Finite Group Databasebeta

← #388012

Subgroups — #388012

Order 512.

918 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1820C211yesmaximal, characteristic
2#11318C212yesmaximal
3#11279C212yesmaximal
4#11070C211yesmaximal, characteristic
5#11070C211yesmaximal, characteristic
6#10936C212yesmaximal
7#10915C212yesmaximal
8#10829C212yesmaximal
9#10736C212yesmaximal
10C22×#117C2211yescharacteristic
11#2315C2211yescharacteristic
12#2315C2211yescharacteristic
13C2×#381C2212yes—
14C2×#381C2212yes—
15C2×#381C2211yescharacteristic
16C2×#381C2211yescharacteristic
17#2273C2212yes—
18#1820C418yescomplemented
19C2×#342C2212yes—
20C2×#342C2212yes—
21C2×#342C2212yes—
22C2×#342C2212yes—
23C2×#342C2212yes—
24C2×#342C2212yes—
25C2×#342C2212yes—
26C2×#342C2211yescharacteristic
27C2×#342C2212yes—
28C2×#342C2211yescharacteristic
29C2×#342C2212yes—
30C2×#342C2212yes—
31C2×#342C2212yes—
32C24×C4C2311yescharacteristic
33C2×#117—22no—
34C2×#117—41no—
35C2×#117—41no—
36C2×#117—41no—
37C2×#117—41no—
38C2×#117C2×C414yes—
39C22×C4⋊C4—21no—
40C22×C22⋊C4C2312yes—
41C22×C22⋊C4C2312yes—
42C22×C22⋊C4C2312yes—
43C22×C22⋊C4C2311yescharacteristic
44C22×C22⋊C4C2311yescharacteristic
45C22×C22⋊C4C2312yes—
46C22×C22⋊C4C2312yes—
47C22×C22⋊C4C2312yes—
48C22×C42—21no—
49#385—24no—
50#385—42no—
51#381—22no—
52#381—22no—
53#381—24no—
54#381—24no—
55#381—41no—
56#381—41no—
57#381—42no—
58#381C2×C414yes—
59#381C2×C414yes—
60#380—41no—
61#380—41no—
62C4×C22⋊C4—24no—
63C4×C22⋊C4—42no—
64C4×C22⋊C4—42no—
65C2×#95—24no—
66C2×#95—41no—
67C2×#95—41no—
68C2×#95—42no—
69#342—24no—
70#342—24no—
71#342—42no—
72#342—42no—
73#342—42no—
74#342—42no—
75#342—41no—
76#342—42no—
77#342—42no—
78#342—42no—
79#342—41no—
80#342C2×C418yes—
81#342C2×C418yes—
82C25C2411yescharacteristic
83C23×C4—22no—
84C23×C4—22no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4—22no—
92C23×C4—22no—
93C23×C4—22no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—22no—
97C23×C4—22no—
98C23×C4C22×C412yes—
99C23×C4#4111yescharacteristic
100C23×C4#4112yes—
101C23×C4#4111yescharacteristic
102C23×C4#4114yes—
103#117—44no—
104#117—44no—
105#117—44no—
106#117—44no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C22⋊C4—22no—
113C2×C22⋊C4—22no—
114C2×C22⋊C4—22no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—22no—
122C2×C22⋊C4—22no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4—22no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—22no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—22no—
133C2×C22⋊C4—22no—
134C2×C22⋊C4—22no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—22no—
140C2×C22⋊C4—22no—
141C2×C22⋊C4—22no—
142C2×C22⋊C4—22no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4C22×C414yes—
152C2×C22⋊C4C22×C412yes—
153C2×C22⋊C4C22×C414yes—
154C2×C22⋊C4C22×C412yes—
155C2×C22⋊C4#4114yes—
156C2×C42—24no—
157C2×C42—42no—
158C2×C42—42no—
159C2×C42—44no—
160#95—44no—
161#95—44no—
162#95—44no—
163#95—44no—
164#95—48no—
165#95—42no—
166#95—44no—
167#95—42no—
168C24—82no—
169C24C23×C411yescharacteristic
170C24C2×#4111yescharacteristic
171C24C2×#4112yes—
172C24C2×#4111yescharacteristic
173C24C2×#4112yes—
174C24H(5,𝔽2)11yescharacteristic
175C24H(5,𝔽2)11yescharacteristic
176C24H(5,𝔽2)12yes—
177C24H(5,𝔽2)11yescharacteristic
178C24H(5,𝔽2)11yescharacteristic
179C242−1+412yes—
180C22×C4—24no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—24no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—24no—
197C22×C4—24no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—24no—
201C22×C4—24no—
202C22×C4—24no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—41no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—41no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—84no—
231C22×C4—84no—
232C22×C4—84no—
233C22×C4—82no—
234C22×C4—82no—
235C22×C4—84no—
236C22×C4—84no—
237C22×C4—84no—
238C22×C4#11712yes—
239C22×C4#11712yes—
240C4⋊C4—48no—
241C4⋊C4—162no—
242C4⋊C4—162no—
243C22⋊C4—24no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—24no—
249C22⋊C4—24no—
250C22⋊C4—24no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—48no—
272C42—164no—
273C23—44no—
274C23—42no—
275C23—42no—
276C23—44no—
277C23—42no—
278C23—81no—
279C23—81no—
280C23—82no—
281C23—81no—
282C23—81no—
283C23—82no—
284C23C2×#11711yescharacteristic
285C23C4×#4112yes—
286C23#51811yescharacteristic
287C23#51811yescharacteristic
288C23#52012yes—
289C23#53811yescharacteristic
290C23#53812yes—
291C23#53811yescharacteristic
292C23#53811yescharacteristic
293C23#53811yescharacteristic
294C23#53912yes—
295C23#54012yes—
296C23#54212yes—
297C23#55112yes—
298C23#55111yescharacteristic
299C23#55112yes—
300C23#55212yes—
301C23#55212yes—
302C23#55312yes—
303C23#55911yescharacteristic
304C23#56011yescharacteristic
305C23#56212yes—
306C23#56311yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—84no—
330C2×C4—84no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—84no—
334C2×C4—84no—
335C2×C4—84no—
336C2×C4—84no—
337C2×C4—84no—
338C2×C4—84no—
339C2×C4—84no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—84no—
343C2×C4—84no—
344C2×C4—84no—
345C2×C4—84no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—162no—
349C2×C4—161no—
350C2×C4—162no—
351C2×C4—161no—
352C2×C4—162no—
353C2×C4—162no—
354C2×C4—162no—
355C22—24no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—24no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—41no—
370C22—42no—
371C22—41no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22#231211yescharacteristic
379C22#233512yes—
380C22#234312yes—
381C22#237411yescharacteristic
382C22#237611yescharacteristic
383C22#275012yes—
384C22#275211yescharacteristic
385C22#276011yescharacteristic
386C22#276112yes—
387C22#276411yescharacteristic
388C22#277111yescharacteristic
389C4—42no—
390C4—42no—
391C4—84no—
392C4—84no—
393C4—82no—
394C4—82no—
395C4—84no—
396C4—84no—
397C4—162no—
398C4—162no—
399C2—21no—
400C2—22no—
401C2—21no—
402C2—21no—
403C2—22no—
404C2—21no—
405C2—22no—
406C2—22no—
407C2—21no—
408C2—21no—
409C2#1450811yescharacteristic
410C2#3270112yes—
subgroupG/H
center, socleC22#2760
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
18. #1820C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18202
#113182
#112792
#110702
#109362
#109152
#108292
#107362