Finite Group Databasebeta

← #32996753

Subgroups — #32996753

Order 18688.

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

normal subgroups only

This group has 434 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#22613190C211yesmaximal, characteristic
2#22608272C211yesmaximal, characteristic
3#22607954C212yesmaximal, complemented
4#22607930C212yesmaximal, complemented
5C73×#1799C211yesmaximal, characteristic
6C2×#14556550C411yescharacteristic, complemented
7#17988644—21no—
8#17988526C411yescharacteristic, complemented
9#17988523C2211yescharacteristic
10#17988517C411yescharacteristic, complemented
11#17988515—21no—
12#17988512C2211yescharacteristic
13#17988501—21no—
14C4×#11924007—21no—
15C4×C22⋊Dic73—21no—
16C4×C22⋊Dic73C411yescharacteristic, complemented
17#17988311—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21#380×C73—21no—
22#342×C73C2212yes—
23#14556550—41no—
24#14556550—41no—
25C2×C4⋊Dic73C2×C411yescharacteristic
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—21no—
28C2×#11924007—21no—
29C2×C22⋊Dic73—21no—
30C2×C22⋊Dic73—21no—
31C2×C22⋊Dic73—21no—
32C2×C22⋊Dic73—21no—
33C2×C4×Dic73—21no—
34C2×C4×Dic73—21no—
35C4⋊#10596831—41no—
36C22⋊#10596831—22no—
37#14556502—41no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C22×D4×C73D411yescharacteristic
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73—41no—
50C2×C4⋊C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73—22no—
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73C2311yescharacteristic
54C2×C42×C73D411yescharacteristic
55#99×C73—42no—
56#95×C73—41no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C2×#10596831—42no—
62C4⋊Dic73—41no—
63C4⋊Dic73—41no—
64#11924007—42no—
65#11924007—42no—
66C22⋊Dic73—42no—
67C22⋊Dic73—42no—
68C22⋊Dic73—42no—
69C22⋊Dic73—41no—
70C22⋊Dic73—41no—
71C4×Dic73—42no—
72C4×Dic73—41no—
73C4×Dic73—41no—
74C24×C73C22⋊C411yescharacteristic
75C24×C73C2×D411yescharacteristic
76C2×D4×C73—21no—
77C2×D4×C73—21no—
78C2×D4×C73—41no—
79C2×D4×C73—41no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—42no—
85C22×C4×C73—42no—
86C22×C4×C73—42no—
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22×C411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C4⋊C4×C73—41no—
93C4⋊C4×C73—82no—
94C22⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—42no—
97C22⋊C4×C73—42no—
98C42×C73—21no—
99C42×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73C2×C22⋊C411yescharacteristic
110C23×C73AGL(1,ℤ/8)11yescharacteristic
111C23×C73#13711yescharacteristic
112D4×C73—42no—
113D4×C73—42no—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—42no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—81no—
128C2×C4×C73—82no—
129C2×C4×C73—82no—
130C2×C4×C73—82no—
131C2×C4×C73#9911yescharacteristic
132C2×C4×C73#9911yescharacteristic
133C2×Dic73—22no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145#10596831—82no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—81no—
158C22×C73—81no—
159C22×C73—81no—
160C22×C73C2×#9911yescharacteristic
161C22×C73#41711yescharacteristic
162C22×C73#42111yescharacteristic
163C4×C73—21no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—162no—
169C4×C73#35212yes—
170Dic73—42no—
171Dic73—81no—
172Dic73—81no—
173Dic73—81no—
174#11822—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73—41no—
178C2×C73—41no—
179C2×C73—81no—
180C2×C73#151311yescharacteristic
181C2×C73C2×#35211yescharacteristic
182C2×C73#212611yescharacteristic
183#2395—731no—
184#1799D7311yescharacteristic
185#1466—731no—
186#1352—732no—
187#1344—732no—
188C73#1182211yescharacteristic, complemented, Sylow
189C2×C4×D4C2×D7311yescharacteristic
190C2×#117—731no—
191#432—1461no—
192C2×#99—21no—
193#400—731no—
194#399—731no—
195#398—731no—
196#397—731no—
197#397—1461no—
198#394—1461no—
199#380—21no—
200C4×C4⋊C4—1461no—
201C4×C22⋊C4—731no—
202C4×C22⋊C4—1461no—
203#342C2×D7312yes—
204#323—732no—
205#323—1461no—
206C22×D4C22⋊D7311yescharacteristic
207C23×C4C4×D7311yescharacteristic
208C23×C4C22⋊D7311yescharacteristic
209C4×D4—41no—
210C4×D4—41no—
211#117—2921no—
212#117—2921no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4C4×D7311yescharacteristic
219C2×C22⋊C4—22no—
220C2×C22⋊C4—1461no—
221C2×C22⋊C4—1461no—
222C2×C22⋊C4—1461no—
223C2×C22⋊C4—1461no—
224C2×C22⋊C4D29211yescharacteristic
225C2×C22⋊C4C22×D7311yescharacteristic
226C2×C42—1461no—
227C2×C42—1461no—
228C2×C42D29211yescharacteristic
229C4⋊C8—2921no—
230#99—42no—
231C22⋊C8—1462no—
232#97—2921no—
233#95—41no—
234#95—731no—
235#95—731no—
236#95—1461no—
237#95—1461no—
238#95—1461no—
239#95—1461no—
240C24#1192400511yescharacteristic
241C24C2×C22⋊D7311yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4#1192400511yescharacteristic
258C22×C4#1192400511yescharacteristic
259C22×C4#1192400511yescharacteristic
260C22×C4C2×C4×D7311yescharacteristic
261C22×C4C2×D29211yescharacteristic
262C2×C8—2922no—
263C4⋊C4—41no—
264C4⋊C4—82no—
265C4⋊C4—2921no—
266C4⋊C4—2921no—
267C4⋊C4—2922no—
268C4⋊C4—2922no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—2922no—
274C22⋊C4—2921no—
275C22⋊C4—2921no—
276C22⋊C4—2922no—
277C22⋊C4—2922no—
278C42—21no—
279C42—21no—
280C42—2922no—
281C42—2921no—
282C42—2921no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23C2×#1192400511yescharacteristic
293C23#1455661711yescharacteristic
294C23#1455662211yescharacteristic
295D4—42no—
296D4—42no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—2921no—
315C2×C4—2921no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—1462no—
326C2×C4#1455650511yescharacteristic
327C2×C4#1455650511yescharacteristic
328C8—5842no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C2×#1455650511yescharacteristic
344C22#1798858611yescharacteristic
345C22#1798860511yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—162no—
352C4—2922no—
353C4—5841no—
354C4—5841no—
355C4—5841no—
356C4#1798837612yes—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—41no—
361C2—81no—
362C2#2260847211yescharacteristic
363C2C2×#1798837611yescharacteristic
364C2#2261159411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1799D73
hypocenterC73#11822
LCSG ▷ C22×C4×C73 ▷ C23×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
3. #22607954C2semidirect
4. #22607930C2semidirect
6. C2×#14556550C4semidirect
8. #17988526C4semidirect
10. #17988517C4semidirect
16. C4×C22⋊Dic73C4semidirect
188. C73#11822semidirect

Maximal subgroups

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

subgroupindex
#226131902
#226082722
#226079542
#226079302
C73×#17992
#1182273