Finite Group Databasebeta

← #102344

Subgroups — #102344

Order 512.

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

normal subgroups only

This group has 438 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#33207C211yesmaximal, characteristic
2#10822C211yesmaximal, characteristic
3#8145C211yesmaximal, characteristic
4#7688C211yesmaximal, characteristic
5#7688C211yesmaximal, characteristic
6#7687C211yesmaximal, characteristic
7#7687C211yesmaximal, characteristic
8C2×#498C411yescharacteristic
9C22×C4×C8C2211yescharacteristic
10#2857C2211yescharacteristic
11#2857C2211yescharacteristic
12#1990C411yescharacteristic
13#1990C411yescharacteristic
14#1941—21no—
15#1941—21no—
16#1844C411yescharacteristic
17#1807—21no—
18#1807—21no—
19C4×C22⋊C8C2211yescharacteristic
20C4×C22⋊C8C2211yescharacteristic
21C2×#341—21no—
22C2×#341—21no—
23#1728C2211yescharacteristic
24#1728C2211yescharacteristic
25C2×#322—21no—
26#1273—21no—
27#1272—22no—
28#1272—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#498—42no—
41C2×#106—21no—
42C2×#106—21no—
43C2×#106—21no—
44C2×#106—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—
78#322—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—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—22no—
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—82no—
117C22⋊Q8—82no—
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—41no—
129C2×C4⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138#106—42no—
139#106—42no—
140#106—42no—
141#106—42no—
142C22⋊C8—24no—
143C22⋊C8—42no—
144C4×C8—22no—
145C4×C8—22no—
146C4×C8—41no—
147C4×C8—41no—
148C4×C8—41no—
149C4×C8—41no—
150C4×C8—41no—
151C4×C8—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156C24#12411yescharacteristic
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—81no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8—81no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C2×C22⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12711yescharacteristic
183C22×C4#13711yescharacteristic
184C22×C4#13711yescharacteristic
185C22×C4#13711yescharacteristic
186C22×C4#13711yescharacteristic
187M16—42no—
188M16—42no—
189M16—42no—
190M16—42no—
191M16—81no—
192M16—81no—
193M16—81no—
194M16—81no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—24no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C2×C8—81no—
221C2×C8#9912yes—
222C2×C8#10412yes—
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—42no—
232C4⋊C4—42no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—82no—
238C4⋊C4—82no—
239C22⋊C4—82no—
240C22⋊C4—82no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—41no—
246C42—41no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23#39011yescharacteristic
254C23#49111yescharacteristic
255C23#49111yescharacteristic
256Q8—162no—
257Q8—162no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
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—21no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4C2×#9911yescharacteristic
291C2×C4#41011yescharacteristic
292C2×C4#41911yescharacteristic
293C2×C4#41911yescharacteristic
294C2×C4C2×#10411yescharacteristic
295C2×C4#42111yescharacteristic
296C2×C4#44312yes—
297C2×C4#44412yes—
298C2×C4#47112yes—
299C2×C4#47112yes—
300C2×C4#49711yescharacteristic
301C2×C4#49711yescharacteristic
302C8—22no—
303C8—22no—
304C8—44no—
305C8—41no—
306C8—41no—
307C8—82no—
308C8—82no—
309C8—82no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#196011yescharacteristic
321C22#196411yescharacteristic
322C22#197411yescharacteristic
323C22#197511yescharacteristic
324C22#197711yescharacteristic
325C22#197711yescharacteristic
326C22#198011yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—161no—
334C4—161no—
335C4—161no—
336C4—161no—
337C4#150611yescharacteristic
338C4#150811yescharacteristic
339C4#151111yescharacteristic
340C4#151511yescharacteristic
341C2—41no—
342C2—41no—
343C2#968311yescharacteristic
344C2#972311yescharacteristic
345C2#972811yescharacteristic
346C2#977611yescharacteristic
347C2#981311yescharacteristic
348C2#981611yescharacteristic
349C2#985911yescharacteristic
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
#332072
#108222
#81452
#76882
#76872