42
FrattiniC22×C4C23×D73
FittingC73×#1765C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556611C22
cosocleC22×C4×C73C24
hypercenter#1765D73
hypocenterC73#20514
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
4. #22618358C2semidirect
5. #22618357C2semidirect
6. #22609832C2semidirect
7. #22609811C2semidirect
8. #22609809C2semidirect
9. #22609778C2semidirect
10. #22609775C2semidirect
11. #22609774C2semidirect
12. #22609743C2semidirect
13. #22609740C2semidirect
14. #22609619C2semidirect
15. C73×#1765C2semidirect
22. #17988702C4semidirect
23. #17988701C4semidirect
24. #17988679C4semidirect
25. #17988678C4semidirect
26. #17988672C4semidirect
27. #17988667C4semidirect
73. #14556599C2×C4semidirect
75. #14556598C2×C4semidirect
77. #14556597C2×C4semidirect
101. #14556526C2×C4semidirect
102. #14556526C2×C4semidirect
105. #14556519C2×C4semidirect
106. #14556518C2×C4semidirect
107. #14556517C2×C4semidirect
121. C4×#10596831C2×C4semidirect
128. C8×Dic73C2×C4semidirect
132. #131×C73C2×C4semidirect
141. #104×C73C2×C4semidirect
314. #1765D73semidirect
318. C73#20514semidirect
383. #131C4×D73semidirect
422. #104C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179887022
C2×#179887012
#226186992
#226183582
#226183572
#226098322
#226098112
#226098092
#226097782
#226097752
#226097742
#226097432
#226097402
#226096192
C73×#17652
#2051473