Finite Group Databasebeta

← #32979611

Subgroups — #32979611

Order 18688.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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#22612871C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607817C212yesmaximal, complemented
4#22607784C212yesmaximal, complemented
5C4×#99×C73C211yesmaximal, characteristic
6#17988551C2212yes—
7#17988480—21no—
8#17988473—21no—
9#17988467—21no—
10#17988455C411yescharacteristic, complemented
11#17988450C2211yescharacteristic
12#17988447C411yescharacteristic, complemented
13C22⋊C4×Dic73—21no—
14C4×C22⋊Dic73C2211yescharacteristic
15#17988433C411yescharacteristic, complemented
16C2×#14556498C411yescharacteristic, complemented
17#17988313—21no—
18#17988311—21no—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21C4×C22⋊C4×C73C2212yes—
22#342×C73—21no—
23C23×Dic73—21no—
24C2×#11924012—22no—
25C2×C4⋊Dic73—21no—
26C2×C22⋊Dic73—21no—
27C2×C22⋊Dic73—21no—
28C2×C22⋊Dic73—21no—
29C2×C4×Dic73—21no—
30C2×C4×Dic73—21no—
31C22⋊#10596831—22no—
32C22⋊#10596831—22no—
33#14556498—21no—
34#14556498—21no—
35#14556498—21no—
36#14556498—21no—
37#14556498—21no—
38#14556498C2×C411yescharacteristic
39#14556498C2×C411yescharacteristic
40#14556498C2×C411yescharacteristic
41#14556498C2×C411yescharacteristic
42C22×D4×C73D411yescharacteristic
43C23×C4×C73C2×C411yescharacteristic
44C23×C4×C73C2311yescharacteristic
45C4×D4×C73—22no—
46C4×D4×C73—22no—
47C2×C4⋊C4×C73D411yescharacteristic
48C2×C22⋊C4×C73—22no—
49C2×C22⋊C4×C73D411yescharacteristic
50C2×C22⋊C4×C73D411yescharacteristic
51C2×C42×C73—22no—
52C2×C42×C73C2×C411yescharacteristic
53#99×C73—24no—
54#95×C73—22no—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—42no—
60C22×Dic73—42no—
61C22×Dic73—81no—
62#11924012—82no—
63C2×#10596831—42no—
64C4⋊Dic73—81no—
65C22⋊Dic73—42no—
66C22⋊Dic73—42no—
67C22⋊Dic73—81no—
68C4×Dic73—42no—
69C4×Dic73—81no—
70C24×C73C22⋊C411yescharacteristic
71C24×C73C2×D411yescharacteristic
72C2×D4×C73—22no—
73C2×D4×C73—22no—
74C2×D4×C73—41no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—42no—
78C22×C4×C73—81no—
79C22×C4×C73—81no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22×C411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73#4112yes—
86C22×C4×C73#4112yes—
87C4⋊C4×C73—22no—
88C22⋊C4×C73—22no—
89C22⋊C4×C73—22no—
90C22⋊C4×C73—24no—
91C22⋊C4×C73—42no—
92C42×C73—21no—
93C42×C73—21no—
94C42×C73—82no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—41no—
100C23×C73—41no—
101C23×C73—41no—
102C23×C73—41no—
103C23×C73#10412yes—
104C23×C73C2×C22⋊C411yescharacteristic
105C23×C73#12312yes—
106D4×C73—44no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—42no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—42no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—44no—
119C2×C4×C73—81no—
120C2×C4×C73—81no—
121C2×C4×C73—82no—
122C2×C4×C73—82no—
123C2×C4×C73#11711yescharacteristic
124C2×C4×C73#11711yescharacteristic
125C2×C4×C73#12312yes—
126C2×Dic73—22no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—84no—
139#10596831—82no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73—22no—
143C22×C73—22no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—42no—
147C22×C73—42no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—81no—
151C22×C73—81no—
152C22×C73#38111yescharacteristic
153C22×C73C2×#10411yescharacteristic
154C22×C73#42111yescharacteristic
155C4×C73—22no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—84no—
162Dic73—42no—
163Dic73—81no—
164Dic73—81no—
165Dic73—81no—
166#8776—731nomaximal, Sylow
167C2×C73—21no—
168C2×C73—21no—
169C2×C73—42no—
170C2×C73—42no—
171C2×C73#182611yescharacteristic
172C2×C73#182711yescharacteristic
173C2×C73#182811yescharacteristic
174#2353—731no—
175C4×#99D7311yescharacteristic
176#1465—731no—
177#1297—732no—
178#1284—732no—
179C73#877611yescharacteristic, complemented, Sylow
180C2×C4×D4C2×D7311yescharacteristic
181C2×#99—21no—
182#407—732no—
183#388—1461no—
184#387—1461no—
185#386—1461no—
186#383—731no—
187#381—731no—
188#380—731no—
189C4×C22⋊C4—731no—
190C4×C22⋊C4—1461no—
191C4×C22⋊C4C2×D7312yes—
192#376—731no—
193C2×#95—731no—
194#342—21no—
195#324—1461no—
196#323—1461no—
197C22×D4C22⋊D7311yescharacteristic
198C23×C4—1461no—
199C23×C4C4×D7311yescharacteristic
200C23×C4C22×D7311yescharacteristic
201C2×M16—1462no—
202C4×D4—22no—
203C4×D4—22no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4D29211yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—1461no—
208C2×C22⋊C4—1461no—
209C2×C22⋊C4—1461no—
210C2×C22⋊C4D29211yescharacteristic
211C2×C22⋊C4C22⋊D7311yescharacteristic
212C2×C42—22no—
213C2×C42—1461no—
214C2×C42—1461no—
215C2×C42C4×D7311yescharacteristic
216#99—24no—
217C22⋊C8—1462no—
218C22⋊C8—1462no—
219#95—22no—
220#95—731no—
221#95—731no—
222#95—731no—
223#95—731no—
224#95—1461no—
225#95—1461no—
226#95—1461no—
227#95—1461no—
228#95—1461no—
229C24#1192400511yescharacteristic
230C24C2×C22⋊D7311yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—2922no—
240C22×C4—2922no—
241C22×C4—5841no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4#1192400511yescharacteristic
247C22×C4#1192400511yescharacteristic
248C22×C4#1192400511yescharacteristic
249C22×C4C2×C4×D7311yescharacteristic
250C22×C4C2×D29211yescharacteristic
251C22×C4#1192402712yes—
252C22×C4#1192402712yes—
253M16—5842no—
254C2×C8—2922no—
255C4⋊C4—22no—
256C4⋊C4—5841no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—42no—
261C22⋊C4—2922no—
262C22⋊C4—2922no—
263C22⋊C4—5841no—
264C42—21no—
265C42—21no—
266C42—82no—
267C42—2922no—
268C42—5841no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#1455651912yes—
278C23C2×#1192400511yescharacteristic
279C23#1455657212yes—
280D4—44no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—2921no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—2921no—
305C2×C4—2921no—
306C2×C4—2921no—
307C2×C4—2921no—
308C2×C4—5844no—
309C2×C4—1462no—
310C2×C4#1455654711yescharacteristic
311C2×C4#1455654711yescharacteristic
312C2×C4#1455657512yes—
313C8—5842no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1798844811yescharacteristic
327C22C2×#1455651911yescharacteristic
328C22#1798860511yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—84no—
336C4—2922no—
337C4—5841no—
338C4—5841no—
339C4—5841no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#2261003111yescharacteristic
345C2#2261003211yescharacteristic
346C2#2261003711yescharacteristic
subgroupG/H
centerC22#17988448
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC4×#99×C73C2
socleC22×C73#381
prime radicalC22×D4×C73D4
cosocleC23×C4×C73C23
hypercenterC4×#99D73
hypocenterC73#8776
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #22607817C2semidirect
4. #22607784C2semidirect
10. #17988455C4semidirect
12. #17988447C4semidirect
15. #17988433C4semidirect
16. C2×#14556498C4semidirect
179. C73#8776semidirect

Maximal subgroups

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

subgroupindex
#226128712
#226082692
#226078172
#226077842
C4×#99×C732
#877673