Finite Group Databasebeta

← #105070

Subgroups — #105070

Order 512.

435 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 92 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#29967C211yesmaximal, characteristic
2#11228C211yesmaximal, characteristic
3#9879C211yesmaximal, characteristic
4#9679C211yesmaximal, characteristic
5#9129C211yesmaximal, characteristic
6#8830C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C22×C4⋊C8C2211yescharacteristic
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11#2099—21no—
12#2088—21no—
13#2088—21no—
14#2058—21no—
15#1853—21no—
16#1824—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#340—21no—
21C2×#340—21no—
22C2×#334—21no—
23C2×#332—21no—
24C2×#328—21no—
25C2×#328—21no—
26C4⋊#95C2211yescharacteristic
27#1296—21no—
28#1280—21no—
29#1280—21no—
30#1277—21no—
31C23×C8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C22⋊Q8—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C42C2311yescharacteristic
39C2×#106—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—42no—
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8D411yescharacteristic
50C2×C22⋊C8D411yescharacteristic
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#384D411yescharacteristic
60#380—21no—
61#380—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—42no—
72#340—42no—
73#336—21no—
74#336—21no—
75#336—21no—
76#334—42no—
77#332—42no—
78#328—42no—
79#328—42no—
80C22×Q8—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—41no—
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4#4111yescharacteristic
87C22×C8—21no—
88C22×C8—22no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C22⋊Q8—41no—
102C22⋊Q8—41no—
103C22⋊Q8—41no—
104C22⋊Q8—41no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
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—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—82no—
129C2×C4⋊C4SD1612yes—
130C2×C22⋊C4—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137#106—81no—
138#106—81no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C22⋊C8—21no—
148C22⋊C8—21no—
149C22⋊C8—21no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8SD1612yes—
155C4×C8—41no—
156C4×C8—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—81no—
164C24#12111yescharacteristic
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—81no—
168C2×Q8—81no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—41no—
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—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4—81no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4#12011yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4#12111yescharacteristic
201C22×C4#12311yescharacteristic
202C22×C4#12311yescharacteristic
203C22×C4#12411yescharacteristic
204C22×C4C2×SD1611yescharacteristic
205C22×C4C2×SD1611yescharacteristic
206C22×C4#13511yescharacteristic
207C22×C4#13511yescharacteristic
208C22×C4AGL(1,ℤ/8)11yescharacteristic
209C22×C4#13711yescharacteristic
210C22×C4#13711yescharacteristic
211C22×C4#13711yescharacteristic
212C2×C8—22no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—42no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—81no—
228C2×C8—81no—
229C2×C8—81no—
230C2×C8—81no—
231C2×C8—81no—
232C2×C8—81no—
233C2×C8—81no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—81no—
253C4⋊C4—82no—
254C4⋊C4—82no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—81no—
258C22⋊C4—81no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—41no—
264C42—41no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23#39411yescharacteristic
270C23#46011yescharacteristic
271C23#46411yescharacteristic
272C23#46511yescharacteristic
273C23#47011yescharacteristic
274C23#47111yescharacteristic
275C23#47311yescharacteristic
276Q8—161no—
277Q8—161no—
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—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—82no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4—161no—
323C2×C4—161no—
324C2×C4—161no—
325C2×C4—161no—
326C2×C4—161no—
327C2×C4#44811yescharacteristic
328C2×C4#45211yescharacteristic
329C2×C4#45411yescharacteristic
330C2×C4#45611yescharacteristic
331C2×C4B(4,𝔽2)11yescharacteristic
332C2×C4#45811yescharacteristic
333C2×C4#46111yescharacteristic
334C2×C4#46311yescharacteristic
335C2×C4#46511yescharacteristic
336C2×C4#46811yescharacteristic
337C2×C4#48311yescharacteristic
338C2×C4#48511yescharacteristic
339C8—42no—
340C8—81no—
341C8—82no—
342C8—81no—
343C8—81no—
344C8—161no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#166611yescharacteristic
358C22#168011yescharacteristic
359C22#169011yescharacteristic
360C22#170411yescharacteristic
361C22#203511yescharacteristic
362C22#203811yescharacteristic
363C22#204411yescharacteristic
364C22#204811yescharacteristic
365C22#205211yescharacteristic
366C22#205311yescharacteristic
367C22#205511yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—82no—
377C4—162no—
378C4—161no—
379C4—161no—
380C4—161no—
381C4#159911yescharacteristic
382C4#160311yescharacteristic
383C4#161111yescharacteristic
384C4#161511yescharacteristic
385C2—21no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2#1040111yescharacteristic
390C2#1046811yescharacteristic
391C2#1048611yescharacteristic
392C2#1050211yescharacteristic
393C2#1051111yescharacteristic
394C2#1056111yescharacteristic
395C2#1056511yescharacteristic
subgroupG/H
center, socleC23#394
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
#299672
#112282
#98792
#96792
#91292
#88302
#70392