Finite Group Databasebeta

← #119957

Subgroups — #119957

Order 512.

950 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#324C211yesmaximal, characteristic
2#14339C211yesmaximal, characteristic
3#14339C211yesmaximal, characteristic
4#8023C212yesmaximal
5C2×#1289C212yesmaximal
6C23×C4⋊C4C2211yescharacteristic
7C22×C22⋊C8C2212yes—
8C2×#381—21no—
9C2×#381—21no—
10C2×#380C2211yescharacteristic
11C2×#380C2212yes—
12C2×#380C2211yescharacteristic
13C2×#324—24no—
14C2×#324—22no—
15#1441—24no—
16#1441—22no—
17#1441C414yescomplemented
18C22⋊#95—21no—
19C22⋊#95—21no—
20#1294—24no—
21#1289—24no—
22C24×C4D411yescharacteristic
23C24×C4D411yescharacteristic
24C24×C4C2311yescharacteristic
25C23×C8—22no—
26C22×C4⋊C4—22no—
27C22×C4⋊C4—22no—
28C22×C4⋊C4—22no—
29C22×C4⋊C4—22no—
30C22×C4⋊C4—22no—
31C22×C4⋊C4—22no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4C2×C412yes—
35C22×C4⋊C4C2×C412yes—
36C22×C4⋊C4D412yes—
37C22×C22⋊C4—21no—
38C22×C22⋊C4—21no—
39C22×C22⋊C4—22no—
40C2×C22⋊C8—22no—
41C2×C22⋊C8—22no—
42C2×C22⋊C8—22no—
43C2×C22⋊C8—22no—
44C2×C22⋊C8—22no—
45C2×C22⋊C8D414yes—
46#381—42no—
47#381—42no—
48#381—42no—
49#381—42no—
50#380—22no—
51#380—22no—
52#380—22no—
53#380—22no—
54#380—22no—
55#380—22no—
56#380—22no—
57#380—22no—
58C2×#95—24no—
59C2×#95—24no—
60C2×#95—21no—
61C2×#95—24no—
62C2×#95—24no—
63C2×#95C2×C412yes—
64C2×#95D414yes—
65#324—28no—
66C25C2×D411yescharacteristic
67C23×C4—21no—
68C23×C4—22no—
69C23×C4—22no—
70C23×C4—21no—
71C23×C4—22no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—22no—
75C23×C4—21no—
76C23×C4—22no—
77C23×C4—22no—
78C23×C4—21no—
79C23×C4—22no—
80C23×C4—22no—
81C23×C4—24no—
82C23×C4—82no—
83C23×C4—82no—
84C23×C4C22⋊C412yes—
85C23×C4C22⋊C412yes—
86C23×C4D812yes—
87C23×C4SD1612yes—
88C23×C4C22×C411yescharacteristic
89C23×C4C2×D412yes—
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D412yes—
92C23×C4#4112yes—
93C23×C4#4112yes—
94C23×C4#4112yes—
95C23×C4#4112yes—
96C22×C8—24no—
97C22×C8—42no—
98C22×C8—42no—
99C22×C8—84no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—24no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—24no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4—84no—
123C2×C4⋊C4—82no—
124C2×C22⋊C4—41no—
125C2×C22⋊C4—42no—
126C2×C22⋊C4—42no—
127C2×C22⋊C4—41no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—42no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—42no—
135C2×C22⋊C4—42no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—42no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—42no—
140C22⋊C8—24no—
141C22⋊C8—24no—
142C22⋊C8—42no—
143C22⋊C8—42no—
144#95—24no—
145#95—24no—
146#95—24no—
147#95—48no—
148#95—48no—
149#95—42no—
150#95—84no—
151#95—84no—
152C24—42no—
153C24—42no—
154C24C2×C22⋊C411yescharacteristic
155C24#12011yescharacteristic
156C24#12112yes—
157C24#12311yescharacteristic
158C24#12312yes—
159C24C2×D811yescharacteristic
160C24C2×SD1611yescharacteristic
161C24#13512yes—
162C24AGL(1,ℤ/8)11yescharacteristic
163C24#13711yescharacteristic
164C24#13712yes—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—24no—
175C22×C4—24no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4—42no—
185C22×C4—44no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—48no—
200C22×C4—44no—
201C22×C4—44no—
202C22×C4—48no—
203C22×C4—44no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—44no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4—44no—
213C22×C4—82no—
214C22×C4—82no—
215C22×C4—82no—
216C22×C4—82no—
217C22×C4—82no—
218C22×C4—84no—
219C22×C4—84no—
220C22×C4#10214yes—
221C22×C4#11711yescharacteristic
222C22×C4#11711yescharacteristic
223C22×C4C4×D412yes—
224C22×C4C4×D412yes—
225C22×C4#12011yescharacteristic
226C22×C4#12112yes—
227C22×C4#12112yes—
228C22×C4#12112yes—
229C22×C4#12312yes—
230C22×C4#12312yes—
231C22×C4#12312yes—
232C22×C4#12311yescharacteristic
233C22×C4#12412yes—
234C22×C4#12412yes—
235C22×C4#12612yes—
236C22×C4#12612yes—
237C2×C8—44no—
238C2×C8—84no—
239C2×C8—84no—
240C2×C8—84no—
241C4⋊C4—44no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—44no—
245C4⋊C4—84no—
246C4⋊C4—82no—
247C4⋊C4—84no—
248C4⋊C4—82no—
249C4⋊C4—84no—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C22⋊C4—82no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C22⋊C4—81no—
257C22⋊C4—82no—
258C22⋊C4—81no—
259C22⋊C4—82no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—42no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—44no—
273C23—42no—
274C23—44no—
275C23—42no—
276C23#38111yescharacteristic
277C23#38611yescharacteristic
278C23#38611yescharacteristic
279C23#39412yes—
280C23#39712yes—
281C23C2×#10211yescharacteristic
282C23#41611yescharacteristic
283C23#41711yescharacteristic
284C23#41911yescharacteristic
285C23#44711yescharacteristic
286C23#44811yescharacteristic
287C23#45212yes—
288C23#46512yes—
289C23#46612yes—
290C23#46812yes—
291C23#47012yes—
292C23#48011yescharacteristic
293C23#48012yes—
294C23#48111yescharacteristic
295C23#48212yes—
296C23#48312yes—
297C23#48512yes—
298C23#48512yes—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—84no—
330C2×C4—84no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—84no—
334C2×C4—82no—
335C2×C4—84no—
336C2×C4—84no—
337C2×C4—88no—
338C2×C4—84no—
339C2×C4—88no—
340C2×C4—84no—
341C2×C4—84no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—84no—
347C2×C4#38812yes—
348C2×C4#38812yes—
349C2×C4#39412yes—
350C2×C4#39712yes—
351C8—84no—
352C22—21no—
353C22—22no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—24no—
362C22—22no—
363C22—24no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22#144011yescharacteristic
379C22#182311yescharacteristic
380C22#182511yescharacteristic
381C22#187311yescharacteristic
382C22#187411yescharacteristic
383C22#189311yescharacteristic
384C22#189411yescharacteristic
385C22#191212yes—
386C22#191312yes—
387C22#203312yes—
388C22#203512yes—
389C22#207512yes—
390C22#207712yes—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—44no—
396C4—82no—
397C4—162no—
398C4—164no—
399C4—162no—
400C2—21no—
401C2—22no—
402C2—22no—
403C2—22no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—22no—
408C2#920212yes—
409C2#920412yes—
410C2#1115611yescharacteristic
411C2#1117211yescharacteristic
412C2#1119911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
17. #1441C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3242
#143392
#80232
C2×#12892