Finite Group Databasebeta

← #32990582

Subgroups — #32990582

Order 18688.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610858C211yesmaximal, characteristic
2#22610736C211yesmaximal, characteristic
3#22610650C211yesmaximal, characteristic, complemented
4C2×#17988339C211yesmaximal, characteristic, complemented
5C2×#17988330C211yesmaximal, characteristic
6#22607814C211yesmaximal, characteristic, complemented
7C73×#1948C211yesmaximal, characteristic, complemented
8C2×#14556588C2211yescharacteristic
9C2×C4⋊#10596831—21no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12C2×#14556511—21no—
13C2×#14556511—21no—
14C2×#14556511—21no—
15C2×#14556511—21no—
16C2×C4×#10596831C2211yescharacteristic
17#17988342—21no—
18#17988339—22no—
19#17988330—22no—
20C2×#106×C73—21no—
21C2×C4⋊C8×C73C2211yescharacteristic
22#384×C73C2211yescharacteristic
23C4×C4⋊C4×C73C2211yescharacteristic
24#340×C73—21no—
25C22×D292—21no—
26C22×D292—21no—
27C22×D292—21no—
28C22×#10596831—21no—
29C22×#10596831—21no—
30C22×#10596831D411yescharacteristic
31C22×#10596831D411yescharacteristic
32#14556588—21no—
33#14556588—21no—
34#14556588—21no—
35#14556588Q812yes—
36C4⋊#10596831—21no—
37C4⋊#10596831—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40C4⋊#10596831—42no—
41#14556511—42no—
42#14556511—42no—
43#14556511—42no—
44#14556511—42no—
45C4×#10596831—21no—
46C4×#10596831—21no—
47C22×C8×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C42×C73—21no—
54C2×C42×C73C2311yescharacteristic
55#106×C73—42no—
56C4⋊C8×C73—21no—
57C4⋊C8×C73D412yes—
58#95×C73—21no—
59C23×D73—41no—
60C2×D292—22no—
61C2×D292—22no—
62C2×D292—22no—
63C2×D292—41no—
64C2×D292—41no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292—41no—
69C2×D292—41no—
70C2×D292—41no—
71C2×D292—41no—
72C2×D292—41no—
73C2×D292—41no—
74C2×D292—81no—
75C2×D292—81no—
76C2×#10596831—21no—
77C2×#10596831—21no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C2×#10596831—21no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C2×#10596831—41no—
85C2×#10596831—41no—
86C2×#10596831—41no—
87C2×#10596831SD1612yes—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—41no—
91C22×C4×C73C2×D411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C22×C4×C73#4111yescharacteristic
94C2×C8×C73—22no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—41no—
103C4⋊C4×C73—41no—
104C4⋊C4×C73—81no—
105C4⋊C4×C73D812yes—
106C42×C73—41no—
107C42×C73—41no—
108C42×C73C2×D411yescharacteristic
109C42×C73C2×Q811yescharacteristic
110C42×C73#4111yescharacteristic
111C42×C73#4111yescharacteristic
112C23×C73#12111yescharacteristic
113C22×D73—42no—
114C22×D73—81no—
115C22×D73—81no—
116C22×D73—81no—
117C22×D73—81no—
118C22×D73—81no—
119C22×D73—81no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—22no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—81no—
129C2×C4×C73—81no—
130C2×C4×C73—81no—
131C2×C4×C73#12111yescharacteristic
132C2×C4×C73#12111yescharacteristic
133C2×C4×C73C22⋊Q811yescharacteristic
134C2×C4×C73C22⋊Q811yescharacteristic
135C2×C4×C73C22⋊Q811yescharacteristic
136C2×C4×C73#12611yescharacteristic
137C2×C4×C73C2×D811yescharacteristic
138C2×C4×C73C2×SD1611yescharacteristic
139C2×C4×C73#13511yescharacteristic
140C2×C4×C73#13511yescharacteristic
141C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C73#13711yescharacteristic
145D292—42no—
146D292—42no—
147D292—42no—
148D292—42no—
149D292—82no—
150D292—82no—
151D292—81no—
152D292—81no—
153D292—81no—
154D292—81no—
155C8×C73—42no—
156#10596831—22no—
157#10596831—41no—
158#10596831—81no—
159#10596831—81no—
160C22×C73#39611yescharacteristic
161C22×C73#46011yescharacteristic
162C22×C73#46311yescharacteristic
163C22×C73#46611yescharacteristic
164C22×C73#46811yescharacteristic
165C22×C73#47111yescharacteristic
166C22×C73#47211yescharacteristic
167C2×D73—82no—
168C2×D73—82no—
169C2×D73—82no—
170C2×D73—161no—
171C2×D73—161no—
172C2×D73—161no—
173C2×D73—161no—
174C4×C73—21no—
175C4×C73—21no—
176C4×C73—42no—
177C4×C73—81no—
178C4×C73—161no—
179C4×C73#45911yescharacteristic
180C4×C73#46411yescharacteristic
181C4×C73#46511yescharacteristic
182C4×C73#46911yescharacteristic
183C4×C73#47411yescharacteristic
184C4×C73#47611yescharacteristic
185C4×C73#47811yescharacteristic
186C4×C73#47811yescharacteristic
187#10599—731nomaximal, Sylow
188C2×C73#166811yescharacteristic
189C2×C73#168111yescharacteristic
190C2×C73#168611yescharacteristic
191C2×C73#169711yescharacteristic
192C2×C73#206311yescharacteristic
193C2×C73#206511yescharacteristic
194C2×C73#206711yescharacteristic
195D73—162no—
196#1982—731no—
197#1957—731no—
198#1948D7311yescharacteristic, complemented
199#1939—731no—
200C2×#335—731no—
201C2×#331—731no—
202#1296—731no—
203C73#1059911yescharacteristic, complemented, Sylow
204C2×#127—731no—
205C2×#106—21no—
206C2×C4⋊C8—731no—
207C2×C4⋊C8—731no—
208C2×C4⋊C8—1461no—
209C2×C4⋊C8C2×D7311yescharacteristic
210C2×#102—1461no—
211C2×#102—1461no—
212C2×#102—1461no—
213C2×#102—1461no—
214C2×C4×C8—731no—
215#384C2×D7311yescharacteristic
216C4×C4⋊C4C2×D7311yescharacteristic
217#340—21no—
218#336—1461no—
219#335—1462no—
220#331—1462no—
221C22×D4—1461no—
222C22×D4—1461no—
223C22×D4—1461no—
224C22×C8—21no—
225C22×C8—731no—
226C22×C8—731no—
227C22×C8—1461no—
228C22×C8—1461no—
229#127—732no—
230#127—1461no—
231#127—1461no—
232#127—1461no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D7311yescharacteristic
237C2×C4⋊C4C22⋊D7311yescharacteristic
238C2×C42—21no—
239C2×C42C22×D7311yescharacteristic
240#106—42no—
241C4⋊C8—21no—
242C4⋊C8—2922no—
243C4⋊C8—1461no—
244C4⋊C8—1461no—
245C4⋊C8—1461no—
246C4⋊C8—1461no—
247C4⋊C8D29212yes—
248#102—2922no—
249#102—2922no—
250#102—2922no—
251#102—2922no—
252C4×C8—1461no—
253C4×C8—1461no—
254#95—21no—
255C24—2921no—
256C2×D4—2921no—
257C2×D4—2921no—
258C2×D4—2921no—
259C2×D4—2921no—
260C2×D4—2921no—
261C2×D4—2921no—
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—2921no—
265C2×D4—2921no—
266C2×D4—2921no—
267C2×D4—5841no—
268C2×D4—5841no—
269C2×D4—1462no—
270C2×D4—1462no—
271C2×D4—1462no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4D4×D7311yescharacteristic
276C22×C4C2×C22⋊D7311yescharacteristic
277C22×C4#1192402711yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—2921no—
282C2×C8—2921no—
283C2×C8—2921no—
284C2×C8—2921no—
285C2×C8—2921no—
286C2×C8—2921no—
287C2×C8—732no—
288C2×C8—1461no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4#1192401312yes—
302C42—41no—
303C42—41no—
304C42C2×D29211yescharacteristic
305C42Q8×D7311yescharacteristic
306C42#1192402811yescharacteristic
307C42#1192402911yescharacteristic
308C23—2922no—
309C23—5841no—
310C23—5841no—
311C23—5841no—
312C23—5841no—
313C23—5841no—
314C23—5841no—
315C23#1455656311yescharacteristic
316D4—2922no—
317D4—2922no—
318D4—2922no—
319D4—2922no—
320D4—5842no—
321D4—5842no—
322D4—5841no—
323D4—5841no—
324D4—5841no—
325D4—5841no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#1455656511yescharacteristic
338C2×C4#1455656611yescharacteristic
339C2×C4#1455656711yescharacteristic
340C2×C4#1455656911yescharacteristic
341C2×C4#1455657111yescharacteristic
342C2×C4#1455658611yescharacteristic
343C2×C4C2×#1192401311yescharacteristic
344C2×C4SD16×D7311yescharacteristic
345C2×C4#1455661111yescharacteristic
346C2×C4#1455661211yescharacteristic
347C2×C4#1455661611yescharacteristic
348C2×C4#1455661811yescharacteristic
349C2×C4#1455661811yescharacteristic
350C2×C4#1455662211yescharacteristic
351C8—42no—
352C8—2921no—
353C8—5841no—
354C8—5841no—
355C8—1462no—
356C22—5842no—
357C22—5842no—
358C22—5842no—
359C22—11681no—
360C22—11681no—
361C22—11681no—
362C22—11681no—
363C22#1798850911yescharacteristic
364C22#1798878511yescharacteristic
365C22#1798880411yescharacteristic
366C22#1798882111yescharacteristic
367C22#1798883511yescharacteristic
368C22#1798885211yescharacteristic
369C22#1798885511yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1798878211yescharacteristic
376C4#1798880911yescharacteristic
377C4#1798881711yescharacteristic
378C4#1798884111yescharacteristic
379C4#1798886411yescharacteristic
380C4#1798887611yescharacteristic
381C4#1798888411yescharacteristic
382C4#1798888611yescharacteristic
383C2—11682no—
384C2#2260928911yescharacteristic
385C2#2260937011yescharacteristic
386C2#2260940511yescharacteristic
387C2#2260946611yescharacteristic
388C2#2261128811yescharacteristic
389C2#2261130011yescharacteristic
390C2#2261131611yescharacteristic
subgroupG/H
centerC23#14556563
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1948C2
socleC23×C73#121
prime radicalC2×#14556588C22
hypercenter#1948D73
hypocenterC73#10599
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #22610650C2semidirect
4. C2×#17988339C2semidirect
6. #22607814C2semidirect
7. C73×#1948C2semidirect
198. #1948D73semidirect
203. C73#10599semidirect

Maximal subgroups

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

subgroupindex
#226108582
#226107362
#226106502
C2×#179883392
C2×#179883302
#226078142
C73×#19482
#1059973