Finite Group Databasebeta

← #32983979

Subgroups — #32983979

Order 18688.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#22618569C211yesmaximal, characteristic
2#22610014C211yesmaximal, characteristic
3#22608261C212yesmaximal
4#22607839C212yesmaximal
5C73×#2484C211yesmaximal, characteristic
6#17988648—24no—
7#17988611—21no—
8#17988551C2212yes—
9#17988551C2212yes—
10C4×#11924012—21no—
11#17988356—21no—
12#17988356—21no—
13#17988313—24no—
14C2×#117×C73C2211yescharacteristic
15C22×C4⋊C4×C73C2211yescharacteristic
16#400×C73—21no—
17#398×C73—21no—
18#387×C73—21no—
19#387×C73—21no—
20#385×C73C411yescharacteristic
21#385×C73C411yescharacteristic
22#381×C73C411yescharacteristic
23#381×C73C411yescharacteristic
24#381×C73C2211yescharacteristic
25C2×#11924012—22no—
26C2×#11924012—22no—
27C4⋊#10596831—24no—
28C22⋊#10596831—22no—
29C22⋊#10596831—22no—
30C22⋊#10596831—22no—
31C22⋊#10596831D414yes—
32#14556502—22no—
33C4×#10596831—22no—
34C23×C4×C73C2×C411yescharacteristic
35C23×C4×C73C2×C411yescharacteristic
36C23×C4×C73C2311yescharacteristic
37#117×C73—22no—
38#117×C73—22no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73—22no—
44C2×C4⋊C4×C73—22no—
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73C2×C411yescharacteristic
48C2×C22⋊C4×C73C2×C411yescharacteristic
49C2×C22⋊C4×C73C2×C411yescharacteristic
50C2×C22⋊C4×C73C2×C411yescharacteristic
51C2×C42×C73D411yescharacteristic
52C2×C42×C73D411yescharacteristic
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61#11924012—42no—
62#11924012—42no—
63#11924012—42no—
64#11924012—42no—
65C2×#10596831—24no—
66C2×#10596831—42no—
67C24×C73C22×C411yescharacteristic
68C22×C4×C73—21no—
69C22×C4×C73—22no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—22no—
74C22×C4×C73—42no—
75C22×C4×C73—41no—
76C22×C4×C73—41no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C2×D412yes—
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73#4112yes—
87C4⋊C4×C73—22no—
88C4⋊C4×C73—22no—
89C4⋊C4×C73—42no—
90C4⋊C4×C73—42no—
91C4⋊C4×C73—41no—
92C4⋊C4×C73—42no—
93C4⋊C4×C73—41no—
94C22⋊C4×C73—22no—
95C22⋊C4×C73—22no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—21no—
101C42×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73C2×C22⋊C411yescharacteristic
107C23×C73C4×D412yes—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—22no—
113C2×C4×C73—24no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—42no—
119C2×C4×C73—42no—
120C2×C4×C73—41no—
121C2×C4×C73—42no—
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—41no—
136C2×C4×C73—82no—
137C2×C4×C73#12011yescharacteristic
138C2×C4×C73#12112yes—
139C2×C4×C73#12311yescharacteristic
140#10596831—44no—
141#10596831—82no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73#38611yescharacteristic
150C22×C73#41011yescharacteristic
151C22×C73#41011yescharacteristic
152C4×C73—21no—
153C4×C73—22no—
154C4×C73—21no—
155C4×C73—42no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—81no—
161C4×C73—81no—
162C4×C73—81no—
163#9514—731nomaximal, Sylow
164C2×C73—21no—
165C2×C73—21no—
166C2×C73—42no—
167C2×C73#189111yescharacteristic
168C2×C73#189911yescharacteristic
169C2×C73#191511yescharacteristic
170#2921—731no—
171#2484D7311yescharacteristic
172#1822—731no—
173#1463—732no—
174#1306—732no—
175C73#951411yescharacteristic, complemented, Sylow
176C2×#117C2×D7311yescharacteristic
177C22×C4⋊C4C2×D7311yescharacteristic
178#433—1464no—
179#423—1461no—
180#407—732no—
181#407—732no—
182C4×M16—1461no—
183#400—21no—
184#398—21no—
185#387—21no—
186#387—21no—
187#385Dic7311yescharacteristic
188#385Dic7311yescharacteristic
189#381Dic7311yescharacteristic
190#381Dic7311yescharacteristic
191#381C2×D7311yescharacteristic
192#343—1461no—
193#343—1461no—
194#324—1464no—
195C23×C4C2×Dic7311yescharacteristic
196C23×C4C2×Dic7311yescharacteristic
197C23×C4C22×D7311yescharacteristic
198C2×M16—1462no—
199C2×M16—1462no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4C22⋊D7311yescharacteristic
209C2×C4⋊C4C22⋊D7311yescharacteristic
210C2×C22⋊C4C2×Dic7311yescharacteristic
211C2×C22⋊C4C2×Dic7311yescharacteristic
212C2×C22⋊C4C2×Dic7311yescharacteristic
213C2×C22⋊C4C2×Dic7311yescharacteristic
214C2×C42C22⋊D7311yescharacteristic
215C2×C42C22⋊D7311yescharacteristic
216C4⋊C8—1464no—
217C22⋊C8—734no—
218C22⋊C8—1462no—
219C22⋊C8—1462no—
220C22⋊C8—1462no—
221#97—1462no—
222C4×C8—1462no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C24C22×Dic7311yescharacteristic
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊Dic7311yescharacteristic
244C22×C4C22⋊Dic7311yescharacteristic
245C22×C4C22⋊Dic7311yescharacteristic
246C22×C4C22⋊Dic7311yescharacteristic
247C22×C4D4×D7312yes—
248C22×C4C2×C22⋊D7311yescharacteristic
249C22×C4C2×C22⋊D7311yescharacteristic
250C22×C4#1192402712yes—
251M16—2922no—
252M16—2922no—
253M16—2922no—
254M16—2922no—
255C2×C8—2922no—
256C2×C8—1464no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×C22⋊Dic7311yescharacteristic
277C23D4×Dic7312yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
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—82no—
307C2×C4#1455655911yescharacteristic
308C2×C4#1455656312yes—
309C2×C4#1455657211yescharacteristic
310C8—2924no—
311C8—5842no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1798846711yescharacteristic
320C22#1798856111yescharacteristic
321C22#1798856111yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2261035011yescharacteristic
337C2#2261039011yescharacteristic
338C2#2261048411yescharacteristic
subgroupG/H
centerC22#17988467
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#2484C2
socleC22×C73#386
cosocleC23×C4×C73C23
hypercenter#2484D73
hypocenterC73#9514
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
175. C73#9514semidirect

Maximal subgroups

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

subgroupindex
#226185692
#226100142
#226082612
#226078392
C73×#24842
#951473