Finite Group Databasebeta

← #33055430

Subgroups — #33055430

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619038C211yesmaximal, characteristic
2#22619010C211yesmaximal, characteristic, complemented
3C4×#14556620C211yesmaximal, characteristic
4#22608751C211yesmaximal, characteristic, complemented
5#22608747C211yesmaximal, characteristic, complemented
6#22608740C211yesmaximal, characteristic, complemented
7#22608737C211yesmaximal, characteristic, complemented
8C8×#11924018C211yesmaximal, characteristic, complemented
9SD16×#10596831C211yesmaximal, characteristic, complemented
10C8×#11924016C211yesmaximal, characteristic, complemented
11#22608682C211yesmaximal, characteristic, complemented
12#22608310C211yesmaximal, characteristic
13Q8⋊C8×D73C211yesmaximal, characteristic, complemented
14#22608210C211yesmaximal, characteristic, complemented
15C73×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#14556620C411yescharacteristic
17C4×#11924027C2211yescharacteristic
18C4×Q8×D73C2211yescharacteristic
19Q8×#10596831C2211yescharacteristic
20C8×Dic146—21no—
21C8×Dic146C2211yescharacteristic
22C8×Dic146C2211yescharacteristic
23#17988711—21no—
24#17988711C2211yescharacteristic
25#17988711C2211yescharacteristic
26#17988693C411yescharacteristic
27#17988691C411yescharacteristic
28#17988688C411yescharacteristic
29#17988684C411yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924018C2211yescharacteristic
32C4×#11924016C2211yescharacteristic
33D4×#10596831C2211yescharacteristic
34C8×C22⋊D73—21no—
35#17988650—21no—
36#17988639—21no—
37#17988639C2211yescharacteristic
38#17988638—21no—
39#17988638C2211yescharacteristic
40#17988637—21no—
41#17988626C411yescharacteristic
42C2×#14556520—21no—
43C4⋊C8×D73C2211yescharacteristic
44#17988594C411yescharacteristic
45#17988585C411yescharacteristic
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988338C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988317C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58C8×#10596831C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924027C2×C411yescharacteristic
68C2×Q8×D73C2×C411yescharacteristic
69#14556620C818yescomplemented
70C2×Dic292C2×C411yescharacteristic
71C2×#11924018C2×C411yescharacteristic
72C2×#11924016C2×C411yescharacteristic
73C2×#11924011C2×C411yescharacteristic
74C2×#11924011C2×C411yescharacteristic
75C22×#10596831—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78Q8×Dic73C2×C411yescharacteristic
79C4×Dic146—21no—
80C4×Dic146C2311yescharacteristic
81C4×Dic146C2311yescharacteristic
82#14556556—21no—
83#14556556C2×C411yescharacteristic
84#14556556C2×C411yescharacteristic
85D4×Dic73C2×C411yescharacteristic
86C4×C22⋊D73—21no—
87#14556551—21no—
88#14556549C2×C411yescharacteristic
89#14556547—21no—
90C4⋊C4×D73—21no—
91C4⋊C4×D73C2×C411yescharacteristic
92C2×C4×Dic73—21no—
93C42×D73—21no—
94C42×D73C2311yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520D411yescharacteristic
107#14556520D411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556515C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556514C2×C411yescharacteristic
113#14556512C2×C411yescharacteristic
114C22⋊#10596831—21no—
115#14556503—21no—
116#14556503D411yescharacteristic
117#14556503D411yescharacteristic
118#14556501C2×C411yescharacteristic
119#14556501C2×C411yescharacteristic
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C8×Dic73—21no—
130C2×SD16×C73C2×C411yescharacteristic
131C22×C8×C73—21no—
132C4×Q8×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#106×C73C2×C411yescharacteristic
135C4⋊C8×C73—21no—
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#103×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924027—22no—
146#11924027C2×C814yes—
147C2×Dic146—21no—
148C2×Dic146C22×C411yescharacteristic
149C2×Dic146C22×C411yescharacteristic
150Q8×D73—22no—
151Q8×D73C2×C814yescomplemented
152C2×C22⋊D73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73C22×C411yescharacteristic
158C2×C4×D73C2×D411yescharacteristic
159C2×C4×D73#4111yescharacteristic
160Dic292C2×C814yescomplemented
161#11924018C2×C814yescomplemented
162#11924016C2×C814yescomplemented
163#11924011—22no—
164#11924011C2×C814yescomplemented
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—81no—
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C2×D411yescharacteristic
172C2×#10596831C2×D411yescharacteristic
173C8×D73—42no—
174C8×D73—81no—
175C4⋊Dic73—21no—
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182#11924007—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73C22×C411yescharacteristic
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73#4111yescharacteristic
194C2×Q8×C73C22×C411yescharacteristic
195C2×D4×C73C22×C411yescharacteristic
196C22×C4×C73—21no—
197SD16×C73C2×C814yescomplemented
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—81no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C2×C8×C73C2×D411yescharacteristic
206C4⋊C4×C73—21no—
207C4⋊C4×C73C22×C411yescharacteristic
208C4⋊C4×C73C22×C411yescharacteristic
209C22⋊C4×C73—21no—
210C42×C73—21no—
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C22×D73C4×D411yescharacteristic
214Q8×C73—21no—
215Q8×C73C22×C812yes—
216D4×C73—21no—
217D4×C73C22×C812yes—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73C23×C411yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C73C2×#4111yescharacteristic
226C22⋊D73—24no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—24no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—81no—
233C2×Dic73C4×D411yescharacteristic
234C2×Dic73C4×D411yescharacteristic
235C2×Dic73C4×D411yescharacteristic
236C4×D73—24no—
237C4×D73—21no—
238C4×D73—21no—
239C4×D73—41no—
240C4×D73—81no—
241C4×D73C22×C812yes—
242C4×D73#13112yes—
243Dic146—21no—
244Dic146—21no—
245Dic146—24no—
246Dic146C22×C812yes—
247Dic146C22×C812yes—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73C22×C812yes—
255#10596831—22no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—41no—
260#10596831—41no—
261#10596831C22×C812yes—
262C22×C73—22no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73C2×C4×D411yescharacteristic
266C2×D73—21no—
267C2×D73—21no—
268C2×D73C8×D412yes—
269C4×C73—22no—
270C4×C73—21no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73C23×C811yescharacteristic
274C4×C73C2×#13111yescharacteristic
275C4×C73#57711yescharacteristic
276C4×C73#57811yescharacteristic
277Dic73—22no—
278Dic73—22no—
279Dic73—21no—
280Dic73—21no—
281Dic73—41no—
282Dic73—41no—
283Dic73C8×D412yes—
284#17853—731nomaximal, Sylow
285C2×C73—42no—
286C2×C73C2×C8×D411yescharacteristic
287C2×C73#294711yescharacteristic
288C2×C73#295611yescharacteristic
289D73—22no—
290#2988—731no—
291#2982—731no—
292C4×#137—731no—
293#1579—731no—
294#1579—731no—
295SD16⋊C8—731no—
296SD16⋊C8D7311yescharacteristic, complemented
297C8×Q16—731no—
298C8×Q16—731no—
299C8×SD16—731no—
300C8×SD16—731no—
301#1565—731no—
302#1476—731no—
303C2×Q8⋊C8—731no—
304C8×M16—731no—
305C73#1785311yescharacteristic, complemented, Sylow
306C2×#137—731no—
307C4×#41—731no—
308C2×C4×Q8—731no—
309C8×Q8—731no—
310C8×Q8—731no—
311C8×Q8—731no—
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8—1461no—
315C8×Q8—1461no—
316C8×Q8C2×D7311yescharacteristic
317#441—731no—
318#441—731no—
319#440—731no—
320#440—731no—
321C4×Q16—731no—
322C4×Q16—731no—
323C4×SD16—731no—
324C4×SD16C2×D7311yescharacteristic
325C8×D4—731no—
326C8×D4—1461no—
327C8×D4—1461no—
328C8×D4C2×D7311yescharacteristic
329#431—731no—
330#431—731no—
331#431—1461no—
332#431—1461no—
333#431—1461no—
334#428—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—1461no—
337#419—731no—
338#417—731no—
339C4×M16—731no—
340C2×C4×C8—731no—
341#335—731no—
342#335C2×D7311yescharacteristic
343#334—731no—
344#334—731no—
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349Q8⋊C8—731no—
350Q8⋊C8C2×D7311yescharacteristic
351D4⋊C8—731no—
352D4⋊C8C2×D7311yescharacteristic
353#322—731no—
354#322C2×D7311yescharacteristic
355C82—731no—
356C82—731no—
357C2×#41—731no—
358C22×Q8—731no—
359#137—738no—
360C2×Q16—731no—
361C2×Q16—731no—
362C2×SD16—731no—
363C2×SD16C4×D7311yescharacteristic
364C2×M16—731no—
365C2×M16—731no—
366C22×C8—21no—
367C22×C8—1461no—
368C22×C8—1461no—
369C22×C8—1461no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—731no—
373C4×Q8—731no—
374C4×Q8—731no—
375C4×Q8—1461no—
376C4×Q8—1461no—
377C4×Q8C22×D7311yescharacteristic
378C4×D4—731no—
379C4×D4—1461no—
380C4×D4—1461no—
381C4×D4C22×D7311yescharacteristic
382#117—731no—
383#117—1461no—
384C2×C4⋊C4—731no—
385C2×C4⋊C4—1461no—
386C2×C42—731no—
387C2×C42—1461no—
388C2×C42—1461no—
389#107—731no—
390#107—731no—
391#106—731no—
392#106C4×D7311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8—1461no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8C22×D7311yescharacteristic
405C4⋊C8C22×D7311yescharacteristic
406#103—731no—
407#103—731no—
408#103—731no—
409#103—731no—
410#103—731no—
411#103C4×D7311yescharacteristic
412#102—731no—
413#102C4×D7311yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—731no—
416C22⋊C8—731no—
417C22⋊C8—1461no—
418C22⋊C8—1461no—
419#97—731no—
420#97—731no—
421C4×C8—21no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—1461no—
426C4×C8—1461no—
427C4×C8—1461no—
428C4×C8—1461no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434C4×C8C22×D7311yescharacteristic
435#41—734no—
436#41—1462no—
437C2×Q8—734no—
438C2×Q8—731no—
439C2×Q8—731no—
440C2×Q8—1461no—
441C2×Q8—1462no—
442C2×Q8C2×C4×D7311yescharacteristic
443C2×D4—1461no—
444C2×D4C2×C4×D7311yescharacteristic
445C22×C4—21no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453Q16—734no—
454Q16—734no—
455SD16—734no—
456SD16C8×D7314yescomplemented
457M16—734no—
458M16—1462no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—2922no—
464C2×C8—5841no—
465C2×C8—5841no—
466C2×C8—731no—
467C2×C8—731no—
468C2×C8—731no—
469C2×C8—731no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8C2×C4×D7311yescharacteristic
474C2×C8C2×C4×D7311yescharacteristic
475C2×C8D4×D7311yescharacteristic
476C2×C8D4×D7311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—731no—
479C4⋊C4—731no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4C2×C4×D7311yescharacteristic
487C4⋊C4C2×C4×D7311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—21no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—1461no—
496C42—1461no—
497C42—1461no—
498C42—1461no—
499C42—1461no—
500C42—1461no—
501C42C23×D7311yescharacteristic
502C23—21no—
503C23—731no—
504Q8—21no—
505Q8—732no—
506Q8—732no—
507Q8—1464no—
508Q8—1461no—
509Q8—1461no—
510Q8C2×C8×D7312yes—
511D4—21no—
512D4—1464no—
513D4C2×C8×D7312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—2921no—
520C2×C4—5841no—
521C2×C4—5841no—
522C2×C4—731no—
523C2×C4—732no—
524C2×C4—732no—
525C2×C4—731no—
526C2×C4—731no—
527C2×C4—1464no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1464no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4C22×C4×D7311yescharacteristic
536C2×C4C2×D4×D7311yescharacteristic
537C2×C4#41×D7311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—2921no—
545C8—2921no—
546C8—732no—
547C8—1462no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C8C2×C8×D7312yes—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—732no—
556C22—1461no—
557C22—1461no—
558C22C4×D4×D7311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—2921no—
564C4—2921no—
565C4—732no—
566C4—1461no—
567C4—1461no—
568C4—1462no—
569C4—1462no—
570C4C22×C8×D7311yescharacteristic
571C4#131×D7311yescharacteristic
572C4#1798939711yescharacteristic
573C4#1798940311yescharacteristic
574C2—42no—
575C2—1462no—
576C2C8×D4×D7311yescharacteristic
577C2#2261877111yescharacteristic
578C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC4×C73C23×C8
FrattiniC42C23×D73
FittingC73×SD16⋊C8C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924027C2×C4
cosocleC42×C73C24
hypercenterSD16⋊C8D73
hypocenterC73#17853
LCSG ▷ 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. #22619010C2semidirect
4. #22608751C2semidirect
5. #22608747C2semidirect
6. #22608740C2semidirect
7. #22608737C2semidirect
8. C8×#11924018C2semidirect
9. SD16×#10596831C2semidirect
10. C8×#11924016C2semidirect
11. #22608682C2semidirect
13. Q8⋊C8×D73C2semidirect
14. #22608210C2semidirect
15. C73×SD16⋊C8C2semidirect
69. #14556620C8semidirect
151. Q8×D73C2×C8semidirect
160. Dic292C2×C8semidirect
161. #11924018C2×C8semidirect
162. #11924016C2×C8semidirect
164. #11924011C2×C8semidirect
197. SD16×C73C2×C8semidirect
296. SD16⋊C8D73semidirect
305. C73#17853semidirect
456. SD16C8×D73semidirect

Maximal subgroups

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

subgroupindex
#226190382
#226190102
C4×#145566202
#226087512
#226087472
#226087402
#226087372
C8×#119240182
SD16×#105968312
C8×#119240162
#226086822
#226083102
Q8⋊C8×D732
#226082102
C73×SD16⋊C82
#1785373