Finite Group Databasebeta

← #32995570

Subgroups — #32995570

Order 18688.

414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 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#22608261C211yesmaximal, characteristic
2C2×#17988313C211yesmaximal, characteristic
3#22607877C212yesmaximal, complemented
4#22607865C212yesmaximal, complemented
5C73×#2502C211yesmaximal, characteristic
6#17988551—21no—
7C2×C22⋊#10596831—21no—
8#17988313—21no—
9#17988313—21no—
10#17988313C2212yes—
11#17988313C2212yes—
12C2×C22⋊Q8×C73C411yescharacteristic
13C22×C4⋊C4×C73C2211yescharacteristic
14#398×C73—21no—
15#398×C73—21no—
16#391×C73C411yescharacteristic
17#391×C73C2211yescharacteristic
18#385×C73—21no—
19#385×C73—21no—
20#384×C73C411yescharacteristic
21#384×C73C2211yescharacteristic
22C4×C22⋊C4×C73C411yescharacteristic
23C2×#11924012—41no—
24C22×#10596831—41no—
25C22⋊#10596831—22no—
26C22⋊#10596831—22no—
27C22⋊#10596831—41no—
28C22⋊#10596831—41no—
29C22×Q8×C73C2×C411yescharacteristic
30C23×C4×C73C2×C411yescharacteristic
31C23×C4×C73D411yescharacteristic
32C23×C4×C73D411yescharacteristic
33C22⋊Q8×C73—41no—
34C22⋊Q8×C73—41no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—41no—
41C2×C4⋊C4×C73—41no—
42C2×C4⋊C4×C73C2×C411yescharacteristic
43C2×C4⋊C4×C73C2×C411yescharacteristic
44C2×C4⋊C4×C73D411yescharacteristic
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73C2311yescharacteristic
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73—21no—
49C2×C42×C73C2×C411yescharacteristic
50C2×C42×C73C2×C411yescharacteristic
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#11924012—82no—
57C2×#10596831—42no—
58C2×#10596831—42no—
59C2×#10596831—82no—
60C24×C73C22⋊C411yescharacteristic
61C2×Q8×C73—22no—
62C2×Q8×C73—41no—
63C2×Q8×C73—41no—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—22no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—41no—
76C22×C4×C73—81no—
77C22×C4×C73—81no—
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22⋊C411yescharacteristic
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22×C411yescharacteristic
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C4⋊C4×C73—41no—
85C4⋊C4×C73—41no—
86C4⋊C4×C73—41no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—42no—
90C4⋊C4×C73—81no—
91C4⋊C4×C73—81no—
92C4⋊C4×C73—81no—
93C4⋊C4×C73—81no—
94C22⋊C4×C73—24no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C42×C73—22no—
98C42×C73—41no—
99C23×C73—22no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—41no—
103C23×C73#9911yescharacteristic
104C23×C73#9911yescharacteristic
105C23×C73C2×C22⋊C411yescharacteristic
106Q8×C73—82no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—22no—
110C2×C4×C73—22no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—42no—
119C2×C4×C73—42no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
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—81no—
137C2×C4×C73—81no—
138C2×C4×C73#13112yes—
139#10596831—82no—
140#10596831—82no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—42no—
149C22×C73—42no—
150C22×C73#35612yes—
151C22×C73#40811yescharacteristic
152C22×C73C2×#9911yescharacteristic
153C22×C73#41311yescharacteristic
154C4×C73—22no—
155C4×C73—42no—
156C4×C73—42no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—81no—
163C4×C73—81no—
164#11555—731nomaximal, Sylow
165C2×C73—21no—
166C2×C73—21no—
167C2×C73—22no—
168C2×C73—41no—
169C2×C73#146811yescharacteristic
170C2×C73#212711yescharacteristic
171C2×C73C2×#35611yescharacteristic
172#2502D7311yescharacteristic
173#1463—731no—
174C2×#324—731no—
175#1325—732no—
176#1319—732no—
177C73#1155511yescharacteristic, complemented, Sylow
178C2×C22⋊Q8Dic7311yescharacteristic
179C22×C4⋊C4C2×D7311yescharacteristic
180#407—1461no—
181C2×C22⋊C8—1461no—
182#398—21no—
183#398—21no—
184#391Dic7311yescharacteristic
185#391C2×D7311yescharacteristic
186#385—21no—
187#385—21no—
188#384Dic7311yescharacteristic
189#384C2×D7311yescharacteristic
190C4×C22⋊C4Dic7311yescharacteristic
191#324—732no—
192#324—732no—
193#324—1461no—
194#324—1461no—
195C22×Q8C2×Dic7311yescharacteristic
196C23×C4C2×Dic7311yescharacteristic
197C23×C4C22⋊D7311yescharacteristic
198C23×C4C22⋊D7311yescharacteristic
199C2×M16—2921no—
200C22×C8—2921no—
201C22⋊Q8—41no—
202C22⋊Q8—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4C2×Dic7311yescharacteristic
211C2×C4⋊C4C2×Dic7311yescharacteristic
212C2×C4⋊C4C22⋊D7311yescharacteristic
213C2×C4⋊C4C22⋊D7311yescharacteristic
214C2×C4⋊C4C22×D7311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42C2×Dic7311yescharacteristic
218C2×C42C2×Dic7311yescharacteristic
219C22⋊C8—2921no—
220C22⋊C8—2921no—
221C22⋊C8—1462no—
222C22⋊C8—1462no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228C24C22⋊Dic7311yescharacteristic
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4C22⋊Dic7311yescharacteristic
247C22×C4C22⋊Dic7311yescharacteristic
248C22×C4C22⋊Dic7311yescharacteristic
249C22×C4C22×Dic7311yescharacteristic
250C22×C4C2×C22⋊D7311yescharacteristic
251C22×C4C2×C22⋊D7311yescharacteristic
252M16—5842no—
253C2×C8—2922no—
254C2×C8—2922no—
255C2×C8—5842no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C22⋊C4—24no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—22no—
270C42—41no—
271C23—22no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23#1455650611yescharacteristic
276C23#1455650611yescharacteristic
277C23C2×C22⋊Dic7311yescharacteristic
278Q8—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
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—81no—
309C2×C4—81no—
310C2×C4#1455659812yes—
311C8—5842no—
312C8—5842no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#1798838612yes—
323C22#1798855411yescharacteristic
324C22C2×#1455650611yescharacteristic
325C22#1798857111yescharacteristic
326C4—22no—
327C4—42no—
328C4—42no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#2260827911yescharacteristic
341C2#2261160011yescharacteristic
342C2C2×#1798838611yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2502C2
socleC22×C73C2×#99
prime radicalC24×C73C22⋊C4
cosocleC2×C4⋊C4×C73C23
hypercenter#2502D73
hypocenterC73#11555
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
3. #22607877C2semidirect
4. #22607865C2semidirect
177. C73#11555semidirect

Maximal subgroups

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

subgroupindex
#226082612
C2×#179883132
#226078772
#226078652
C73×#25022
#1155573