Finite Group Databasebeta

← #33057159

Subgroups — #33057159

Order 18688.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619998C211yesmaximal, characteristic
2#22619054C211yesmaximal, characteristic
3#22619031C211yesmaximal, characteristic, complemented
4#22608829C211yesmaximal, characteristic, complemented
5#22608825C211yesmaximal, characteristic, complemented
6#22608802C211yesmaximal, characteristic, complemented
7#22608801C211yesmaximal, characteristic, complemented
8#22608789C211yesmaximal, characteristic, complemented
9#22608788C211yesmaximal, characteristic, complemented
10#22608734C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608384C211yesmaximal, characteristic, complemented
13#22608310C211yesmaximal, characteristic
14#22608213C211yesmaximal, characteristic, complemented
15C8×SD16×C73C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17C4×#11924027C2211yescharacteristic
18#17988931C411yescharacteristic
19#17988927C411yescharacteristic
20#17988871C411yescharacteristic
21#17988865C411yescharacteristic
22#17988796C411yescharacteristic
23#17988790C411yescharacteristic
24#17988750C411yescharacteristic
25#17988746C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988717C2211yescharacteristic
29#17988716—21no—
30#17988714C2211yescharacteristic
31C8×Dic146—21no—
32#17988711C2211yescharacteristic
33C4×Dic292C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36#17988658—21no—
37#17988655—21no—
38D4×#10596831C2211yescharacteristic
39#17988647—21no—
40#17988646—21no—
41#17988641—21no—
42#17988639C2211yescharacteristic
43#17988638C2211yescharacteristic
44#17988638C2211yescharacteristic
45#17988609C2211yescharacteristic
46C2×#14556520—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54#17988317C2211yescharacteristic
55#17988317C2211yescharacteristic
56D4⋊#10596831C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59C8×#10596831C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924027C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C2×C8×D73—21no—
74#14556590C2×C411yescharacteristic
75#14556589C2×C411yescharacteristic
76#14556581—21no—
77#14556571C2×C411yescharacteristic
78#14556569—21no—
79#14556567C2×C411yescharacteristic
80C4×Dic146—21no—
81C4×Dic146C2311yescharacteristic
82C4×Dic146C2311yescharacteristic
83#14556556C2×C411yescharacteristic
84D4×Dic73C2×C411yescharacteristic
85C4×C22⋊D73—21no—
86#14556551—21no—
87#14556549C2×C411yescharacteristic
88#14556548—21no—
89#14556547—21no—
90C2×C4×Dic73—21no—
91C42×D73C2311yescharacteristic
92#14556525C2×C411yescharacteristic
93#14556524C2×C411yescharacteristic
94#14556522C2×C411yescharacteristic
95C4⋊#10596831—21no—
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520D411yescharacteristic
106#14556520D411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113C22⋊#10596831—21no—
114#14556503—21no—
115#14556503C2×C411yescharacteristic
116#14556503C2×C411yescharacteristic
117#14556503D411yescharacteristic
118#14556503D411yescharacteristic
119#14556502—21no—
120#14556501—21no—
121#14556501—21no—
122#14556501—21no—
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
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
144#11924027—22no—
145#11924027—41no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×C22⋊D73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C2×C4×D73C22×C411yescharacteristic
153C2×C4×D73C2×D411yescharacteristic
154C2×C4×D73#4111yescharacteristic
155Dic292—41no—
156#11924018—41no—
157#11924016—22no—
158#11924011—81no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—81no—
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C8×D73—24no—
168C4⋊Dic73—21no—
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73#4111yescharacteristic
189C2×Q8×C73C22×C411yescharacteristic
190C2×D4×C73C22×C411yescharacteristic
191C22×C4×C73—21no—
192SD16×C73—22no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—81no—
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C4⋊C4×C73—21no—
202C4⋊C4×C73C22×C411yescharacteristic
203C4⋊C4×C73C22×C411yescharacteristic
204C22⋊C4×C73—21no—
205C42×C73—21no—
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C22×D73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211D4×C73—21no—
212D4×C73#13112yes—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73C23×C411yescharacteristic
219C2×C4×C73C22×D411yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C22⋊D73—42no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73C4×D411yescharacteristic
229C2×Dic73C4×D411yescharacteristic
230C2×Dic73C4×D411yescharacteristic
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—22no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146—21no—
240Dic146—42no—
241C8×C73—22no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—41no—
247C8×C73—41no—
248#10596831—22no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—22no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73C2×C4×D411yescharacteristic
259C2×D73—21no—
260C2×D73—21no—
261C2×D73—21no—
262C4×C73—21no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73C2×#13111yescharacteristic
267C4×C73#56811yescharacteristic
268C4×C73#57711yescharacteristic
269C4×C73#57811yescharacteristic
270Dic73—21no—
271Dic73—21no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73#44312yes—
277#18016—731nomaximal, Sylow
278C2×C73—42no—
279C2×C73#293311yescharacteristic
280C2×C73#294711yescharacteristic
281C2×C73C2×#44311yescharacteristic
282D73—41no—
283#3107—731no—
284#2990—731no—
285#2986—731no—
286#1591—731no—
287#1591—731no—
288#1587—731no—
289#1587—731no—
290#1585—731no—
291#1585—731no—
292C8×SD16—731no—
293C8×SD16D7311yescharacteristic, complemented
294#1574—731no—
295#1493—731no—
296#1476—731no—
297#1450—731no—
298C73#1801611yescharacteristic, complemented, Sylow
299#533—731no—
300C4×#41—731no—
301#485—731no—
302#485—731no—
303#475—731no—
304#474—731no—
305#462—731no—
306#461—731no—
307#452—731no—
308#452—731no—
309#446—731no—
310#446—731no—
311#446—731no—
312#446—731no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—1461no—
316C8×Q8C2×D7311yescharacteristic
317C4×Q16—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16C2×D7311yescharacteristic
321#435—1461no—
322#435—1461no—
323C8×D4—731no—
324C8×D4C2×D7311yescharacteristic
325#433—1461no—
326#433—1461no—
327#432—1461no—
328#431—731no—
329#431—731no—
330#431—731no—
331#423—731no—
332C2×C4⋊C8—1461no—
333C2×C4×C8—731no—
334#335—731no—
335#335—731no—
336#334—731no—
337#334C2×D7311yescharacteristic
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8C2×D7311yescharacteristic
344D4⋊C8—731no—
345D4⋊C8C2×D7311yescharacteristic
346#322—731no—
347#322—731no—
348C82—731no—
349C82C2×D7311yescharacteristic
350C2×#41—731no—
351C2×Q16—731no—
352C2×Q16—731no—
353C2×SD16—731no—
354C2×SD16C4×D7311yescharacteristic
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—1461no—
358C22×C8—1461no—
359C4⋊Q8—731no—
360C4⋊Q8—731no—
361#125—1461no—
362C22⋊Q8—731no—
363C22⋊Q8—731no—
364C22⋊Q8—1461no—
365C4×Q8—731no—
366C4×Q8—731no—
367C4×Q8—731no—
368C4×Q8—1461no—
369C4×Q8C22×D7311yescharacteristic
370C4×D4—731no—
371C4×D4—1461no—
372C4×D4—1461no—
373C4×D4C22×D7311yescharacteristic
374#117—731no—
375#117—1461no—
376#117—1461no—
377C2×C42—731no—
378C2×C42—1461no—
379#107—731no—
380#107—731no—
381#106—731no—
382#106C4×D7311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8C22×D7311yescharacteristic
397C4⋊C8C22×D7311yescharacteristic
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103C4×D7311yescharacteristic
404#102—731no—
405#102C4×D7311yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—731no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416#97—1461no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427#41—2921no—
428#41—1462no—
429C2×Q8—731no—
430C2×Q8—731no—
431C2×Q8—1461no—
432C2×Q8C2×C4×D7311yescharacteristic
433C2×D4—1461no—
434C2×D4C2×C4×D7311yescharacteristic
435C22×C4—21no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—1461no—
440C22×C4—1461no—
441Q16—2921no—
442Q16—2921no—
443SD16—22no—
444SD16—1462no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—81no—
450C2×C8—5841no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—1464no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8C2×C4×D7311yescharacteristic
460C2×C8C2×C4×D7311yescharacteristic
461C2×C8D4×D7311yescharacteristic
462C2×C8D4×D7311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—731no—
465C4⋊C4—731no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4C2×C4×D7311yescharacteristic
475C4⋊C4C2×C4×D7311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—731no—
483C42—731no—
484C42—731no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42—1461no—
489C42C23×D7311yescharacteristic
490C23—21no—
491C23—731no—
492Q8—21no—
493Q8—21no—
494Q8—2922no—
495Q8—1461no—
496Q8—1461no—
497Q8—1461no—
498Q8—1461no—
499D4—21no—
500D4—2922no—
501D4#1455659712yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—2922no—
508C2×C4—2922no—
509C2×C4—731no—
510C2×C4—731no—
511C2×C4—731no—
512C2×C4—1462no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4#41×D7311yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—2921no—
532C8—2921no—
533C8—1462no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—1461no—
542C22—1461no—
543C22—1461no—
544C22C4×D4×D7311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4—2921no—
553C4—732no—
554C4—1461no—
555C4—1461no—
556C4C2×#1455659711yescharacteristic
557C4#1798935211yescharacteristic
558C4#1798939311yescharacteristic
559C4#1798940111yescharacteristic
560C2—42no—
561C2—2921no—
562C2#2261865111yescharacteristic
563C2#2261876711yescharacteristic
564C2#443×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC8×SD16×C73C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924027C2×C4
cosocleC42×C73C24
hypercenterC8×SD16D73
hypocenterC73#18016
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #22619031C2semidirect
4. #22608829C2semidirect
5. #22608825C2semidirect
6. #22608802C2semidirect
7. #22608801C2semidirect
8. #22608789C2semidirect
9. #22608788C2semidirect
10. #22608734C2semidirect
11. #22608718C2semidirect
12. #22608384C2semidirect
14. #22608213C2semidirect
15. C8×SD16×C73C2semidirect
293. C8×SD16D73semidirect
298. C73#18016semidirect

Maximal subgroups

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

subgroupindex
#226199982
#226190542
#226190312
#226088292
#226088252
#226088022
#226088012
#226087892
#226087882
#226087342
#226087182
#226083842
#226083102
#226082132
C8×SD16×C732
#1801673