Finite Group Databasebeta

← #33068291

Subgroups — #33068291

Order 18688.

716 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620253C211yesmaximal, characteristic, complemented
2#22619939C211yesmaximal, characteristic, complemented
3C2×D4×#10596831C211yesmaximal, characteristic, complemented
4#22609380C212yesmaximal, complemented
5#22609366C212yesmaximal, complemented
6#22609352C212yesmaximal, complemented
7#22609338C212yesmaximal, complemented
8#22608677C211yesmaximal, characteristic, complemented
9#22608586C211yesmaximal, characteristic, complemented
10#22608580C211yesmaximal, characteristic, complemented
11C73×#3100C211yesmaximal, characteristic
12C23×#10596831—21no—
13#17989144C2211yescharacteristic
14#17988941—21no—
15#17988941—21no—
16#17988937C2211yescharacteristic, complemented
17#17988937C2211yescharacteristic, complemented
18#17988933C2211yescharacteristic, complemented
19#17988933C2211yescharacteristic, complemented
20#17988917—21no—
21#17988877C2212yes—
22#17988792C2212yes—
23#17988738—21no—
24C4×#11924016—22no—
25D4×#10596831—21no—
26D4×#10596831—21no—
27D4×#10596831C2212yes—
28D4×#10596831C2212yes—
29#17988640C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31#17988583—21no—
32#17988583—21no—
33C2×C22⋊#10596831—21no—
34C2×C4×#10596831C2211yescharacteristic
35#17988339C2212yescomplemented
36#17988337C2212yescomplemented
37#17988335C2212yescomplemented
38#17988334C2212yescomplemented
39#17988333C2212yescomplemented
40#17988331C2212yescomplemented
41#532×C73C2211yescharacteristic
42C2×C4×D4×C73C2211yescharacteristic
43#480×C73—21no—
44#474×C73C2212yes—
45#459×C73C2212yes—
46#447×C73—21no—
47C4×D8×C73—22no—
48#431×C73C2211yescharacteristic
49C2×#11924016—22no—
50C22×#10596831—22no—
51C22×#10596831—22no—
52C22×#10596831—21no—
53C22×#10596831—44no—
54C22×#10596831D411yescharacteristic
55C22×#10596831D411yescharacteristic
56#14556591C2311yescharacteristic
57#14556591C2311yescharacteristic
58#14556583—21no—
59#14556570—21no—
60#14556570—21no—
61C4×Dic146—21no—
62C4×Dic146—21no—
63#14556550—21no—
64#14556522—22no—
65C4⋊#10596831—21no—
66C4⋊#10596831C2312yes—
67C4⋊#10596831C2312yes—
68#14556515—21no—
69#14556515—21no—
70#14556515—21no—
71#14556515—21no—
72#14556514—22no—
73#14556512—21no—
74#14556512—21no—
75#14556512—21no—
76#14556512—21no—
77#14556512—22no—
78C22⋊#10596831—22no—
79C22⋊#10596831—22no—
80C22⋊#10596831—21no—
81C4×#10596831—21no—
82C4×#10596831D411yescharacteristic
83C4×#10596831D411yescharacteristic
84C4×#10596831C2311yescharacteristic
85C4×#10596831C2311yescharacteristic
86C2×#41×C73—21no—
87C22×D4×C73D411yescharacteristic
88C23×C4×C73—21no—
89C2×D8×C73—22no—
90C4⋊Q8×C73C2311yescharacteristic
91#127×C73C2311yescharacteristic
92#124×C73—21no—
93#121×C73—21no—
94#121×C73—21no—
95C4×D4×C73—21no—
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73D412yes—
100C4×D4×C73C2312yes—
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C22⋊C4×C73—21no—
103C2×C42×C73C2311yescharacteristic
104#107×C73—22no—
105C4⋊C8×C73C2312yes—
106#102×C73—22no—
107#102×C73—22no—
108C22⋊C8×C73—21no—
109C4×C8×C73—21no—
110C2×Dic146—21no—
111C2×Dic146—21no—
112#11924016—44no—
113C2×#10596831—22no—
114C2×#10596831—22no—
115C2×#10596831—22no—
116C2×#10596831—22no—
117C2×#10596831—44no—
118C2×#10596831—44no—
119C2×#10596831—42no—
120C2×#10596831C2×D411yescharacteristic
121C2×#10596831C2×D411yescharacteristic
122C2×#10596831C2×D411yescharacteristic
123C2×#10596831C2×D411yescharacteristic
124C4⋊Dic73—21no—
125C4⋊Dic73—21no—
126C4⋊Dic73—21no—
127C4⋊Dic73—21no—
128#11924007—41no—
129#11924007—41no—
130C22⋊Dic73—41no—
131C4×Dic73—41no—
132C24×C73—21no—
133#41×C73—42no—
134#41×C73—42no—
135C2×Q8×C73—21no—
136C2×D4×C73—24no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73—41no—
142C2×D4×C73C2×D412yes—
143C22×C4×C73—21no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—42no—
147C22×C4×C73—42no—
148C22×C4×C73—41no—
149C22×C4×C73C2×D411yescharacteristic
150C22×C4×C73C2×D411yescharacteristic
151C22×C4×C73#4111yescharacteristic
152D8×C73—44no—
153C2×C8×C73—22no—
154C4⋊C4×C73—21no—
155C4⋊C4×C73—21no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73C2×D412yes—
158C22⋊C4×C73—22no—
159C22⋊C4×C73—22no—
160C22⋊C4×C73—41no—
161C22⋊C4×C73—41no—
162C42×C73C2×D411yescharacteristic
163C42×C73C2×D411yescharacteristic
164C42×C73#4111yescharacteristic
165C42×C73C2411yescharacteristic
166C23×C73—24no—
167C23×C73—22no—
168C23×C73—42no—
169C23×C73—42no—
170C23×C73—41no—
171C23×C73#12111yescharacteristic
172Q8×C73—41no—
173Q8×C73—41no—
174D4×C73—24no—
175D4×C73—22no—
176D4×C73—42no—
177D4×C73—41no—
178D4×C73—41no—
179D4×C73—81no—
180D4×C73—82no—
181D4×C73#13514yes—
182C2×C4×C73—22no—
183C2×C4×C73—22no—
184C2×C4×C73—41no—
185C2×C4×C73—42no—
186C2×C4×C73—42no—
187C2×C4×C73—42no—
188C2×C4×C73—44no—
189C2×C4×C73—41no—
190C2×C4×C73—82no—
191C2×C4×C73#12111yescharacteristic
192C2×C4×C73#12111yescharacteristic
193C2×C4×C73#12111yescharacteristic
194C2×C4×C73#13512yes—
195C2×C4×C73AGL(1,ℤ/8)12yes—
196C2×C4×C73C22×D411yescharacteristic
197C2×C4×C73C22×D411yescharacteristic
198C2×C4×C73C2×#4111yescharacteristic
199C2×Dic73—41no—
200C2×Dic73—41no—
201Dic146—42no—
202Dic146—81no—
203C8×C73—42no—
204#10596831—21no—
205#10596831—21no—
206#10596831—21no—
207#10596831—21no—
208#10596831—42no—
209#10596831—42no—
210C22×C73—21no—
211C22×C73—21no—
212C22×C73—24no—
213C22×C73—48no—
214C22×C73—42no—
215C22×C73—42no—
216C22×C73—81no—
217C22×C73—81no—
218C22×C73—81no—
219C22×C73#46312yes—
220C22×C73C2×#12111yescharacteristic
221C4×C73—21no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—42no—
225C4×C73—81no—
226C4×C73#46312yes—
227C4×C73C2×#13511yescharacteristic
228C4×C73C2×#13512yes—
229C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
230Dic73—81no—
231Dic73—81no—
232#19110—731nomaximal, Sylow
233C2×C73—22no—
234C2×C73—44no—
235C2×C73—161no—
236C2×C73C2×#46311yescharacteristic
237C2×C73#305011yescharacteristic
238C2×C73#306711yescharacteristic
239#3131—731no—
240#3101—731no—
241#3100D7311yescharacteristic
242C2×C8×D4—731no—
243#1683—732no—
244#1681—732no—
245#1679—732no—
246#1677—732no—
247#1564—731no—
248#1542—731no—
249#1540—731no—
250C73#1911011yescharacteristic, complemented, Sylow
251C23×C8—1461no—
252#533—731no—
253#532C2×D7311yescharacteristic
254C2×C4×D4C2×D7311yescharacteristic
255#488—1461no—
256#488—1461no—
257#487—731no—
258#487—731no—
259#486—731no—
260#486—731no—
261#483—1461no—
262#480—21no—
263#476—732no—
264#474C2×D7312yes—
265#461—732no—
266#459C2×D7312yes—
267#450—1461no—
268#447—21no—
269C4×SD16—1462no—
270C4×D8—22no—
271C8×D4—732no—
272C8×D4—732no—
273C8×D4—1461no—
274C8×D4—1461no—
275#431—731no—
276#431C2×D7311yescharacteristic
277C2×C4⋊C8—731no—
278#416—1461no—
279#416—1461no—
280C2×C22⋊C8—1461no—
281C2×C4×C8—731no—
282#335—732no—
283#334—732no—
284#333—732no—
285#332—732no—
286#332—732no—
287#331—732no—
288C2×#41—21no—
289C22×D4C22⋊D7311yescharacteristic
290C23×C4—21no—
291C2×SD16—1462no—
292C2×D8—22no—
293C22×C8—2924no—
294C22×C8—731no—
295C22×C8—731no—
296C22×C8—1462no—
297C22×C8—1462no—
298C22×C8—1461no—
299C4⋊Q8—731no—
300C4⋊Q8—731no—
301C4⋊Q8C22×D7311yescharacteristic
302#127C22×D7311yescharacteristic
303#125—1461no—
304#124—21no—
305C22⋊Q8—1461no—
306C22⋊Q8—1461no—
307#121—21no—
308#121—21no—
309C4×Q8—1461no—
310C4×Q8—1461no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C22⋊D7312yes—
316C4×D4C22×D7312yes—
317#117—1461no—
318C2×C4⋊C4C22⋊D7311yescharacteristic
319C2×C22⋊C4—21no—
320C2×C42C22×D7311yescharacteristic
321#107—22no—
322#106—1462no—
323C4⋊C8—732no—
324C4⋊C8—732no—
325C4⋊C8—1461no—
326C4⋊C8C22×D7312yes—
327#103—1461no—
328#103—1461no—
329#103—1461no—
330#103—1461no—
331#103—1462no—
332#102—22no—
333#102—22no—
334#102—1461no—
335#102—1461no—
336#102—1461no—
337#102—1461no—
338#102—1462no—
339C22⋊C8—21no—
340C22⋊C8—1462no—
341C22⋊C8—1462no—
342C22⋊C8—1461no—
343C4×C8—21no—
344C4×C8—731no—
345C4×C8—731no—
346C4×C8—731no—
347C4×C8—731no—
348C4×C8—1461no—
349C24—21no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—1461no—
354C2×Q8—1461no—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4C2×C22⋊D7312yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—41no—
368C22×C4D4×D7311yescharacteristic
369C22×C4C2×C22⋊D7311yescharacteristic
370C22×C4#1192402711yescharacteristic
371SD16—2924no—
372D8—44no—
373C2×C8—22no—
374C2×C8—2922no—
375C2×C8—2924no—
376C2×C8—2924no—
377C2×C8—731no—
378C2×C8—731no—
379C2×C8—731no—
380C2×C8—731no—
381C2×C8—1462no—
382C2×C8—1462no—
383C2×C8—1462no—
384C2×C8—1462no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—2921no—
389C4⋊C4—2921no—
390C4⋊C4—1461no—
391C4⋊C4—1461no—
392C4⋊C4—1461no—
393C4⋊C4—1461no—
394C4⋊C4C2×C22⋊D7312yes—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—2921no—
400C42—2921no—
401C42D4×D7311yescharacteristic
402C42C2×C22⋊D7311yescharacteristic
403C42#1192402711yescharacteristic
404C42C23×D7311yescharacteristic
405C23—24no—
406C23—22no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23#1455656311yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—2922no—
414Q8—5841no—
415D4—24no—
416D4—22no—
417D4—41no—
418D4—42no—
419D4—41no—
420D4—81no—
421D4—82no—
422D4#1455661114yes—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—2921no—
433C2×C4—2921no—
434C2×C4#1455656311yescharacteristic
435C2×C4#1455656311yescharacteristic
436C2×C4#1455656311yescharacteristic
437C2×C4#1455661012yes—
438C2×C4#1455661512yes—
439C2×C4C2×D4×D7311yescharacteristic
440C2×C4C22×C22⋊D7311yescharacteristic
441C2×C4C2×#1192402711yescharacteristic
442C8—42no—
443C8—2922no—
444C8—2922no—
445C8—1461no—
446C8—1461no—
447C8—1461no—
448C8—1461no—
449C22—21no—
450C22—21no—
451C22—24no—
452C22—48no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#1798880012yes—
459C22C2×#1455656311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—5841no—
466C4—5841no—
467C4#1798880012yes—
468C4C2×#1455661011yescharacteristic
469C4C2×#1455661112yes—
470C4C2×#1455661511yescharacteristic
471C2—22no—
472C2—44no—
473C2—161no—
474C2C2×#1798880011yescharacteristic
475C2#2261950911yescharacteristic
476C2#2261964811yescharacteristic
subgroupG/H
centerC2×C4#14556563
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
Fitting, prime radicalC73×#3100C2
socleC22×C73C2×#121
hypercenter#3100D73
hypocenterC73#19110
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #22620253C2semidirect
2. #22619939C2semidirect
3. C2×D4×#10596831C2semidirect
4. #22609380C2semidirect
5. #22609366C2semidirect
6. #22609352C2semidirect
7. #22609338C2semidirect
8. #22608677C2semidirect
9. #22608586C2semidirect
10. #22608580C2semidirect
16. #17988937C22semidirect
17. #17988937C22semidirect
18. #17988933C22semidirect
19. #17988933C22semidirect
35. #17988339C22semidirect
36. #17988337C22semidirect
37. #17988335C22semidirect
38. #17988334C22semidirect
39. #17988333C22semidirect
40. #17988331C22semidirect
250. C73#19110semidirect

Maximal subgroups

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

subgroupindex
#226202532
#226199392
C2×D4×#105968312
#226093802
#226093662
#226093522
#226093382
#226086772
#226085862
#226085802
C73×#31002
#1911073