Finite Group Databasebeta

← #103344

Subgroups — #103344

Order 512.

522 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 88 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#33149C211yesmaximal, characteristic
2#29329C211yesmaximal, characteristic
3#15111C211yesmaximal, characteristic
4#9911C211yesmaximal, characteristic
5#8707C211yesmaximal, characteristic
6#7641C211yesmaximal, characteristic
7#7024C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#2100—21no—
12#2043—21no—
13#1987—21no—
14#1947—21no—
15#1933—22no—
16#1921—22no—
17#1872—21no—
18#1872—21no—
19#1852—21no—
20#1824—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24#1445—21no—
25#1445—21no—
26#1442—21no—
27#1442—21no—
28#1436—22no—
29#1434C2211yescharacteristic
30#1294—22no—
31#1279—22no—
32#1271—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C22⋊Q8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42C2×#107—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×#103—22no—
46C2×#103—22no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C4×C8D412yes—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384D411yescharacteristic
59#380—21no—
60#380—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C2×#95—22no—
66C2×#95—22no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95D412yes—
74#340—22no—
75#340—22no—
76#340—22no—
77#340—22no—
78#340—22no—
79#336—21no—
80#336—21no—
81#336D412yes—
82C22×Q8—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—22no—
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—41no—
94C4⋊Q8—42no—
95C22⋊Q8—44no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4Q1612yes—
121C2×C22⋊C4—41no—
122C2×C42—42no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—82no—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130#107—44no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133#103—44no—
134#103—82no—
135C22⋊C8—42no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—42no—
139C4×C8—42no—
140#95—22no—
141#95—22no—
142#95—42no—
143#95—44no—
144#95—44no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—82no—
154#95—82no—
155C24#12011yescharacteristic
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4#12011yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4#12711yescharacteristic
201C22×C4C2×Q1611yescharacteristic
202C22×C4#13511yescharacteristic
203C22×C4#13512yes—
204C22×C4#13711yescharacteristic
205C22×C4#13711yescharacteristic
206C22×C4#13712yes—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—81no—
214C2×C8—81no—
215C2×C8—81no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C22⋊C4—82no—
240C42—22no—
241C42—22no—
242C42—41no—
243C42—41no—
244C42—82no—
245C42—82no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#39211yescharacteristic
251C23#45111yescharacteristic
252C23#45212yes—
253C23#45211yescharacteristic
254C23#45412yes—
255Q8—84no—
256C2×C4—21no—
257C2×C4—21no—
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—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4#45111yescharacteristic
310C2×C4#45211yescharacteristic
311C2×C4#45812yes—
312C2×C4#46412yes—
313C2×C4#46711yescharacteristic
314C2×C4#47011yescharacteristic
315C2×C4#49511yescharacteristic
316C2×C4#49711yescharacteristic
317C8—82no—
318C8—82no—
319C8—161no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22#163612yes—
329C22#163812yes—
330C22#200111yescharacteristic
331C22#200311yescharacteristic
332C22#200811yescharacteristic
333C22#201011yescharacteristic
334C22#201011yescharacteristic
335C22#201511yescharacteristic
336C22#202211yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—21no—
345C4—41no—
346C4—82no—
347C4—82no—
348C4—82no—
349C4—162no—
350C4—161no—
351C4—161no—
352C4—161no—
353C2—22no—
354C2—22no—
355C2#994111yescharacteristic
356C2#995811yescharacteristic
357C2#1000211yescharacteristic
358C2#1001611yescharacteristic
359C2#1001911yescharacteristic
360C2#1006111yescharacteristic
361C2#1032511yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#120
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
#331492
#293292
#151112
#99112
#87072
#76412
#70242