Finite Group Databasebeta

← #134339

Subgroups — #134339

Order 512.

522 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 96 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#14049C211yesmaximal, characteristic
2C2×#1325C212yesmaximal
3#8560C211yesmaximal, characteristic
4#8558C211yesmaximal, characteristic
5#7189C212yesmaximal
6C2×#389C411yescharacteristic
7C2×#387—21no—
8C2×#387—21no—
9C2×#384C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1797—21no—
12#1797—21no—
13C2×#324C2212yes—
14C2×#324C2212yes—
15#1445—21no—
16#1445—21no—
17C4⋊#95C411yescharacteristic
18C4⋊#95C411yescharacteristic
19C4⋊#95C2211yescharacteristic
20C4×#95C411yescharacteristic
21#1325—24no—
22#1280—21no—
23#1280—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2311yescharacteristic
31C22×C42C2×C411yescharacteristic
32C22×C42C2×C411yescharacteristic
33C22×C42C2×C411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42D411yescharacteristic
36C2×C4⋊C8—41no—
37C2×C4⋊C8—41no—
38C2×C22⋊C8—22no—
39C2×C22⋊C8—22no—
40#389—41no—
41#389—41no—
42#387—44no—
43#387—44no—
44#384—21no—
45#384—21no—
46#384D412yes—
47#384Q812yes—
48C4×C4⋊C4—41no—
49C4×C4⋊C4—41no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95D411yescharacteristic
60C2×#95D411yescharacteristic
61#336—41no—
62#336—41no—
63#324—22no—
64#324—22no—
65#324—22no—
66#324—22no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22×C411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C22×C8—42no—
79C22×C8—42no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4C4⋊C412yes—
104C2×C4⋊C4C2×D411yescharacteristic
105C2×C4⋊C4C2×Q811yescharacteristic
106C2×C4⋊C4#4111yescharacteristic
107C2×C4⋊C4#4111yescharacteristic
108C2×C42—22no—
109C2×C42—22no—
110C2×C42—21no—
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—22no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—22no—
119C2×C42—41no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—41no—
123C2×C42—41no—
124C2×C42C4⋊C412yes—
125C4⋊C8—82no—
126C4⋊C8—82no—
127C22⋊C8—42no—
128C22⋊C8—42no—
129C22⋊C8—42no—
130C22⋊C8—42no—
131#95—24no—
132#95—41no—
133#95—41no—
134#95—42no—
135#95—42no—
136#95—42no—
137#95—42no—
138#95—42no—
139#95—42no—
140#95—42no—
141#95—42no—
142C24C2×C22⋊C411yescharacteristic
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
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#9911yescharacteristic
202C22×C4#9911yescharacteristic
203C22×C4#10112yes—
204C22×C4C2×C4⋊C411yescharacteristic
205C22×C4#11711yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12111yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4C22⋊Q811yescharacteristic
210C22×C4#13112yes—
211C22×C4#13112yes—
212C2×C8—82no—
213C2×C8—82no—
214C2×C8—82no—
215C2×C8—82no—
216C2×C8—82no—
217C2×C8—82no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—44no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—44no—
226C4⋊C4—44no—
227C4⋊C4—44no—
228C4⋊C4—44no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—82no—
232C42—24no—
233C42—42no—
234C42—42no—
235C42—42no—
236C42—42no—
237C42—42no—
238C42—81no—
239C42—81no—
240C42—82no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23#38011yescharacteristic
246C23#40811yescharacteristic
247C23#40811yescharacteristic
248C23C2×#9911yescharacteristic
249C23#41011yescharacteristic
250C23C2×#10111yescharacteristic
251C23#41311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4#35312yes—
325C2×C4#42412yes—
326C2×C4#43312yes—
327C8—162no—
328C8—162no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22#146811yescharacteristic
342C22#147011yescharacteristic
343C22#147211yescharacteristic
344C22#147311yescharacteristic
345C22#179811yescharacteristic
346C22#179911yescharacteristic
347C22#180111yescharacteristic
348C22C2×#35311yescharacteristic
349C22#212611yescharacteristic
350C22#213311yescharacteristic
351C22#213511yescharacteristic
352C4—22no—
353C4—22no—
354C4—22no—
355C4—44no—
356C4—41no—
357C4—42no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—161no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2#856211yescharacteristic
372C2#1154911yescharacteristic
373C2#1155211yescharacteristic
374C2#1157011yescharacteristic
375C2#1157111yescharacteristic
376C2#1279711yescharacteristic
377C2#1280411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#140492
C2×#13252
#85602
#85582
#71892