Finite Group Databasebeta

← #102338

Subgroups — #102338

Order 512.

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

normal subgroups only

This group has 450 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
1#33043C211yesmaximal, characteristic
2#10822C211yesmaximal, characteristic
3C8×C22⋊C8C211yesmaximal, characteristic
4#7688C211yesmaximal, characteristic
5#7687C211yesmaximal, characteristic
6#7685C211yesmaximal, characteristic
7#7685C211yesmaximal, characteristic
8C2×#487C411yescharacteristic
9C22×C4×C8C2211yescharacteristic
10#2857C2211yescharacteristic
11#2857C2211yescharacteristic
12#1990C411yescharacteristic
13#1956C411yescharacteristic
14#1933—21no—
15#1933—21no—
16#1892—21no—
17#1892—21no—
18#1834C411yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C4×C22⋊C8C2211yescharacteristic
21C2×#341—21no—
22C2×#341—21no—
23#1728C2211yescharacteristic
24#1728C2211yescharacteristic
25C2×C82—21no—
26#1273—21no—
27#1272—22no—
28#1271—22no—
29#1271—22no—
30#1271—22no—
31C22×M16—21no—
32C22×M16—21no—
33C23×C8D411yescharacteristic
34C23×C8D411yescharacteristic
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C22⋊Q8—21no—
38C2×C22⋊Q8—21no—
39C22×C42C2311yescharacteristic
40#487—42no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#103—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8—42no—
50C2×C4×C8C2×C411yescharacteristic
51C2×C4×C8C2×C411yescharacteristic
52C2×C4×C8D411yescharacteristic
53C2×C4×C8D411yescharacteristic
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384C2×C411yescharacteristic
61#384C2×C411yescharacteristic
62#380—21no—
63#380—21no—
64#380—21no—
65#380—21no—
66#341—24no—
67#341—42no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336D412yes—
77#336D412yes—
78C82—42no—
79C22×Q8—21no—
80C22×Q8—21no—
81C23×C4C2×D411yescharacteristic
82C23×C4#4111yescharacteristic
83C23×C4#4111yescharacteristic
84C2×M16—22no—
85C2×M16—22no—
86C2×M16—41no—
87C2×M16—41no—
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8C22⋊C411yescharacteristic
109C22×C8C22⋊C411yescharacteristic
110C22×C8C22⋊C411yescharacteristic
111C22×C8C22⋊C411yescharacteristic
112C4⋊Q8—41no—
113C4⋊Q8—41no—
114C4⋊Q8—41no—
115C4⋊Q8—41no—
116C22⋊Q8—41no—
117C22⋊Q8—41no—
118C22⋊Q8—41no—
119C22⋊Q8—41no—
120C22⋊Q8—82no—
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—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C42—41no—
136C2×C42—41no—
137C2×C42C22×C411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141#103—42no—
142#103—42no—
143#103—42no—
144#103—42no—
145C22⋊C8—24no—
146C22⋊C8—24no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—41no—
150C4×C8—41no—
151C4×C8—41no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—41no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159C24#12411yescharacteristic
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—42no—
167C2×Q8—81no—
168C2×Q8—81no—
169C22×C4—21no—
170C22×C4—21no—
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—41no—
183C22×C4C2×C22⋊C411yescharacteristic
184C22×C4C4×D411yescharacteristic
185C22×C4C4×D411yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4#12111yescharacteristic
188C22×C4#12711yescharacteristic
189C22×C4#13511yescharacteristic
190C22×C4#13511yescharacteristic
191C22×C4#13511yescharacteristic
192C22×C4#13511yescharacteristic
193M16—42no—
194M16—42no—
195M16—42no—
196M16—42no—
197M16—81no—
198M16—81no—
199M16—81no—
200M16—81no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—24no—
206C2×C8—24no—
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8#9912yes—
228C2×C8#10412yes—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—82no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C22⋊C4—82no—
246C22⋊C4—81no—
247C22⋊C4—81no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—41no—
253C42—41no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23#39011yescharacteristic
261C23#48811yescharacteristic
262C23#48811yescharacteristic
263Q8—81no—
264Q8—81no—
265Q8—81no—
266Q8—81no—
267Q8—162no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C2×#9911yescharacteristic
301C2×C4#41011yescharacteristic
302C2×C4#41611yescharacteristic
303C2×C4#41611yescharacteristic
304C2×C4C2×#10411yescharacteristic
305C2×C4#42111yescharacteristic
306C2×C4#44312yes—
307C2×C4#44312yes—
308C2×C4#47112yes—
309C2×C4#47312yes—
310C2×C4#49511yescharacteristic
311C2×C4#49511yescharacteristic
312C8—22no—
313C8—22no—
314C8—44no—
315C8—44no—
316C8—41no—
317C8—41no—
318C8—82no—
319C8—82no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#195811yescharacteristic
331C22#196411yescharacteristic
332C22#197411yescharacteristic
333C22#197411yescharacteristic
334C22#197711yescharacteristic
335C22#197911yescharacteristic
336C22#198011yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—161no—
344C4—161no—
345C4—161no—
346C4—161no—
347C4#150011yescharacteristic
348C4#150111yescharacteristic
349C4#151611yescharacteristic
350C4#152111yescharacteristic
351C2—41no—
352C2—41no—
353C2#968111yescharacteristic
354C2#972311yescharacteristic
355C2#972511yescharacteristic
356C2#977011yescharacteristic
357C2#981311yescharacteristic
358C2#981411yescharacteristic
359C2#985711yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×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
#330432
#108222
C8×C22⋊C82
#76882
#76872
#76852