Finite Group Databasebeta

← #33055322

Subgroups — #33055322

Order 18688.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619058C211yesmaximal, characteristic
2#22619052C211yesmaximal, characteristic
3#22618895C211yesmaximal, characteristic
4#22608713C211yesmaximal, characteristic, complemented
5#22608713C211yesmaximal, characteristic, complemented
6#22608710C211yesmaximal, characteristic, complemented
7#22608706C211yesmaximal, characteristic, complemented
8#22608704C211yesmaximal, characteristic, complemented
9#22608699C211yesmaximal, characteristic, complemented
10#22608695C211yesmaximal, characteristic, complemented
11#22608693C211yesmaximal, characteristic, complemented
12#22608684C211yesmaximal, characteristic, complemented
13#22608680C211yesmaximal, characteristic, complemented
14#335×D73C211yesmaximal, characteristic, complemented
15C73×#1572C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988717—21no—
18#17988716C411yescharacteristic
19#17988716C411yescharacteristic
20#17988715—21no—
21#17988662C411yescharacteristic
22#17988662C411yescharacteristic
23#17988661—21no—
24#17988661—21no—
25#17988661C411yescharacteristic
26#17988661C411yescharacteristic
27#17988660—21no—
28#17988657C411yescharacteristic
29#17988657C411yescharacteristic
30#17988655—21no—
31C8×D292—21no—
32#17988650—21no—
33#17988643C2211yescharacteristic
34#17988643C2211yescharacteristic
35#17988643C2211yescharacteristic
36#17988639C2211yescharacteristic
37#17988638C2211yescharacteristic
38#17988638C2211yescharacteristic
39#17988611C2211yescharacteristic
40#17988609C2211yescharacteristic
41C2×C4⋊#10596831C2211yescharacteristic
42C4⋊C8×D73C2211yescharacteristic
43C4⋊C8×D73C2211yescharacteristic
44C4⋊C8×D73C2211yescharacteristic
45C4×#11924012C2211yescharacteristic
46C4×#11924011C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988340C2211yescharacteristic
51#17988340C2211yescharacteristic
52#17988339C2211yescharacteristic
53#17988339C2211yescharacteristic
54#17988339C2211yescharacteristic
55#17988339C2211yescharacteristic
56#17988337C2211yescharacteristic
57#17988337C2211yescharacteristic
58#17988337C2211yescharacteristic
59#17988337C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028Q811yescharacteristic
68C2×#11924012—21no—
69C2×#11924012C2×C411yescharacteristic
70C2×#11924012C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×#11924011C2×C411yescharacteristic
73C2×#11924011C2×C411yescharacteristic
74C22×#10596831—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78C2×C8×D73C2×C411yescharacteristic
79C2×C8×D73C2×C411yescharacteristic
80C4×Dic146C2×C411yescharacteristic
81C4×Dic146D411yescharacteristic
82C4×D292C2×C411yescharacteristic
83C4×D292D411yescharacteristic
84C4×C22⋊D73C2×C411yescharacteristic
85C4×C22⋊D73C2×C411yescharacteristic
86C4×C22⋊D73D411yescharacteristic
87C4×C22⋊D73D411yescharacteristic
88#14556550Q811yescharacteristic
89#14556548Q811yescharacteristic
90#14556548Q811yescharacteristic
91C42×D73C2311yescharacteristic
92C42×D73C2311yescharacteristic
93C4⋊#10596831—21no—
94C4⋊#10596831—21no—
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520C2×C411yescharacteristic
106#14556520C2×C411yescharacteristic
107#14556503—21no—
108#14556503—21no—
109#14556503—21no—
110#14556503—21no—
111#14556503C2×C411yescharacteristic
112#14556503C2×C411yescharacteristic
113#14556503C2×C411yescharacteristic
114#14556503C2×C411yescharacteristic
115#14556502C2×C411yescharacteristic
116#14556502C2×C411yescharacteristic
117#14556501—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501C2×C411yescharacteristic
121#14556501C2×C411yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C8×Dic73C2×C411yescharacteristic
126C8×Dic73C2×C411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73C2×C411yescharacteristic
129C4⋊C8×C73C2×C411yescharacteristic
130C4⋊C8×C73C2311yescharacteristic
131C4⋊C8×C73C2311yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73C2×C411yescharacteristic
137C22⋊C8×C73C2×C411yescharacteristic
138#97×C73—21no—
139C4×C8×C73—21no—
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142#11924028—42no—
143C2×Dic146C4⋊C411yescharacteristic
144C2×D292C4⋊C411yescharacteristic
145C2×C22⋊D73C4⋊C411yescharacteristic
146C2×C22⋊D73C4⋊C411yescharacteristic
147C2×C4×D73C22×C411yescharacteristic
148C2×C4×D73C22×C411yescharacteristic
149C2×C4×D73C2×D411yescharacteristic
150C2×C4×D73C2×D411yescharacteristic
151C2×C4×D73C2×Q811yescharacteristic
152C2×C4×D73C2×Q811yescharacteristic
153#11924012—22no—
154#11924012—41no—
155#11924012—81no—
156#11924011—22no—
157#11924011—41no—
158#11924011—81no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—81no—
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C8×D73—22no—
169C8×D73—41no—
170C8×D73—81no—
171C8×D73—81no—
172C8×D73—81no—
173C4⋊Dic73C4⋊C411yescharacteristic
174C4⋊Dic73C4⋊C411yescharacteristic
175#11924007C4⋊C411yescharacteristic
176#11924007C4⋊C411yescharacteristic
177#11924007C4⋊C411yescharacteristic
178#11924007C4⋊C411yescharacteristic
179C22⋊Dic73C4⋊C411yescharacteristic
180C22⋊Dic73C4⋊C411yescharacteristic
181#11924005C4⋊C411yescharacteristic
182#11924005C4⋊C411yescharacteristic
183#11924005C4⋊C411yescharacteristic
184#11924005C4⋊C411yescharacteristic
185C4×Dic73C22×C411yescharacteristic
186C4×Dic73C22×C411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73C2×Q811yescharacteristic
190C4×Dic73C2×Q811yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×Q811yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C42×C73C22×C411yescharacteristic
203C42×C73C2×D411yescharacteristic
204C42×C73C2×Q811yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73C2×C4⋊C411yescharacteristic
207C22×D73C2×C4⋊C411yescharacteristic
208C22×D73C2×C4⋊C411yescharacteristic
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—41no—
214C2×C4×C73C2×C4⋊C411yescharacteristic
215C2×C4×C73C2×C4⋊C411yescharacteristic
216C2×C4×C73C2×C4⋊C411yescharacteristic
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C22×Q811yescharacteristic
220C22⋊D73—22no—
221C22⋊D73—41no—
222C2×Dic73C2×C4⋊C411yescharacteristic
223C2×Dic73C2×C4⋊C411yescharacteristic
224C2×Dic73C2×C4⋊C411yescharacteristic
225C2×Dic73C2×C4⋊C411yescharacteristic
226C2×Dic73C2×C4⋊C411yescharacteristic
227C2×Dic73C2×C4⋊C411yescharacteristic
228D292—22no—
229C4×D73—22no—
230C4×D73—21no—
231C4×D73—21no—
232C4×D73—21no—
233C4×D73—21no—
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—41no—
239Dic146—41no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13112yes—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73C22×C4⋊C411yescharacteristic
260C2×D73—21no—
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C2×D73—21no—
265C2×D73#43012yes—
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—21no—
269C4×C73—21no—
270C4×C73C2×#13111yescharacteristic
271C4×C73#56811yescharacteristic
272C4×C73#57611yescharacteristic
273C4×C73#57811yescharacteristic
274Dic73—21no—
275Dic73—21no—
276Dic73—21no—
277Dic73—21no—
278Dic73—21no—
279Dic73—21no—
280#17840—731nomaximal, Sylow
281C2×C73—41no—
282C2×C73#290611yescharacteristic
283C2×C73#291311yescharacteristic
284C2×C73C2×#43011yescharacteristic
285D73—22no—
286D73—41no—
287#2990—731no—
288#2990—731no—
289#2965—731no—
290#1573—731no—
291#1573—731no—
292#1572—731no—
293#1572D7311yescharacteristic, complemented
294#1571—731no—
295#1571—731no—
296#1569—731no—
297#1569—731no—
298#1568—731no—
299#1565—731no—
300#1565—731no—
301C2×#335—731no—
302C73#1784011yescharacteristic, complemented, Sylow
303C4×#41—731no—
304#446—731no—
305#446—731no—
306#446—1461no—
307#446—1461no—
308#436—731no—
309#436—731no—
310#435—731no—
311#435—731no—
312#435—731no—
313#435—731no—
314#435—1461no—
315#435—1461no—
316#435—1461no—
317#435—1461no—
318C8×D4—1461no—
319C8×D4—1461no—
320#432—731no—
321#432—731no—
322#432—731no—
323#432C2×D7311yescharacteristic
324#431—731no—
325#431—731no—
326#431—731no—
327#431C2×D7311yescharacteristic
328#431C2×D7311yescharacteristic
329#423—731no—
330#423—731no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C4×M16—731no—
336C4×M16—731no—
337C2×C4×C8—731no—
338#335—731no—
339#335—731no—
340#335—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346#335C2×D7311yescharacteristic
347#335C2×D7311yescharacteristic
348#334—731no—
349#334—731no—
350#334—731no—
351#334—731no—
352#334C2×D7311yescharacteristic
353#334C2×D7311yescharacteristic
354C2×#41—731no—
355C2×M16—731no—
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—731no—
359C2×M16—1461no—
360C2×M16—1461no—
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—1461no—
364C22×C8—1461no—
365C22×C8—1461no—
366C22×C8—1461no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×D4—731no—
370C4×D4—731no—
371C4×D4—731no—
372C4×D4—731no—
373C4×D4—731no—
374C4×D4—731no—
375#117—731no—
376#117—731no—
377#117—731no—
378C2×C42—731no—
379C2×C42—731no—
380C2×C42C22×D7311yescharacteristic
381C4⋊C8—731no—
382C4⋊C8—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⋊C8C4×D7311yescharacteristic
396C4⋊C8C4×D7311yescharacteristic
397C4⋊C8C22×D7311yescharacteristic
398C4⋊C8C22×D7311yescharacteristic
399C4⋊C8C22×D7311yescharacteristic
400C4⋊C8C22×D7311yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—731no—
404C22⋊C8—731no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C4×D7311yescharacteristic
412C22⋊C8C4×D7311yescharacteristic
413#97—21no—
414#97—731no—
415#97—731no—
416#97—731no—
417#97—731no—
418#97—1461no—
419#97—1461no—
420#97—1461no—
421C4×C8—21no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—1461no—
427C4×C8C22×D7311yescharacteristic
428C4×C8C22×D7311yescharacteristic
429#41—2922no—
430C2×Q8—731no—
431C2×D4—731no—
432C2×D4—731no—
433C2×D4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4C2×C4×D7311yescharacteristic
441C22×C4D4×D7311yescharacteristic
442C22×C4Q8×D7311yescharacteristic
443M16—2921no—
444M16—2921no—
445M16—5841no—
446M16—5841no—
447M16—1462no—
448M16—1462no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—2921no—
454C2×C8—5841no—
455C2×C8—5841no—
456C2×C8—5841no—
457C2×C8—5841no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—1462no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8C2×C4×D7311yescharacteristic
468C2×C8C2×C4×D7311yescharacteristic
469C2×C8C2×C4×D7311yescharacteristic
470C2×C8C2×C4×D7311yescharacteristic
471C4⋊C4—731no—
472C4⋊C4—731no—
473C4⋊C4—731no—
474C4⋊C4—731no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C22⋊C4—731no—
478C22⋊C4—731no—
479C22⋊C4—731no—
480C22⋊C4—731no—
481C22⋊C4—731no—
482C22⋊C4—731no—
483C42—731no—
484C42—731no—
485C42—731no—
486C42—731no—
487C42—731no—
488C42—731no—
489C42C2×C4×D7311yescharacteristic
490C42D4×D7311yescharacteristic
491C42Q8×D7311yescharacteristic
492C42C23×D7311yescharacteristic
493C23—731no—
494C23—731no—
495C23C4⋊C4×D7311yescharacteristic
496Q8—2921no—
497D4—2921no—
498D4—1462no—
499D4—1462no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—2921no—
506C2×C4—731no—
507C2×C4—731no—
508C2×C4—731no—
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×C4C4⋊C4×D7311yescharacteristic
522C2×C4C4⋊C4×D7311yescharacteristic
523C2×C4C4⋊C4×D7311yescharacteristic
524C2×C4C22×C4×D7311yescharacteristic
525C2×C4C2×D4×D7311yescharacteristic
526C2×C4C2×Q8×D7311yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—2921no—
536C8—2921no—
537C8—2921no—
538C8—2921no—
539C8—732no—
540C8—1461no—
541C8—1461no—
542C8—1461no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—732no—
547C22—1461no—
548C22—1461no—
549C22—1461no—
550C22—1461no—
551C22—1461no—
552C22C2×C4⋊C4×D7311yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—1461no—
558C4—1461no—
559C4—1461no—
560C4—1461no—
561C4—1461no—
562C4—1461no—
563C4#131×D7311yescharacteristic
564C4#1798935211yescharacteristic
565C4#1798938911yescharacteristic
566C4#1798940111yescharacteristic
567C2—41no—
568C2—2921no—
569C2—1462no—
570C2#2261849811yescharacteristic
571C2#2261852811yescharacteristic
572C2#430×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1572C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028Q8
cosocleC42×C73C24
hypercenter#1572D73
hypocenterC73#17840
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #22608713C2semidirect
5. #22608713C2semidirect
6. #22608710C2semidirect
7. #22608706C2semidirect
8. #22608704C2semidirect
9. #22608699C2semidirect
10. #22608695C2semidirect
11. #22608693C2semidirect
12. #22608684C2semidirect
13. #22608680C2semidirect
14. #335×D73C2semidirect
15. C73×#1572C2semidirect
293. #1572D73semidirect
302. C73#17840semidirect

Maximal subgroups

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

subgroupindex
#226190582
#226190522
#226188952
#226087132
#226087102
#226087062
#226087042
#226086992
#226086952
#226086932
#226086842
#226086802
#335×D732
C73×#15722
#1784073