Finite Group Databasebeta

← #32990744

Subgroups — #32990744

Order 18688.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610724C211yesmaximal, characteristic
2#22610058C211yesmaximal, characteristic, complemented
3#22609932C211yesmaximal, characteristic
4#22609928C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic, complemented
6#22607765C211yesmaximal, characteristic, complemented
7C73×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D292C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×#14556513—21no—
11C2×#14556511—21no—
12C2×#14556503—21no—
13C2×#14556503—21no—
14C2×C4×#10596831C2211yescharacteristic
15#17988457C2211yescharacteristic
16#17988350—21no—
17#17988349—21no—
18#17988349—21no—
19#17988349—21no—
20C2×C4⋊C8×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22#384×C73C2211yescharacteristic
23C22×D292D411yescharacteristic
24C22×C4×D73—21no—
25C22×#10596831—21no—
26C22×#10596831D411yescharacteristic
27C22×#10596831D411yescharacteristic
28C4×D292—21no—
29C4×D292—21no—
30C4×D292—21no—
31C4×D292—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×#11924005—21no—
37C4⋊#10596831—21no—
38C4⋊#10596831—21no—
39#14556513—42no—
40#14556511—42no—
41#14556503—42no—
42#14556503—42no—
43C4×#10596831—21no—
44C4×#10596831—21no—
45C22×C8×C73—21no—
46C22×C8×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C42×C73C2311yescharacteristic
51C4⋊C8×C73—21no—
52C4⋊C8×C73—21no—
53C4⋊C8×C73—21no—
54C4⋊C8×C73—21no—
55C23×D73—21no—
56C2×D292—21no—
57C2×D292—21no—
58C2×D292—21no—
59C2×D292—21no—
60C2×D292—21no—
61C2×D292SD1612yes—
62C22×Dic73—21no—
63C22×Dic73—41no—
64C2×C4×D73—41no—
65C2×C4×D73—41no—
66C2×C4×D73—41no—
67C2×C4×D73—41no—
68C2×C4×D73—41no—
69C2×C4×D73—41no—
70C2×#10596831—21no—
71C2×#10596831—21no—
72C2×#10596831—21no—
73C2×#10596831—21no—
74C2×#10596831—21no—
75C2×#10596831—21no—
76C2×#10596831—41no—
77C2×#10596831—41no—
78C2×#10596831—41no—
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73—41no—
82C4⋊Dic73—41no—
83C4⋊Dic73—41no—
84C4⋊Dic73—41no—
85C4⋊Dic73—81no—
86#11924005—41no—
87#11924005—41no—
88C22×C4×C73—41no—
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73#4111yescharacteristic
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C2×C8×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—41no—
102C4⋊C4×C73—81no—
103C42×C73#4111yescharacteristic
104C42×C73#4111yescharacteristic
105C42×C73#4111yescharacteristic
106C42×C73#4111yescharacteristic
107C23×C73#12111yescharacteristic
108C22×D73—22no—
109C22×D73—41no—
110C22×D73—41no—
111C22×D73—41no—
112C22×D73—41no—
113C22×D73—41no—
114C22×D73—41no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—81no—
118C2×C4×C73—81no—
119C2×C4×C73—81no—
120C2×C4×C73#12311yescharacteristic
121C2×C4×C73#12311yescharacteristic
122C2×C4×C73#12311yescharacteristic
123C2×C4×C73#12411yescharacteristic
124C2×C4×C73#12611yescharacteristic
125C2×C4×C73#12611yescharacteristic
126C2×C4×C73C2×SD1611yescharacteristic
127C2×C4×C73#13511yescharacteristic
128C2×C4×C73#13511yescharacteristic
129C2×C4×C73#13511yescharacteristic
130C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C73#13711yescharacteristic
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—81no—
138C2×Dic73—81no—
139C2×Dic73—81no—
140D292—22no—
141D292—22no—
142D292—41no—
143D292—41no—
144C4×D73—81no—
145C4×D73—81no—
146C4×D73—81no—
147C4×D73—81no—
148C8×C73—81no—
149C8×C73—81no—
150#10596831—41no—
151#10596831—41no—
152#10596831—81no—
153C22×C73#39711yescharacteristic
154C22×C73#46311yescharacteristic
155C22×C73#46311yescharacteristic
156C22×C73#46511yescharacteristic
157C22×C73#46811yescharacteristic
158C22×C73#47211yescharacteristic
159C22×C73#47311yescharacteristic
160C2×D73—42no—
161C2×D73—42no—
162C2×D73—42no—
163C2×D73—81no—
164C2×D73—81no—
165C2×D73—81no—
166C2×D73—81no—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—161no—
170C4×C73#48111yescharacteristic
171C4×C73#48211yescharacteristic
172C4×C73#48211yescharacteristic
173C4×C73#48211yescharacteristic
174C4×C73#48311yescharacteristic
175C4×C73#48511yescharacteristic
176C4×C73#48811yescharacteristic
177C4×C73#49011yescharacteristic
178Dic73—81no—
179Dic73—161no—
180#10625—731nomaximal, Sylow
181C2×C73#167711yescharacteristic
182C2×C73#167911yescharacteristic
183C2×C73#169711yescharacteristic
184C2×C73#169911yescharacteristic
185C2×C73#207311yescharacteristic
186C2×C73#207711yescharacteristic
187C2×C73#207811yescharacteristic
188D73—82no—
189#1954—731no—
190#1834—731no—
191#1802—731no—
192#1802—731no—
193#1296—731no—
194#1296D7311yescharacteristic, complemented
195#1277—731no—
196C73#1062511yescharacteristic, complemented, Sylow
197C2×C4×D4—731no—
198C2×C4⋊C8—731no—
199C2×C4⋊C8C2×D7311yescharacteristic
200C2×C4⋊C8C2×D7311yescharacteristic
201C2×#102—1461no—
202C2×#102—1461no—
203C2×C22⋊C8—1461no—
204C2×C22⋊C8—1461no—
205C2×C4×C8—731no—
206#384—731no—
207#384C2×D7311yescharacteristic
208#340—1461no—
209#340—1461no—
210#340—1461no—
211#340—1461no—
212C22×D4—731no—
213C23×C4—1461no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—731no—
217C22×C8—731no—
218C22×C8—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221C4×D4—1461no—
222C4×D4—1461no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—1461no—
228C2×C4⋊C4—1461no—
229C2×C4⋊C4—1461no—
230C2×C22⋊C4—1461no—
231C2×C42C22×D7311yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1461no—
237C4⋊C8—1461no—
238#102—2922no—
239#102—2922no—
240C22⋊C8—2922no—
241C22⋊C8—2922no—
242C4×C8—1461no—
243C4×C8—1461no—
244C24—1461no—
245C2×D4—732no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4—1461no—
251C22×C4—41no—
252C22×C4—2921no—
253C22×C4—2921no—
254C22×C4—2921no—
255C22×C4—2921no—
256C22×C4—2921no—
257C22×C4—2921no—
258C22×C4—2921no—
259C22×C4—1461no—
260C22×C4D4×D7311yescharacteristic
261C22×C4D4×D7311yescharacteristic
262C22×C4#1192402811yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—2921no—
270C2×C8—2921no—
271C2×C8—2921no—
272C2×C8—1461no—
273C2×C8—1461no—
274C2×C8—1461no—
275C2×C8—1461no—
276C2×C8—1461no—
277C2×C8—1461no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—2921no—
284C4⋊C4—2921no—
285C4⋊C4—2921no—
286C4⋊C4—2921no—
287C4⋊C4—5841no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C22⋊C4—2921no—
291C22⋊C4—2921no—
292C42#1192402711yescharacteristic
293C42#1192402811yescharacteristic
294C42#1192402811yescharacteristic
295C42#1192402911yescharacteristic
296C23—2921no—
297C23—2921no—
298C23—2921no—
299C23—2921no—
300C23—2921no—
301C23—2921no—
302C23—1462no—
303C23#1455656411yescharacteristic
304D4—2921no—
305D4—2921no—
306D4—1462no—
307D4—1462no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—2921no—
316C2×C4—5841no—
317C2×C4—5841no—
318C2×C4—5841no—
319C2×C4—5841no—
320C2×C4—5841no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4#1455657311yescharacteristic
324C2×C4#1455657611yescharacteristic
325C2×C4#1455657611yescharacteristic
326C2×C4#1455657711yescharacteristic
327C2×C4#1455658511yescharacteristic
328C2×C4#1455658611yescharacteristic
329C2×C4SD16×D7311yescharacteristic
330C2×C4#1455661211yescharacteristic
331C2×C4#1455661411yescharacteristic
332C2×C4#1455661411yescharacteristic
333C2×C4#1455661511yescharacteristic
334C2×C4#1455661511yescharacteristic
335C2×C4#1455661811yescharacteristic
336C2×C4#1455662011yescharacteristic
337C8—81no—
338C8—81no—
339C8—2921no—
340C8—2921no—
341C8—5841no—
342C22—2922no—
343C22—2922no—
344C22—2922no—
345C22—5841no—
346C22—5841no—
347C22—5841no—
348C22—5841no—
349C22#1798851611yescharacteristic
350C22#1798880111yescharacteristic
351C22#1798880511yescharacteristic
352C22#1798881911yescharacteristic
353C22#1798883211yescharacteristic
354C22#1798885611yescharacteristic
355C22#1798886111yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—5841no—
360C4—11681no—
361C4#1798890411yescharacteristic
362C4#1798891311yescharacteristic
363C4#1798891411yescharacteristic
364C4#1798891411yescharacteristic
365C4#1798891911yescharacteristic
366C4#1798892711yescharacteristic
367C4#1798894311yescharacteristic
368C4#1798895011yescharacteristic
369C2—5842no—
370C2#2260934311yescharacteristic
371C2#2260935311yescharacteristic
372C2#2260946311yescharacteristic
373C2#2260948111yescharacteristic
374C2#2261134811yescharacteristic
375C2#2261137011yescharacteristic
376C2#2261137511yescharacteristic
subgroupG/H
centerC23#14556564
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1296C2
socleC23×C73#121
prime radicalC22×D292D4
hypercenter#1296D73
hypocenterC73#10625
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #22610058C2semidirect
5. #22607815C2semidirect
6. #22607765C2semidirect
7. C73×#1296C2semidirect
194. #1296D73semidirect
196. C73#10625semidirect

Maximal subgroups

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

subgroupindex
#226107242
#226100582
#226099322
#226099282
#226078152
#226077652
C73×#12962
#1062573