Finite Group Databasebeta

← #190194

Subgroups — #190194

Order 512.

771 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34378C211yesmaximal, characteristic
2#17394C211yesmaximal, characteristic
3#17394C211yesmaximal, characteristic
4#8758C214yesmaximal
5#8757C214yesmaximal
6#8110C211yesmaximal, characteristic
7#8109C211yesmaximal, characteristic
8#8106C211yesmaximal, characteristic
9#8105C211yesmaximal, characteristic
10C22×#125C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13#2920C2211yescharacteristic
14#2920C2211yescharacteristic
15#2382—22no—
16#2370—22no—
17#2345C412yes—
18#2344C412yes—
19#2344C414yes—
20#2336—22no—
21#2330—22no—
22#2316C2212yes—
23#2313C2212yes—
24#2285C2211yescharacteristic
25#2283C2211yescharacteristic
26#1470—22no—
27#1470—22no—
28#1470—22no—
29#1470—22no—
30#1463C2214yes—
31#1463C2214yes—
32#1305C2212yes—
33#1305C2212yes—
34#1305C2214yes—
35#1305C2214yes—
36#1305C2212yes—
37#1305C2212yes—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125—21no—
46C2×#125D412yes—
47C2×#125D412yes—
48C2×#125D412yes—
49C2×#125D412yes—
50C2×#117C2×C414yes—
51C2×#117C2×C412yes—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2312yes—
56C22×C42C2311yescharacteristic
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432—21no—
64#432—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#431—21no—
70#431—21no—
71#431—21no—
72#431—21no—
73#423—21no—
74#423—21no—
75#423—21no—
76#423—21no—
77#407C2312yes—
78#407C2312yes—
79#407C2312yes—
80#407C2312yes—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16—21no—
85#389—22no—
86#389—24no—
87#389—22no—
88#389—24no—
89#389—24no—
90#387—24no—
91#387—24no—
92#387—24no—
93#387—24no—
94#387—24no—
95#387—24no—
96#384—21no—
97#383—21no—
98#382—21no—
99#382—21no—
100#381C2×C414yes—
101#381C2×C412yes—
102#380C2×C414yes—
103#380C2×C412yes—
104#380C2311yescharacteristic
105#380C2312yes—
106#380C2311yescharacteristic
107C4×C4⋊C4—22no—
108C4×C4⋊C4—22no—
109C4×C4⋊C4—24no—
110C4×C4⋊C4—21no—
111C4×C4⋊C4—21no—
112C4×C4⋊C4—21no—
113C4×C22⋊C4C2×C414yes—
114C4×C22⋊C4C2×C412yes—
115#376—21no—
116#324—28no—
117#324—28no—
118C23×C4C22×C412yes—
119C23×C4C22×C412yes—
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C2411yescharacteristic
123C2×M16—22no—
124C2×M16—22no—
125C2×M16—22no—
126C2×M16—22no—
127#125—22no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132#125—22no—
133#125—22no—
134#125—22no—
135#125—22no—
136#125—22no—
137#125—22no—
138#125—22no—
139#125—22no—
140#125—22no—
141#125—22no—
142#125—22no—
143#117—84no—
144#117—82no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C22⋊C414yes—
169C2×C4⋊C4C22⋊C412yes—
170C2×C4⋊C4C22⋊C412yes—
171C2×C4⋊C4C22⋊C412yes—
172C2×C4⋊C4C22⋊C412yes—
173C2×C4⋊C4C22⋊C414yes—
174C2×C4⋊C4C2×D414yes—
175C2×C4⋊C4C2×D414yes—
176C2×C22⋊C4C22×C412yes—
177C2×C22⋊C4C22×C414yes—
178C2×C22⋊C4C22×C412yes—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—24no—
182C2×C42—24no—
183C2×C42C2×D411yescharacteristic
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42#4111yescharacteristic
188C2×C42#4111yescharacteristic
189C2×C42#4111yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C4⋊C8—41no—
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211#97—41no—
212#97—41no—
213#97—41no—
214#97—41no—
215C4×C8—41no—
216C4×C8—41no—
217C4×C8—41no—
218C4×C8—41no—
219#95—22no—
220#95—22no—
221#95—24no—
222#95—22no—
223#95—22no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—21no—
228#95—21no—
229#95—22no—
230C24C23×C411yescharacteristic
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—24no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—81no—
244C22×C4—82no—
245C22×C4C2×C22⋊C414yes—
246C22×C4C2×C22⋊C411yescharacteristic
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C2×C22⋊C411yescharacteristic
249C22×C4C2×C22⋊C414yes—
250C22×C4C2×C22⋊C411yescharacteristic
251C22×C4#11711yescharacteristic
252C22×C4#11711yescharacteristic
253C22×C4#11711yescharacteristic
254C22×C4#11711yescharacteristic
255C22×C4#11711yescharacteristic
256C22×C4#11711yescharacteristic
257C22×C4#11711yescharacteristic
258C22×C4#11711yescharacteristic
259C22×C4C22×D411yescharacteristic
260C22×C4C22×D411yescharacteristic
261C22×C4C2×#4111yescharacteristic
262C22×C4C2×#4111yescharacteristic
263C22×C4C2×#4111yescharacteristic
264C22×C4C2×#4111yescharacteristic
265M16—82no—
266M16—82no—
267M16—82no—
268M16—82no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—44no—
290C4⋊C4—82no—
291C4⋊C4—84no—
292C4⋊C4—81no—
293C4⋊C4—82no—
294C4⋊C4—81no—
295C4⋊C4—84no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—44no—
299C42—44no—
300C42—82no—
301C42—84no—
302C42—84no—
303C42#12311yescharacteristic
304C42#12311yescharacteristic
305C42#12311yescharacteristic
306C42#12311yescharacteristic
307C42#12311yescharacteristic
308C42#12311yescharacteristic
309C42#12311yescharacteristic
310C42#12311yescharacteristic
311C42#12311yescharacteristic
312C42#12311yescharacteristic
313C42#12311yescharacteristic
314C42#12311yescharacteristic
315C42#12311yescharacteristic
316C42#12311yescharacteristic
317C42#12311yescharacteristic
318C42#12311yescharacteristic
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23C22×C22⋊C411yescharacteristic
324C23C2×#11711yescharacteristic
325C23C2×#11711yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#38111yescharacteristic
365C2×C4#38111yescharacteristic
366C2×C4#38111yescharacteristic
367C2×C4#38111yescharacteristic
368C2×C4#38111yescharacteristic
369C2×C4#38111yescharacteristic
370C2×C4#38111yescharacteristic
371C2×C4#38111yescharacteristic
372C2×C4C2×#12311yescharacteristic
373C2×C4C2×#12311yescharacteristic
374C2×C4C2×#12311yescharacteristic
375C2×C4C2×#12311yescharacteristic
376C8—82no—
377C8—82no—
378C8—82no—
379C8—82no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22C2×#38111yescharacteristic
391C22#288811yescharacteristic
392C22#288911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—44no—
405C4—44no—
406C4—82no—
407C4—84no—
408C4—82no—
409C4#183012yes—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—41no—
414C2#2069511yescharacteristic
415C2#2071011yescharacteristic
416C2C2×#183011yescharacteristic
subgroupG/H
center, socleC22C2×#381
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#343782
#173942
#87582
#87572
#81102
#81092
#81062
#81052