Finite Group Databasebeta

← #33057247

Subgroups — #33057247

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#22619018C211yesmaximal, characteristic, complemented
3#22608838C211yesmaximal, characteristic, complemented
4#22608833C211yesmaximal, characteristic, complemented
5#22608781C211yesmaximal, characteristic, complemented
6#22608779C211yesmaximal, characteristic, complemented
7#22608772C211yesmaximal, characteristic, complemented
8#22608767C211yesmaximal, characteristic, complemented
9#22608748C211yesmaximal, characteristic, complemented
10#22608743C211yesmaximal, characteristic, complemented
11#22608714C211yesmaximal, characteristic, complemented
12#22608391C211yesmaximal, characteristic
13C2×#17988317C211yesmaximal, characteristic, complemented
14#22608224C211yesmaximal, characteristic, complemented
15C73×#2994C211yesmaximal, characteristic
16C2×C4×Dic146C2211yescharacteristic
17#17988915C411yescharacteristic
18#17988898C411yescharacteristic
19#17988891C411yescharacteristic
20#17988891C411yescharacteristic
21#17988806C411yescharacteristic
22#17988806C411yescharacteristic
23#17988742C411yescharacteristic
24#17988725C411yescharacteristic
25#17988717C2211yescharacteristic
26#17988717C2211yescharacteristic
27#17988716—21no—
28#17988716—21no—
29C8×Dic146C2211yescharacteristic
30C8×Dic146C2211yescharacteristic
31C4×#11924018C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C4×#11924016C2211yescharacteristic
35#17988644C2211yescharacteristic
36#17988641—21no—
37#17988640C2211yescharacteristic
38#17988637—21no—
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50D4⋊#10596831C2211yescharacteristic
51D4⋊#10596831C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55#17988308C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73C2211yescharacteristic
60#435×C73—21no—
61C8×D4×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#424×C73—21no—
66C2×C4⋊C8×C73C2211yescharacteristic
67C22×Dic146C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924016C2×C411yescharacteristic
72C22×#10596831—21no—
73C4×Dic146—21no—
74C4×Dic146—21no—
75C4×Dic146C2×C411yescharacteristic
76C4×Dic146C2×C411yescharacteristic
77C4×Dic146C2311yescharacteristic
78C4×Dic146C2311yescharacteristic
79C2×C4⋊Dic73C2×C411yescharacteristic
80C2×#11924007—21no—
81C2×C4×Dic73—21no—
82#14556524C2×C411yescharacteristic
83#14556524C2×C411yescharacteristic
84#14556522C2×C411yescharacteristic
85#14556522C2×C411yescharacteristic
86C4⋊#10596831C2×C411yescharacteristic
87C4⋊#10596831C2×C411yescharacteristic
88C4⋊#10596831C2311yescharacteristic
89C4⋊#10596831C2311yescharacteristic
90#14556520—21no—
91#14556520—21no—
92#14556520—21no—
93#14556520—21no—
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831C2×C411yescharacteristic
104C22⋊#10596831C2×C411yescharacteristic
105#14556502—21no—
106#14556501—21no—
107#14556501—21no—
108C4×#10596831—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×M16×C73—21no—
116C22×C8×C73—21no—
117C22×C8×C73—21no—
118#126×C73—21no—
119#125×C73C2×C411yescharacteristic
120#124×C73C2×C411yescharacteristic
121#123×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123#121×C73C2×C411yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—21no—
126C4×D4×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
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—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—42no—
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C4⋊Dic73—21no—
165C4⋊Dic73C22×C411yescharacteristic
166C4⋊Dic73C22×C411yescharacteristic
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C2×Q8×C73C22×C411yescharacteristic
176C2×D4×C73—21no—
177C2×D4×C73C22×C411yescharacteristic
178C22×C4×C73—21no—
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4111yescharacteristic
182M16×C73—81no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—81no—
186C2×C8×C73—81no—
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
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—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—41no—
246C8×C73—41no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
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#2994D7311yescharacteristic
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#1494—731no—
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—1461no—
312#446—1461no—
313#446C2×D7311yescharacteristic
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8C2×D7311yescharacteristic
317C4×Q16—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16—731no—
321#436C2×D7311yescharacteristic
322#435—21no—
323C8×D4—21no—
324C8×D4C2×D7311yescharacteristic
325#433—21no—
326#432—731no—
327#432—1461no—
328#431—731no—
329#431—1461no—
330#431C2×D7311yescharacteristic
331#424—21no—
332C2×C4⋊C8C2×D7311yescharacteristic
333C2×C4×C8—731no—
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⋊C8—731no—
343Q8⋊C8—731no—
344D4⋊C8—731no—
345D4⋊C8—731no—
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—21no—
356C22×C8—21no—
357C22×C8—21no—
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—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
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⋊C8C22⋊D7311yescharacteristic
395C4⋊C8C22⋊D7311yescharacteristic
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—21no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—1461no—
411C22⋊C8C22⋊D7311yescharacteristic
412C22⋊C8C22⋊D7311yescharacteristic
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×C4C2×C22⋊D7311yescharacteristic
440C22×C4#1192402811yescharacteristic
441Q16—2921no—
442Q16—1462no—
443SD16—2921no—
444SD16—1462no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—2922no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8C2×C22⋊D7311yescharacteristic
460C2×C8C2×C22⋊D7311yescharacteristic
461C2×C8C2×C22⋊D7311yescharacteristic
462C2×C8C2×C22⋊D7311yescharacteristic
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
487C42C2×C22⋊D7311yescharacteristic
488C42#1192402811yescharacteristic
489C42C23×D7311yescharacteristic
490C23—21no—
491C23C4×C22⋊D7311yescharacteristic
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×C4C4×C22⋊D7311yescharacteristic
519C2×C4C4×C22⋊D7311yescharacteristic
520C2×C4C4×C22⋊D7311yescharacteristic
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C22×C22⋊D7311yescharacteristic
523C2×C4C2×#1192402811yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—2921no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1798870712yes—
544C22C2×C4×C22⋊D7311yescharacteristic
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#1798939811yescharacteristic
559C4#1798940211yescharacteristic
560C2—22no—
561C2—81no—
562C2#2261865311yescharacteristic
563C2#2261877011yescharacteristic
564C2C2×#1798870711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2994C2
socleC22×C73C2×C4×D4
prime radical#121×C73C2×C4
cosocleC42×C73C24
hypercenter#2994D73
hypocenterC73#18023
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #22619018C2semidirect
3. #22608838C2semidirect
4. #22608833C2semidirect
5. #22608781C2semidirect
6. #22608779C2semidirect
7. #22608772C2semidirect
8. #22608767C2semidirect
9. #22608748C2semidirect
10. #22608743C2semidirect
11. #22608714C2semidirect
13. C2×#17988317C2semidirect
14. #22608224C2semidirect
298. C73#18023semidirect

Maximal subgroups

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

subgroupindex
#226200072
#226190182
#226088382
#226088332
#226087812
#226087792
#226087722
#226087672
#226087482
#226087432
#226087142
#226083912
C2×#179883172
#226082242
C73×#29942
#1802373