Finite Group Databasebeta

← #102091

Subgroups — #102091

Order 512.

498 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C2×#1933C211yesmaximal, characteristic
2#9878C211yesmaximal, characteristic
3#9650C211yesmaximal, characteristic
4#8596C211yesmaximal, characteristic
5#8145C211yesmaximal, characteristic
6#7575C211yesmaximal, characteristic
7#7573C211yesmaximal, characteristic
8C22×#103C411yescharacteristic
9C22×#103C411yescharacteristic
10C22×C4×C8C2211yescharacteristic
11C2×#391C2211yescharacteristic
12C2×#389C2211yescharacteristic
13#1933—21no—
14#1933—21no—
15#1933—21no—
16#1933—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C4×C22⋊C8C2211yescharacteristic
21C2×#340C411yescharacteristic
22C2×#340C411yescharacteristic
23C2×#335—21no—
24C2×#324—22no—
25C2×#322—21no—
26#1280—22no—
27#1277—21no—
28#1273—21no—
29#1272—22no—
30#1271—22no—
31C23×Q8C2×C411yescharacteristic
32C23×C8C2×C411yescharacteristic
33C23×C8C2×C411yescharacteristic
34C22×C4⋊C4—21no—
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C42C2311yescharacteristic
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×#103—22no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#103—22no—
45C2×#103—21no—
46C2×#103—21no—
47C2×#103—42no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8D412yes—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—42no—
55C2×C4×C8D411yescharacteristic
56C2×C4×C8D411yescharacteristic
57C2×C4×C8D411yescharacteristic
58C2×C4×C8D411yescharacteristic
59#391—21no—
60#391—21no—
61#391—21no—
62#391—21no—
63#389—21no—
64#389—21no—
65#389—21no—
66#389—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336D412yes—
78#335—42no—
79#324—44no—
80#322—42no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—41no—
89C22×Q8—41no—
90C22×Q8M1612yes—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C22×C8—22no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8C22⋊C411yescharacteristic
111C22×C8C22⋊C411yescharacteristic
112C22×C8C22⋊C411yescharacteristic
113C22×C8C22⋊C411yescharacteristic
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—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4M1612yes—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42#4111yescharacteristic
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142#103—24no—
143#103—24no—
144#103—42no—
145#103—42no—
146C22⋊C8—24no—
147C22⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—42no—
150C22⋊C8—42no—
151C4×C8—22no—
152C4×C8—22no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—41no—
158C4×C8—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165C24C4×D411yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—81no—
179C2×Q8—81no—
180C2×Q8—81no—
181C2×Q8—81no—
182C2×Q8—81no—
183C2×Q8—81no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4C2×C22⋊C411yescharacteristic
212C22×C4C4×D411yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12111yescharacteristic
215C22×C4#12411yescharacteristic
216C22×C4#12711yescharacteristic
217C22×C4C2×M1611yescharacteristic
218C22×C4C2×M1611yescharacteristic
219C22×C4#13111yescharacteristic
220C22×C4#13111yescharacteristic
221C22×C4AGL(1,ℤ/8)12yes—
222C22×C4#13712yes—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—24no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—81no—
247C2×C8—81no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8#9912yes—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—82no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—41no—
269C42—41no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23#39011yescharacteristic
275C23#43511yescharacteristic
276C23#43511yescharacteristic
277C23#44012yes—
278C23#44312yes—
279Q8—42no—
280Q8—42no—
281Q8—82no—
282Q8—82no—
283Q8—81no—
284Q8—81no—
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—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—82no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—162no—
324C2×C4—162no—
325C2×C4#40711yescharacteristic
326C2×C4#40811yescharacteristic
327C2×C4C2×#9911yescharacteristic
328C2×C4#41011yescharacteristic
329C2×C4#41311yescharacteristic
330C2×C4#41311yescharacteristic
331C2×C4#43511yescharacteristic
332C2×C4#43511yescharacteristic
333C2×C4#46812yes—
334C2×C4#47312yes—
335C2×C4#49611yescharacteristic
336C2×C4#49711yescharacteristic
337C8—22no—
338C8—44no—
339C8—41no—
340C8—41no—
341C8—41no—
342C8—82no—
343C8—161no—
344C8—161no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#158512yes—
354C22#158812yes—
355C22#195511yescharacteristic
356C22#196411yescharacteristic
357C22#196711yescharacteristic
358C22#197311yescharacteristic
359C22#197411yescharacteristic
360C22#197611yescharacteristic
361C22#197911yescharacteristic
362C4—22no—
363C4—21no—
364C4—21no—
365C4—22no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—82no—
370C4—82no—
371C4—161no—
372C4—161no—
373C4#146411yescharacteristic
374C4#146511yescharacteristic
375C4#146811yescharacteristic
376C4#147311yescharacteristic
377C2—22no—
378C2—22no—
379C2#965211yescharacteristic
380C2#966611yescharacteristic
381C2#967111yescharacteristic
382C2#978611yescharacteristic
383C2#978911yescharacteristic
384C2#980911yescharacteristic
385C2#981411yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ 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
C2×#19332
#98782
#96502
#85962
#81452
#75752
#75732