Finite Group Databasebeta

← #32981069

Subgroups — #32981069

Order 18688.

516 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 111 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#22619016C211yesmaximal, characteristic, complemented
2C4×#14556510C211yesmaximal, characteristic, complemented
3#22608374C212yesmaximal
4#22607824C212yesmaximal, complemented
5C73×#2398C211yesmaximal, characteristic
6#17988718—24no—
7#17988644—21no—
8#17988644C2212yes—
9#17988640—21no—
10C2×#14556510—21no—
11C4×#11924012C2212yes—
12#17988356—21no—
13D4⋊#10596831—24no—
14C2×C4×Q8×C73C2211yescharacteristic
15C2×C4×D4×C73C2211yescharacteristic
16#400×C73C411yescharacteristic
17#400×C73C411yescharacteristic
18#397×C73—21no—
19#394×C73C411yescharacteristic
20#394×C73C411yescharacteristic
21#393×C73—21no—
22C4×C22⋊C4×C73—21no—
23C4×C22⋊C4×C73—21no—
24#376×C73C2211yescharacteristic
25C2×#11924012—22no—
26C4⋊#10596831—22no—
27C4⋊#10596831—22no—
28C4⋊#10596831D414yes—
29#14556510—24no—
30C22⋊#10596831—22no—
31#14556502—22no—
32#14556502—22no—
33#14556502—22no—
34C4×#10596831—22no—
35C4×#10596831—22no—
36C22×Q8×C73D411yescharacteristic
37C22×D4×C73C2×C411yescharacteristic
38C23×C4×C73—21no—
39C4×Q8×C73—22no—
40C4×Q8×C73—22no—
41C4×D4×C73—22no—
42C4×D4×C73—22no—
43C2×C4⋊C4×C73C2×C411yescharacteristic
44C2×C4⋊C4×C73C2×C411yescharacteristic
45C2×C4⋊C4×C73C2×C411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73—21no—
49C2×C22⋊C4×C73—21no—
50C2×C22⋊C4×C73—21no—
51C2×C22⋊C4×C73—21no—
52C2×C42×C73—21no—
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73C2311yescharacteristic
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61#95×C73C2×C411yescharacteristic
62#95×C73C2×C411yescharacteristic
63#11924012—24no—
64#11924012—42no—
65C2×#10596831—24no—
66C2×#10596831—42no—
67C24×C73—21no—
68C2×Q8×C73—22no—
69C2×Q8×C73—22no—
70C2×Q8×C73—41no—
71C2×D4×C73—22no—
72C2×D4×C73—42no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—42no—
77C22×C4×C73—42no—
78C22×C4×C73—41no—
79C22×C4×C73—41no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22×C411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C4⋊C4×C73—22no—
88C4⋊C4×C73—22no—
89C4⋊C4×C73—22no—
90C4⋊C4×C73—22no—
91C22⋊C4×C73—42no—
92C22⋊C4×C73—42no—
93C22⋊C4×C73—42no—
94C22⋊C4×C73—42no—
95C22⋊C4×C73—42no—
96C42×C73—21no—
97C42×C73—21no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—42no—
101C42×C73C2×D412yes—
102C42×C73#4112yes—
103C23×C73—22no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73—41no—
110C23×C73C2×C22⋊C411yescharacteristic
111Q8×C73—44no—
112D4×C73—24no—
113D4×C73—42no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—22no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
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—82no—
138C2×C4×C73#10412yes—
139C2×C4×C73C4×D412yes—
140C2×C4×C73#12011yescharacteristic
141C2×C4×C73#12112yes—
142C2×C4×C73#12311yescharacteristic
143#10596831—44no—
144#10596831—44no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73—42no—
150C22×C73—81no—
151C22×C73—81no—
152C22×C73—81no—
153C22×C73—81no—
154C22×C73#38611yescharacteristic
155C22×C73C2×#10411yescharacteristic
156C22×C73#42111yescharacteristic
157C4×C73—22no—
158C4×C73—22no—
159C4×C73—21no—
160C4×C73—22no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—81no—
165C4×C73—81no—
166C4×C73—81no—
167C4×C73#45412yes—
168#9032—731nomaximal, Sylow
169C2×C73—21no—
170C2×C73—21no—
171C2×C73—82no—
172C2×C73#187111yescharacteristic
173C2×C73#188811yescharacteristic
174C2×C73#189111yescharacteristic
175#2983—731no—
176#2398D7311yescharacteristic
177C4×#101—731no—
178#1490—732no—
179#1300—732no—
180C73#903211yescharacteristic, complemented, Sylow
181C2×C4×Q8C2×D7311yescharacteristic
182C2×C4×D4C2×D7311yescharacteristic
183#446—1464no—
184#432—732no—
185#432—1461no—
186#431—1461no—
187C2×#101—1461no—
188C4×M16—732no—
189#400Dic7311yescharacteristic
190#400Dic7311yescharacteristic
191#397—21no—
192#394Dic7311yescharacteristic
193#394Dic7311yescharacteristic
194#393—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197#376C2×D7311yescharacteristic
198#343—1461no—
199D4⋊C8—1464no—
200C22×Q8C22⋊D7311yescharacteristic
201C22×D4C2×Dic7311yescharacteristic
202C23×C4—21no—
203C2×M16—1462no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×D4—22no—
207C4×D4—22no—
208C2×C4⋊C4C2×Dic7311yescharacteristic
209C2×C4⋊C4C2×Dic7311yescharacteristic
210C2×C4⋊C4C2×Dic7311yescharacteristic
211C2×C4⋊C4C22⋊D7311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42—21no—
218C2×C42C22⋊D7311yescharacteristic
219C2×C42C22⋊D7311yescharacteristic
220C2×C42C22×D7311yescharacteristic
221C4⋊C8—734no—
222C4⋊C8—1462no—
223C4⋊C8—1462no—
224#101—1464no—
225C22⋊C8—1462no—
226#97—1462no—
227#97—1462no—
228#97—1462no—
229C4×C8—1462no—
230C4×C8—1462no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C2×Dic7311yescharacteristic
237#95C2×Dic7311yescharacteristic
238C24—21no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×D4—22no—
243C2×D4—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C22⋊Dic7311yescharacteristic
252C22×C4C22⋊Dic7311yescharacteristic
253C22×C4C22⋊Dic7311yescharacteristic
254C22×C4C22⋊Dic7311yescharacteristic
255C22×C4C22×Dic7311yescharacteristic
256C22×C4C2×C22⋊D7311yescharacteristic
257C22×C4C2×C22⋊D7311yescharacteristic
258M16—2922no—
259M16—1464no—
260C2×C8—2922no—
261C2×C8—1464no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42D4×D7312yes—
277C42#1192402712yes—
278C23—22no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C2×C22⋊Dic7311yescharacteristic
286Q8—44no—
287D4—24no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
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—82no—
312C2×C4—82no—
313C2×C4#1455651812yes—
314C2×C4D4×Dic7312yes—
315C2×C4#1455655911yescharacteristic
316C2×C4#1455656312yes—
317C2×C4#1455657211yescharacteristic
318C8—2924no—
319C8—2924no—
320C22—21no—
321C22—21no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1798846711yescharacteristic
330C22C2×#1455651811yescharacteristic
331C22#1798860411yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#1798875912yes—
343C2—21no—
344C2—21no—
345C2—82no—
346C2#2261023411yescharacteristic
347C2#2261033511yescharacteristic
348C2#2261035011yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2398C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC2×C42×C73C23
hypercenter#2398D73
hypocenterC73#9032
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #22619016C2semidirect
2. C4×#14556510C2semidirect
4. #22607824C2semidirect
180. C73#9032semidirect

Maximal subgroups

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

subgroupindex
#226190162
C4×#145565102
#226083742
#226078242
C73×#23982
#903273