Finite Group Databasebeta

← #33091094

Subgroups — #33091094

Order 18688.

1430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989137C211yesmaximal, characteristic
2C4×#14556550C211yesmaximal, characteristic, complemented
3#22610882C212yesmaximal, complemented
4#22610857C212yesmaximal, complemented
5#22610251C214yesmaximal, complemented
6#22609757C214yesmaximal, complemented
7C2×#432×C73C211yesmaximal, characteristic, complemented
8C22×#11924028—21no—
9#17989137—24no—
10#17989137C418yescomplemented
11C2×#14556591C2211yescharacteristic
12C2×#14556588C2211yescharacteristic
13C2×#14556579—21no—
14C2×#14556565—21no—
15C2×#14556565C2212yes—
16C2×C4×D292—21no—
17C2×C4×D292C2212yes—
18C2×#14556550C2212yes—
19C2×#14556513C2218yes—
20C4×C4⋊Dic73C2212yes—
21C4×C4⋊Dic73C2212yes—
22C4×C22⋊Dic73—21no—
23C4×C22⋊Dic73—21no—
24#17988433—21no—
25C42×Dic73—21no—
26#17988350C2218yes—
27C22×C42×C73C2211yescharacteristic
28#432×C73—24no—
29C2×C4⋊C8×C73C2212yes—
30C2×C22⋊C8×C73C2212yes—
31C2×#97×C73C2212yes—
32C2×#11924028—28no—
33C2×#11924028—48no—
34C22×Dic146—21no—
35C22×D292—21no—
36C22×D292—21no—
37C22×D292C2312yes—
38C22×C22⋊D73—22no—
39C22×C4×D73—22no—
40#14556591—22no—
41#14556591C2×C414yes—
42#14556588—22no—
43#14556588C2×C414yes—
44#14556579—28no—
45#14556565—28no—
46#14556565—24no—
47#14556565C2×C418yes—
48C4×D292—28no—
49C4×D292—24no—
50C4×D292C2×C418yes—
51#14556550—28no—
52C2×C4⋊Dic73—21no—
53C2×C4⋊Dic73C2312yes—
54C2×C4⋊Dic73C2314yes—
55C2×C22⋊Dic73—22no—
56C2×#11924005—22no—
57C2×#11924005—22no—
58C2×C4×Dic73—22no—
59C2×C4×Dic73—22no—
60C2×C4×Dic73—22no—
61#14556513—216no—
62#14556498—22no—
63#14556498—22no—
64C23×C4×C73D411yescharacteristic
65C23×C4×C73D411yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C22×C8×C73C2314yes—
68C2×C42×C73C2×C414yes—
69C2×C42×C73D411yescharacteristic
70C2×C42×C73D411yescharacteristic
71C2×C42×C73D414yes—
72C2×C42×C73C2311yescharacteristic
73C2×C42×C73C2311yescharacteristic
74C4⋊C8×C73—24no—
75C22⋊C8×C73—24no—
76#97×C73—24no—
77C23×D73—22no—
78#11924028—432no—
79C2×Dic146—24no—
80C2×Dic146—44no—
81C2×D292—28no—
82C2×D292—24no—
83C2×D292—24no—
84C2×D292—22no—
85C2×D292—44no—
86C2×D292—44no—
87C2×D292C22×C414yes—
88C2×C22⋊D73—28no—
89C2×C22⋊D73—48no—
90C22×Dic73—24no—
91C22×Dic73—22no—
92C2×C4×D73—28no—
93C2×C4×D73—48no—
94C4⋊Dic73—24no—
95C4⋊Dic73—22no—
96C4⋊Dic73—24no—
97C4⋊Dic73C22×C414yes—
98C4⋊Dic73#4118yescomplemented
99C22⋊Dic73—28no—
100#11924005—28no—
101#11924005—28no—
102C4×Dic73—28no—
103C4×Dic73—44no—
104C4×Dic73—44no—
105C24×C73C2×D411yescharacteristic
106C22×C4×C73—24no—
107C22×C4×C73—24no—
108C22×C4×C73—42no—
109C22×C4×C73C22⋊C414yes—
110C22×C4×C73C22⋊C414yes—
111C22×C4×C73C22×C412yes—
112C22×C4×C73C2×D412yes—
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73C2411yescharacteristic
119C2×C8×C73—24no—
120C2×C8×C73—28no—
121C42×C73C22⋊C414yes—
122C42×C73C22⋊C414yes—
123C42×C73C22×C412yes—
124C42×C73C22×C412yes—
125C42×C73C2×D412yes—
126C42×C73C2×D412yes—
127C23×C73—22no—
128C23×C73—22no—
129C23×C73—22no—
130C23×C73C2×C22⋊C412yes—
131C23×C73C22×D411yescharacteristic
132C22×D73—24no—
133C22×D73—44no—
134C22×D73—44no—
135C22×D73—44no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73—22no—
140C2×C4×C73—24no—
141C2×C4×C73—24no—
142C2×C4×C73—28no—
143C2×C4×C73—44no—
144C2×C4×C73C2×C22⋊C412yes—
145C2×C4×C73C2×C22⋊C412yes—
146C2×C4×C73C2×C22⋊C412yes—
147C2×C4×C73C2×C22⋊C412yes—
148C2×C4×C73C2×C22⋊C412yes—
149C2×C4×C73AGL(1,ℤ/8)14yes—
150C2×C4×C73C23×C411yescharacteristic
151C2×C4×C73C22×D411yescharacteristic
152C2×C4×C73C2×#4114yes—
153C22⋊D73—416no—
154C2×Dic73—24no—
155C2×Dic73—28no—
156C2×Dic73—44no—
157C2×Dic73—44no—
158C2×Dic73—44no—
159D292—28no—
160D292—48no—
161D292—44no—
162D292—48no—
163C4×D73—416no—
164Dic146—48no—
165C8×C73—44no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—44no—
170C22×C73C22×C22⋊C411yescharacteristic
171C22×C73#52512yes—
172C22×C73C2×AGL(1,ℤ/8)12yes—
173C22×C73#57512yes—
174C2×D73—44no—
175C2×D73—44no—
176C2×D73—44no—
177C2×D73—88no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—22no—
181C4×C73—22no—
182C4×C73#41814yes—
183C4×C73C4×#4112yes—
184C4×C73#53212yes—
185Dic73—48no—
186Dic73—44no—
187#21393—731nomaximal, Sylow
188C2×C73—42no—
189C2×C73#229711yescharacteristic
190C2×C73C2×#41811yescharacteristic
191C2×C73#289611yescharacteristic
192C2×C73#311514yes—
193D73—84no—
194C2×#532—731no—
195C2×#432D7311yescharacteristic, complemented
196C4×#117—731no—
197#1988—732no—
198#1982—732no—
199#1875—734no—
200#1762—734no—
201C73#2139311yescharacteristic, complemented, Sylow
202C22×#41—1461no—
203#532—738no—
204#532—1464no—
205C2×C4⋊Q8—731no—
206C2×#127—731no—
207C2×#124—1461no—
208C2×#121—732no—
209C2×#121—1461no—
210C2×C4×D4—732no—
211C2×C4×D4—1461no—
212C2×#117—732no—
213C22×C42C2×D7311yescharacteristic
214#432—24no—
215C2×C4⋊C8C2×D7312yes—
216C2×#102—738no—
217C2×C22⋊C8C2×D7312yes—
218C2×#97C2×D7312yes—
219C4×C4⋊C4—732no—
220C4×C4⋊C4—732no—
221C4×C22⋊C4—1461no—
222C4×C22⋊C4—1461no—
223#376—1461no—
224C43—1461no—
225#340—738no—
226C2×#41—2928no—
227C2×#41—1468no—
228C22×Q8—1461no—
229C22×D4—732no—
230C22×D4—1462no—
231C22×D4—1461no—
232C22×D4—1461no—
233C23×C4—1462no—
234C23×C4D29211yescharacteristic
235C23×C4D29211yescharacteristic
236C23×C4C22×D7311yescharacteristic
237C22×C8C22×D7314yes—
238C4⋊Q8—734no—
239C4⋊Q8—1462no—
240#127—734no—
241#127—1462no—
242#124—1468no—
243#121—738no—
244#121—1468no—
245#121—1464no—
246C4×D4—738no—
247C4×D4—1468no—
248C4×D4—1464no—
249#117—1468no—
250C2×C4⋊C4—734no—
251C2×C4⋊C4—732no—
252C2×C4⋊C4—1461no—
253C2×C22⋊C4—1462no—
254C2×C22⋊C4—1462no—
255C2×C22⋊C4—1462no—
256C2×C42—1462no—
257C2×C42—1462no—
258C2×C42—1462no—
259C2×C42C4×D7314yes—
260C2×C42D29211yescharacteristic
261C2×C42D29211yescharacteristic
262C2×C42C22⋊D7314yes—
263C2×C42C22×D7311yescharacteristic
264C2×C42C22×D7311yescharacteristic
265C4⋊C8—24no—
266#102—14616no—
267C22⋊C8—24no—
268#97—24no—
269#95—1462no—
270#95—1462no—
271C24—1462no—
272C24C2×D29211yescharacteristic
273#41—29232no—
274C2×Q8—2924no—
275C2×Q8—1464no—
276C2×D4—2924no—
277C2×D4—2928no—
278C2×D4—2924no—
279C2×D4—734no—
280C2×D4—1468no—
281C2×D4—1464no—
282C2×D4—1464no—
283C2×D4—1462no—
284C2×D4—1468no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—42no—
288C22×C4—2928no—
289C22×C4—1464no—
290C22×C4—1462no—
291C22×C4—1468no—
292C22×C4#1192400514yes—
293C22×C4#1192400514yes—
294C22×C4C2×C4×D7312yes—
295C22×C4C2×C22⋊D7312yes—
296C22×C4C2×D29211yescharacteristic
297C22×C4C2×D29211yescharacteristic
298C22×C4C2×D29211yescharacteristic
299C22×C4C2×D29211yescharacteristic
300C22×C4C2×D29211yescharacteristic
301C22×C4C23×D7311yescharacteristic
302C2×C8—24no—
303C2×C8—28no—
304C4⋊C4—734no—
305C4⋊C4—738no—
306C4⋊C4—1464no—
307C4⋊C4—1462no—
308C4⋊C4—1464no—
309C22⋊C4—1468no—
310C22⋊C4—1468no—
311C22⋊C4—1468no—
312C42—2924no—
313C42—2924no—
314C42—1468no—
315C42#1192400514yes—
316C42#1192400514yes—
317C42C2×C4×D7312yes—
318C42C2×C4×D7312yes—
319C42C2×C22⋊D7312yes—
320C42C2×C22⋊D7312yes—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—2924no—
325C23—2924no—
326C23—2924no—
327C23—1464no—
328C23C2×#1192400512yes—
329C23C22×D29211yescharacteristic
330Q8—2928no—
331D4—2928no—
332D4—29216no—
333D4—2924no—
334D4—2928no—
335D4—1468no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—44no—
344C2×C4—29216no—
345C2×C4—2924no—
346C2×C4—2924no—
347C2×C4—2924no—
348C2×C4—1464no—
349C2×C4—1468no—
350C2×C4C2×#1192400512yes—
351C2×C4C2×#1192400512yes—
352C2×C4C2×#1192400512yes—
353C2×C4C2×#1192400512yes—
354C2×C4C2×#1192400512yes—
355C2×C4#1455661914yes—
356C2×C4C22×C4×D7311yescharacteristic
357C2×C4C22×C22⋊D7311yescharacteristic
358C2×C4#41×D7314yes—
359C8—44no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—2924no—
365C22—2924no—
366C22—2924no—
367C22—5848no—
368C22C22×#1192400511yescharacteristic
369C22#1798909912yes—
370C22C2×#1455661912yes—
371C22#1798938712yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—2924no—
377C4—2928no—
378C4#1798859314yes—
379C4#1798905512yes—
380C4#1798913312yes—
381C2—42no—
382C2—5844no—
383C2#2261241911yescharacteristic
384C2C2×#1798859311yescharacteristic
385C2#2261845111yescharacteristic
386C2#2262008314yes—
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#432×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989137C2
cosocleC22×C4×C73C24
hypercenterC2×#432D73
hypocenterC73#21393
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
2. C4×#14556550C2semidirect
3. #22610882C2semidirect
4. #22610857C2semidirect
5. #22610251C2semidirect
6. #22609757C2semidirect
7. C2×#432×C73C2semidirect
10. #17989137C4semidirect
98. C4⋊Dic73#41semidirect
195. C2×#432D73semidirect
201. C73#21393semidirect

Maximal subgroups

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

subgroupindex
C2×#179891372
C4×#145565502
#226108822
#226108572
#226102512
#226097572
C2×#432×C732
#2139373