Finite Group Databasebeta

← #32996343

Subgroups — #32996343

Order 18688.

442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556506C211yesmaximal, characteristic
2#22608249C211yesmaximal, characteristic
3#22607955C212yesmaximal, complemented
4#22607931C212yesmaximal, complemented
5C73×#2633C211yesmaximal, characteristic
6C2×#14556506—21no—
7C2×C22⋊#10596831—21no—
8C4×C22⋊Dic73—21no—
9#17988354C2212yes—
10#17988313—21no—
11#17988311C2212yes—
12C2×#125×C73C411yescharacteristic, complemented
13C2×C4×D4×C73C2211yescharacteristic
14#399×C73C411yescharacteristic, complemented
15#399×C73C2211yescharacteristic
16#398×C73—21no—
17#397×C73C411yescharacteristic, complemented
18#397×C73C2211yescharacteristic
19#394×C73—21no—
20#385×C73—21no—
21#385×C73—21no—
22#383×C73C411yescharacteristic, complemented
23C22×#10596831—41no—
24C2×C22⋊Dic73—22no—
25C2×C4×Dic73—41no—
26#14556506—24no—
27C22⋊#10596831—22no—
28C22⋊#10596831—41no—
29#14556498—41no—
30C22×D4×C73D411yescharacteristic
31C23×C4×C73D411yescharacteristic
32C23×C4×C73D411yescharacteristic
33#125×C73—41no—
34#125×C73—41no—
35C4×D4×C73—41no—
36C4×D4×C73—41no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2×C411yescharacteristic
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C22⋊C4×C73—21no—
45C2×C22⋊C4×C73—21no—
46C2×C22⋊C4×C73—21no—
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73C2×C411yescharacteristic
49C2×C22⋊C4×C73C2311yescharacteristic
50C2×C42×C73C2×C411yescharacteristic
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73C2×C411yescharacteristic
56#95×C73C2×C411yescharacteristic
57C22×Dic73—42no—
58C2×#10596831—42no—
59C2×#10596831—82no—
60C22⋊Dic73—24no—
61C22⋊Dic73—42no—
62C4×Dic73—82no—
63C24×C73C22⋊C411yescharacteristic
64C24×C73C2×D411yescharacteristic
65C2×D4×C73—22no—
66C2×D4×C73—22no—
67C2×D4×C73—41no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—81no—
77C22×C4×C73—81no—
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C4⋊C4×C73—41no—
84C4⋊C4×C73—41no—
85C4⋊C4×C73—41no—
86C4⋊C4×C73—42no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—81no—
90C4⋊C4×C73—81no—
91C22⋊C4×C73—41no—
92C22⋊C4×C73—41no—
93C22⋊C4×C73—42no—
94C22⋊C4×C73—42no—
95C22⋊C4×C73—81no—
96C22⋊C4×C73—81no—
97C42×C73—21no—
98C42×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73#10412yes—
108C23×C73C2×C22⋊C411yescharacteristic
109C23×C73#13512yes—
110D4×C73—44no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—41no—
118C2×C4×C73—42no—
119C2×C4×C73—42no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—81no—
136C2×C4×C73—81no—
137C2×C4×C73#9911yescharacteristic
138C2×C4×C73#9911yescharacteristic
139C2×Dic73—44no—
140C2×Dic73—82no—
141C2×Dic73—82no—
142#10596831—82no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—81no—
154C22×C73—81no—
155C22×C73C2×#9911yescharacteristic
156C22×C73#41611yescharacteristic
157C22×C73C2×#10411yescharacteristic
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—81no—
165C4×C73—81no—
166C4×C73—81no—
167C4×C73—81no—
168Dic73—84no—
169#11732—731nomaximal, Sylow
170C2×C73—21no—
171C2×C73—21no—
172C2×C73—42no—
173C2×C73—42no—
174C2×C73#150111yescharacteristic
175C2×C73#212311yescharacteristic
176C2×C73#212711yescharacteristic
177#2633D7311yescharacteristic
178C4×#99—731no—
179#1459—731no—
180#1352—732no—
181#1344—732no—
182C73#1173211yescharacteristic, complemented, Sylow
183C2×#125Dic7311yescharacteristic, complemented
184C2×C4×D4C2×D7311yescharacteristic
185C2×#99—1461no—
186C2×C22⋊C8—1461no—
187#399Dic7311yescharacteristic, complemented
188#399C2×D7311yescharacteristic
189#398—21no—
190#397Dic7311yescharacteristic, complemented
191#397C2×D7311yescharacteristic
192#394—21no—
193#385—21no—
194#385—21no—
195#383Dic7311yescharacteristic, complemented
196C4×C22⋊C4—1461no—
197#342—732no—
198#324—1461no—
199#323—732no—
200C22×D4C22⋊D7311yescharacteristic
201C23×C4C22⋊D7311yescharacteristic
202C23×C4C22⋊D7311yescharacteristic
203C22×C8—2921no—
204#125—41no—
205#125—41no—
206C4×D4—41no—
207C4×D4—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×Dic7311yescharacteristic
213C2×C4⋊C4C2×Dic7311yescharacteristic
214C2×C4⋊C4C22⋊D7311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—1462no—
220C2×C22⋊C4C2×Dic7311yescharacteristic
221C2×C22⋊C4C22×D7311yescharacteristic
222C2×C42—2921no—
223C2×C42C2×Dic7311yescharacteristic
224#99—1464no—
225C22⋊C8—2921no—
226C22⋊C8—1462no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—2921no—
232#95C2×Dic7311yescharacteristic
233#95C2×Dic7311yescharacteristic
234C24C22⋊Dic7311yescharacteristic
235C24C2×C22⋊D7311yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—41no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—2922no—
250C22×C4C22⋊Dic7311yescharacteristic
251C22×C4C22⋊Dic7311yescharacteristic
252C22×C4C22⋊Dic7311yescharacteristic
253C22×C4C22×Dic7311yescharacteristic
254C22×C4C2×C22⋊D7311yescharacteristic
255C2×C8—2922no—
256C2×C8—5842no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—81no—
270C22⋊C4—81no—
271C22⋊C4—2922no—
272C22⋊C4—1464no—
273C42—21no—
274C42—21no—
275C42—5842no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#1455651812yes—
285C23C2×C22⋊Dic7311yescharacteristic
286C23#1455661112yes—
287D4—44no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—2924no—
315C2×C4—5842no—
316C2×C4—5842no—
317C2×C4#1455650611yescharacteristic
318C2×C4#1455650611yescharacteristic
319C8—5842no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—81no—
332C22C2×#1455650611yescharacteristic
333C22#1798858311yescharacteristic
334C22C2×#1455651811yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—5844no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—42no—
350C2#2260842211yescharacteristic
351C2#2261158511yescharacteristic
352C2#2261160011yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#2633C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#2633D73
hypocenterC73#11732
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2633

Complements

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

NH ≅ G/Ntype
3. #22607955C2semidirect
4. #22607931C2semidirect
12. C2×#125×C73C4semidirect
14. #399×C73C4semidirect
17. #397×C73C4semidirect
22. #383×C73C4semidirect
182. C73#11732semidirect
183. C2×#125Dic73semidirect
187. #399Dic73semidirect
190. #397Dic73semidirect
195. #383Dic73semidirect

Maximal subgroups

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

subgroupindex
C4×#145565062
#226082492
#226079552
#226079312
C73×#26332
#1173273