Finite Group Databasebeta

← #108273

Subgroups — #108273

Order 512.

781 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34239C211yesmaximal, characteristic
2#21830C211yesmaximal, characteristic
3C2×#1470C211yesmaximal, characteristic
4#7951C211yesmaximal, characteristic
5#7949C211yesmaximal, characteristic
6#7869C211yesmaximal, characteristic
7#7857C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13#2371—22no—
14#2370—22no—
15#2345—21no—
16#2344—21no—
17#2344—22no—
18#2336—22no—
19#2313C412yes—
20C4×#125—22no—
21#2283C2211yescharacteristic
22#2274C412yes—
23C4×#117C2211yescharacteristic
24#1998—22no—
25#1998C414yescomplemented
26#1821—21no—
27#1821—21no—
28#1470—22no—
29#1470C414yescomplemented
30C2×#324—22no—
31#1285—22no—
32#1285—22no—
33#1276—22no—
34#1274—22no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125C2×C412yes—
44C2×#125C2×C412yes—
45C2×#125D412yes—
46C2×#125Q812yes—
47C2×#117—22no—
48C2×#117—21no—
49C22×C4⋊C4C2×C412yes—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4D412yes—
53C22×C42C2311yescharacteristic
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432C2×C412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#431C2×C412yes—
70#423—21no—
71#423C2×C412yes—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74#407—21no—
75#407—21no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C4×M16—21no—
79C4×M16C2×C412yes—
80C2×#97—21no—
81C2×C4×C8—21no—
82#389—22no—
83#389—22no—
84#389—24no—
85#387—24no—
86#387—24no—
87#387—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#383—21no—
92#382—21no—
93#381—22no—
94#381—21no—
95#380—22no—
96#380—21no—
97C4×C4⋊C4—22no—
98C4×C4⋊C4—24no—
99C4×C4⋊C4—22no—
100C4×C4⋊C4—24no—
101C4×C4⋊C4—24no—
102C4×C4⋊C4—21no—
103C4×C4⋊C4D412yes—
104C4×C4⋊C4D412yes—
105C4×C22⋊C4—22no—
106C4×C22⋊C4—21no—
107C4×C22⋊C4C2×C411yescharacteristic
108C4×C22⋊C4C2×C412yes—
109C4×C22⋊C4C2×C411yescharacteristic
110#376—21no—
111#376D412yes—
112C43D412yes—
113#343—24no—
114#343—24no—
115#324—28no—
116C23×C4C22⋊C412yes—
117C23×C4C22⋊C412yes—
118C23×C4C22×C411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C2×M16—22no—
122C2×M16—22no—
123C22×C8—41no—
124C22×C8—41no—
125#125—22no—
126#125—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#117—44no—
142#117—48no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4C4214yes—
164C2×C4⋊C4C22⋊C414yes—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C4⋊C414yes—
168C2×C4⋊C4C4⋊C412yes—
169C2×C4⋊C4C4⋊C412yes—
170C2×C4⋊C4C4⋊C414yes—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—21no—
174C2×C42—24no—
175C2×C42—22no—
176C2×C42—22no—
177C2×C42—24no—
178C2×C42C22⋊C412yes—
179C2×C42C22⋊C412yes—
180C2×C42C22⋊C414yes—
181C2×C42C22×C411yescharacteristic
182C2×C42C22×C411yescharacteristic
183C2×C42C2×D411yescharacteristic
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×Q811yescharacteristic
189C2×C42#4111yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C4⋊C8—22no—
194C4⋊C8—22no—
195C4⋊C8—22no—
196C4⋊C8—22no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206C22⋊C8—41no—
207C22⋊C8—41no—
208C22⋊C8—41no—
209#97—22no—
210#97—22no—
211#97—41no—
212#97—41no—
213C4×C8—22no—
214C4×C8—22no—
215C4×C8—41no—
216C4×C8—41no—
217#95—24no—
218#95—24no—
219#95—24no—
220#95—24no—
221#95—21no—
222#95—21no—
223#95—22no—
224#95—22no—
225#95—22no—
226#95—22no—
227#95—22no—
228C24C2×C22⋊C411yescharacteristic
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4#9514yes—
242C22×C4#9514yes—
243C22×C4C2×C4211yescharacteristic
244C22×C4C2×C22⋊C411yescharacteristic
245C22×C4C2×C22⋊C411yescharacteristic
246C22×C4C2×C22⋊C411yescharacteristic
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C2×C4⋊C411yescharacteristic
249C22×C4C2×C4⋊C411yescharacteristic
250C22×C4C2×C4⋊C411yescharacteristic
251C22×C4#11711yescharacteristic
252C22×C4#11711yescharacteristic
253C22×C4#12011yescharacteristic
254C22×C4#12011yescharacteristic
255C22×C4#12011yescharacteristic
256C22×C4#12011yescharacteristic
257C22×C4#12311yescharacteristic
258C22×C4#12311yescharacteristic
259C22×C4#12311yescharacteristic
260C22×C4#12311yescharacteristic
261M16—44no—
262M16—44no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—82no—
268C2×C8—82no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—44no—
286C4⋊C4—44no—
287C4⋊C4—48no—
288C4⋊C4—84no—
289C22⋊C4—24no—
290C22⋊C4—44no—
291C22⋊C4—42no—
292C42—42no—
293C42—44no—
294C42—42no—
295C42—44no—
296C42—44no—
297C42—48no—
298C42—84no—
299C42C4×D411yescharacteristic
300C42C4×D411yescharacteristic
301C42C4×D411yescharacteristic
302C42C4×D411yescharacteristic
303C42C4×D411yescharacteristic
304C42C4×D411yescharacteristic
305C42C4×D411yescharacteristic
306C42C4×D411yescharacteristic
307C42#12111yescharacteristic
308C42#12111yescharacteristic
309C42#12111yescharacteristic
310C42#12111yescharacteristic
311C42C22⋊Q811yescharacteristic
312C42C22⋊Q811yescharacteristic
313C42C22⋊Q811yescharacteristic
314C42C22⋊Q811yescharacteristic
315C23—22no—
316C23—22no—
317C23—41no—
318C23C2×#9511yescharacteristic
319C23#37911yescharacteristic
320C23#38111yescharacteristic
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4C4×C22⋊C411yescharacteristic
358C2×C4C4×C22⋊C411yescharacteristic
359C2×C4#38011yescharacteristic
360C2×C4#38011yescharacteristic
361C2×C4#38511yescharacteristic
362C2×C4#38511yescharacteristic
363C2×C4#38511yescharacteristic
364C2×C4#38511yescharacteristic
365C2×C4#38611yescharacteristic
366C2×C4#38611yescharacteristic
367C2×C4#38611yescharacteristic
368C2×C4#38611yescharacteristic
369C8—82no—
370C8—82no—
371C8—82no—
372C8—82no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—44no—
381C22C22⋊#9511yescharacteristic
382C22#179112yes—
383C22#182712yes—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—44no—
396C4—44no—
397C4—44no—
398C4—82no—
399C4—84no—
400C4#191212yes—
401C2—22no—
402C2—22no—
403C2—41no—
404C2#1074111yescharacteristic
405C2#1074711yescharacteristic
406C2#1075811yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
25. #1998C4semidirect
29. #1470C4semidirect

Maximal subgroups

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

subgroupindex
#342392
#218302
C2×#14702
#79512
#79492
#78692
#78572