Finite Group Databasebeta

← #99868

Subgroups — #99868

Order 512.

436 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#477C211yesmaximal, characteristic
2#21339C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#8564C211yesmaximal, characteristic
5#7571C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#477C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1987C411yescharacteristic
12#1984—21no—
13#1947C411yescharacteristic
14#1939—21no—
15#1921—21no—
16#1916—22no—
17#1863—21no—
18#1842C2211yescharacteristic
19#1803C411yescharacteristic
20C4×#107—21no—
21C4×C4⋊C8—21no—
22C4×C4⋊C8C2211yescharacteristic
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×#103—21no—
26#1744—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1279—21no—
30#1279—21no—
31#1279—21no—
32#1272—22no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#477—22no—
39#477—22no—
40C2×#107—21no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—22no—
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—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57C2×C4×C8D411yescharacteristic
58C2×C4×C8D411yescharacteristic
59#391—21no—
60#389—21no—
61#389—21no—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4C2×C411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C4×C4⋊C4D411yescharacteristic
71C43—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—22no—
79#336—22no—
80#336—21no—
81#336—21no—
82#336D412yes—
83Q8⋊C8—42no—
84C22×Q8—21no—
85C22×Q8C22⋊C411yescharacteristic
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—41no—
92C22×C8—41no—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8—21no—
96C4⋊Q8M1612yes—
97C4×Q8—21no—
98C4×Q8—21no—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—41no—
104C4×Q8—41no—
105C4×Q8—81no—
106C4×Q8—81no—
107C4×Q8SD1612yes—
108C4×Q8Q1612yes—
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⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—41no—
128C2×C42C22×C411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42#4111yescharacteristic
134C2×C42#4111yescharacteristic
135#107—24no—
136#107—42no—
137C4⋊C8—22no—
138C4⋊C8—21no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—44no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—81no—
150C4⋊C8M1612yes—
151#103—24no—
152#103—42no—
153C4×C8—21no—
154C4×C8—21no—
155C4×C8—21no—
156C4×C8—41no—
157C4×C8—41no—
158C4×C8—42no—
159C4×C8—41no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—41no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8Q1612yes—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—41no—
170#95—41no—
171C2×Q8—21no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—22no—
177C2×Q8—41no—
178C2×Q8—81no—
179C2×Q8—81no—
180C2×Q8#10312yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4C2×C22⋊C411yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4C4×D411yescharacteristic
190C22×C4#12011yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12111yescharacteristic
193C22×C4#12311yescharacteristic
194C2×C8—22no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—81no—
211C2×C8—81no—
212C2×C8—81no—
213C2×C8—81no—
214C2×C8—81no—
215C4⋊C4—21no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—81no—
234C4⋊C4—82no—
235C4⋊C4#10312yes—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—22no—
241C42—22no—
242C42—21no—
243C42—21no—
244C42—41no—
245C42—42no—
246C42—42no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42—81no—
254C42—81no—
255C42C2×M1611yescharacteristic
256C42C2×M1611yescharacteristic
257C42#13111yescharacteristic
258C42#13111yescharacteristic
259C42C2×SD1611yescharacteristic
260C42C2×Q1611yescharacteristic
261C42C2×Q1611yescharacteristic
262C42#13511yescharacteristic
263C42#13511yescharacteristic
264C42#13511yescharacteristic
265C42#13711yescharacteristic
266C42#13711yescharacteristic
267C23#38611yescharacteristic
268Q8—22no—
269Q8—22no—
270Q8—41no—
271Q8—41no—
272Q8—82no—
273Q8—82no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4#40711yescharacteristic
302C2×C4#40811yescharacteristic
303C2×C4C2×#10311yescharacteristic
304C2×C4#41611yescharacteristic
305C2×C4#42111yescharacteristic
306C2×C4#42111yescharacteristic
307C2×C4#43511yescharacteristic
308C2×C4#43511yescharacteristic
309C2×C4#43611yescharacteristic
310C2×C4#43611yescharacteristic
311C2×C4C4×Q1611yescharacteristic
312C2×C4#44111yescharacteristic
313C2×C4#44311yescharacteristic
314C2×C4#44411yescharacteristic
315C2×C4#45111yescharacteristic
316C2×C4#45211yescharacteristic
317C2×C4#46211yescharacteristic
318C2×C4#46411yescharacteristic
319C2×C4#46511yescharacteristic
320C2×C4#46511yescharacteristic
321C2×C4#46711yescharacteristic
322C2×C4#46711yescharacteristic
323C2×C4#47111yescharacteristic
324C2×C4#47211yescharacteristic
325C8—42no—
326C8—42no—
327C8—42no—
328C8—82no—
329C8—82no—
330C8—81no—
331C8—161no—
332C22#187011yescharacteristic
333C22#187611yescharacteristic
334C22#187811yescharacteristic
335C22#189211yescharacteristic
336C22#189711yescharacteristic
337C22#190611yescharacteristic
338C22#190711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—41no—
348C4—81no—
349C4—82no—
350C4—81no—
351C4—161no—
352C4#148111yescharacteristic
353C4#148211yescharacteristic
354C4#148711yescharacteristic
355C4#148811yescharacteristic
356C4#158411yescharacteristic
357C4#158711yescharacteristic
358C4#159111yescharacteristic
359C4#159311yescharacteristic
360C4#167211yescharacteristic
361C4#167611yescharacteristic
362C4#167811yescharacteristic
363C4#168411yescharacteristic
364C2#895011yescharacteristic
365C2#907511yescharacteristic
366C2#909711yescharacteristic
367C2#920711yescharacteristic
368C2#921311yescharacteristic
369C2#921611yescharacteristic
370C2#923611yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
C4×#4772
#213392
#98702
#85642
#75712
#70312
#70152