Finite Group Databasebeta

← #101483

Subgroups — #101483

Order 512.

396 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 82 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#29388C211yesmaximal, characteristic
2#21267C211yesmaximal, characteristic
3#9647C211yesmaximal, characteristic, complemented
4#7642C211yesmaximal, characteristic
5#7625C211yesmaximal, characteristic, complemented
6#7041C211yesmaximal, characteristic, complemented
7#7019C211yesmaximal, characteristic, complemented
8C2×#433—21no—
9C4×C4⋊Q8C2211yescharacteristic
10#2293C2211yescharacteristic
11#2083C411yescharacteristic
12#2071C411yescharacteristic
13#2057C411yescharacteristic
14#2023C411yescharacteristic
15#1955—21no—
16#1940—21no—
17#1925—21no—
18#1924—22no—
19#1918—21no—
20#1918—21no—
21#1862—21no—
22#1839C2211yescharacteristic
23#1839C2211yescharacteristic
24#1831C2211yescharacteristic
25#1767C2211yescharacteristic
26#1750—21no—
27C4×#97C2211yescharacteristic
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30#1271—21no—
31#1271—22no—
32#1270—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×D4D411yescharacteristic
36C2×#117—21no—
37#433—42no—
38#433—42no—
39C2×#107—21no—
40C2×#107—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#102—21no—
45C2×#102—21no—
46C2×C22⋊C8—22no—
47C2×C22⋊C8—22no—
48C2×#97—21no—
49C2×#97—21no—
50C2×#97—21no—
51C2×C4×C8D411yescharacteristic
52C2×C4×C8D411yescharacteristic
53#391—21no—
54#390C2×C411yescharacteristic
55#390D411yescharacteristic
56#389—21no—
57#389—21no—
58#389C2×C411yescharacteristic
59#389D411yescharacteristic
60#388—21no—
61#388—21no—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4D411yescharacteristic
66C4×C22⋊C4—21no—
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—22no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336C2×C411yescharacteristic
81#336C2×C411yescharacteristic
82#336D412yes—
83Q8⋊C8—42no—
84Q8⋊C8—42no—
85C22×Q8—21no—
86C22×D4C22⋊C411yescharacteristic
87C23×C4—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—22no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—42no—
96C4×Q8—41no—
97C4×Q8—41no—
98C4×Q8—41no—
99C4×Q8—41no—
100C4×D4—41no—
101C4×D4—41no—
102#117—41no—
103#117—41no—
104#117—41no—
105#117—41no—
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—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C22⋊C4—21no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—21no—
121C2×C22⋊C4—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#107—42no—
132#107—42no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—44no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138#102—42no—
139#102—42no—
140C22⋊C8—44no—
141C22⋊C8—44no—
142#97—41no—
143#97—41no—
144#97—42no—
145#97—41no—
146#97—41no—
147C4×C8—21no—
148C4×C8—21no—
149C4×C8—21no—
150C4×C8D812yes—
151#95—21no—
152#95—21no—
153#95—21no—
154#95—41no—
155#95—41no—
156C24—21no—
157C2×Q8—22no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4C2×C22⋊C411yescharacteristic
177C22×C4C4×D411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4#12011yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12311yescharacteristic
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—41no—
191C2×C8—42no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C22⋊C4—42no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—81no—
229C22⋊C4—81no—
230C42—21no—
231C42—21no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—81no—
240C42—81no—
241C42C2×D811yescharacteristic
242C42#13511yescharacteristic
243C42AGL(1,ℤ/8)11yescharacteristic
244C42AGL(1,ℤ/8)11yescharacteristic
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23#38611yescharacteristic
253Q8—42no—
254Q8—42no—
255Q8—81no—
256Q8—81no—
257D4—42no—
258D4—81no—
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—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4#42111yescharacteristic
294C2×C4#42111yescharacteristic
295C2×C4C4×D811yescharacteristic
296C2×C4#44211yescharacteristic
297C2×C4#44711yescharacteristic
298C2×C4#44911yescharacteristic
299C2×C4#45911yescharacteristic
300C2×C4#46311yescharacteristic
301C8—42no—
302C8—42no—
303C8—82no—
304C8—81no—
305C8—81no—
306C8—161no—
307C8—161no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22#187911yescharacteristic
316C22#188111yescharacteristic
317C22#189111yescharacteristic
318C22#189711yescharacteristic
319C22#190211yescharacteristic
320C22#190611yescharacteristic
321C22#190911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—82no—
337C4—161no—
338C2—161no—
339C2#904911yescharacteristic
340C2#923711yescharacteristic
341C2#929111yescharacteristic
342C2#931411yescharacteristic
343C2#936911yescharacteristic
344C2#949311yescharacteristic
345C2#953111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #9647C2semidirect
5. #7625C2semidirect
6. #7041C2semidirect
7. #7019C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#293882
#212672
#96472
#76422
#76252
#70412
#70192