Finite Group Databasebeta

← #33057257

Subgroups — #33057257

Order 18688.

592 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#22620007C211yesmaximal, characteristic
2#22619091C211yesmaximal, characteristic
3#22619021C211yesmaximal, characteristic, complemented
4#22608837C211yesmaximal, characteristic, complemented
5#22608830C211yesmaximal, characteristic, complemented
6#22608784C211yesmaximal, characteristic, complemented
7#22608778C211yesmaximal, characteristic, complemented
8#22608777C211yesmaximal, characteristic, complemented
9#22608764C211yesmaximal, characteristic, complemented
10#22608747C211yesmaximal, characteristic, complemented
11#22608740C211yesmaximal, characteristic, complemented
12#22608717C211yesmaximal, characteristic, complemented
13C2×#17988319C211yesmaximal, characteristic, complemented
14#22608223C211yesmaximal, characteristic, complemented
15C73×#1494C211yesmaximal, characteristic
16C2×C4×Dic146C2211yescharacteristic
17#17988915C411yescharacteristic
18#17988898C411yescharacteristic
19#17988891C411yescharacteristic
20#17988891C411yescharacteristic
21#17988806C411yescharacteristic
22#17988806C411yescharacteristic
23#17988742C411yescharacteristic
24#17988725C411yescharacteristic
25#17988718C2211yescharacteristic
26#17988715—21no—
27#17988715—21no—
28#17988714C2211yescharacteristic
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31#17988711C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×#11924018C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924016C2211yescharacteristic
36C4×#11924016C2211yescharacteristic
37#17988665C2211yescharacteristic
38#17988659—21no—
39D4×#10596831—21no—
40D4×#10596831C2211yescharacteristic
41#17988648—21no—
42#17988641—21no—
43#17988640C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988637—21no—
46#17988614—21no—
47C2×C4⋊#10596831C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60#529×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C22×Dic146C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924016C2×C411yescharacteristic
72C2×#11924012—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C4×Dic146—21no—
76C4×Dic146—21no—
77C4×Dic146C2×C411yescharacteristic
78C4×Dic146C2×C411yescharacteristic
79C4×Dic146C2311yescharacteristic
80C4×Dic146C2311yescharacteristic
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×#11924007—21no—
83C2×C4×Dic73—21no—
84#14556524C2×C411yescharacteristic
85#14556524C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2×C411yescharacteristic
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556514C2×C411yescharacteristic
104#14556514C2×C411yescharacteristic
105#14556514C2×C411yescharacteristic
106#14556514C2×C411yescharacteristic
107#14556512C2×C411yescharacteristic
108#14556512C2×C411yescharacteristic
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831C2×C411yescharacteristic
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831D411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115#14556502—21no—
116#14556501—21no—
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C22×C8×C73—21no—
126#126×C73—21no—
127#125×C73C2×C411yescharacteristic
128#124×C73C2×C411yescharacteristic
129#123×C73—21no—
130C22⋊Q8×C73C2×C411yescharacteristic
131#121×C73C2×C411yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133C4×D4×C73—21no—
134C4×D4×C73C2311yescharacteristic
135#117×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—22no—
145C2×Dic146—21no—
146C2×Dic146—41no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C22×Dic73—21no—
150C22×Dic73—21no—
151#11924018—22no—
152#11924018—41no—
153#11924016—22no—
154#11924016—41no—
155#11924012—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—81no—
159C2×#10596831—81no—
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C4⋊Dic73—21no—
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C2×Q8×C73C22×C411yescharacteristic
180C2×D4×C73—21no—
181C2×D4×C73C22×C411yescharacteristic
182C22×C4×C73—21no—
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73#4111yescharacteristic
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—42no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73C22×C411yescharacteristic
196C4⋊C4×C73C22×C411yescharacteristic
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211D4×C73—21no—
212D4×C73—21no—
213D4×C73—42no—
214C2×C4×C73—22no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—42no—
235C2×Dic73—42no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146—42no—
240Dic146#13112yes—
241C8×C73—41no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245#10596831—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73#44412yes—
261C22×C73C2×C4×D411yescharacteristic
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73C2×#13111yescharacteristic
270C4×C73#56811yescharacteristic
271C4×C73#57711yescharacteristic
272C4×C73#57811yescharacteristic
273Dic73—22no—
274Dic73—41no—
275Dic73—41no—
276Dic73—41no—
277#18023—731nomaximal, Sylow
278C2×C73—22no—
279C2×C73—81no—
280C2×C73#293311yescharacteristic
281C2×C73#294711yescharacteristic
282C2×C73C2×#44411yescharacteristic
283#3108—731no—
284#2994—731no—
285#2984—731no—
286#1593—731no—
287#1592—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1579—731no—
293SD16⋊C8—731no—
294#1573—731no—
295#1494D7311yescharacteristic
296C2×Q8⋊C8—731no—
297#1452—731no—
298C73#1802311yescharacteristic, complemented, Sylow
299#529C2×D7311yescharacteristic
300C2×C4×Q8—731no—
301#483—731no—
302#480—731no—
303#479—731no—
304#479—731no—
305#464—731no—
306#464—731no—
307#451—731no—
308#448—731no—
309#446—731no—
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C4×Q16—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16—731no—
321#436—731no—
322#435—1461no—
323C8×D4—731no—
324C8×D4—1461no—
325#433—1461no—
326#432—1461no—
327#432C2×D7311yescharacteristic
328#431—731no—
329#431—731no—
330#431—1461no—
331#424—1461no—
332C2×C4⋊C8—731no—
333C2×C4×C8C2×D7311yescharacteristic
334#335—731no—
335#335—731no—
336#334—731no—
337#334—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8C2×D7311yescharacteristic
343Q8⋊C8C2×D7311yescharacteristic
344D4⋊C8C2×D7311yescharacteristic
345D4⋊C8C2×D7311yescharacteristic
346#322—731no—
347#322—731no—
348#322—731no—
349#322—731no—
350C22×Q8—731no—
351C2×Q16—731no—
352C2×Q16—731no—
353C2×SD16—731no—
354C2×SD16—731no—
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—1461no—
358C22×C8—1461no—
359#126—21no—
360#125C4×D7311yescharacteristic
361#124C4×D7311yescharacteristic
362#123—21no—
363C22⋊Q8C4×D7311yescharacteristic
364#121C4×D7311yescharacteristic
365C4×Q8—731no—
366C4×Q8—731no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×Q8—1461no—
370C4×Q8—1461no—
371C4×Q8C22×D7311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D7311yescharacteristic
374#117—21no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—1461no—
377C2×C42—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
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#103—731no—
404#102—731no—
405#102—731no—
406C22⋊C8—21no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—731no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—1461no—
415#97—1461no—
416#97—1461no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427C2×Q8—2921no—
428C2×Q8—731no—
429C2×Q8—731no—
430C2×Q8—1462no—
431C2×Q8—1461no—
432C2×Q8C2×C4×D7311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D7311yescharacteristic
435C22×C4—21no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4C2×C4×D7311yescharacteristic
439C22×C4D4×D7311yescharacteristic
440C22×C4#1192402711yescharacteristic
441Q16—2921no—
442Q16—1462no—
443SD16—2921no—
444SD16—1462no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—5841no—
452C2×C8—5841no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—1461no—
462C2×C8—1461no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—731no—
468C4⋊C4—731no—
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—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42C2×C4×D7311yescharacteristic
487C42D4×D7311yescharacteristic
488C42#1192402711yescharacteristic
489C42C23×D7311yescharacteristic
490C23—21no—
491C23#1455655111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—2922no—
495Q8—732no—
496Q8—1461no—
497Q8—1461no—
498Q8—1461no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—2922no—
513C2×C4—2922no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4#1455655111yescharacteristic
519C2×C4#1455655111yescharacteristic
520C2×C4#1455655111yescharacteristic
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4C2×#1192402711yescharacteristic
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—2921no—
529C8—2921no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1798870612yes—
544C22C2×#1455655111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—2921no—
553C4—2921no—
554C4—2921no—
555C4—1462no—
556C4#131×D7311yescharacteristic
557C4#1798935211yescharacteristic
558C4#1798939411yescharacteristic
559C4#1798940111yescharacteristic
560C2—22no—
561C2—81no—
562C2#2261866111yescharacteristic
563C2#2261877711yescharacteristic
564C2C2×#1798870611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1494C2
socleC22×C73C2×C4×D4
prime radical#121×C73C2×C4
cosocleC42×C73C24
hypercenter#1494D73
hypocenterC73#18023
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #22619021C2semidirect
4. #22608837C2semidirect
5. #22608830C2semidirect
6. #22608784C2semidirect
7. #22608778C2semidirect
8. #22608777C2semidirect
9. #22608764C2semidirect
10. #22608747C2semidirect
11. #22608740C2semidirect
12. #22608717C2semidirect
13. C2×#17988319C2semidirect
14. #22608223C2semidirect
298. C73#18023semidirect

Maximal subgroups

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

subgroupindex
#226200072
#226190912
#226190212
#226088372
#226088302
#226087842
#226087782
#226087772
#226087642
#226087472
#226087402
#226087172
C2×#179883192
#226082232
C73×#14942
#1802373