Finite Group Databasebeta

← #99321

Subgroups — #99321

Order 512.

436 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21916C211yesmaximal, characteristic
2#11202C211yesmaximal, characteristic
3#8830C211yesmaximal, characteristic
4#8829C211yesmaximal, characteristic
5C4×#324C211yesmaximal, characteristic
6#7029C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C22×C4⋊C8C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1917—21no—
11#1917—21no—
12#1917—21no—
13#1917—21no—
14#1817—21no—
15#1797C2211yescharacteristic
16#1797C2211yescharacteristic
17#1749—21no—
18C4×C22⋊C8C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#336—21no—
21C2×#336—21no—
22C2×#336C2211yescharacteristic
23C2×#335—21no—
24C2×#334—21no—
25C2×#324C411yescharacteristic
26C2×#324C411yescharacteristic
27#1280C411yescharacteristic
28#1280C411yescharacteristic
29#1277—21no—
30#1277—21no—
31C23×C8—21no—
32C23×C8—21no—
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C4⋊C4Q811yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—42no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8C2×C411yescharacteristic
48C2×C22⋊C8C2×C411yescharacteristic
49C2×C22⋊C8C2×C411yescharacteristic
50C2×C22⋊C8C2×C411yescharacteristic
51C2×#97—21no—
52C2×#97—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C4×C4⋊C4—21no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C2×#95C2×C411yescharacteristic
60C2×#95Q811yescharacteristic
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—42no—
74#336—42no—
75#335—42no—
76#334—42no—
77#324—22no—
78#324—22no—
79C23×C4C4⋊C411yescharacteristic
80C23×C4C4⋊C411yescharacteristic
81C23×C4C4⋊C411yescharacteristic
82C23×C4C4⋊C411yescharacteristic
83C23×C4C22×C411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×Q811yescharacteristic
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C2×C4⋊C4—22no—
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×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42#4111yescharacteristic
133C2×C42#4111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C22⋊C8—21no—
143C22⋊C8—21no—
144C22⋊C8—21no—
145C22⋊C8—21no—
146C22⋊C8—21no—
147C22⋊C8—21no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8M1612yes—
153C22⋊C8M1612yes—
154#97—81no—
155#97—81no—
156C4×C8—41no—
157C4×C8—41no—
158C4×C8—41no—
159C4×C8—41no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164C24C2×C4⋊C411yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4#10812yes—
197C22×C4C4×D411yescharacteristic
198C22×C4C4×D411yescharacteristic
199C22×C4#12011yescharacteristic
200C22×C4C22⋊Q811yescharacteristic
201C22×C4C22⋊Q811yescharacteristic
202C22×C4#12311yescharacteristic
203C22×C4C2×M1611yescharacteristic
204C22×C4C2×M1611yescharacteristic
205C22×C4#13111yescharacteristic
206C22×C4#13111yescharacteristic
207C22×C4#13511yescharacteristic
208C22×C4#13511yescharacteristic
209C22×C4AGL(1,ℤ/8)11yescharacteristic
210C22×C4#13711yescharacteristic
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—81no—
247C2×C8—81no—
248C2×C8—81no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—81no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23#38511yescharacteristic
273C23#42311yescharacteristic
274C23#42411yescharacteristic
275C23#42711yescharacteristic
276C23#42811yescharacteristic
277C23C2×#10811yescharacteristic
278C23#43011yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
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—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4#43511yescharacteristic
328C2×C4#43511yescharacteristic
329C2×C4#43611yescharacteristic
330C2×C4#43611yescharacteristic
331C2×C4#44911yescharacteristic
332C2×C4#45211yescharacteristic
333C2×C4#45411yescharacteristic
334C2×C4#45611yescharacteristic
335C2×C4B(4,𝔽2)11yescharacteristic
336C2×C4#45811yescharacteristic
337C2×C4#48211yescharacteristic
338C2×C4#48511yescharacteristic
339C8—42no—
340C8—42no—
341C8—81no—
342C8—81no—
343C8—82no—
344C8—81no—
345C8—82no—
346C8—81no—
347C8—81no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#156811yescharacteristic
362C22#156911yescharacteristic
363C22#157211yescharacteristic
364C22#157311yescharacteristic
365C22#185111yescharacteristic
366C22#185411yescharacteristic
367C22#185511yescharacteristic
368C22#185711yescharacteristic
369C22#185811yescharacteristic
370C22#186711yescharacteristic
371C22#186811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4#159711yescharacteristic
385C4#160311yescharacteristic
386C4#160911yescharacteristic
387C4#161511yescharacteristic
388C2—21no—
389C2—21no—
390C2—21no—
391C2—21no—
392C2#883411yescharacteristic
393C2#883811yescharacteristic
394C2#885211yescharacteristic
395C2#885511yescharacteristic
396C2#886011yescharacteristic
397C2#886311yescharacteristic
398C2#886511yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C2×C4⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#219162
#112022
#88302
#88292
C4×#3242
#70292