Finite Group Databasebeta

← #101621

Subgroups — #101621

Order 512.

381 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 84 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#27614C211yesmaximal, characteristic
2#22628C211yesmaximal, characteristic
3#9883C211yesmaximal, characteristic
4#8727C211yesmaximal, characteristic
5#7641C211yesmaximal, characteristic
6#7044C211yesmaximal, characteristic
7#7033C211yesmaximal, characteristic
8C2×#389C2211yescharacteristic
9#2285C2211yescharacteristic
10#2100—21no—
11#2083—21no—
12#1940—21no—
13#1921—21no—
14#1921—21no—
15#1917—21no—
16#1916—21no—
17#1852C411yescharacteristic
18#1852C411yescharacteristic
19#1824C411yescharacteristic
20#1824C411yescharacteristic
21#1817C2211yescharacteristic
22#1798—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1797C2211yescharacteristic
26#1771—21no—
27#1750—21no—
28#1749C2211yescharacteristic
29#1296—21no—
30#1296—21no—
31#1280—21no—
32#1280—21no—
33#1271—21no—
34#1271—21no—
35C2×#117—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C42C2311yescharacteristic
40C2×#107—21no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8C2×C411yescharacteristic
51C2×C22⋊C8C2×C411yescharacteristic
52C2×C22⋊C8D411yescharacteristic
53C2×C22⋊C8D411yescharacteristic
54C2×#97—21no—
55C2×#97—21no—
56C2×C4×C8—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384D411yescharacteristic
62#384D411yescharacteristic
63#382—21no—
64#380—21no—
65#380C2×C411yescharacteristic
66#380C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C2×#95—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336D411yescharacteristic
87#336D411yescharacteristic
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C22×C411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4#4111yescharacteristic
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101#117—81no—
102#117—81no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—81no—
117C2×C4⋊C4—81no—
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C22⋊C4—21no—
123C2×C22⋊C4—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132#107—42no—
133#107—42no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—81no—
141C4⋊C8—81no—
142C22⋊C8—21no—
143C22⋊C8—21no—
144C22⋊C8—21no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—81no—
152C22⋊C8Q1612yes—
153#97—41no—
154#97—41no—
155#97—81no—
156C4×C8—81no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—41no—
162#95—41no—
163C24C4×D411yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
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—42no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4C2×C22⋊C411yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4#12011yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12311yescharacteristic
193C22×C4C2×Q1611yescharacteristic
194C22×C4#13511yescharacteristic
195C22×C4#13711yescharacteristic
196C22×C4#13711yescharacteristic
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—81no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C2×C8—81no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—82no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C22⋊C4—81no—
241C22⋊C4—81no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23#38611yescharacteristic
259C23C4×Q1611yescharacteristic
260C23#44111yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—162no—
304C2×C4#41011yescharacteristic
305C2×C4#41011yescharacteristic
306C2×C4#45111yescharacteristic
307C2×C4#45211yescharacteristic
308C2×C4#46211yescharacteristic
309C2×C4#46411yescharacteristic
310C2×C4#47111yescharacteristic
311C2×C4#47211yescharacteristic
312C8—42no—
313C8—81no—
314C8—81no—
315C8—81no—
316C8—81no—
317C8—81no—
318C8—161no—
319C8—161no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#187811yescharacteristic
331C22#188111yescharacteristic
332C22#189111yescharacteristic
333C22#189911yescharacteristic
334C22#190411yescharacteristic
335C22#190711yescharacteristic
336C22#191511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—82no—
350C4—81no—
351C4—81no—
352C4—161no—
353C2—41no—
354C2—41no—
355C2#904811yescharacteristic
356C2#925711yescharacteristic
357C2#927011yescharacteristic
358C2#933511yescharacteristic
359C2#934811yescharacteristic
360C2#951411yescharacteristic
361C2#952911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
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
#276142
#226282
#98832
#87272
#76412
#70442
#70332