Finite Group Databasebeta

← #32974195

Subgroups — #32974195

Order 18688.

506 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22609999C211yesmaximal, characteristic
2#22609693C211yesmaximal, characteristic
3#22607757C212yesmaximal, complemented
4#22607754C212yesmaximal, complemented
5C4×C22⋊Q8×C73C211yesmaximal, characteristic
6C2×C22⋊#10596831—21no—
7C2×C22⋊#10596831—21no—
8C2×#14556502—21no—
9#17988342—21no—
10#17988342C2212yes—
11#17988342C2212yes—
12C2×C22⋊Q8×C73C411yescharacteristic
13C2×C4×Q8×C73C411yescharacteristic
14C22×C42×C73C2211yescharacteristic
15#391×C73C2211yescharacteristic
16#389×C73C2211yescharacteristic
17#387×C73—21no—
18#385×C73—21no—
19#380×C73C411yescharacteristic
20C4×C4⋊C4×C73—21no—
21C4×C4⋊C4×C73C411yescharacteristic
22C4×C22⋊C4×C73—21no—
23C22×#10596831—22no—
24C22×#10596831—22no—
25C22⋊#10596831—24no—
26C22⋊#10596831—42no—
27#14556502—42no—
28C22×Q8×C73C2×C411yescharacteristic
29C23×C4×C73C2×C411yescharacteristic
30C23×C4×C73D411yescharacteristic
31C23×C4×C73D411yescharacteristic
32C22⋊Q8×C73—22no—
33C22⋊Q8×C73—22no—
34C4×Q8×C73—42no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73C2×C411yescharacteristic
39C2×C4⋊C4×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C22⋊C4×C73—21no—
42C2×C22⋊C4×C73—21no—
43C2×C42×C73—21no—
44C2×C42×C73—21no—
45C2×C42×C73—42no—
46C2×C42×C73C2×C411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C2×C42×C73D411yescharacteristic
49C2×C42×C73C2311yescharacteristic
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55C2×#10596831—24no—
56C2×#10596831—42no—
57C2×#10596831—42no—
58C2×#10596831—42no—
59C2×#10596831—42no—
60C2×#10596831—42no—
61C24×C73C22⋊C411yescharacteristic
62C2×Q8×C73—21no—
63C2×Q8×C73—41no—
64C2×Q8×C73—41no—
65C2×Q8×C73M1612yes—
66C22×C4×C73—22no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—22no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—22no—
73C22×C4×C73—22no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—41no—
77C22×C4×C73—41no—
78C22×C4×C73—41no—
79C22×C4×C73—41no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22×C411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C4⋊C4×C73—24no—
87C4⋊C4×C73—21no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—42no—
91C4⋊C4×C73—42no—
92C4⋊C4×C73M1612yes—
93C22⋊C4×C73—24no—
94C22⋊C4×C73—42no—
95C42×C73—22no—
96C42×C73—22no—
97C42×C73—41no—
98C42×C73—41no—
99C42×C73—42no—
100C42×C73—42no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73#10412yes—
108C23×C73C2×C22⋊C411yescharacteristic
109Q8×C73—42no—
110Q8×C73—42no—
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—21no—
119C2×C4×C73—22no—
120C2×C4×C73—22no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—44no—
128C2×C4×C73—44no—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73#9912yes—
142C2×C4×C73C2×M1611yescharacteristic
143C2×C4×C73C2×M1611yescharacteristic
144C2×C4×C73#13512yes—
145C2×C4×C73#13712yes—
146#10596831—44no—
147#10596831—82no—
148C22×C73—22no—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73#40711yescharacteristic
156C22×C73C2×#9911yescharacteristic
157C22×C73#41311yescharacteristic
158C22×C73#41611yescharacteristic
159C22×C73#41911yescharacteristic
160C22×C73C2×#10411yescharacteristic
161C22×C73#42111yescharacteristic
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—22no—
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—41no—
168C4×C73—42no—
169C4×C73—42no—
170C4×C73—41no—
171C4×C73—81no—
172C4×C73—81no—
173#7623—731nomaximal, Sylow
174C2×C73—42no—
175C2×C73#146511yescharacteristic
176C2×C73#148811yescharacteristic
177C2×C73#149111yescharacteristic
178C2×C73#150111yescharacteristic
179C2×C73#151111yescharacteristic
180C2×C73#153211yescharacteristic
181C2×C73#155411yescharacteristic
182C4×C22⋊Q8D7311yescharacteristic
183#1817—731no—
184#1749—731no—
185#1272—732no—
186#1271—732no—
187C73#762311yescharacteristic, complemented, Sylow
188C2×C22⋊Q8Dic7311yescharacteristic
189C2×C4×Q8Dic7311yescharacteristic
190C22×C42C2×D7311yescharacteristic
191C2×C22⋊C8—1461no—
192C2×C22⋊C8—1461no—
193C2×#97—1461no—
194#391C2×D7311yescharacteristic
195#389C2×D7311yescharacteristic
196#387—21no—
197#385—21no—
198#380Dic7311yescharacteristic
199C4×C4⋊C4—21no—
200C4×C4⋊C4Dic7311yescharacteristic
201C4×C22⋊C4—21no—
202#336—732no—
203#336—732no—
204#336—1461no—
205C22×Q8C2×Dic7311yescharacteristic
206C23×C4C2×Dic7311yescharacteristic
207C23×C4C22⋊D7311yescharacteristic
208C23×C4C22⋊D7311yescharacteristic
209C22×C8—1462no—
210C22×C8—1462no—
211C22⋊Q8—22no—
212C22⋊Q8—22no—
213C4×Q8—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×Dic7311yescharacteristic
218C2×C4⋊C4C2×Dic7311yescharacteristic
219C2×C4⋊C4C2×Dic7311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—42no—
225C2×C42C2×Dic7311yescharacteristic
226C2×C42C22⋊D7311yescharacteristic
227C2×C42C22⋊D7311yescharacteristic
228C2×C42C22×D7311yescharacteristic
229C22⋊C8—2922no—
230C22⋊C8—1464no—
231#97—2922no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C24C22⋊Dic7311yescharacteristic
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8#1192401212yes—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C22⋊Dic7311yescharacteristic
257C22×C4C22⋊Dic7311yescharacteristic
258C22×C4C22⋊Dic7311yescharacteristic
259C22×C4C22×Dic7311yescharacteristic
260C22×C4C2×C22⋊D7311yescharacteristic
261C22×C4C2×C22⋊D7311yescharacteristic
262C2×C8—2922no—
263C2×C8—2922no—
264C2×C8—2922no—
265C2×C8—2922no—
266C2×C8—2922no—
267C2×C8—1464no—
268C4⋊C4—24no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4#1192401212yes—
275C22⋊C4—24no—
276C22⋊C4—42no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#1455651812yes—
290C23C2×C22⋊Dic7311yescharacteristic
291Q8—42no—
292Q8—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4#1455650612yes—
324C2×C4C2×#1192401211yescharacteristic
325C2×C4C2×#1192401211yescharacteristic
326C2×C4#1455661112yes—
327C2×C4#1455662212yes—
328C8—2924no—
329C8—5842no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22#1798855111yescharacteristic
338C22C2×#1455650611yescharacteristic
339C22#1798857111yescharacteristic
340C22#1798858311yescharacteristic
341C22#1798859611yescharacteristic
342C22C2×#1455651811yescharacteristic
343C22#1798860411yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—42no—
353C4—81no—
354C4—81no—
355C2—42no—
356C2#2260826911yescharacteristic
357C2#2260836511yescharacteristic
358C2#2260837811yescharacteristic
359C2#2260842211yescharacteristic
360C2#2260846411yescharacteristic
361C2#2260855111yescharacteristic
362C2#2260864111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC4×C22⋊Q8×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenterC4×C22⋊Q8D73
hypocenterC73#7623
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #22607757C2semidirect
4. #22607754C2semidirect
187. C73#7623semidirect

Maximal subgroups

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

subgroupindex
#226099992
#226096932
#226077572
#226077542
C4×C22⋊Q8×C732
#762373