Finite Group Databasebeta

← #102346

Subgroups — #102346

Order 512.

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

normal subgroups only

This group has 460 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#10864C211yesmaximal, characteristic
3#8145C211yesmaximal, characteristic
4#7688C211yesmaximal, characteristic
5#7687C211yesmaximal, characteristic
6#7685C211yesmaximal, characteristic
7#7685C211yesmaximal, characteristic
8C2×#487C411yescharacteristic
9C22×#108—21no—
10C22×C4×C8C2211yescharacteristic
11#2857C2211yescharacteristic
12#2857C2211yescharacteristic
13#1990C411yescharacteristic
14#1956C411yescharacteristic
15#1933—21no—
16#1933—21no—
17#1892—21no—
18#1892—21no—
19#1834C411yescharacteristic
20C4×C22⋊C8C2211yescharacteristic
21C4×C22⋊C8C2211yescharacteristic
22C2×#341—21no—
23#1728C2211yescharacteristic
24#1728C2211yescharacteristic
25C2×#322—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×#108—24no—
42C2×#108—42no—
43C2×#108—42no—
44C2×#103—21no—
45C2×#103—21no—
46C2×#103—21no—
47C2×#103—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8—42no—
53C2×C4×C8C2×C411yescharacteristic
54C2×C4×C8C2×C411yescharacteristic
55C2×C4×C8D411yescharacteristic
56C2×C4×C8D411yescharacteristic
57#391—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#384C2×C411yescharacteristic
64#384C2×C411yescharacteristic
65#380—21no—
66#380—21no—
67#380—21no—
68#380—21no—
69#341—42no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336D412yes—
79#336D412yes—
80#322—42no—
81C22×Q8—21no—
82C22×Q8—21no—
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C23×C4#4111yescharacteristic
86C2×M16—22no—
87C2×M16—22no—
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—41no—
97C2×M16—41no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—22no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8C22⋊C411yescharacteristic
111C22×C8C22⋊C411yescharacteristic
112C22×C8C22⋊C411yescharacteristic
113C22×C8C22⋊C411yescharacteristic
114C4⋊Q8—41no—
115C4⋊Q8—41no—
116C4⋊Q8—41no—
117C4⋊Q8—41no—
118C22⋊Q8—41no—
119C22⋊Q8—41no—
120C22⋊Q8—41no—
121C22⋊Q8—41no—
122C22⋊Q8—82no—
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—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C42—41no—
138C2×C42—41no—
139C2×C42C22×C411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×D411yescharacteristic
143#108—48no—
144#103—42no—
145#103—42no—
146#103—42no—
147#103—42no—
148C22⋊C8—24no—
149C22⋊C8—42no—
150C4×C8—22no—
151C4×C8—22no—
152C4×C8—41no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162C24#12411yescharacteristic
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—42no—
170C2×Q8—81no—
171C2×Q8—81no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4C2×C22⋊C411yescharacteristic
187C22×C4C4×D411yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12711yescharacteristic
192C22×C4AGL(1,ℤ/8)11yescharacteristic
193C22×C4AGL(1,ℤ/8)11yescharacteristic
194C22×C4#13711yescharacteristic
195C22×C4#13711yescharacteristic
196M16—42no—
197M16—42no—
198M16—42no—
199M16—42no—
200M16—81no—
201M16—81no—
202M16—81no—
203M16—81no—
204C2×C8—24no—
205C2×C8—24no—
206C2×C8—21no—
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8—24no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C2×C8—81no—
230C2×C8#9912yes—
231C2×C8#10412yes—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—82no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C22⋊C4—82no—
249C22⋊C4—81no—
250C22⋊C4—81no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—41no—
256C42—41no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23#39011yescharacteristic
264C23#48911yescharacteristic
265C23#48911yescharacteristic
266Q8—81no—
267Q8—81no—
268Q8—81no—
269Q8—81no—
270Q8—162no—
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—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—44no—
290C2×C4—44no—
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×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C2×#9911yescharacteristic
304C2×C4#41011yescharacteristic
305C2×C4#41711yescharacteristic
306C2×C4#41711yescharacteristic
307C2×C4C2×#10411yescharacteristic
308C2×C4#42111yescharacteristic
309C2×C4#44312yes—
310C2×C4#44412yes—
311C2×C4#47112yes—
312C2×C4#47312yes—
313C2×C4#49611yescharacteristic
314C2×C4#49711yescharacteristic
315C8—22no—
316C8—22no—
317C8—44no—
318C8—41no—
319C8—41no—
320C8—82no—
321C8—82no—
322C8—82no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22#195911yescharacteristic
334C22#196411yescharacteristic
335C22#197411yescharacteristic
336C22#197511yescharacteristic
337C22#197711yescharacteristic
338C22#197911yescharacteristic
339C22#198011yescharacteristic
340C4—22no—
341C4—22no—
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—161no—
347C4—161no—
348C4—161no—
349C4—161no—
350C4#150411yescharacteristic
351C4#150911yescharacteristic
352C4#151211yescharacteristic
353C4#151311yescharacteristic
354C2—41no—
355C2—41no—
356C2#968211yescharacteristic
357C2#972511yescharacteristic
358C2#972811yescharacteristic
359C2#977511yescharacteristic
360C2#981311yescharacteristic
361C2#981711yescharacteristic
362C2#985811yescharacteristic
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
#108642
#81452
#76882
#76872
#76852