Finite Group Databasebeta

← #118200

Subgroups — #118200

Order 512.

586 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21830C211yesmaximal, characteristic
2C2×#1989C211yesmaximal, characteristic
3#17807C211yesmaximal, characteristic
4#17667C211yesmaximal, characteristic
5#8098C211yesmaximal, characteristic
6#8082C211yesmaximal, characteristic
7#7950C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1998—22no—
16#1998—21no—
17#1998—21no—
18#1989—22no—
19#1989—22no—
20#1821—21no—
21#1821—21no—
22C2×#340—21no—
23C2×#340—21no—
24#1573—22no—
25#1571—21no—
26#1570—21no—
27#1565—22no—
28#1534C414yescomplemented
29#1528—22no—
30#1528—22no—
31#1303—22no—
32#1301—22no—
33#1285—22no—
34C23×C8—21no—
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×#125—21no—
44C2×#125—21no—
45C2×#125C2×C412yes—
46C2×#125Q812yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C42—21no—
53C22×C42C2311yescharacteristic
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432C2×C412yes—
60#432C2×C412yes—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#431—21no—
70#423—21no—
71#423—21no—
72#423D412yes—
73#423D411yescharacteristic
74#423D411yescharacteristic
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8D412yes—
81#407—21no—
82#407—21no—
83#407—21no—
84#407—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16D412yes—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4D412yes—
93C2×#95—21no—
94#343—22no—
95#343—22no—
96#343—22no—
97#343—22no—
98#340—24no—
99#340—24no—
100#335—24no—
101#334—24no—
102#330—28no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—41no—
106C23×C4C2×D411yescharacteristic
107C23×C4#4111yescharacteristic
108C23×C4#4111yescharacteristic
109C2×M16—22no—
110C2×M16—21no—
111C2×M16—21no—
112C2×M16—22no—
113C2×M16—41no—
114C22×C8—22no—
115C22×C8—44no—
116C22×C8—41no—
117C22×C8—41no—
118#125—22no—
119#125—22no—
120#125—22no—
121#125—22no—
122#125—22no—
123#125—22no—
124#125—22no—
125#125—22no—
126#125—41no—
127#125—41no—
128#125—41no—
129#125—41no—
130#125—41no—
131#125—41no—
132#125—41no—
133#125—41no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4C4⋊C412yes—
161C2×C4⋊C4C4⋊C412yes—
162C2×C42—22no—
163C2×C42—41no—
164C2×C42—82no—
165C2×C42C22×C411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×Q811yescharacteristic
173C2×C42#4111yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—21no—
180C4⋊C8—22no—
181C4⋊C8—21no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199#97—22no—
200#97—41no—
201#97—41no—
202#97C22⋊C414yes—
203C4×C8—22no—
204C4×C8—41no—
205C4×C8—41no—
206C4×C8—41no—
207#95—22no—
208#95—41no—
209C24#12311yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4—42no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—82no—
224C22×C4—82no—
225C22×C4—81no—
226C22×C4—81no—
227C22×C4—82no—
228C22×C4C2×C4⋊C411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12011yescharacteristic
232C22×C4#12011yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4#12311yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12411yescharacteristic
243C22×C4#12411yescharacteristic
244C22×C4#12611yescharacteristic
245C22×C4#12611yescharacteristic
246M16—44no—
247M16—42no—
248M16—42no—
249M16—42no—
250M16—42no—
251M16—81no—
252M16—81no—
253C2×C8—24no—
254C2×C8—44no—
255C2×C8—42no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—82no—
261C2×C8—82no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—44no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C42—82no—
282C42—82no—
283C42C2×C22⋊C411yescharacteristic
284C42#11711yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42#12011yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42C22⋊Q811yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42#12311yescharacteristic
297C42#12411yescharacteristic
298C42#12711yescharacteristic
299C23—21no—
300C23—21no—
301C23—22no—
302C23—22no—
303C23#38511yescharacteristic
304C23#39411yescharacteristic
305C23#39711yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
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—44no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—88no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4#38011yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38611yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#39011yescharacteristic
346C2×C4#39211yescharacteristic
347C2×C4#39311yescharacteristic
348C2×C4#39411yescharacteristic
349C2×C4#39611yescharacteristic
350C2×C4#39611yescharacteristic
351C2×C4#39911yescharacteristic
352C2×C4#45412yes—
353C2×C4#45612yes—
354C8—44no—
355C8—82no—
356C8—82no—
357C8—81no—
358C8—81no—
359C8—82no—
360C22—24no—
361C22—24no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22#143911yescharacteristic
369C22#185712yes—
370C22#204811yescharacteristic
371C22#204911yescharacteristic
372C22#208012yes—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—84no—
384C4—82no—
385C4—82no—
386C4#200311yescharacteristic
387C4#200511yescharacteristic
388C4#203812yes—
389C2—21no—
390C2—21no—
391C2—22no—
392C2—22no—
393C2#1108611yescharacteristic
394C2#1112011yescharacteristic
395C2#1113611yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ 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
28. #1534C4semidirect

Maximal subgroups

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

subgroupindex
#218302
C2×#19892
#178072
#176672
#80982
#80822
#79502