Finite Group Databasebeta

← #100494

Subgroups — #100494

Order 512.

397 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33202C211yesmaximal, characteristic
2#22828C211yesmaximal, characteristic
3#8566C211yesmaximal, characteristic
4#7662C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#477C411yescharacteristic
9C2×#475C411yescharacteristic
10#2862C2211yescharacteristic
11C42×Q8C2211yescharacteristic
12#1988C411yescharacteristic
13#1987C411yescharacteristic
14#1984—21no—
15#1949—21no—
16#1949—21no—
17#1916—22no—
18#1842C2211yescharacteristic
19#1839—21no—
20#1831C2211yescharacteristic
21#1831C2211yescharacteristic
22#1805—21no—
23#1805—21no—
24C8×C4⋊C4—21no—
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1744—21no—
28C2×Q8⋊C8—21no—
29#1279—21no—
30#1272—21no—
31#1272—21no—
32#1272—22no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4⋊Q8C2×C411yescharacteristic
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#477—42no—
39#475—42no—
40C2×#107—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8C2×C411yescharacteristic
49C2×C4⋊C8C2×C411yescharacteristic
50C2×#103—21no—
51C2×#103—21no—
52C2×C4×C8—22no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55#391—21no—
56#391—21no—
57#391—21no—
58#391—21no—
59#382—21no—
60#382—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4C2×C411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C43—21no—
68C43C2311yescharacteristic
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#336—22no—
74#336—22no—
75#336—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81#336D411yescharacteristic
82#336D411yescharacteristic
83Q8⋊C8—42no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8C22⋊C411yescharacteristic
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—41no—
93C22×C8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4×Q8—21no—
99C4×Q8—21no—
100C4×Q8—22no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—41no—
106C4×Q8SD1612yes—
107C4×Q8Q1612yes—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
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#106—42no—
133C4⋊C8—22no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—42no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146#103—42no—
147#103—42no—
148C4×C8—44no—
149C4×C8—41no—
150C4×C8—41no—
151C4×C8—41no—
152C4×C8—41no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—81no—
172C2×Q8#10312yes—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C2×C22⋊C411yescharacteristic
180C22×C4C4×D411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4#12011yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12311yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—81no—
203C2×C8—81no—
204C2×C8—81no—
205C2×C8—81no—
206C2×C8—81no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—42no—
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#10012yes—
223C4⋊C4#10312yes—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—22no—
229C42—22no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—42no—
234C42—42no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—81no—
240C42C2×SD1611yescharacteristic
241C42C2×Q1611yescharacteristic
242C42#13511yescharacteristic
243C42#13511yescharacteristic
244C42#13511yescharacteristic
245C42#13511yescharacteristic
246C42#13711yescharacteristic
247C42#13711yescharacteristic
248C23#38611yescharacteristic
249Q8—22no—
250Q8—22no—
251Q8—41no—
252Q8—41no—
253Q8—161no—
254Q8—161no—
255Q8—162no—
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—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C2×#10011yescharacteristic
288C2×C4#41311yescharacteristic
289C2×C4C2×#10311yescharacteristic
290C2×C4#41611yescharacteristic
291C2×C4#41611yescharacteristic
292C2×C4#41911yescharacteristic
293C2×C4#44311yescharacteristic
294C2×C4#44411yescharacteristic
295C2×C4#45211yescharacteristic
296C2×C4#45211yescharacteristic
297C2×C4#46511yescharacteristic
298C2×C4#46511yescharacteristic
299C2×C4#46711yescharacteristic
300C2×C4#46711yescharacteristic
301C2×C4#48511yescharacteristic
302C2×C4#48511yescharacteristic
303C8—42no—
304C8—81no—
305C8—82no—
306C8—82no—
307C8—81no—
308C8—81no—
309C8—161no—
310C22#187311yescharacteristic
311C22#187611yescharacteristic
312C22#188111yescharacteristic
313C22#189211yescharacteristic
314C22#190011yescharacteristic
315C22#190511yescharacteristic
316C22#190611yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—42no—
329C4—42no—
330C4—42no—
331C4—81no—
332C4—161no—
333C4—161no—
334C4#154211yescharacteristic
335C4#154311yescharacteristic
336C4#154811yescharacteristic
337C4#155411yescharacteristic
338C2#899411yescharacteristic
339C2#912811yescharacteristic
340C2#917811yescharacteristic
341C2#920711yescharacteristic
342C2#924411yescharacteristic
343C2#930411yescharacteristic
344C2#934911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332022
#228282
#85662
#76622
#70402
#70312