Finite Group Databasebeta

← #32990739

Subgroups — #32990739

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#22610725C211yesmaximal, characteristic
2#22609928C211yesmaximal, characteristic
3#22609928C211yesmaximal, characteristic
4#22607814C211yesmaximal, characteristic, complemented
5#22607814C211yesmaximal, characteristic, complemented
6#22607766C211yesmaximal, characteristic, complemented
7C73×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D292C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×C4⋊#10596831C2211yescharacteristic
12C2×#14556511—21no—
13C2×#14556511—21no—
14C2×#14556503—21no—
15C2×#14556503—21no—
16#17988349—21no—
17#17988349—21no—
18C2×C4×C8×C73C2211yescharacteristic
19#384×C73C2211yescharacteristic
20#384×C73C2211yescharacteristic
21#340×C73—21no—
22#340×C73—21no—
23C22×D292D411yescharacteristic
24C22×C4×D73—21no—
25C22×#10596831—21no—
26C22×#10596831—21no—
27C22×#10596831—21no—
28C4×D292—21no—
29C4×D292—21no—
30C4×D292—21no—
31C4×D292—21no—
32C2×C4⋊Dic73D411yescharacteristic
33C2×#11924005—21no—
34C4⋊#10596831—21no—
35C4⋊#10596831—21no—
36C4⋊#10596831—21no—
37C4⋊#10596831—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40#14556511—42no—
41#14556511—42no—
42#14556503—42no—
43#14556503—42no—
44C22×C8×C73D411yescharacteristic
45C22×C8×C73D411yescharacteristic
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C42×C73C2311yescharacteristic
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—
63C2×C4×D73—41no—
64C2×C4×D73—41no—
65C2×C4×D73—41no—
66C2×C4×D73—41no—
67C2×C4×D73—41no—
68C2×C4×D73—41no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C2×#10596831—41no—
76C2×#10596831—41no—
77C2×#10596831—41no—
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80#11924005—41no—
81#11924005—41no—
82C22×C4×C73—41no—
83C22×C4×C73—41no—
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73#4111yescharacteristic
87C2×C8×C73—21no—
88C2×C8×C73—21no—
89C2×C8×C73—21no—
90C2×C8×C73—21no—
91C2×C8×C73—21no—
92C2×C8×C73—21no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73—41no—
97C4⋊C4×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—81no—
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—81no—
121C2×C4×C73—81no—
122C2×C4×C73—81no—
123C2×C4×C73#12311yescharacteristic
124C2×C4×C73#12311yescharacteristic
125C2×C4×C73#12311yescharacteristic
126C2×C4×C73#12411yescharacteristic
127C2×C4×C73#12611yescharacteristic
128C2×C4×C73#12611yescharacteristic
129C2×C4×C73C2×SD1611yescharacteristic
130C2×C4×C73#13511yescharacteristic
131C2×C4×C73#13511yescharacteristic
132C2×C4×C73#13511yescharacteristic
133C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C73#13711yescharacteristic
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140D292—22no—
141D292—22no—
142D292—41no—
143D292—41no—
144C4×D73—81no—
145C4×D73—81no—
146C4×D73—81no—
147C4×D73—81no—
148C8×C73—41no—
149C8×C73—41no—
150#10596831—81no—
151#10596831—81no—
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—161no—
171C4×C73#48111yescharacteristic
172C4×C73#48211yescharacteristic
173C4×C73#48211yescharacteristic
174C4×C73#48211yescharacteristic
175C4×C73#48311yescharacteristic
176C4×C73#48511yescharacteristic
177C4×C73#48811yescharacteristic
178C4×C73#49011yescharacteristic
179Dic73—81no—
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#1834D7311yescharacteristic, complemented
191#1802—731no—
192#1802—731no—
193#1296—731no—
194#1296—731no—
195#1277—731no—
196C73#1062511yescharacteristic, complemented, Sylow
197C2×C4×D4—731no—
198C2×C4⋊C8—731no—
199C2×C4⋊C8—731no—
200C2×C4⋊C8—731no—
201C2×#102—1461no—
202C2×#102—1461no—
203C2×C22⋊C8—1461no—
204C2×C22⋊C8—1461no—
205C2×C4×C8C2×D7311yescharacteristic
206#384C2×D7311yescharacteristic
207#384C2×D7311yescharacteristic
208#340—21no—
209#340—21no—
210#340—1461no—
211#340—1461no—
212C22×D4—731no—
213C23×C4—1461no—
214C22×C8—1461no—
215C22×C8—1461no—
216C22×C8—1461no—
217C22×C8C22⋊D7311yescharacteristic
218C22×C8C22⋊D7311yescharacteristic
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—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—731no—
230C2×C22⋊C4—1461no—
231C2×C42C22×D7311yescharacteristic
232C4⋊C8—1461no—
233C4⋊C8—1461no—
234C4⋊C8—1461no—
235C4⋊C8—1461no—
236C4⋊C8—1461no—
237C4⋊C8—1461no—
238#102—2922no—
239#102—2922no—
240C22⋊C8—2922no—
241C22⋊C8—2922no—
242C4×C8—21no—
243C4×C8—21no—
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—41no—
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×C4C2×C22⋊D7311yescharacteristic
262C22×C4#1192402711yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—2921no—
270C2×C8—2921no—
271C2×C8—2921no—
272C2×C8—2921no—
273C2×C8—2921no—
274C2×C8—2921no—
275C2×C8—2921no—
276C2×C8—2921no—
277C2×C8—2921no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C22⋊C4—2921no—
291C22⋊C4—2921no—
292C42#1192402811yescharacteristic
293C42#1192402811yescharacteristic
294C42#1192402911yescharacteristic
295C42#1192402911yescharacteristic
296C23—2921no—
297C23—2921no—
298C23—2921no—
299C23—2921no—
300C23—2921no—
301C23—2921no—
302C23—1462no—
303C23#1455656211yescharacteristic
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—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—5841no—
320C2×C4—5841no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4#1455657411yescharacteristic
324C2×C4#1455657611yescharacteristic
325C2×C4#1455657611yescharacteristic
326C2×C4#1455658011yescharacteristic
327C2×C4#1455658611yescharacteristic
328C2×C4#1455658611yescharacteristic
329C2×C4SD16×D7311yescharacteristic
330C2×C4#1455661111yescharacteristic
331C2×C4#1455661111yescharacteristic
332C2×C4#1455661211yescharacteristic
333C2×C4#1455661611yescharacteristic
334C2×C4#1455661611yescharacteristic
335C2×C4#1455661811yescharacteristic
336C2×C4#1455662011yescharacteristic
337C8—41no—
338C8—41no—
339C8—5841no—
340C8—5841no—
341C8—5841no—
342C22—2922no—
343C22—2922no—
344C22—2922no—
345C22—5841no—
346C22—5841no—
347C22—5841no—
348C22—5841no—
349C22#1798851311yescharacteristic
350C22#1798879911yescharacteristic
351C22#1798879911yescharacteristic
352C22#1798881311yescharacteristic
353C22#1798883011yescharacteristic
354C22#1798885411yescharacteristic
355C22#1798885911yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—5841no—
361C4#1798890711yescharacteristic
362C4#1798891111yescharacteristic
363C4#1798891111yescharacteristic
364C4#1798891311yescharacteristic
365C4#1798891911yescharacteristic
366C4#1798893111yescharacteristic
367C4#1798894411yescharacteristic
368C4#1798895311yescharacteristic
369C2—5842no—
370C2#2260933711yescharacteristic
371C2#2260935111yescharacteristic
372C2#2260946111yescharacteristic
373C2#2260947511yescharacteristic
374C2#2261134511yescharacteristic
375C2#2261136511yescharacteristic
376C2#2261137211yescharacteristic
subgroupG/H
centerC23#14556562
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1834C2
socleC23×C73#121
prime radicalC22×D292D4
hypercenter#1834D73
hypocenterC73#10625
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #22607814C2semidirect
5. #22607814C2semidirect
6. #22607766C2semidirect
7. C73×#1834C2semidirect
190. #1834D73semidirect
196. C73#10625semidirect

Maximal subgroups

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

subgroupindex
#226107252
#226099282
#226078142
#226077662
C73×#18342
#1062573