Finite Group Databasebeta

← #34000476

Subgroups — #34000476

Order 18688.

372 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 66 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#22625795C211yesmaximal, characteristic
2#22625791C211yesmaximal, characteristic
3#22610223C211yesmaximal, characteristic
4#17989590—21no—
5C2×#14556651—21no—
6C2×#14556649—21no—
7#17989529—21no—
8#17989467C412yescomplemented
9#17989465C412yes—
10C2×C4×C22⋊D73C2211yescharacteristic
11C2×C22⋊#10596831C411yescharacteristic, complemented
12C2×#14556503—21no—
13#17988341—21no—
14C23×C8×C73C411yescharacteristic, complemented
15C2×#11924037—22no—
16C2×C4⋊#64408—41no—
17C2×C22⋊#64408—22no—
18#14556658—41no—
19C4⋊#10596833—41no—
20#14556651—41no—
21#14556651—41no—
22#14556649—41no—
23#14556649—41no—
24(C2×#64408)⋊C4—41no—
25C22×C22⋊D73D411yescharacteristic
26C22×C4×D73D411yescharacteristic
27C22×#10596831—21no—
28C4×C22⋊D73—41no—
29C4×C22⋊D73—41no—
30C2×#11924007C2×C411yescharacteristic
31C2×C22⋊Dic73Q811yescharacteristic
32C2×#11924005C2×C411yescharacteristic
33C2×C4×Dic73D411yescharacteristic
34C22⋊#10596831—41no—
35#14556503—42no—
36C23×C4×C73C2×C411yescharacteristic
37C22×C8×C73—21no—
38C22×C8×C73—42no—
39C22×C8×C73—41no—
40C22×#64408—42no—
41#11924037—42no—
42#11924037—42no—
43C2×#10596833—42no—
44C4⋊#64408—81no—
45C4⋊#64408—81no—
46C22⋊#64408—42no—
47C22⋊#64408—42no—
48C23×D73C22⋊C411yescharacteristic
49C2×C22⋊D73—41no—
50C2×C22⋊D73—41no—
51C2×C22⋊D73D811yescharacteristic
52C2×C22⋊D73SD1611yescharacteristic
53C2×C22⋊D73SD1611yescharacteristic
54C2×C22⋊D73Q1611yescharacteristic
55C22×Dic73C22⋊C411yescharacteristic
56C22×Dic73C4⋊C411yescharacteristic
57C22×Dic73C4⋊C411yescharacteristic
58C2×C4×D73—21no—
59C2×C4×D73—21no—
60C2×C4×D73—41no—
61C2×C4×D73—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65#11924007—41no—
66C22⋊Dic73—41no—
67#11924005—41no—
68C4×Dic73—21no—
69C4×Dic73—21no—
70C24×C73C4⋊C411yescharacteristic
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—41no—
74C22×C4×C73—41no—
75C22×C4×C73C4211yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C2×C8×C73—22no—
78C2×C8×C73—41no—
79C2×C8×C73—42no—
80C2×C8×C73—41no—
81C2×C8×C73—42no—
82C23×C73—21no—
83C23×C73—21no—
84C23×C73—41no—
85C23×C73—41no—
86C23×C73#9511yescharacteristic
87C23×C73#10611yescharacteristic
88C23×C73#10711yescharacteristic
89C22×D73—21no—
90C22×D73—21no—
91C22×D73—41no—
92C22×D73—41no—
93C22×D73#10211yescharacteristic
94C22×D73#10311yescharacteristic
95C2×#64408—82no—
96C2×#64408—82no—
97C2×#64408—82no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—42no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73#9911yescharacteristic
106C2×C4×C73#9911yescharacteristic
107C22⋊D73—41no—
108C22⋊D73—41no—
109C22⋊D73—41no—
110C22⋊D73—41no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—41no—
116C2×Dic73—41no—
117C2×Dic73#10211yescharacteristic
118C2×Dic73#10311yescharacteristic
119C4×D73—41no—
120C4×D73—41no—
121C4×D73—81no—
122#10596833—82no—
123C8×C73—42no—
124#10596831—81no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—41no—
130C22×C73—41no—
131C22×C73—42no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73H(3,ℤ/4)11yescharacteristic
135C22×C73#34011yescharacteristic
136C22×C73#34211yescharacteristic
137C2×D73—21no—
138C2×D73—21no—
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—41no—
142C2×D73—41no—
143C2×D73—81no—
144#64408—162no—
145C4×C73—21no—
146C4×C73—41no—
147C4×C73AΣL(1,𝔽16)11yescharacteristic
148C4×C73#35211yescharacteristic
149Dic73—21no—
150Dic73—21no—
151Dic73—41no—
152Dic73—41no—
153#7236—731nomaximal, Sylow
154C2×C73—21no—
155C2×C73—21no—
156C2×C73—41no—
157C2×C73—41no—
158C2×C73#128911yescharacteristic
159C2×C73#139011yescharacteristic
160C2×C73#139511yescharacteristic
161D73—41no—
162D73—41no—
163#1869—731no—
164#1800—731no—
165#1799—731no—
166C73#723611yescharacteristic, complemented, Sylow
167C23×C8#6440811yescharacteristic, complemented
168C2×C4×D4—731no—
169#423—1461no—
170C2×#100—1461no—
171C2×#99—1461no—
172C2×C22⋊C8—731no—
173C2×C22⋊C8—1461no—
174#380—1461no—
175#343—732no—
176#342—732no—
177#336—1461no—
178C22×D4—731no—
179C23×C4—731no—
180C23×C4C2×#6440811yescharacteristic
181C2×M16—1462no—
182C22×C8—21no—
183C22×C8—42no—
184C22×C8—41no—
185C22×C8—1461no—
186C4×D4—2921no—
187C4×D4—2921no—
188C2×C4⋊C4—2921no—
189C2×C4⋊C4—731no—
190C2×C22⋊C4—731no—
191C2×C22⋊C4—731no—
192C2×C22⋊C4—1462no—
193C2×C42—731no—
194C4⋊C8—2921no—
195C4⋊C8—2921no—
196#100—2921no—
197#100—2921no—
198#99—2921no—
199#99—2921no—
200C22⋊C8—2922no—
201C22⋊C8—2921no—
202#95—2921no—
203C24—731no—
204C24C4⋊#6440811yescharacteristic
205C2×D4—2921no—
206C2×D4—2921no—
207C2×D4—731no—
208C2×D4—731no—
209C2×D4—731no—
210C2×D4—731no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—2921no—
216C22×C4—2921no—
217C22×C4—2922no—
218C22×C4—731no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4C4×#6440811yescharacteristic
224C22×C4C22⋊#6440811yescharacteristic
225M16—2922no—
226M16—2922no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—2921no—
233C2×C8—2921no—
234C2×C8—2922no—
235C2×C8—2921no—
236C4⋊C4—2921no—
237C4⋊C4—5841no—
238C4⋊C4—5841no—
239C22⋊C4—2921no—
240C22⋊C4—2922no—
241C22⋊C4—2922no—
242C22⋊C4—2921no—
243C42—1461no—
244C42—1461no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—2921no—
250C23—2921no—
251C23—731no—
252C23—731no—
253C23—1461no—
254C23—1461no—
255C23(C2×#64408)⋊C411yescharacteristic
256C23#1455665911yescharacteristic
257C23#1455666011yescharacteristic
258D4—2921no—
259D4—2921no—
260D4—2921no—
261D4—2921no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—2921no—
270C2×C4—2921no—
271C2×C4—2921no—
272C2×C4—2921no—
273C2×C4—5841no—
274C2×C4—5842no—
275C2×C4—5842no—
276C2×C4—5842no—
277C2×C4—731no—
278C2×C4—731no—
279C2×C4—1461no—
280C2×C4—1461no—
281C2×C4—1461no—
282C2×C4—1461no—
283C2×C4#1455664911yescharacteristic
284C2×C4#1455665011yescharacteristic
285C8—42no—
286C8—5841no—
287C8—5842no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—2921no—
298C22—2921no—
299C22—2921no—
300C22—2921no—
301C22—5841no—
302C22—1461no—
303C22—1461no—
304C22#1798945511yescharacteristic
305C22#1798946111yescharacteristic
306C22#1798946511yescharacteristic
307C4—21no—
308C4—41no—
309C4—2921no—
310C4—2921no—
311C4—11682no—
312C4—1461no—
313C4—1461no—
314C4#1798948711yescharacteristic
315C4#1798948911yescharacteristic
316C2—21no—
317C2—21no—
318C2—41no—
319C2—41no—
320C2—2921no—
321C2—2921no—
322C2#2262479411yescharacteristic
323C2#2262501511yescharacteristic
324C2#2262503111yescharacteristic
subgroupG/H
centerC22#17989465
commutatorC22×C4×C73C42
FrattiniC23×C4C2×#64408
FittingC23×C8×C73C4
socleC22×C73#342
prime radicalC22×C22⋊D73D4
cosocleC2×C4×C22⋊D73C22
hypercenterC23×C8#64408
hypocenterC73#7236
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
8. #17989467C4semidirect
11. C2×C22⋊#10596831C4semidirect
14. C23×C8×C73C4semidirect
166. C73#7236semidirect
167. C23×C8#64408semidirect

Maximal subgroups

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

subgroupindex
#226257952
#226257912
#226102232
#723673