Finite Group Databasebeta

← #33052151

Subgroups — #33052151

Order 18688.

1012 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#22618960C212yesmaximal, complemented
2#22608291C214yesmaximal, complemented
3#22608279C214yesmaximal, complemented
4#22608272C212yesmaximal, complemented
5#22608265C212yesmaximal, complemented
6C2×#540×C73C211yesmaximal, characteristic
7#17988659—28no—
8#17988644C2214yes—
9#17988551C2214yes—
10C2×C22⋊#10596831C2214yes—
11#17988313C2214yes—
12#17988311C2214yes—
13#17988311C2218yes—
14#540×C73—28no—
15C2×#127×C73C411yescharacteristic
16C2×#125×C73C411yescharacteristic
17C2×#123×C73C412yes—
18C2×#123×C73C2212yes—
19C2×#121×C73C412yes—
20C2×#121×C73C411yescharacteristic
21C2×#121×C73C411yescharacteristic
22C2×#121×C73C2212yes—
23C2×C4×D4×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26C2×#11924012—24no—
27C22×#10596831—24no—
28C4⋊#10596831—24no—
29C22⋊#10596831—24no—
30C22⋊#10596831—24no—
31C22⋊#10596831C2318yes—
32#14556502—24no—
33C22×D4×C73C2×C411yescharacteristic
34C22×D4×C73C2×C412yes—
35C22×D4×C73C2×C412yes—
36C22×D4×C73C2×C412yes—
37C22×D4×C73C2×C412yes—
38C22×D4×C73C2×C411yescharacteristic
39C23×C4×C73C2×C411yescharacteristic
40C23×C4×C73C2×C412yes—
41C23×C4×C73C2312yes—
42#127×C73—24no—
43#125×C73—24no—
44#123×C73—24no—
45#123×C73—24no—
46#123×C73—28no—
47#121×C73—24no—
48#121×C73—24no—
49#121×C73—24no—
50#121×C73—24no—
51#121×C73—28no—
52C4×D4×C73—24no—
53C4×D4×C73D418yes—
54#117×C73—24no—
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C4⋊C4×C73C2×C411yescharacteristic
57C2×C4⋊C4×C73C2×C412yes—
58C2×C4⋊C4×C73C2×C412yes—
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C4⋊C4×C73C2311yescharacteristic
61C2×C22⋊C4×C73C2×C411yescharacteristic
62C2×C22⋊C4×C73C2×C412yes—
63C2×C22⋊C4×C73C2×C412yes—
64C2×C22⋊C4×C73C2×C412yes—
65C2×C22⋊C4×C73C2311yescharacteristic
66C2×C22⋊C4×C73C2312yes—
67C2×C42×C73C2×C411yescharacteristic
68C2×C42×C73C2311yescharacteristic
69#11924012—84no—
70C2×#10596831—28no—
71C2×#10596831—84no—
72C24×C73C22×C411yescharacteristic
73C24×C73C22×C412yes—
74C24×C73C22×C412yes—
75C2×D4×C73—24no—
76C2×D4×C73—24no—
77C2×D4×C73—24no—
78C2×D4×C73—22no—
79C2×D4×C73—24no—
80C2×D4×C73—42no—
81C2×D4×C73—42no—
82C2×D4×C73—82no—
83C2×D4×C73—82no—
84C2×D4×C73—82no—
85C2×D4×C73—82no—
86C2×D4×C73C22⋊C414yes—
87C22×C4×C73—22no—
88C22×C4×C73—24no—
89C22×C4×C73—42no—
90C22×C4×C73—82no—
91C22×C4×C73—82no—
92C22×C4×C73C22×C411yescharacteristic
93C22×C4×C73C22×C411yescharacteristic
94C22×C4×C73C22×C411yescharacteristic
95C22×C4×C73C22×C411yescharacteristic
96C22×C4×C73C22×C412yes—
97C22×C4×C73C22×C411yescharacteristic
98C22×C4×C73C22×C412yes—
99C22×C4×C73C2×D414yes—
100C22×C4×C73C2×D414yes—
101C22×C4×C73C2411yescharacteristic
102C4⋊C4×C73—22no—
103C4⋊C4×C73—22no—
104C4⋊C4×C73—24no—
105C4⋊C4×C73—24no—
106C4⋊C4×C73—22no—
107C4⋊C4×C73C22⋊C414yes—
108C22⋊C4×C73—24no—
109C22⋊C4×C73—22no—
110C22⋊C4×C73—24no—
111C22⋊C4×C73—22no—
112C22⋊C4×C73—22no—
113C22⋊C4×C73—22no—
114C22⋊C4×C73C22⋊C418yes—
115C42×C73—22no—
116C42×C73C2×D414yes—
117C23×C73—24no—
118C23×C73—21no—
119C23×C73—22no—
120C23×C73—22no—
121C23×C73—24no—
122C23×C73—42no—
123C23×C73—42no—
124C23×C73—42no—
125C23×C73—41no—
126C23×C73—42no—
127C23×C73—41no—
128C23×C73C2×C22⋊C414yes—
129C23×C73C23×C411yescharacteristic
130D4×C73—44no—
131D4×C73—44no—
132D4×C73—84no—
133D4×C73—84no—
134D4×C73—84no—
135D4×C73—84no—
136C2×C4×C73—22no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—22no—
141C2×C4×C73—22no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—42no—
145C2×C4×C73—44no—
146C2×C4×C73—44no—
147C2×C4×C73—44no—
148C2×C4×C73—42no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73—84no—
152C2×C4×C73C2×C22⋊C412yes—
153C2×C4×C73C2×C22⋊C412yes—
154C2×C4×C73C2×C22⋊C414yes—
155C2×C4×C73C22×D412yes—
156#10596831—48no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—24no—
160C22×C73—24no—
161C22×C73—24no—
162C22×C73—41no—
163C22×C73—42no—
164C22×C73—41no—
165C22×C73—42no—
166C22×C73—42no—
167C22×C73—41no—
168C22×C73—84no—
169C22×C73—82no—
170C22×C73—84no—
171C22×C73C22×C22⋊C411yescharacteristic
172C22×C73#56812yes—
173C4×C73—22no—
174C4×C73—22no—
175C4×C73—24no—
176C4×C73—22no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73—42no—
180C4×C73—41no—
181#17408—731nomaximal, Sylow
182C2×C73—22no—
183C2×C73—44no—
184C2×C73—81no—
185C2×C73—82no—
186C2×C73#287911yescharacteristic
187C2×C73#288311yescharacteristic
188C2×C73#288811yescharacteristic
189C2×#540D7311yescharacteristic
190#2973—732no—
191#1471—734no—
192#1468—734no—
193#1466—732no—
194#1464—732no—
195C73#1740811yescharacteristic, complemented, Sylow
196#540—28no—
197C2×#127Dic7311yescharacteristic
198C2×#125Dic7311yescharacteristic
199C2×#123Dic7312yes—
200C2×#123C2×D7312yes—
201C2×#121Dic7312yes—
202C2×#121Dic7311yescharacteristic
203C2×#121Dic7311yescharacteristic
204C2×#121C2×D7312yes—
205C2×C4×D4C2×D7311yescharacteristic
206C2×C4×D4C2×D7311yescharacteristic
207C2×#117C2×D7311yescharacteristic
208#435—1468no—
209#432—734no—
210#407—734no—
211C2×C22⋊C8—734no—
212#324—734no—
213#323—734no—
214#323—738no—
215C22×D4C2×Dic7311yescharacteristic
216C22×D4C2×Dic7312yes—
217C22×D4C2×Dic7312yes—
218C22×D4C2×Dic7312yes—
219C22×D4C2×Dic7312yes—
220C22×D4C2×Dic7311yescharacteristic
221C23×C4C2×Dic7311yescharacteristic
222C23×C4C2×Dic7312yes—
223C23×C4C22×D7312yes—
224C2×M16—1464no—
225C22×C8—1464no—
226#127—24no—
227#125—24no—
228#123—24no—
229#123—24no—
230#123—28no—
231#121—24no—
232#121—24no—
233#121—24no—
234#121—24no—
235#121—28no—
236C4×D4—24no—
237C4×D4C22⋊D7318yes—
238#117—24no—
239C2×C4⋊C4C2×Dic7311yescharacteristic
240C2×C4⋊C4C2×Dic7311yescharacteristic
241C2×C4⋊C4C2×Dic7312yes—
242C2×C4⋊C4C2×Dic7312yes—
243C2×C4⋊C4C2×Dic7311yescharacteristic
244C2×C4⋊C4C22×D7311yescharacteristic
245C2×C22⋊C4C2×Dic7311yescharacteristic
246C2×C22⋊C4C2×Dic7312yes—
247C2×C22⋊C4C2×Dic7312yes—
248C2×C22⋊C4C2×Dic7312yes—
249C2×C22⋊C4C22×D7311yescharacteristic
250C2×C22⋊C4C22×D7312yes—
251C2×C42C2×Dic7311yescharacteristic
252C2×C42C22×D7311yescharacteristic
253C4⋊C8—1464no—
254C22⋊C8—738no—
255C22⋊C8—1464no—
256C22⋊C8—1464no—
257#97—1464no—
258C24C22×Dic7311yescharacteristic
259C24C22×Dic7312yes—
260C24C22×Dic7312yes—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—24no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—82no—
269C2×D4—82no—
270C2×D4—82no—
271C2×D4—82no—
272C2×D4C22⋊Dic7314yes—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—42no—
276C22×C4—82no—
277C22×C4—82no—
278C22×C4C22×Dic7311yescharacteristic
279C22×C4C22×Dic7311yescharacteristic
280C22×C4C22×Dic7311yescharacteristic
281C22×C4C22×Dic7311yescharacteristic
282C22×C4C22×Dic7312yes—
283C22×C4C22×Dic7311yescharacteristic
284C22×C4C22×Dic7312yes—
285C22×C4C2×C22⋊D7314yes—
286C22×C4C2×C22⋊D7314yes—
287C22×C4C23×D7311yescharacteristic
288M16—5844no—
289C2×C8—5844no—
290C2×C8—1468no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—22no—
296C4⋊C4C22⋊Dic7314yes—
297C22⋊C4—24no—
298C22⋊C4—22no—
299C22⋊C4—24no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4C22⋊Dic7318yes—
304C42—22no—
305C42C2×C22⋊D7314yes—
306C23—24no—
307C23—21no—
308C23—22no—
309C23—22no—
310C23—24no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—41no—
315C23—42no—
316C23—41no—
317C23C2×C22⋊Dic7314yes—
318C23C23×Dic7311yescharacteristic
319D4—44no—
320D4—44no—
321D4—84no—
322D4—84no—
323D4—84no—
324D4—84no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4C2×C22⋊Dic7312yes—
342C2×C4C2×C22⋊Dic7312yes—
343C2×C4C2×C22⋊Dic7314yes—
344C2×C4C22×C22⋊D7312yes—
345C8—2928no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—24no—
350C22—24no—
351C22—41no—
352C22—42no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—84no—
358C22—82no—
359C22—84no—
360C22C22×C22⋊Dic7311yescharacteristic
361C22#1798935412yes—
362C4—22no—
363C4—22no—
364C4—24no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—42no—
369C4—41no—
370C2—22no—
371C2—44no—
372C2—81no—
373C2—82no—
374C2#2261837611yescharacteristic
375C2#2261839211yescharacteristic
376C2#2261841011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#540×C73C2
socleC22×C73C22×C22⋊C4
cosocleC22×C4×C73C24
hypercenterC2×#540D73
hypocenterC73#17408
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #22618960C2semidirect
2. #22608291C2semidirect
3. #22608279C2semidirect
4. #22608272C2semidirect
5. #22608265C2semidirect
195. C73#17408semidirect

Maximal subgroups

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

subgroupindex
#226189602
#226082912
#226082792
#226082722
#226082652
C2×#540×C732
#1740873