Finite Group Databasebeta

← #33004627

Subgroups — #33004627

Order 18688.

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

normal subgroups only

This group has 484 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#22614248C211yesmaximal, characteristic
2C4×#14556508C211yesmaximal, characteristic
3#22608048C214yesmaximal
4C73×#1799C211yesmaximal, characteristic
5C22×C4⋊Dic73C411yescharacteristic, complemented
6C2×#14556508C2212yes—
7C4×#11924012—21no—
8#17988526—21no—
9#17988523—21no—
10#17988485—21no—
11#17988467C2212yes—
12#17988459C412yescomplemented
13#17988447—21no—
14#17988447C411yescharacteristic, complemented
15#17988356—21no—
16C2×C4×D4×C73C2211yescharacteristic
17C2×#99×C73C2212yes—
18#380×C73—21no—
19#342×C73—21no—
20C23×Dic73C2×C412yes—
21C2×#11924012—22no—
22C2×C4⋊Dic73—21no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—41no—
26C2×C4⋊Dic73—41no—
27C2×#11924007—22no—
28C2×C22⋊Dic73—22no—
29C2×C22⋊Dic73C2×C412yes—
30#14556508—22no—
31#14556508Q814yes—
32#14556502—41no—
33C4×#10596831—41no—
34#14556498—22no—
35#14556498—21no—
36#14556498—22no—
37C22×D4×C73C2311yescharacteristic
38C23×C4×C73C2×C411yescharacteristic
39C23×C4×C73D411yescharacteristic
40C4×D4×C73—41no—
41C4×D4×C73—41no—
42C2×C4⋊C4×C73—41no—
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C22⋊C4×C73—22no—
45C2×C22⋊C4×C73C2×C411yescharacteristic
46C2×C22⋊C4×C73D411yescharacteristic
47C2×C42×C73D411yescharacteristic
48#99×C73—24no—
49#95×C73—41no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52C22×Dic73—42no—
53C22×Dic73—82no—
54#11924012—24no—
55#11924012—42no—
56C2×#10596831—42no—
57C4⋊Dic73—42no—
58C4⋊Dic73—42no—
59C4⋊Dic73—41no—
60C4⋊Dic73—41no—
61#11924007—82no—
62C22⋊Dic73—42no—
63C22⋊Dic73—82no—
64C24×C73C22×C411yescharacteristic
65C24×C73C2×D411yescharacteristic
66C2×D4×C73—41no—
67C2×D4×C73—41no—
68C2×D4×C73C2×Q812yes—
69C2×D4×C73#4112yes—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—42no—
75C22×C4×C73—42no—
76C22×C4×C73—42no—
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C2×D411yescharacteristic
82C4⋊C4×C73—41no—
83C4⋊C4×C73—82no—
84C22⋊C4×C73—41no—
85C22⋊C4×C73—41no—
86C22⋊C4×C73—42no—
87C22⋊C4×C73—42no—
88C42×C73—21no—
89C42×C73—21no—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—41no—
95C23×C73—41no—
96C23×C73—41no—
97C23×C73—41no—
98C23×C73C2×C22⋊C411yescharacteristic
99C23×C73C4×Q812yes—
100C23×C73#12411yescharacteristic
101C23×C73C4⋊Q811yescharacteristic
102D4×C73—42no—
103D4×C73—42no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—22no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—42no—
111C2×C4×C73—42no—
112C2×C4×C73—42no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—81no—
117C2×C4×C73—82no—
118C2×C4×C73—82no—
119C2×C4×C73—82no—
120C2×C4×C73#9911yescharacteristic
121C2×C4×C73#9911yescharacteristic
122C2×C4×C73C22⋊Q812yes—
123C2×Dic73—42no—
124C2×Dic73—42no—
125C2×Dic73—42no—
126C2×Dic73—42no—
127C2×Dic73—42no—
128C2×Dic73—42no—
129C2×Dic73—84no—
130#10596831—44no—
131C22×C73—21no—
132C22×C73—21no—
133C22×C73—21no—
134C22×C73—22no—
135C22×C73—21no—
136C22×C73—42no—
137C22×C73—41no—
138C22×C73—41no—
139C22×C73—42no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73—81no—
145C22×C73#39111yescharacteristic
146C22×C73C2×#9911yescharacteristic
147C22×C73#41011yescharacteristic
148C4×C73—21no—
149C4×C73—22no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73—162no—
154C4×C73#35212yes—
155Dic73—82no—
156Dic73—82no—
157#13292—731nomaximal, Sylow
158C2×C73—21no—
159C2×C73—21no—
160C2×C73—41no—
161C2×C73—42no—
162C2×C73—41no—
163C2×C73#199611yescharacteristic
164C2×C73C2×#35211yescharacteristic
165C2×C73#212211yescharacteristic
166#2487—731no—
167#1799D7311yescharacteristic
168C4×#100—731no—
169#1390—734no—
170C73#1329211yescharacteristic, complemented, Sylow
171C2×C4×D4C2×D7311yescharacteristic
172C22×C4⋊C4—731no—
173C2×#100—732no—
174C2×#99C2×D7312yes—
175C4×M16—1461no—
176#400—1461no—
177#399—1461no—
178#389—1461no—
179#386—732no—
180#385—732no—
181#380—21no—
182#380—731no—
183#380—1461no—
184#343—1461no—
185#342—21no—
186C22×D4C22×D7311yescharacteristic
187C23×C4—732no—
188C23×C4C4×D7311yescharacteristic
189C23×C4C22⋊D7311yescharacteristic
190C2×M16—1462no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—2921no—
195C2×C4⋊C4—2921no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4—1461no—
199C2×C4⋊C4—1462no—
200C2×C4⋊C4D29211yescharacteristic
201C2×C22⋊C4—22no—
202C2×C22⋊C4—732no—
203C2×C22⋊C4—1462no—
204C2×C22⋊C4C4×D7311yescharacteristic
205C2×C22⋊C4C22⋊D7311yescharacteristic
206C2×C42D29211yescharacteristic
207#100—734no—
208#100—1462no—
209#99—24no—
210#97—2921no—
211C4×C8—2921no—
212#95—41no—
213#95—1461no—
214#95—1462no—
215#95—1462no—
216C24C2×C4×D7311yescharacteristic
217C24C2×C22⋊D7311yescharacteristic
218C2×D4—41no—
219C2×D4—41no—
220C2×D4Q8×D7312yes—
221C2×D4#1192402712yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—2922no—
230C22×C4—5842no—
231C22×C4—1462no—
232C22×C4—1462no—
233C22×C4#1192400511yescharacteristic
234C22×C4#1192400511yescharacteristic
235C22×C4#1192400511yescharacteristic
236C22×C4#1192400511yescharacteristic
237C22×C4C2×D29211yescharacteristic
238M16—2922no—
239M16—1464no—
240C2×C8—2922no—
241C4⋊C4—41no—
242C4⋊C4—82no—
243C4⋊C4—2922no—
244C4⋊C4—2922no—
245C4⋊C4—2921no—
246C4⋊C4—2921no—
247C4⋊C4—5842no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—2922no—
253C22⋊C4—5842no—
254C42—21no—
255C42—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C2×#1192400511yescharacteristic
265C23#1455655612yes—
266C23#1455657811yescharacteristic
267C23#1455658911yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—2922no—
287C2×C4—2922no—
288C2×C4—2922no—
289C2×C4—2922no—
290C2×C4—2922no—
291C2×C4—2922no—
292C2×C4—5844no—
293C2×C4#1455650511yescharacteristic
294C2×C4#1455650511yescharacteristic
295C2×C4#1455657112yes—
296C8—2924no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22#1798849211yescharacteristic
312C22C2×#1455650511yescharacteristic
313C22#1798856011yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—162no—
320C4—5842no—
321C4—5842no—
322C4#1798837612yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#2261091511yescharacteristic
329C2C2×#1798837611yescharacteristic
330C2#2261158011yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#1799D73
hypocenterC73#13292
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
5. C22×C4⋊Dic73C4semidirect
12. #17988459C4semidirect
14. #17988447C4semidirect
170. C73#13292semidirect

Maximal subgroups

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

subgroupindex
#226142482
C4×#145565082
#226080482
C73×#17992
#1329273