Finite Group Databasebeta

← #34001913

Subgroups — #34001913

Order 18688.

420 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 94 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#22625847C211yesmaximal, characteristic, complemented
2#22625846C211yesmaximal, characteristic, complemented
3#22624750C212yesmaximal, complemented
4#22624747C212yesmaximal
5#22618295C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×C4⋊#10596833—21no—
8#17989453—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×#14556584—21no—
13#17988490C411yescharacteristic
14#17988490C2211yescharacteristic
15#17988486C411yescharacteristic
16#17988485C411yescharacteristic
17#17988483C2211yescharacteristic
18#17988481—21no—
19#17988480—21no—
20#17988475—21no—
21C42×Dic73C2211yescharacteristic
22#390×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556658—42no—
26C4⋊#10596833—42no—
27#14556584—42no—
28#14556584—42no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37C2×C22⋊Dic73—21no—
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42C2×C4×Dic73D411yescharacteristic
43C2×C4×Dic73C2311yescharacteristic
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C22×D4×C73C2×C411yescharacteristic
48C2×C4⋊C4×C73C2×C411yescharacteristic
49C2×C22⋊C4×C73—21no—
50C2×C22⋊C4×C73—21no—
51C2×C42×C73C2×C411yescharacteristic
52C2×#10596833—42no—
53C2×#10596833—42no—
54C2×#10596833—42no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73C22⋊C411yescharacteristic
61C22×Dic73C22⋊C411yescharacteristic
62C22×Dic73C2×D411yescharacteristic
63C22×Dic73C2×D411yescharacteristic
64C4⋊Dic73—22no—
65C4⋊Dic73—42no—
66C4⋊Dic73—41no—
67#11924007—42no—
68#11924007—41no—
69#11924007—41no—
70C22⋊Dic73—42no—
71C22⋊Dic73—42no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74C22⋊Dic73—41no—
75C22⋊Dic73—41no—
76C4×Dic73—21no—
77C4×Dic73—21no—
78C4×Dic73—41no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C4×Dic73—41no—
82C4×Dic73D812yes—
83C4×Dic73SD1612yes—
84C24×C73—21no—
85C2×D4×C73—22no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
88C22×C4×C73—21no—
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C22×C411yescharacteristic
92C4⋊C4×C73—41no—
93C22⋊C4×C73—42no—
94C22⋊C4×C73—42no—
95C42×C73—22no—
96C23×C73—41no—
97C23×C73—41no—
98C23×C73—41no—
99C23×C73—41no—
100C23×C73—41no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73C2×C22⋊C411yescharacteristic
104D4×C73—82no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73#10212yes—
116C2×C4×C73#13112yes—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73#10212yes—
133C2×Dic73C2×D811yescharacteristic
134C2×Dic73C2×SD1611yescharacteristic
135C2×Dic73AGL(1,ℤ/8)11yescharacteristic
136C2×Dic73#13711yescharacteristic
137#10596833—82no—
138#10596833—82no—
139C22×C73—81no—
140C22×C73—81no—
141C22×C73—81no—
142C22×C73—81no—
143C22×C73—81no—
144C22×C73—81no—
145C22×C73—81no—
146C22×C73#40811yescharacteristic
147C22×C73#41011yescharacteristic
148C22×C73#41311yescharacteristic
149C22×C73C2×#10211yescharacteristic
150C22×C73#41711yescharacteristic
151C22×C73#42111yescharacteristic
152C22×C73#42111yescharacteristic
153C4×C73—22no—
154C4×C73—22no—
155C4×C73—41no—
156C4×C73—81no—
157Dic73—22no—
158Dic73—21no—
159Dic73—21no—
160Dic73—21no—
161Dic73—21no—
162Dic73—41no—
163Dic73—81no—
164Dic73—81no—
165#7732—731nomaximal, Sylow
166C2×C73—161no—
167C2×C73#147311yescharacteristic
168C2×C73#148011yescharacteristic
169C2×C73#149511yescharacteristic
170C2×C73#151211yescharacteristic
171C2×C73#151711yescharacteristic
172C2×C73#153511yescharacteristic
173C2×C73#154711yescharacteristic
174#2860—731no—
175#1831—731no—
176#1831—731no—
177#1271—732no—
178#1270—732no—
179C73#773211yescharacteristic, complemented, Sylow
180C2×#126—1461no—
181C2×C4⋊C8—1461no—
182C2×C4⋊C8—1461no—
183#390—731no—
184#390—731no—
185#390#6440811yescharacteristic
186#389—731no—
187#389—731no—
188#389—731no—
189#388—1461no—
190#388—1461no—
191#388—1461no—
192C43—731no—
193#336—732no—
194#336—732no—
195#336—1461no—
196#336—1461no—
197C22×D4C2×#6440811yescharacteristic
198C22×C8—1462no—
199C22×C8—1462no—
200#126—2922no—
201#126—2922no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4C2×#6440811yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—1461no—
211C2×C22⋊C4—1461no—
212C2×C22⋊C4—1461no—
213C2×C22⋊C4—1461no—
214C2×C42—731no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42—731no—
218C2×C42—731no—
219C2×C42—731no—
220C2×C42C2×#6440811yescharacteristic
221C4⋊C8—2922no—
222C4⋊C8—2922no—
223#95—1461no—
224#95—1461no—
225#95—1461no—
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4C22⋊#6440811yescharacteristic
238C22×C4C22⋊#6440811yescharacteristic
239C22×C4C22×#6440811yescharacteristic
240C2×C8—2922no—
241C2×C8—2922no—
242C2×C8—2922no—
243C2×C8—2922no—
244C2×C8—2922no—
245C2×C8—2922no—
246C4⋊C4—41no—
247C4⋊C4—2921no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2922no—
251C4⋊C4—2922no—
252C4⋊C4—1462no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—2921no—
256C22⋊C4—2921no—
257C22⋊C4—2921no—
258C22⋊C4—2922no—
259C22⋊C4—2921no—
260C22⋊C4—2922no—
261C42—22no—
262C42—2921no—
263C42—2921no—
264C42—2921no—
265C42—2921no—
266C42—732no—
267C42—732no—
268C42—1461no—
269C42—1461no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊#6440811yescharacteristic
278D4—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—2921no—
290C2×C4—2921no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—731no—
296C2×C4—732no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4#1455665312yes—
310C2×C4#1455667812yes—
311C8—5842no—
312C8—5842no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#1798956011yescharacteristic
321C22#1798956711yescharacteristic
322C22#1798957311yescharacteristic
323C22C2×#1455665311yescharacteristic
324C22#1798957811yescharacteristic
325C22#1798958411yescharacteristic
326C22#1798958511yescharacteristic
327C4—22no—
328C4—22no—
329C4—41no—
330C4—81no—
331C4—2921no—
332C4—5841no—
333C4—5841no—
334C4—1461no—
335C4—1461no—
336C4—1461no—
337C4—1461no—
338C4—1462no—
339C2—161no—
340C2#2262521311yescharacteristic
341C2#2262523611yescharacteristic
342C2#2262528611yescharacteristic
343C2#2262534311yescharacteristic
344C2#2262536011yescharacteristic
345C2#2262541511yescharacteristic
346C2#2262544211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#390×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC22×D4×C73C2×C4
cosocleC2×C4×Dic73C23
hypercenter#390#64408
hypocenterC73#7732
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #22625847C2semidirect
2. #22625846C2semidirect
3. #22624750C2semidirect
179. C73#7732semidirect

Maximal subgroups

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

subgroupindex
#226258472
#226258462
#226247502
#226247472
#226182952
#773273