Finite Group Databasebeta

← #122193

Subgroups — #122193

Order 512.

685 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37481C211yesmaximal, characteristic
2#8108C211yesmaximal, characteristic
3#8108C211yesmaximal, characteristic
4#8104C211yesmaximal, characteristic
5#7927C211yesmaximal, characteristic
6#7925C211yesmaximal, characteristic
7#7925C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2842C412yes—
13#2842C412yes—
14#2667—22no—
15#2667—22no—
16#2629—22no—
17#2608—22no—
18#2441—22no—
19#2441—22no—
20#2280C2211yescharacteristic
21#2280C2211yescharacteristic
22#2280C2211yescharacteristic
23#1305—22no—
24#1305—22no—
25#1305—22no—
26#1282—22no—
27#1282—22no—
28#1282—22no—
29C24×C4C2311yescharacteristic
30C22×M16—21no—
31C22×M16—21no—
32C22×M16Q812yes—
33C23×C8—21no—
34C2×#125—22no—
35C2×#117—21no—
36C2×#117—21no—
37C2×#117—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407—21no—
48#407—21no—
49#407Q812yes—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8Q812yes—
61C2×C22⋊C8Q812yes—
62#399—24no—
63#399—24no—
64#398—24no—
65#398—24no—
66#396—24no—
67#396—24no—
68#396—24no—
69#396—24no—
70#389—24no—
71#389—24no—
72#389—22no—
73#389—22no—
74#387—24no—
75#387—24no—
76#384—22no—
77#381—21no—
78#381—21no—
79#381—21no—
80#380—21no—
81#380—21no—
82#380—21no—
83#380D412yes—
84#380D412yes—
85#380D412yes—
86#379C2×C411yescharacteristic
87#379C2×C411yescharacteristic
88#379C2×C412yes—
89#379C2×C412yes—
90C4×C22⋊C4—21no—
91C4×C22⋊C4—21no—
92C4×C22⋊C4—21no—
93C4×C22⋊C4D412yes—
94C4×C22⋊C4D412yes—
95C4×C22⋊C4D412yes—
96C25C22×C411yescharacteristic
97C23×C4—82no—
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×Q811yescharacteristic
105C23×C4C2×Q811yescharacteristic
106C23×C4C2×Q811yescharacteristic
107C23×C4C2×Q811yescharacteristic
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—82no—
119C2×M16—82no—
120C2×M16—82no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—41no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—82no—
128#125—84no—
129#117—82no—
130#117—82no—
131#117—82no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—22no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—22no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4C22⋊C414yes—
150C2×C22⋊C4C22⋊C412yes—
151C2×C22⋊C4C22⋊C414yes—
152C2×C22⋊C4C22⋊C412yes—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—22no—
156C22⋊C8—22no—
157C22⋊C8—22no—
158C22⋊C8—22no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C22⋊C8—41no—
172#95—24no—
173#95—24no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180C24—42no—
181C24—81no—
182C24—81no—
183C24C2×C22⋊C411yescharacteristic
184C24C2×C22⋊C411yescharacteristic
185C24C2×C22⋊C411yescharacteristic
186C24C4×Q811yescharacteristic
187C24C4×Q811yescharacteristic
188C24C4×Q811yescharacteristic
189C24C4×Q811yescharacteristic
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—24no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—81no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4—81no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4#12011yescharacteristic
209C22×C4#12011yescharacteristic
210C22×C4#12011yescharacteristic
211C22×C4#12011yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4C22⋊Q811yescharacteristic
218C22×C4C22⋊Q811yescharacteristic
219C22×C4C22⋊Q811yescharacteristic
220C22×C4C22⋊Q811yescharacteristic
221C22×C4C22⋊Q811yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4#12411yescharacteristic
225C22×C4#12411yescharacteristic
226C22×C4#12411yescharacteristic
227C22×C4#12411yescharacteristic
228C22×C4#12411yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4C4⋊Q811yescharacteristic
231C22×C4C4⋊Q811yescharacteristic
232C22×C4C4⋊Q811yescharacteristic
233C22×C4C4⋊Q811yescharacteristic
234C22×C4C4⋊Q811yescharacteristic
235C22×C4C4⋊Q811yescharacteristic
236M16—82no—
237M16—82no—
238M16—82no—
239M16—82no—
240M16—82no—
241M16—82no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—82no—
249C2×C8—82no—
250C2×C8—82no—
251C2×C8—82no—
252C4⋊C4—44no—
253C4⋊C4—44no—
254C4⋊C4—84no—
255C4⋊C4—84no—
256C4⋊C4—84no—
257C4⋊C4—84no—
258C4⋊C4—82no—
259C4⋊C4—84no—
260C4⋊C4—84no—
261C22⋊C4—44no—
262C22⋊C4—42no—
263C22⋊C4—44no—
264C22⋊C4—42no—
265C22⋊C4—82no—
266C22⋊C4—81no—
267C22⋊C4—82no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C22⋊C4—81no—
271C22⋊C4—82no—
272C22⋊C4—82no—
273C42—44no—
274C42—82no—
275C42—82no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—88no—
298C23#37911yescharacteristic
299C23#39111yescharacteristic
300C23#39111yescharacteristic
301C23#39111yescharacteristic
302C23#39111yescharacteristic
303C23#39111yescharacteristic
304C23#39111yescharacteristic
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
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—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4#39311yescharacteristic
346C2×C4#39311yescharacteristic
347C2×C4#39311yescharacteristic
348C2×C4#39311yescharacteristic
349C2×C4#39511yescharacteristic
350C2×C4#39511yescharacteristic
351C2×C4#39511yescharacteristic
352C2×C4#39511yescharacteristic
353C8—82no—
354C8—82no—
355C8—82no—
356C8—82no—
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—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—44no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22#144611yescharacteristic
385C22#179112yes—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—82no—
394C4—82no—
395C4—84no—
396C4—84no—
397C4#203212yes—
398C2—22no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2—41no—
403C2—41no—
404C2—41no—
405C2#1139111yescharacteristic
406C2#1139411yescharacteristic
407C2#1139511yescharacteristic
subgroupG/H
center, socleC22#1446
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#374812
#81082
#81042
#79272
#79252