Finite Group Databasebeta

← #102455

Subgroups — #102455

Order 512.

514 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 94 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#33146C211yesmaximal, characteristic
2#33108C211yesmaximal, characteristic
3#30187C211yesmaximal, characteristic
4#11346C211yesmaximal, characteristic
5#7668C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7020C211yesmaximal, characteristic
8C2×#483—21no—
9#2857C2211yescharacteristic
10#2857C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12#2100—21no—
13#2072—21no—
14#2043—21no—
15#2024—21no—
16#1988—21no—
17#1981—21no—
18#1948—21no—
19#1947—21no—
20#1927—22no—
21#1918—22no—
22#1892—22no—
23#1872—21no—
24#1852—21no—
25#1823—21no—
26#1797C2211yescharacteristic
27#1797C2211yescharacteristic
28C2×#336—22no—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1271—22no—
32#1271—22no—
33C23×C8—21no—
34C23×C8D412yes—
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×C22⋊Q8—21no—
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C42—21no—
42C22×C42C2311yescharacteristic
43#483—42no—
44#483—42no—
45C2×#107—22no—
46C2×#106—22no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×#103—22no—
50C2×#103—22no—
51C2×#103—22no—
52C2×#103—22no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55#391—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384D411yescharacteristic
62#384D411yescharacteristic
63#380—21no—
64#380—21no—
65#380—21no—
66#380—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C2×#95—21no—
72#340—22no—
73#340—22no—
74#340—22no—
75#340—22no—
76#340—22no—
77#340—22no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—44no—
83#336D412yes—
84#336D412yes—
85C22×Q8—21no—
86C22×Q8—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4#4111yescharacteristic
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—22no—
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—42no—
99C22×C8—42no—
100C22×C8—41no—
101C22×C8—42no—
102C22×C8—41no—
103C22×C8—42no—
104C4⋊Q8—42no—
105C4⋊Q8—42no—
106C22⋊Q8—41no—
107C22⋊Q8—42no—
108C22⋊Q8—41no—
109C22⋊Q8—42no—
110C22⋊Q8—41no—
111C22⋊Q8—41no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4SD1612yes—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C42—42no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42—42no—
139C2×C42—42no—
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144#107—44no—
145#106—44no—
146C4⋊C8—42no—
147C4⋊C8—42no—
148#103—44no—
149#103—44no—
150#103—82no—
151#103—82no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162C24#12111yescharacteristic
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—42no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—41no—
188C22×C4—42no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4#12011yescharacteristic
194C22×C4#12011yescharacteristic
195C22×C4#12011yescharacteristic
196C22×C4#12111yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12711yescharacteristic
199C22×C4C2×SD1611yescharacteristic
200C22×C4#13512yes—
201C22×C4#13511yescharacteristic
202C22×C4AGL(1,ℤ/8)12yes—
203C22×C4AGL(1,ℤ/8)11yescharacteristic
204C22×C4#13711yescharacteristic
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—44no—
211C2×C8—44no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—81no—
218C2×C8—82no—
219C2×C8—81no—
220C2×C8—82no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C22⋊C4—82no—
246C22⋊C4—81no—
247C22⋊C4—81no—
248C42—22no—
249C42—22no—
250C42—41no—
251C42—41no—
252C42—82no—
253C42—81no—
254C42—81no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23#39211yescharacteristic
260C23#46312yes—
261C23#46511yescharacteristic
262C23#46811yescharacteristic
263C23#47312yes—
264Q8—82no—
265Q8—82no—
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
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—81no—
310C2×C4—81no—
311C2×C4#44811yescharacteristic
312C2×C4#44911yescharacteristic
313C2×C4#44912yes—
314C2×C4#45011yescharacteristic
315C2×C4#45211yescharacteristic
316C2×C4#45511yescharacteristic
317C2×C4#45611yescharacteristic
318C2×C4#45812yes—
319C2×C4#49511yescharacteristic
320C2×C4#49611yescharacteristic
321C8—82no—
322C8—82no—
323C8—82no—
324C8—82no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22#167912yes—
334C22#169912yes—
335C22#200011yescharacteristic
336C22#200711yescharacteristic
337C22#201011yescharacteristic
338C22#201211yescharacteristic
339C22#201711yescharacteristic
340C22#202011yescharacteristic
341C22#202211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—82no—
351C4—82no—
352C4—161no—
353C4—161no—
354C4—161no—
355C4—161no—
356C4#160912yes—
357C4#161212yes—
358C2—22no—
359C2—22no—
360C2#997111yescharacteristic
361C2#997911yescharacteristic
362C2#1003111yescharacteristic
363C2#1003311yescharacteristic
364C2#1025711yescharacteristic
365C2#1027011yescharacteristic
366C2#1032311yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C22×C42 ▷ 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
#331462
#331082
#301872
#113462
#76682
#76652
#70202