Finite Group Databasebeta

← #33056123

Subgroups — #33056123

Order 18688.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619937C211yesmaximal, characteristic
2#22619022C211yesmaximal, characteristic, complemented
3#22618952C211yesmaximal, characteristic
4#22608789C211yesmaximal, characteristic, complemented
5#22608787C211yesmaximal, characteristic, complemented
6#22608770C211yesmaximal, characteristic, complemented
7#22608764C211yesmaximal, characteristic, complemented
8#22608745C211yesmaximal, characteristic, complemented
9C8×#11924015C211yesmaximal, characteristic, complemented
10C8×#11924016C211yesmaximal, characteristic, complemented
11#22608710C211yesmaximal, characteristic, complemented
12#22608372C211yesmaximal, characteristic
13#22608350C211yesmaximal, characteristic, complemented
14#22608227C211yesmaximal, characteristic, complemented
15C73×SD16⋊C8C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×D4×D73C2211yescharacteristic
18#17988919C411yescharacteristic
19#17988916C411yescharacteristic
20#17988876C411yescharacteristic
21#17988875C411yescharacteristic
22#17988791C411yescharacteristic
23#17988790C411yescharacteristic
24#17988739C411yescharacteristic
25#17988736C411yescharacteristic
26#17988718C2211yescharacteristic, complemented
27#17988717—21no—
28#17988716—21no—
29#17988714C2211yescharacteristic, complemented
30C8×Dic146C2211yescharacteristic, complemented
31C4×#11924017C2211yescharacteristic
32C4×#11924015C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C8×D292C2211yescharacteristic
35D4×#10596831C2211yescharacteristic
36#17988652C2211yescharacteristic
37C8×C22⋊D73—21no—
38#17988650—21no—
39#17988647—21no—
40#17988646—21no—
41#17988643C2211yescharacteristic
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45C2×#14556503—21no—
46C22⋊C8×D73—21no—
47C4×#11924011C2211yescharacteristic
48#17988340C2211yescharacteristic, complemented
49#17988337C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988319C2211yescharacteristic, complemented
52Q8⋊#10596831C2211yescharacteristic, complemented
53#17988317C2211yescharacteristic, complemented
54#17988316C2211yescharacteristic
55D4⋊#10596831C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic, complemented
58#17988309C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C8×Q8×C73C2211yescharacteristic, complemented
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic, complemented
67C2×D4×D73C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924017C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924015C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76#14556590C2×C411yescharacteristic
77#14556589C2×C411yescharacteristic
78#14556581—21no—
79#14556571C2×C411yescharacteristic
80#14556569—21no—
81#14556567C2×C411yescharacteristic
82C4×Dic146—21no—
83C4×Dic146C2311yescharacteristic
84C4×D292C2311yescharacteristic
85D4×Dic73C2×C411yescharacteristic
86#14556553C2×C411yescharacteristic
87C4×C22⋊D73—21no—
88#14556551—21no—
89#14556548—21no—
90C4⋊C4×D73C2×C411yescharacteristic
91C22⋊C4×D73—21no—
92C42×D73C2311yescharacteristic
93#14556523C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95#14556522C2×C411yescharacteristic
96C4⋊#10596831—21no—
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520C2×C411yescharacteristic
102#14556520C2×C411yescharacteristic
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556516C2×C411yescharacteristic
106#14556515C2×C411yescharacteristic
107#14556514C2×C411yescharacteristic
108#14556513C2×C411yescharacteristic
109#14556512C2×C411yescharacteristic
110#14556511C2×C411yescharacteristic
111C22⋊#10596831—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503C2×C411yescharacteristic
117#14556503C2×C411yescharacteristic
118#14556503D411yescharacteristic
119#14556503D411yescharacteristic
120#14556502—21no—
121#14556501—21no—
122#14556501—21no—
123#14556501—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×SD16×C73C2×C411yescharacteristic
130C22×C8×C73—21no—
131C4×Q8×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133#106×C73C2×C411yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139C22⋊C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×Dic146—21no—
146C2×Dic146C22×C411yescharacteristic
147C2×D292C22×C411yescharacteristic
148C2×C22⋊D73—21no—
149D4×D73—22no—
150D4×D73—22no—
151C22×Dic73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157C2×C4×D73C22×C411yescharacteristic
158C2×C4×D73C2×D411yescharacteristic
159C2×C4×D73#4111yescharacteristic
160#11924017—22no—
161#11924016—22no—
162#11924015—22no—
163#11924011—42no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—81no—
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C2×D411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C8×D73—81no—
173C8×D73—81no—
174C4⋊Dic73—21no—
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188C4×Dic73—21no—
189C4×Dic73C22×C411yescharacteristic
190C4×Dic73C2×D411yescharacteristic
191C4×Dic73#4111yescharacteristic
192C2×Q8×C73C22×C411yescharacteristic
193C2×D4×C73C22×C411yescharacteristic
194C22×C4×C73—21no—
195SD16×C73—22no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—81no—
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C4⋊C4×C73—21no—
205C4⋊C4×C73C22×C411yescharacteristic
206C4⋊C4×C73C22×C411yescharacteristic
207C22⋊C4×C73—21no—
208C42×C73—21no—
209C42×C73C2411yescharacteristic
210C23×C73—21no—
211C22×D73—21no—
212C22×D73—24no—
213C22×D73—81no—
214C22×D73—81no—
215C22×D73C4×D411yescharacteristic
216Q8×C73—21no—
217Q8×C73—21no—
218D4×C73—21no—
219D4×C73#13112yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73C23×C411yescharacteristic
226C2×C4×C73C22×D411yescharacteristic
227C2×C4×C73C2×#4111yescharacteristic
228C22⋊D73—24no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—81no—
233C2×Dic73C4×D411yescharacteristic
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236D292—21no—
237D292#13112yes—
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—21no—
242C4×D73—41no—
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—81no—
246C4×D73—81no—
247Dic146—21no—
248Dic146—21no—
249Dic146—81no—
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73—21no—
254C8×C73—41no—
255C8×C73—41no—
256C8×C73—41no—
257#10596831—22no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—21no—
262#10596831—41no—
263#10596831—41no—
264C22×C73—22no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73C2×C4×D411yescharacteristic
268C2×D73—21no—
269C2×D73—22no—
270C2×D73—21no—
271C2×D73—21no—
272C2×D73—41no—
273C2×D73—41no—
274C2×D73—84no—
275C4×C73—21no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73C2×#13111yescharacteristic
280C4×C73C2×#13111yescharacteristic
281C4×C73#57711yescharacteristic
282C4×C73#57711yescharacteristic
283Dic73—21no—
284Dic73—21no—
285Dic73—21no—
286Dic73—41no—
287Dic73—41no—
288Dic73—41no—
289#17924—731nomaximal, Sylow
290C2×C73—42no—
291C2×C73#292911yescharacteristic
292C2×C73#294911yescharacteristic
293C2×C73#295611yescharacteristic
294D73—41no—
295D73—42no—
296#3101—731no—
297#2985—731no—
298#2972—731no—
299#1585—731no—
300#1585—731no—
301#1582—731no—
302#1582—731no—
303SD16⋊C8—731no—
304SD16⋊C8D7311yescharacteristic, complemented
305C8×SD16—731no—
306C8×SD16—731no—
307#1572—731no—
308#1490—731no—
309#1485—731no—
310#1453—731no—
311C73#1792411yescharacteristic, complemented, Sylow
312#533—731no—
313C2×C4×D4—731no—
314#483—731no—
315#483—731no—
316#476—731no—
317#476—731no—
318#461—731no—
319#461—731no—
320#450—731no—
321#450—731no—
322#446—731no—
323#446—731no—
324#446—1461no—
325#446—1461no—
326C8×Q8—731no—
327C8×Q8C2×D7311yescharacteristic, complemented
328C4×SD16—731no—
329C4×SD16—731no—
330C4×SD16—731no—
331C4×SD16C2×D7311yescharacteristic
332C8×D4—731no—
333C8×D4—731no—
334C8×D4—731no—
335C8×D4—1461no—
336C8×D4—1461no—
337C8×D4C2×D7311yescharacteristic
338#433—1461no—
339#433—1461no—
340#432—731no—
341#431—731no—
342#431—731no—
343#431—731no—
344C2×C22⋊C8—1461no—
345C2×C22⋊C8—1461no—
346C4×M16—731no—
347#335—731no—
348#335C2×D7311yescharacteristic, complemented
349#334—731no—
350#334—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353Q8⋊C8—731no—
354Q8⋊C8C2×D7311yescharacteristic, complemented
355D4⋊C8—731no—
356D4⋊C8—731no—
357D4⋊C8—731no—
358D4⋊C8C2×D7311yescharacteristic
359#322—731no—
360#322—731no—
361#322C2×D7311yescharacteristic, complemented
362C82—731no—
363C22×D4—731no—
364C23×C4—1461no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×SD16—731no—
368C2×SD16C4×D7311yescharacteristic
369C2×M16—1461no—
370C22×C8—21no—
371C22×C8—1461no—
372C22×C8—1461no—
373C22×C8—1461no—
374C4⋊Q8—731no—
375C4⋊Q8—731no—
376#125—1461no—
377C22⋊Q8—731no—
378C22⋊Q8—731no—
379C22⋊Q8—1461no—
380C4×Q8—731no—
381C4×Q8—1461no—
382C4×Q8C22×D7311yescharacteristic
383C4×D4—731no—
384C4×D4—731no—
385C4×D4—731no—
386C4×D4—1461no—
387C4×D4—1461no—
388C4×D4C22×D7311yescharacteristic
389#117—1461no—
390C2×C4⋊C4—731no—
391C2×C22⋊C4—1461no—
392C2×C42—731no—
393#106—731no—
394#106—731no—
395#106—731no—
396#106C4×D7311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—731no—
402C4⋊C8—731no—
403C4⋊C8—731no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8—1461no—
407C4⋊C8C22×D7311yescharacteristic
408C4⋊C8C22×D7311yescharacteristic
409#103—731no—
410#103—731no—
411#103—731no—
412#103C4×D7311yescharacteristic
413#102—731no—
414#102—731no—
415#102—731no—
416#102C4×D7311yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—731no—
421C22⋊C8—731no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427#97—1461no—
428#97—1461no—
429#97—1461no—
430#97—1461no—
431C4×C8—21no—
432C4×C8—731no—
433C4×C8—731no—
434C4×C8—731no—
435C4×C8—1461no—
436C4×C8—1461no—
437C4×C8C22×D7311yescharacteristic
438C4×C8C22×D7311yescharacteristic
439C4×C8C22×D7311yescharacteristic
440C24—1461no—
441C2×Q8—731no—
442C2×Q8—1461no—
443C2×Q8C2×C4×D7311yescharacteristic
444C2×D4—731no—
445C2×D4—1461no—
446C2×D4—1462no—
447C2×D4—1462no—
448C2×D4C2×C4×D7311yescharacteristic
449C22×C4—21no—
450C22×C4—5841no—
451C22×C4—5841no—
452C22×C4—731no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459SD16—22no—
460SD16—1462no—
461SD16—1462no—
462SD16—1462no—
463M16—2922no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—5841no—
469C2×C8—5841no—
470C2×C8—5841no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—731no—
474C2×C8—731no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8C2×C4×D7311yescharacteristic
479C2×C8C2×C4×D7311yescharacteristic
480C2×C8D4×D7311yescharacteristic
481C2×C8D4×D7311yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—731no—
484C4⋊C4—731no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C4⋊C4—1461no—
492C4⋊C4C2×C4×D7311yescharacteristic
493C4⋊C4C2×C4×D7311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—1461no—
496C22⋊C4—1461no—
497C22⋊C4—1461no—
498C22⋊C4—1461no—
499C22⋊C4—1461no—
500C42—21no—
501C42—731no—
502C42—731no—
503C42—731no—
504C42—1461no—
505C42C23×D7311yescharacteristic
506C23—21no—
507C23—5841no—
508C23—5841no—
509C23—731no—
510C23—1464no—
511C23—1461no—
512Q8—21no—
513Q8—21no—
514Q8—5841no—
515Q8—1461no—
516Q8—1461no—
517D4—21no—
518D4—732no—
519D4—1464no—
520D4—1461no—
521D4#1455659712yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—5841no—
531C2×C4—5841no—
532C2×C4—5841no—
533C2×C4—731no—
534C2×C4—731no—
535C2×C4—731no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4C22×C4×D7311yescharacteristic
544C2×C4C2×D4×D7311yescharacteristic
545C2×C4#41×D7311yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—2921no—
554C8—2921no—
555C8—1462no—
556C8—1461no—
557C8—1461no—
558C8—1461no—
559C8—1461no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—2921no—
564C22—2921no—
565C22—5844no—
566C22—1461no—
567C22—1461no—
568C22—1461no—
569C22—1462no—
570C22C4×D4×D7311yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—2921no—
576C4—2921no—
577C4—2921no—
578C4—1461no—
579C4—1461no—
580C4—1461no—
581C4#131×D7311yescharacteristic
582C4C2×#1455659711yescharacteristic
583C4#1798939611yescharacteristic
584C4#1798939711yescharacteristic
585C2—42no—
586C2—2922no—
587C2—2921no—
588C2#2261862011yescharacteristic
589C2#2261878711yescharacteristic
590C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×SD16⋊C8C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenterSD16⋊C8D73
hypocenterC73#17924
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #22619022C2semidirect
4. #22608789C2semidirect
5. #22608787C2semidirect
6. #22608770C2semidirect
7. #22608764C2semidirect
8. #22608745C2semidirect
9. C8×#11924015C2semidirect
10. C8×#11924016C2semidirect
11. #22608710C2semidirect
13. #22608350C2semidirect
14. #22608227C2semidirect
15. C73×SD16⋊C8C2semidirect
26. #17988718C22semidirect
29. #17988714C22semidirect
30. C8×Dic146C22semidirect
48. #17988340C22semidirect
49. #17988337C22semidirect
50. #17988337C22semidirect
51. #17988319C22semidirect
52. Q8⋊#10596831C22semidirect
53. #17988317C22semidirect
57. #17988309C22semidirect
58. #17988309C22semidirect
59. C8×#10596831C22semidirect
60. C8×Q8×C73C22semidirect
63. #335×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
66. #322×C73C22semidirect
304. SD16⋊C8D73semidirect
311. C73#17924semidirect
327. C8×Q8C2×D73semidirect
348. #335C2×D73semidirect
354. Q8⋊C8C2×D73semidirect
361. #322C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199372
#226190222
#226189522
#226087892
#226087872
#226087702
#226087642
#226087452
C8×#119240152
C8×#119240162
#226087102
#226083722
#226083502
#226082272
C73×SD16⋊C82
#1792473