Finite Group Databasebeta

← #109963

Subgroups — #109963

Order 512.

556 conjugacy classes of subgroups.

The subgroup lattice has 385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20534C211yesmaximal, characteristic
2C2×#1573C211yesmaximal, characteristic
3#10835C211yesmaximal, characteristic
4C2×#1302C211yesmaximal, characteristic
5C2×#1302C211yesmaximal, characteristic
6#7908C211yesmaximal, characteristic
7#7879C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×#97C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1771—21no—
16#1771—21no—
17#1771—21no—
18#1771—21no—
19#1749—21no—
20C4×C22⋊C8—21no—
21C2×#336—21no—
22C2×#336—21no—
23#1573—22no—
24#1573C414yescomplemented
25C2×#335—21no—
26C2×#334—21no—
27#1302—22no—
28#1302C414yescomplemented
29#1280C414yes—
30#1277—21no—
31#1277—21no—
32C23×C8—21no—
33C23×C8—21no—
34C22×C4⋊C4Q812yes—
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38#432—21no—
39#432—21no—
40#432—21no—
41#432—21no—
42#432C2×C412yes—
43#432C2×C412yes—
44#432D412yes—
45#432Q812yes—
46#431—21no—
47#431—21no—
48#431—21no—
49#431—21no—
50#431—21no—
51#431—21no—
52#431C2×C412yes—
53#431C2×C412yes—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8C2×C412yes—
62C2×C4⋊C8D411yescharacteristic
63C2×C4⋊C8D411yescharacteristic
64C2×C4⋊C8D411yescharacteristic
65C2×C4⋊C8D411yescharacteristic
66C2×C22⋊C8—21no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8C2×C412yes—
69C2×C22⋊C8C2×C412yes—
70C2×#97—21no—
71C2×#97—21no—
72C2×#97—21no—
73C2×#97—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97C2×C412yes—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C2×#95C2×C412yes—
89#336—21no—
90#336—21no—
91#336—21no—
92#336—21no—
93#336—42no—
94#336—42no—
95#335—24no—
96#334—24no—
97C23×C4C4⋊C412yes—
98C23×C4C4⋊C412yes—
99C23×C4C22×C411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×Q811yescharacteristic
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—21no—
107C22×C8—21no—
108C22×C8—21no—
109C22×C8—21no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—42no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C22×C411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×Q811yescharacteristic
140C2×C42#4111yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—21no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C4⋊C8C22⋊C412yes—
159C4⋊C8C22⋊C412yes—
160C4⋊C8C4⋊C412yes—
161C4⋊C8C4⋊C412yes—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—22no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8C4214yes—
170#97—22no—
171#97—22no—
172#97—22no—
173#97—22no—
174#97—22no—
175#97—22no—
176#97—41no—
177#97—41no—
178#97—81no—
179#97—81no—
180C4×C8—22no—
181C4×C8—22no—
182C4×C8—41no—
183C4×C8—41no—
184C4×C8—81no—
185C4×C8—81no—
186#95—22no—
187#95—22no—
188C24C2×C4⋊C411yescharacteristic
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4#10814yes—
206C22×C4C2×C4211yescharacteristic
207C22×C4#11711yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4C4×D411yescharacteristic
212C22×C4C4×D411yescharacteristic
213C22×C4C4×Q811yescharacteristic
214C22×C4C4×Q811yescharacteristic
215C22×C4C4×Q811yescharacteristic
216C22×C4#12011yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4C22⋊Q811yescharacteristic
219C22×C4C22⋊Q811yescharacteristic
220C22×C4C22⋊Q811yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12511yescharacteristic
223C22×C4C4⋊Q811yescharacteristic
224C2×C8—24no—
225C2×C8—24no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—44no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—44no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—81no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—81no—
254C4⋊C4—44no—
255C4⋊C4—44no—
256C42—41no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—81no—
261C42—81no—
262C42C2×C22⋊C411yescharacteristic
263C42C2×C4⋊C411yescharacteristic
264C42#11711yescharacteristic
265C42#11711yescharacteristic
266C42C4×D411yescharacteristic
267C42C4×D411yescharacteristic
268C42C4×D411yescharacteristic
269C42C4×Q811yescharacteristic
270C42#12111yescharacteristic
271C42C22⋊Q811yescharacteristic
272C42#12311yescharacteristic
273C42#12311yescharacteristic
274C42#12411yescharacteristic
275C42#12511yescharacteristic
276C42#12611yescharacteristic
277C42#12611yescharacteristic
278C23—21no—
279C23—21no—
280C23—22no—
281C23C4×C4⋊C411yescharacteristic
282C23#38511yescharacteristic
283C23#38911yescharacteristic
284C23C2×#10812yes—
285C23#43012yes—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
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—21no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4C4×C22⋊C411yescharacteristic
321C2×C4C4×C4⋊C411yescharacteristic
322C2×C4#38511yescharacteristic
323C2×C4#38611yescharacteristic
324C2×C4#38711yescharacteristic
325C2×C4#38711yescharacteristic
326C2×C4#38711yescharacteristic
327C2×C4#38711yescharacteristic
328C2×C4#38811yescharacteristic
329C2×C4#38811yescharacteristic
330C2×C4#38911yescharacteristic
331C2×C4#39111yescharacteristic
332C2×C4#45311yescharacteristic
333C2×C4#45411yescharacteristic
334C2×C4#45511yescharacteristic
335C2×C4#45611yescharacteristic
336C8—44no—
337C8—44no—
338C8—42no—
339C8—42no—
340C8—42no—
341C8—42no—
342C8—82no—
343C8—82no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22#143611yescharacteristic
353C22C4×#10811yescharacteristic
354C22#177811yescharacteristic
355C22#185512yes—
356C22#185611yescharacteristic
357C22#185711yescharacteristic
358C22#186812yes—
359C22#195012yes—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—44no—
371C4—82no—
372C4#185911yescharacteristic
373C4#186011yescharacteristic
374C4#188211yescharacteristic
375C4#188311yescharacteristic
376C2—22no—
377C2—21no—
378C2—21no—
379C2#886412yes—
380C2#886512yes—
381C2#1089911yescharacteristic
382C2#1091111yescharacteristic
383C2#1092011yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C2×C4⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
24. #1573C4semidirect
28. #1302C4semidirect

Maximal subgroups

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

subgroupindex
#205342
C2×#15732
#108352
C2×#13022
#79082
#78792