Finite Group Databasebeta

← #32995672

Subgroups — #32995672

Order 18688.

426 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 83 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#22615274C211yesmaximal, characteristic
2#22608249C211yesmaximal, characteristic
3#22607880C212yesmaximal, complemented
4#22607878C212yesmaximal, complemented
5C73×#1466C211yesmaximal, characteristic
6C22×#11924007C411yescharacteristic
7C2×C22⋊#10596831—21no—
8#17988520—21no—
9#17988510—21no—
10#17988471—21no—
11#17988467C411yescharacteristic
12#17988467C411yescharacteristic
13#17988460—21no—
14#17988459C2211yescharacteristic
15#17988459C2211yescharacteristic
16#17988447C411yescharacteristic
17#17988313—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20#432×C73—21no—
21#323×C73—21no—
22#323×C73C2212yes—
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C22×#10596831—41no—
26C2×C4⋊Dic73—21no—
27C2×#11924007—21no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—41no—
32C2×#11924007—41no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73C2×C411yescharacteristic
36C2×C22⋊Dic73C2×C411yescharacteristic
37C22⋊#10596831—22no—
38C22⋊#10596831—41no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44C22×D4×C73C2×C411yescharacteristic
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C22⋊C4×C73D411yescharacteristic
51C2×C22⋊C4×C73C2311yescharacteristic
52C2×C42×C73D411yescharacteristic
53C4⋊C8×C73—41no—
54C22⋊C8×C73—22no—
55#97×C73—41no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—42no—
61C22×Dic73—41no—
62C22×Dic73—41no—
63C22×Dic73—81no—
64C2×#10596831—42no—
65C2×#10596831—82no—
66C4⋊Dic73—81no—
67#11924007—42no—
68#11924007—42no—
69#11924007—41no—
70#11924007—41no—
71#11924007—81no—
72C22⋊Dic73—22no—
73C22⋊Dic73—22no—
74C22⋊Dic73—42no—
75C22⋊Dic73—81no—
76C24×C73C22⋊C411yescharacteristic
77C24×C73C22×C411yescharacteristic
78C2×D4×C73—22no—
79C2×D4×C73—22no—
80C2×D4×C73—41no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—81no—
86C22×C4×C73—81no—
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C2×C8×C73—42no—
93C4⋊C4×C73—41no—
94C22⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C42×C73—21no—
97C42×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—41no—
103C23×C73—41no—
104C23×C73—41no—
105C23×C73—41no—
106C23×C73#10112yes—
107C23×C73C2×C22⋊C411yescharacteristic
108C23×C73#13112yes—
109D4×C73—44no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—41no—
117C2×C4×C73—42no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—81no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73#9911yescharacteristic
125C2×C4×C73#9911yescharacteristic
126C2×Dic73—22no—
127C2×Dic73—41no—
128C2×Dic73—42no—
129C2×Dic73—41no—
130C2×Dic73—42no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—82no—
141C8×C73—82no—
142#10596831—82no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—42no—
148C22×C73—42no—
149C22×C73—42no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—81no—
155C22×C73#40811yescharacteristic
156C22×C73C2×#9911yescharacteristic
157C22×C73C2×#10111yescharacteristic
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164Dic73—42no—
165Dic73—81no—
166Dic73—81no—
167Dic73—81no—
168#11578—731nomaximal, Sylow
169C2×C73—21no—
170C2×C73—21no—
171C2×C73—42no—
172C2×C73—42no—
173C2×C73#147211yescharacteristic
174C2×C73#212011yescharacteristic
175C2×C73#212111yescharacteristic
176#2579—731no—
177#1466D7311yescharacteristic
178#1459—731no—
179#1326—732no—
180#1326—732no—
181C73#1157811yescharacteristic, complemented, Sylow
182C2×C4×D4C2×D7311yescharacteristic
183C22×C4⋊C4—731no—
184#432—21no—
185C2×C22⋊C8—1461no—
186#398—1461no—
187#396—1461no—
188#387—1461no—
189#386—731no—
190#386—731no—
191#385—731no—
192#385—731no—
193#385—1461no—
194#380—731no—
195#324—1461no—
196#323—21no—
197#323—732no—
198#323C2×D7312yes—
199C22×D4C4×D7311yescharacteristic
200C23×C4—731no—
201C23×C4—731no—
202C23×C4C4×D7311yescharacteristic
203C23×C4D29211yescharacteristic
204C22×C8—2921no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—2921no—
208C2×C4⋊C4—2921no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4—1461no—
212C2×C4⋊C4—1461no—
213C2×C4⋊C4—1461no—
214C2×C4⋊C4D29211yescharacteristic
215C2×C22⋊C4—731no—
216C2×C22⋊C4—731no—
217C2×C22⋊C4—1461no—
218C2×C22⋊C4—1461no—
219C2×C22⋊C4C22⋊D7311yescharacteristic
220C2×C22⋊C4C22×D7311yescharacteristic
221C2×C42C22⋊D7311yescharacteristic
222C4⋊C8—41no—
223C22⋊C8—22no—
224C22⋊C8—2921no—
225C22⋊C8—1462no—
226#97—41no—
227#95—1461no—
228#95—1461no—
229#95—1461no—
230#95—1461no—
231#95—1461no—
232C24#1192400511yescharacteristic
233C24C2×C4×D7311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4—2921no—
244C22×C4—2922no—
245C22×C4—2921no—
246C22×C4—5841no—
247C22×C4—1461no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4#1192400511yescharacteristic
252C22×C4#1192400511yescharacteristic
253C22×C4#1192400511yescharacteristic
254C22×C4C2×C22⋊D7311yescharacteristic
255C22×C4C2×D29211yescharacteristic
256C2×C8—42no—
257C2×C8—2922no—
258C2×C8—5842no—
259C4⋊C4—41no—
260C4⋊C4—2922no—
261C4⋊C4—2922no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—5841no—
265C4⋊C4—5841no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—2922no—
269C22⋊C4—5841no—
270C22⋊C4—1462no—
271C22⋊C4—1462no—
272C42—21no—
273C42—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1455650912yes—
283C23C2×#1192400511yescharacteristic
284C23#1455659912yes—
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—2921no—
301C2×C4—2922no—
302C2×C4—2921no—
303C2×C4—2922no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2921no—
307C2×C4—2921no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—5842no—
314C2×C4—1462no—
315C2×C4#1455650511yescharacteristic
316C2×C4#1455650511yescharacteristic
317C8—82no—
318C8—5842no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1798855511yescharacteristic
332C22C2×#1455650511yescharacteristic
333C22C2×#1455650911yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2922no—
341C4—5841no—
342C4—5841no—
343C4—5841no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#2260829611yescharacteristic
349C2#2261157011yescharacteristic
350C2#2261157811yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1466C2
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC2×C22⋊C4×C73C23
hypercenter#1466D73
hypocenterC73#11578
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #22607880C2semidirect
4. #22607878C2semidirect
181. C73#11578semidirect

Maximal subgroups

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

subgroupindex
#226152742
#226082492
#226078802
#226078782
C73×#14662
#1157873