Finite Group Databasebeta

← #102420

Subgroups — #102420

Order 512.

718 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14709C211yesmaximal, characteristic
2#10832C211yesmaximal, characteristic
3#10693C211yesmaximal, characteristic
4#7025C212yesmaximal
5#7025C212yesmaximal
6C22×#125C411yescharacteristic
7C22×C4⋊C8—21no—
8C22×#97—21no—
9C2×#382C411yescharacteristic
10C2×C43C2211yescharacteristic
11C2×#336—21no—
12C2×#336—21no—
13C2×#336C2212yes—
14C2×#336C2212yes—
15#1436—21no—
16#1436—21no—
17#1436—21no—
18#1436—21no—
19C4⋊#95C411yescharacteristic
20C4⋊#95C411yescharacteristic
21C4⋊#95C2211yescharacteristic
22C4⋊#95C2211yescharacteristic
23C23×C8—22no—
24C23×C8—22no—
25C2×#125—22no—
26C2×#125—22no—
27C2×#125—42no—
28C2×#125—42no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C4⋊C4C2×C411yescharacteristic
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C42C2×C411yescharacteristic
36C22×C42C2×C411yescharacteristic
37C22×C42D411yescharacteristic
38C22×C42D411yescharacteristic
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C22×C42C2311yescharacteristic
42C2×C4⋊C8—24no—
43C2×C4⋊C8—42no—
44C2×C4⋊C8—42no—
45C2×#97—24no—
46C2×#97—42no—
47C2×#97—42no—
48#382—42no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C43—42no—
60#336—24no—
61#336—22no—
62#336—24no—
63#336—42no—
64#336Q814yes—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22×C411yescharacteristic
74C23×C4C2×D411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C22×C8—24no—
77C22×C8—24no—
78C22×C8—24no—
79C22×C8—24no—
80C22×C8—42no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8—42no—
84C22×C8—42no—
85C22×C8—42no—
86C22×C8—42no—
87C22×C8—42no—
88C22×C8—42no—
89C22×C8—42no—
90#125—48no—
91#125—48no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—24no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4M1612yes—
111C2×C4⋊C4M1612yes—
112C2×C42—22no—
113C2×C42—22no—
114C2×C42—22no—
115C2×C42—22no—
116C2×C42—22no—
117C2×C42—22no—
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—22no—
125C2×C42—22no—
126C2×C42—22no—
127C2×C42—22no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42C2×Q812yes—
137C2×C42#4112yes—
138C4⋊C8—48no—
139#97—48no—
140#95—42no—
141#95—42no—
142#95—42no—
143#95—42no—
144#95—42no—
145#95—42no—
146#95—42no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153C24C2×C22⋊C411yescharacteristic
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4#9912yes—
217C22×C4#10012yes—
218C22×C4#10112yes—
219C22×C4#10412yes—
220C22×C4#10412yes—
221C22×C4#10412yes—
222C22×C4C4×Q812yes—
223C22×C4C22⋊Q812yes—
224C22×C4#12411yescharacteristic
225C22×C4C4⋊Q811yescharacteristic
226C22×C4C2×M1611yescharacteristic
227C22×C4C2×M1611yescharacteristic
228C22×C4#13112yes—
229C22×C4#13512yes—
230C22×C4AGL(1,ℤ/8)11yescharacteristic
231C22×C4AGL(1,ℤ/8)11yescharacteristic
232C22×C4AGL(1,ℤ/8)11yescharacteristic
233C22×C4#13711yescharacteristic
234C22×C4#13711yescharacteristic
235C22×C4#13711yescharacteristic
236C2×C8—28no—
237C2×C8—44no—
238C2×C8—44no—
239C2×C8—44no—
240C2×C8—44no—
241C2×C8—44no—
242C2×C8—44no—
243C2×C8—44no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—82no—
249C2×C8—82no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—48no—
255C4⋊C4—48no—
256C4⋊C4—82no—
257C4⋊C4—82no—
258C42—24no—
259C42—24no—
260C42—24no—
261C42—24no—
262C42—24no—
263C42—24no—
264C42—42no—
265C42—42no—
266C42—44no—
267C42—44no—
268C42—42no—
269C42—42no—
270C23#39111yescharacteristic
271C23#40711yescharacteristic
272C23#40811yescharacteristic
273C23C2×#9911yescharacteristic
274C23#41011yescharacteristic
275C23C2×#10011yescharacteristic
276C23C2×#10111yescharacteristic
277C23#41611yescharacteristic
278C23#41711yescharacteristic
279C23#41711yescharacteristic
280C23#41711yescharacteristic
281C23C2×#10411yescharacteristic
282C23C2×#10411yescharacteristic
283C23C2×#10411yescharacteristic
284C23#42111yescharacteristic
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
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—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4#33014yes—
369C2×C4#44612yes—
370C2×C4#44612yes—
371C2×C4#47812yes—
372C2×C4#47912yes—
373C2×C4#49011yescharacteristic
374C2×C4#49111yescharacteristic
375C2×C4#50111yescharacteristic
376C2×C4#50111yescharacteristic
377C8—48no—
378C8—84no—
379C22#146211yescharacteristic
380C22#146711yescharacteristic
381C22#146911yescharacteristic
382C22#147211yescharacteristic
383C22#148311yescharacteristic
384C22#148311yescharacteristic
385C22#148811yescharacteristic
386C22#148911yescharacteristic
387C22#148911yescharacteristic
388C22#148911yescharacteristic
389C22#149411yescharacteristic
390C22#149511yescharacteristic
391C22#150011yescharacteristic
392C22#150111yescharacteristic
393C22#150411yescharacteristic
394C22#150411yescharacteristic
395C22#150911yescharacteristic
396C22#150911yescharacteristic
397C22#151211yescharacteristic
398C22#151311yescharacteristic
399C22C2×#33011yescharacteristic
400C22#152511yescharacteristic
401C22#152811yescharacteristic
402C22#153011yescharacteristic
403C22#155111yescharacteristic
404C22#155211yescharacteristic
405C22#156011yescharacteristic
406C22#156111yescharacteristic
407C22#198511yescharacteristic
408C22#198611yescharacteristic
409C22#198911yescharacteristic
410C22#199211yescharacteristic
411C22#199411yescharacteristic
412C22#199611yescharacteristic
413C22#199711yescharacteristic
414C4—24no—
415C4—22no—
416C4—22no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—22no—
423C4—42no—
424C4—42no—
425C4—42no—
426C4—82no—
427C4—82no—
428C4—161no—
429C4—161no—
430C2#761211yescharacteristic
431C2#761911yescharacteristic
432C2#763111yescharacteristic
433C2#763611yescharacteristic
434C2#767611yescharacteristic
435C2#769111yescharacteristic
436C2#769611yescharacteristic
437C2#771111yescharacteristic
438C2#986711yescharacteristic
439C2#987611yescharacteristic
440C2#988211yescharacteristic
441C2#988711yescharacteristic
442C2#989111yescharacteristic
443C2#990611yescharacteristic
444C2#991011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#147092
#108322
#106932
#70252