Finite Group Databasebeta

← #98513

Subgroups — #98513

Order 512.

642 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×#2514C211yesmaximal, characteristic
2#8719C212yesmaximal
3#8153C211yesmaximal, characteristic
4#8153C211yesmaximal, characteristic
5#7629C212yesmaximal
6#2514—24no—
7#2514—24no—
8C2×#401—21no—
9C2×#400—21no—
10C2×#391C411yescharacteristic
11C2×#391C411yescharacteristic
12C2×#391C2211yescharacteristic
13C2×#389C411yescharacteristic
14C2×#387—21no—
15C2×#383—21no—
16C2×#382C2211yescharacteristic
17C2×C4×C4⋊C4C411yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19#1749C2212yes—
20#1749C2212yes—
21C2×#324—21no—
22C2×#324—21no—
23#1295—24no—
24#1280—21no—
25#1280—21no—
26#1272—24no—
27C23×Q8C2×C411yescharacteristic
28C22×C4⋊C4—21no—
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C4⋊C4D411yescharacteristic
33C22×C4⋊C4D411yescharacteristic
34C22×C42—21no—
35C22×C42C2×C411yescharacteristic
36C22×C42C2×C411yescharacteristic
37C22×C42C2311yescharacteristic
38C2×C22⋊C8—22no—
39C2×C22⋊C8—22no—
40C2×#97—22no—
41C2×#97—22no—
42#401—28no—
43#400—28no—
44#391—22no—
45#391—22no—
46#391—22no—
47#391—22no—
48#391—22no—
49#391D414yes—
50#389—22no—
51#389—22no—
52#387—28no—
53#383—28no—
54#382—22no—
55#382D414yes—
56C4×C4⋊C4—22no—
57C4×C4⋊C4—22no—
58C4×C4⋊C4—22no—
59C4×C4⋊C4—22no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95D411yescharacteristic
71C2×#95D411yescharacteristic
72#336—22no—
73#336—22no—
74#324—24no—
75#324—24no—
76C22×Q8—21no—
77C22×Q8—42no—
78C22×Q8—42no—
79C22×Q8—41no—
80C22×Q8—41no—
81C22×Q8C22⋊C412yes—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22⋊C411yescharacteristic
89C23×C4C22⋊C411yescharacteristic
90C23×C4C22×C411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C22×C8—42no—
94C22×C8—42no—
95C2×C4⋊C4—24no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4C22⋊C412yes—
112C2×C4⋊C4C22⋊C412yes—
113C2×C4⋊C4C22⋊C412yes—
114C2×C42—24no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—42no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—42no—
125C2×C42C2×D412yes—
126C2×C42C2×D412yes—
127C22⋊C8—24no—
128C22⋊C8—24no—
129C22⋊C8—42no—
130C22⋊C8—42no—
131#97—44no—
132#97—44no—
133#95—24no—
134#95—24no—
135#95—24no—
136#95—24no—
137#95—24no—
138#95—24no—
139#95—24no—
140#95—24no—
141#95—24no—
142#95—24no—
143#95—22no—
144#95—22no—
145C24C2×C22⋊C411yescharacteristic
146C2×Q8—24no—
147C2×Q8—42no—
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—84no—
153C2×Q8—84no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4#10412yes—
209C22×C4#10412yes—
210C22×C4C2×C22⋊C411yescharacteristic
211C22×C4C2×C22⋊C411yescharacteristic
212C22×C4#12012yes—
213C22×C4#12012yes—
214C2×C8—44no—
215C2×C8—44no—
216C2×C8—82no—
217C2×C8—82no—
218C2×C8—82no—
219C2×C8—82no—
220C4⋊C4—44no—
221C4⋊C4—44no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—48no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C42—24no—
230C42—42no—
231C42—42no—
232C42—42no—
233C42—42no—
234C42—48no—
235C42—42no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23#37911yescharacteristic
241C23#41311yescharacteristic
242C23#41311yescharacteristic
243C23C2×#10411yescharacteristic
244C23C2×#10411yescharacteristic
245C23#42111yescharacteristic
246C23#42111yescharacteristic
247Q8—84no—
248Q8—84no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4#41012yes—
310C2×C4#41312yes—
311C8—84no—
312C8—84no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22#152411yescharacteristic
326C22#152911yescharacteristic
327C22#153211yescharacteristic
328C22#153511yescharacteristic
329C22#178211yescharacteristic
330C22#178511yescharacteristic
331C22#178511yescharacteristic
332C22#178911yescharacteristic
333C22#178911yescharacteristic
334C22#179611yescharacteristic
335C22#179611yescharacteristic
336C4—22no—
337C4—22no—
338C4—42no—
339C4—42no—
340C4—42no—
341C4—42no—
342C4—81no—
343C4—82no—
344C4—82no—
345C4—81no—
346C4—82no—
347C4—82no—
348C2—21no—
349C2—21no—
350C2—21no—
351C2—21no—
352C2#833611yescharacteristic
353C2#836311yescharacteristic
354C2#836511yescharacteristic
355C2#836811yescharacteristic
356C2#836811yescharacteristic
357C2#852711yescharacteristic
358C2#855611yescharacteristic
subgroupG/H
center, socleC23#379
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25142
#87192
#81532
#76292