Finite Group Databasebeta

← #32996587

Subgroups — #32996587

Order 18688.

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

normal subgroups only

This group has 460 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#22615285C211yesmaximal, characteristic
2#22608269C211yesmaximal, characteristic
3#22607954C212yesmaximal, complemented
4#22607951C212yesmaximal, complemented
5C4×#99×C73C211yesmaximal, characteristic
6C2×C4×Dic146C411yescharacteristic, complemented
7#17988551—21no—
8#17988523C411yescharacteristic, complemented
9#17988523C2211yescharacteristic
10#17988499C411yescharacteristic, complemented
11#17988499C2211yescharacteristic
12#17988490—21no—
13#17988483—21no—
14#17988460—21no—
15#17988460—21no—
16#17988453C411yescharacteristic, complemented
17#17988313—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21C4×C22⋊C4×C73—21no—
22#342×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C2×#11924012—41no—
25C4×Dic146—41no—
26C4×Dic146—41no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C4×Dic73—21no—
37C22⋊#10596831—22no—
38C22⋊#10596831—41no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C22×D4×C73D411yescharacteristic
45C23×C4×C73D411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C22⋊C4×C73—22no—
51C2×C22⋊C4×C73C2×C411yescharacteristic
52C2×C22⋊C4×C73C2311yescharacteristic
53C2×C42×C73—41no—
54C2×C42×C73C2×C411yescharacteristic
55#99×C73—24no—
56#95×C73—41no—
57C2×Dic146—41no—
58C2×Dic146—42no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63#11924012—82no—
64C2×#10596831—42no—
65C4⋊Dic73—42no—
66C4⋊Dic73—41no—
67#11924007—41no—
68#11924007—41no—
69#11924007—81no—
70#11924007—81no—
71C22⋊Dic73—42no—
72C22⋊Dic73—42no—
73C22⋊Dic73—81no—
74C22⋊Dic73—81no—
75C4×Dic73—42no—
76C24×C73C22⋊C411yescharacteristic
77C24×C73C2×D411yescharacteristic
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—42no—
86C22×C4×C73—81no—
87C22×C4×C73—81no—
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C22×C411yescharacteristic
92C22×C4×C73C2×D411yescharacteristic
93C4⋊C4×C73—41no—
94C22⋊C4×C73—24no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—42no—
98C42×C73—21no—
99C42×C73—21no—
100C42×C73—82no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73—41no—
110C23×C73C2×C22⋊C411yescharacteristic
111C23×C73#13712yes—
112D4×C73—44no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—41no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—44no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73—82no—
128C2×C4×C73—82no—
129C2×C4×C73#9911yescharacteristic
130C2×C4×C73#9911yescharacteristic
131C2×C4×C73#10412yes—
132C2×Dic73—22no—
133C2×Dic73—41no—
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—
144Dic146—42no—
145Dic146—42no—
146#10596831—82no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—22no—
150C22×C73—42no—
151C22×C73—42no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—81no—
158C22×C73—81no—
159C22×C73C2×#9911yescharacteristic
160C22×C73#41911yescharacteristic
161C22×C73C2×#10411yescharacteristic
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—22no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—84no—
169Dic73—42no—
170Dic73—81no—
171Dic73—81no—
172Dic73—81no—
173#11784—731nomaximal, Sylow
174C2×C73—21no—
175C2×C73—21no—
176C2×C73—42no—
177C2×C73—81no—
178C2×C73#150811yescharacteristic
179C2×C73#212011yescharacteristic
180C2×C73#212711yescharacteristic
181#2580—731no—
182C4×#99D7311yescharacteristic
183#1465—731no—
184#1352—732no—
185#1351—732no—
186C73#1178411yescharacteristic, complemented, Sylow
187C2×C4×Q8—731no—
188C2×C4×D4C2×D7311yescharacteristic
189C2×#99—21no—
190#407—1461no—
191#399—731no—
192#399—731no—
193#393—731no—
194#393—731no—
195#390—1461no—
196#389—1461no—
197#385—1461no—
198#385—1461no—
199#382—731no—
200C4×C22⋊C4—21no—
201#342C2×D7312yes—
202#324—1461no—
203#323—732no—
204C22×Q8—731no—
205C22×D4C22⋊D7311yescharacteristic
206C23×C4D29211yescharacteristic
207C23×C4C22⋊D7311yescharacteristic
208C2×M16—2921no—
209C4×Q8—2921no—
210C4×Q8—2921no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—1461no—
215C2×C4⋊C4—1461no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4D29211yescharacteristic
219C2×C22⋊C4—22no—
220C2×C22⋊C4—1461no—
221C2×C22⋊C4—1461no—
222C2×C22⋊C4—1461no—
223C2×C22⋊C4—1461no—
224C2×C22⋊C4C4×D7311yescharacteristic
225C2×C22⋊C4C22×D7311yescharacteristic
226C2×C42—41no—
227C2×C42—1461no—
228C2×C42C4×D7311yescharacteristic
229#99—24no—
230C22⋊C8—2921no—
231C22⋊C8—1462no—
232#95—41no—
233#95—731no—
234#95—731no—
235#95—1461no—
236#95—1461no—
237#95—1461no—
238C24#1192400511yescharacteristic
239C24C2×C22⋊D7311yescharacteristic
240C2×Q8—2921no—
241C2×Q8—2922no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4#1192400511yescharacteristic
257C22×C4#1192400511yescharacteristic
258C22×C4#1192400511yescharacteristic
259C22×C4C2×C4×D7311yescharacteristic
260C22×C4C2×D29211yescharacteristic
261M16—5842no—
262C2×C8—2922no—
263C4⋊C4—41no—
264C4⋊C4—2921no—
265C4⋊C4—2921no—
266C4⋊C4—2921no—
267C4⋊C4—2922no—
268C4⋊C4—5841no—
269C4⋊C4—5841no—
270C22⋊C4—24no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—2922no—
275C22⋊C4—2922no—
276C22⋊C4—5841no—
277C22⋊C4—5841no—
278C42—21no—
279C42—21no—
280C42—82no—
281C42—2922no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×#1192400511yescharacteristic
292C23#1455662112yes—
293Q8—2922no—
294Q8—2922no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—2921no—
313C2×C4—2921no—
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—1462no—
324C2×C4#1455650511yescharacteristic
325C2×C4#1455650511yescharacteristic
326C2×C4#1455651912yes—
327C8—5842no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#1455650511yescharacteristic
341C22#1798859511yescharacteristic
342C22C2×#1455651911yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—84no—
350C4—2922no—
351C4—5841no—
352C4—5841no—
353C4—5841no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#2260845011yescharacteristic
359C2#2261157011yescharacteristic
360C2#2261159811yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC4×#99×C73C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenterC4×#99D73
hypocenterC73#11784
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #22607954C2semidirect
4. #22607951C2semidirect
6. C2×C4×Dic146C4semidirect
8. #17988523C4semidirect
10. #17988499C4semidirect
16. #17988453C4semidirect
186. C73#11784semidirect

Maximal subgroups

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

subgroupindex
#226152852
#226082692
#226079542
#226079512
C4×#99×C732
#1178473