Finite Group Databasebeta

← #99437

Subgroups — #99437

Order 512.

448 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22295C211yesmaximal, characteristic
2#11255C211yesmaximal, characteristic
3#8937C211yesmaximal, characteristic
4#8830C211yesmaximal, characteristic
5C4×#328C211yesmaximal, characteristic
6#7028C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×C4⋊C8C2211yescharacteristic
9C4×C22⋊Q8C2211yescharacteristic
10#1985—21no—
11#1940—21no—
12#1917—21no—
13#1917—21no—
14#1850—21no—
15#1797C2211yescharacteristic
16#1752—21no—
17C4×C22⋊C8C2211yescharacteristic
18C4×C22⋊C8C2211yescharacteristic
19C2×#336—21no—
20C2×#336—21no—
21C2×#336C2211yescharacteristic
22C2×#334—21no—
23C2×#328C411yescharacteristic
24C2×#328C411yescharacteristic
25C2×Q8⋊C8—21no—
26C4×#95C2211yescharacteristic
27#1294C411yescharacteristic
28#1294C411yescharacteristic
29#1279—21no—
30#1277—21no—
31C23×C8—21no—
32C23×C8D411yescharacteristic
33C23×C8D411yescharacteristic
34C2×C22⋊Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C22×C42—21no—
37C22×C42C2311yescharacteristic
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—42no—
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8C2×C411yescharacteristic
48C2×C22⋊C8C2×C411yescharacteristic
49C2×#97—21no—
50C2×#97—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#391Q811yescharacteristic
54#389Q811yescharacteristic
55#387—21no—
56#385—21no—
57#380C2×C411yescharacteristic
58C4×C4⋊C4—21no—
59C4×C4⋊C4D411yescharacteristic
60C4×C22⋊C4—21no—
61C2×#95—21no—
62C2×#95C2×C411yescharacteristic
63C2×#95C2×C411yescharacteristic
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#334—42no—
76#328—22no—
77#328—22no—
78Q8⋊C8—42no—
79C22×Q8C4⋊C411yescharacteristic
80C23×C4—21no—
81C23×C4—21no—
82C23×C4C22×C411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—22no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—41no—
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×C8SD1612yes—
107C22⋊Q8—21no—
108C22⋊Q8—21no—
109C22⋊Q8—21no—
110C22⋊Q8—21no—
111C4×Q8—41no—
112C4×Q8—41no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4C4⋊C411yescharacteristic
117C2×C4⋊C4C4⋊C411yescharacteristic
118C2×C4⋊C4C4⋊C411yescharacteristic
119C2×C22⋊C4—21no—
120C2×C22⋊C4—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×Q811yescharacteristic
134C2×C42#4111yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—81no—
142C4⋊C8—81no—
143C22⋊C8—21no—
144C22⋊C8—22no—
145C22⋊C8—21no—
146C22⋊C8—21no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8M1612yes—
151#97—81no—
152#97—81no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—42no—
166#95M1612yes—
167C24C4×D411yescharacteristic
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—41no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—41no—
185C22×C4—41no—
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—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4C2×C4⋊C411yescharacteristic
201C22×C4C4×D411yescharacteristic
202C22×C4#12011yescharacteristic
203C22×C4C22⋊Q811yescharacteristic
204C22×C4C22⋊Q811yescharacteristic
205C22×C4#12311yescharacteristic
206C22×C4C2×M1611yescharacteristic
207C22×C4C2×M1611yescharacteristic
208C22×C4#13111yescharacteristic
209C22×C4#13111yescharacteristic
210C22×C4C2×SD1611yescharacteristic
211C22×C4#13511yescharacteristic
212C22×C4#13711yescharacteristic
213C22×C4#13711yescharacteristic
214C2×C8—22no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—42no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8—41no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—42no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—81no—
239C2×C8—81no—
240C2×C8—81no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C2×C8—81no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—81no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—81no—
269C42—81no—
270C42—81no—
271C42—81no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#38511yescharacteristic
277C23#43511yescharacteristic
278C23#43611yescharacteristic
279C23C4×SD1611yescharacteristic
280C23#44111yescharacteristic
281C23#44311yescharacteristic
282C23#44411yescharacteristic
283Q8—42no—
284Q8—81no—
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—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#42311yescharacteristic
338C2×C4#42411yescharacteristic
339C2×C4#43511yescharacteristic
340C2×C4#43611yescharacteristic
341C2×C4#44811yescharacteristic
342C2×C4#45211yescharacteristic
343C2×C4#45411yescharacteristic
344C2×C4#45511yescharacteristic
345C2×C4B(4,𝔽2)11yescharacteristic
346C2×C4#45811yescharacteristic
347C2×C4#47511yescharacteristic
348C2×C4#47911yescharacteristic
349C8—42no—
350C8—42no—
351C8—81no—
352C8—82no—
353C8—82no—
354C8—81no—
355C8—81no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22#158211yescharacteristic
370C22#158711yescharacteristic
371C22#159011yescharacteristic
372C22#159311yescharacteristic
373C22#185111yescharacteristic
374C22#186011yescharacteristic
375C22#186111yescharacteristic
376C22#186511yescharacteristic
377C22#186611yescharacteristic
378C22#186711yescharacteristic
379C22#186811yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—82no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4#159911yescharacteristic
395C4#160611yescharacteristic
396C4#160811yescharacteristic
397C4#161511yescharacteristic
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#884211yescharacteristic
403C2#885011yescharacteristic
404C2#885211yescharacteristic
405C2#887211yescharacteristic
406C2#887411yescharacteristic
407C2#887711yescharacteristic
408C2#888111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C4×D4
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
#222952
#112552
#89372
#88302
C4×#3282
#70282
#70162