Finite Group Databasebeta

← #33056842

Subgroups — #33056842

Order 18688.

544 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620514C211yesmaximal, characteristic
2#22619027C211yesmaximal, characteristic
3#22619022C211yesmaximal, characteristic
4#22608804C211yesmaximal, characteristic, complemented
5#22608803C211yesmaximal, characteristic, complemented
6#22608801C211yesmaximal, characteristic, complemented
7#22608784C211yesmaximal, characteristic, complemented
8#22608781C211yesmaximal, characteristic, complemented
9#22608779C211yesmaximal, characteristic, complemented
10#22608778C211yesmaximal, characteristic, complemented
11#22608691C211yesmaximal, characteristic
12#22608402C211yesmaximal, characteristic
13#22608402C211yesmaximal, characteristic
14#22608222C211yesmaximal, characteristic
15C73×#1587C211yesmaximal, characteristic, complemented
16#17989141C2211yescharacteristic
17#17989141C2211yescharacteristic
18#17988991C411yescharacteristic
19#17988965C411yescharacteristic
20#17988936C411yescharacteristic
21#17988936C411yescharacteristic
22#17988829C411yescharacteristic
23#17988827C411yescharacteristic
24#17988827C411yescharacteristic
25#17988825C411yescharacteristic
26#17988718C2211yescharacteristic
27#17988717—21no—
28#17988717C2211yescharacteristic
29#17988716—21no—
30#17988715—21no—
31#17988714—21no—
32#17988714C2211yescharacteristic
33Q8×#10596831C2211yescharacteristic
34C8×Dic146C2211yescharacteristic
35#17988711C2211yescharacteristic
36C4×Dic292C2211yescharacteristic
37C4×#11924018C2211yescharacteristic
38C4×#11924018C2211yescharacteristic
39#17988649—21no—
40#17988647—21no—
41#17988647—21no—
42#17988646—21no—
43#17988643C2211yescharacteristic
44#17988643C2211yescharacteristic
45#17988638C2211yescharacteristic
46#17988638C2211yescharacteristic
47C4×C8×D73C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988319C2211yescharacteristic
52#17988319C2211yescharacteristic
53Q8⋊#10596831C2211yescharacteristic
54Q8⋊#10596831C2211yescharacteristic
55#17988317C2211yescharacteristic
56#17988317C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988308C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×Dic292C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924018C2×C411yescharacteristic
70C2×C8×D73C2×C411yescharacteristic
71C2×C8×D73C2×C411yescharacteristic
72#14556590C2×C411yescharacteristic
73#14556590C2×C411yescharacteristic
74#14556589C2×C411yescharacteristic
75#14556589C2×C411yescharacteristic
76#14556581—21no—
77#14556581—21no—
78#14556571C2×C411yescharacteristic
79#14556571C2×C411yescharacteristic
80#14556569—21no—
81#14556569—21no—
82#14556567C2×C411yescharacteristic
83#14556567C2×C411yescharacteristic
84C4×Dic146—21no—
85C4×Dic146—21no—
86C4×Dic146C2311yescharacteristic
87C4×Dic146C2311yescharacteristic
88#14556548—21no—
89#14556548—21no—
90C42×D73C2311yescharacteristic
91#14556525C2×C411yescharacteristic
92#14556524C2×C411yescharacteristic
93#14556524C2×C411yescharacteristic
94C4⋊#10596831—21no—
95C4⋊#10596831—21no—
96C4⋊#10596831C2311yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98#14556520—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520D411yescharacteristic
104#14556520D411yescharacteristic
105#14556516C2×C411yescharacteristic
106#14556516C2×C411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556514C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556503—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503D411yescharacteristic
115#14556503D411yescharacteristic
116#14556502—21no—
117#14556501—21no—
118#14556501—21no—
119#14556501—21no—
120#14556501—21no—
121C4×#10596831—21no—
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73C2×C411yescharacteristic
128C8×Dic73C2×C411yescharacteristic
129C2×Q16×C73C2×C411yescharacteristic
130C4×Q8×C73C2311yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132#107×C73C2×C411yescharacteristic
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137#103×C73C2×C411yescharacteristic
138#103×C73C2×C411yescharacteristic
139#97×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×C4×D73C22×C411yescharacteristic
149C2×C4×D73C2×D411yescharacteristic
150C2×C4×D73#4111yescharacteristic
151Dic292—41no—
152#11924018—41no—
153#11924018—41no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C8×D73—41no—
162C8×D73—41no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73C22×C411yescharacteristic
166C4⋊Dic73C22×C411yescharacteristic
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924005—21no—
178#11924005—21no—
179#11924005—21no—
180#11924005—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73C22×C411yescharacteristic
184C4×Dic73C2×D411yescharacteristic
185C4×Dic73#4111yescharacteristic
186C2×Q8×C73C22×C411yescharacteristic
187C2×Q8×C73C22×C411yescharacteristic
188Q16×C73—41no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73C22×C411yescharacteristic
193C2×C8×C73C22×C411yescharacteristic
194C2×C8×C73C2×D411yescharacteristic
195C2×C8×C73C2×D411yescharacteristic
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73C22×C411yescharacteristic
199C4⋊C4×C73C22×C411yescharacteristic
200C42×C73—21no—
201C42×C73—21no—
202C42×C73C2411yescharacteristic
203C22×D73C4×D411yescharacteristic
204Q8×C73—21no—
205Q8×C73—21no—
206Q8×C73—21no—
207Q8×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73C23×C411yescharacteristic
213C2×C4×C73C22×D411yescharacteristic
214C2×C4×C73C2×#4111yescharacteristic
215C2×Dic73—21no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—21no—
219C2×Dic73C4×D411yescharacteristic
220C2×Dic73C4×D411yescharacteristic
221C2×Dic73C4×D411yescharacteristic
222C4×D73—21no—
223C4×D73—21no—
224C4×D73—21no—
225C4×D73—21no—
226C4×D73—41no—
227Dic146—21no—
228Dic146—21no—
229Dic146—21no—
230Dic146—21no—
231Dic146—81no—
232Dic146—81no—
233C8×C73—21no—
234C8×C73—21no—
235C8×C73—21no—
236C8×C73—21no—
237C8×C73—41no—
238C8×C73—41no—
239C8×C73—41no—
240#10596831—21no—
241#10596831—21no—
242#10596831—21no—
243#10596831—21no—
244#10596831—41no—
245#10596831—41no—
246#10596831—41no—
247C22×C73C2×C4×D411yescharacteristic
248C2×D73—21no—
249C2×D73—21no—
250C2×D73—21no—
251C4×C73—21no—
252C4×C73—41no—
253C4×C73—41no—
254C4×C73—41no—
255C4×C73—41no—
256C4×C73#56811yescharacteristic
257C4×C73#56811yescharacteristic
258C4×C73#57811yescharacteristic
259C4×C73#57811yescharacteristic
260Dic73—21no—
261Dic73—21no—
262Dic73—21no—
263Dic73—41no—
264Dic73—41no—
265Dic73—41no—
266Dic73—41no—
267#17991—731nomaximal, Sylow
268C2×C73#293211yescharacteristic
269C2×C73#295011yescharacteristic
270C2×C73#295711yescharacteristic
271D73—41no—
272#3170—731no—
273#2985—731no—
274#2985—731no—
275#1587—731no—
276#1587—731no—
277#1587—731no—
278#1587D7311yescharacteristic, complemented
279#1584—731no—
280#1584—731no—
281#1584—731no—
282#1584—731no—
283#1568—731no—
284#1497—731no—
285#1497—731no—
286#1452—731no—
287C73#1799111yescharacteristic, complemented, Sylow
288#533—731no—
289#533—731no—
290#500—731no—
291#494—731no—
292#487—731no—
293#487—731no—
294#467—731no—
295#467—731no—
296#467—731no—
297#467—731no—
298#446—731no—
299#446—731no—
300#446—731no—
301#446—1461no—
302#446—1461no—
303#446—1461no—
304#446—1461no—
305#446C2×D7311yescharacteristic
306C8×Q8—731no—
307C8×Q8—731no—
308C8×Q8—731no—
309C8×Q8C2×D7311yescharacteristic
310C4×Q16—731no—
311C4×Q16—731no—
312C4×Q16—731no—
313C4×Q16C2×D7311yescharacteristic
314#433—1461no—
315#433—1461no—
316#433—1461no—
317#433—1461no—
318#432—731no—
319#432—731no—
320#431—731no—
321#431—731no—
322C2×C4×C8—731no—
323#335—731no—
324#335—731no—
325#334—731no—
326#334C2×D7311yescharacteristic
327Q8⋊C8—731no—
328Q8⋊C8—731no—
329Q8⋊C8—731no—
330Q8⋊C8—731no—
331Q8⋊C8—731no—
332Q8⋊C8—731no—
333Q8⋊C8C2×D7311yescharacteristic
334Q8⋊C8C2×D7311yescharacteristic
335#322—731no—
336#322—731no—
337#322—731no—
338#322C2×D7311yescharacteristic
339C2×Q16—731no—
340C2×Q16—731no—
341C2×Q16—731no—
342C2×Q16C4×D7311yescharacteristic
343C22×C8—731no—
344C22×C8—731no—
345C4⋊Q8—731no—
346C4⋊Q8—731no—
347C4⋊Q8—731no—
348C4⋊Q8—731no—
349#125—1461no—
350#125—1461no—
351C22⋊Q8—731no—
352C22⋊Q8—731no—
353C22⋊Q8—731no—
354C22⋊Q8—731no—
355C22⋊Q8—1461no—
356C22⋊Q8—1461no—
357C4×Q8—731no—
358C4×Q8—731no—
359C4×Q8—1461no—
360C4×Q8—1461no—
361C4×Q8C22×D7311yescharacteristic
362C4×Q8C22×D7311yescharacteristic
363#117—1461no—
364#117—1461no—
365C2×C42—731no—
366#107—731no—
367#107—731no—
368#107—731no—
369#107C4×D7311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—731no—
373C4⋊C8—731no—
374C4⋊C8—731no—
375C4⋊C8—731no—
376C4⋊C8—1461no—
377C4⋊C8—1461no—
378C4⋊C8—1461no—
379C4⋊C8—1461no—
380C4⋊C8—1461no—
381C4⋊C8—1461no—
382C4⋊C8—1461no—
383C4⋊C8C22×D7311yescharacteristic
384C4⋊C8C22×D7311yescharacteristic
385#103—731no—
386#103—731no—
387#103—731no—
388#103—731no—
389#103—731no—
390#103—731no—
391#103C4×D7311yescharacteristic
392#103C4×D7311yescharacteristic
393C22⋊C8—731no—
394C22⋊C8—731no—
395C22⋊C8—1461no—
396C22⋊C8—1461no—
397C22⋊C8—1461no—
398#97—21no—
399#97—1461no—
400#97—1461no—
401#97—1461no—
402#97—1461no—
403#97—1461no—
404C4×C8—21no—
405C4×C8—731no—
406C4×C8—731no—
407C4×C8—731no—
408C4×C8—731no—
409C4×C8—731no—
410C4×C8—1461no—
411C4×C8—1461no—
412C4×C8—1461no—
413C4×C8C22×D7311yescharacteristic
414C4×C8C22×D7311yescharacteristic
415C4×C8C22×D7311yescharacteristic
416C2×Q8—731no—
417C2×Q8—731no—
418C2×Q8—1461no—
419C2×Q8—1461no—
420C2×Q8C2×C4×D7311yescharacteristic
421C2×Q8C2×C4×D7311yescharacteristic
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425Q16—41no—
426Q16—2921no—
427Q16—2921no—
428Q16—2921no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—2921no—
433C2×C8—2921no—
434C2×C8—731no—
435C2×C8—731no—
436C2×C8—731no—
437C2×C8—731no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8C2×C4×D7311yescharacteristic
442C2×C8C2×C4×D7311yescharacteristic
443C2×C8D4×D7311yescharacteristic
444C2×C8D4×D7311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—731no—
448C4⋊C4—731no—
449C4⋊C4—1461no—
450C4⋊C4—1461no—
451C4⋊C4—1461no—
452C4⋊C4—1461no—
453C4⋊C4—1461no—
454C4⋊C4—1461no—
455C4⋊C4—1461no—
456C4⋊C4—1461no—
457C4⋊C4—1461no—
458C4⋊C4—1461no—
459C4⋊C4—1461no—
460C4⋊C4—1461no—
461C4⋊C4C2×C4×D7311yescharacteristic
462C4⋊C4C2×C4×D7311yescharacteristic
463C22⋊C4—1461no—
464C22⋊C4—1461no—
465C22⋊C4—1461no—
466C22⋊C4—1461no—
467C42—21no—
468C42—21no—
469C42—731no—
470C42—731no—
471C42—731no—
472C42—1461no—
473C42—1461no—
474C42C23×D7311yescharacteristic
475C23—731no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—5841no—
481Q8—5841no—
482Q8—1461no—
483Q8—1461no—
484Q8—1461no—
485Q8—1461no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—2921no—
491C2×C4—731no—
492C2×C4—731no—
493C2×C4—731no—
494C2×C4—1461no—
495C2×C4—1461no—
496C2×C4—1461no—
497C2×C4—1461no—
498C2×C4—1461no—
499C2×C4—1461no—
500C2×C4—1461no—
501C2×C4—1461no—
502C2×C4C22×C4×D7311yescharacteristic
503C2×C4C2×D4×D7311yescharacteristic
504C2×C4#41×D7311yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—2921no—
513C8—2921no—
514C8—2921no—
515C8—1461no—
516C8—1461no—
517C8—1461no—
518C8—1461no—
519C22—1461no—
520C22—1461no—
521C22—1461no—
522C22C4×D4×D7311yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—2921no—
529C4—2921no—
530C4—2921no—
531C4—2921no—
532C4—1461no—
533C4—1461no—
534C4—1461no—
535C4#1798935211yescharacteristic
536C4#1798935311yescharacteristic
537C4#1798940311yescharacteristic
538C4#1798940311yescharacteristic
539C2—2921no—
540C2#2261864511yescharacteristic
541C2#2261879611yescharacteristic
542C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1587C2
socleC22×C73C2×C4×D4
prime radicalC22×D73C4×D4
cosocleC42×C73C24
hypercenter#1587D73
hypocenterC73#17991
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #22608804C2semidirect
5. #22608803C2semidirect
6. #22608801C2semidirect
7. #22608784C2semidirect
8. #22608781C2semidirect
9. #22608779C2semidirect
10. #22608778C2semidirect
15. C73×#1587C2semidirect
278. #1587D73semidirect
287. C73#17991semidirect

Maximal subgroups

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

subgroupindex
#226205142
#226190272
#226190222
#226088042
#226088032
#226088012
#226087842
#226087812
#226087792
#226087782
#226086912
#226084022
#226082222
C73×#15872
#1799173