Finite Group Databasebeta

← #96935

Subgroups — #96935

Order 512.

790 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2863C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4C2×#1272C212yesmaximal
5C2×#1271C212yesmaximal
6#2863—24no—
7#2863—24no—
8C2×#391C411yescharacteristic
9C2×#391C411yescharacteristic
10C2×#391C2211yescharacteristic
11C2×#389C411yescharacteristic
12C2×#389C411yescharacteristic
13C2×#389C2211yescharacteristic
14C2×#387—21no—
15C2×#387—21no—
16C2×#387—21no—
17C2×#383—21no—
18C2×C43C2211yescharacteristic
19C2×#336—21no—
20C2×#336—21no—
21C2×#336—21no—
22C2×#336—21no—
23C2×#336C2212yes—
24C2×#336C2212yes—
25#1272—24no—
26#1271—24no—
27C23×Q8C2×C411yescharacteristic
28C23×C8—22no—
29C23×C8—22no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C42C2×C411yescharacteristic
37C22×C42C2×C411yescharacteristic
38C22×C42D411yescharacteristic
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C22×C42D411yescharacteristic
42C22×C42C2311yescharacteristic
43#391—22no—
44#391—22no—
45#391—22no—
46#391—22no—
47#391—22no—
48#391D414yes—
49#389—22no—
50#389—22no—
51#389—22no—
52#389—22no—
53#389—22no—
54#389D414yes—
55#387—28no—
56#387—28no—
57#387—28no—
58#383—28no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C43—22no—
69C43—22no—
70#336—24no—
71#336—24no—
72#336—22no—
73#336—22no—
74#336—22no—
75#336—22no—
76#336—42no—
77#336—42no—
78C22×Q8—21no—
79C22×Q8—22no—
80C22×Q8—22no—
81C22×Q8—41no—
82C22×Q8—41no—
83C22×Q8—41no—
84C22×Q8—41no—
85C22×Q8C22⋊C412yes—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C22⋊C411yescharacteristic
91C23×C4C22⋊C411yescharacteristic
92C23×C4C22⋊C411yescharacteristic
93C23×C4C22⋊C411yescharacteristic
94C23×C4C22×C411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C22×C8—24no—
98C22×C8—24no—
99C22×C8—42no—
100C22×C8—42no—
101C22×C8—42no—
102C22×C8—42no—
103C22×C8—42no—
104C22×C8—42no—
105C22×C8—42no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—42no—
109C22×C8—42no—
110C22×C8—42no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—24no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4C22⋊C412yes—
131C2×C4⋊C4C22⋊C412yes—
132C2×C4⋊C4C22⋊C412yes—
133C2×C42—22no—
134C2×C42—22no—
135C2×C42—22no—
136C2×C42—22no—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—21no—
140C2×C42—21no—
141C2×C42—22no—
142C2×C42—22no—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—41no—
150C2×C42—41no—
151C2×C42—41no—
152C2×C42—41no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42SD1612yes—
156C2×C42Q1612yes—
157C2×C42C2×D412yes—
158C2×C42C2×D412yes—
159#95—24no—
160#95—24no—
161#95—24no—
162#95—24no—
163#95—24no—
164#95—24no—
165#95—24no—
166#95—24no—
167#95—24no—
168C24C2×C22⋊C411yescharacteristic
169C2×Q8—24no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—42no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8—82no—
176C2×Q8—82no—
177C2×Q8—82no—
178C2×Q8—82no—
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—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4#10312yes—
244C22×C4#10312yes—
245C22×C4#10412yes—
246C22×C4#10412yes—
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C2×C22⋊C411yescharacteristic
249C22×C4#12012yes—
250C22×C4#12012yes—
251C22×C4#13112yes—
252C22×C4#13112yes—
253C22×C4C2×SD1611yescharacteristic
254C22×C4C2×Q1611yescharacteristic
255C22×C4#13512yes—
256C22×C4AGL(1,ℤ/8)11yescharacteristic
257C22×C4#13712yes—
258C22×C4#13711yescharacteristic
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—44no—
264C2×C8—44no—
265C2×C8—82no—
266C2×C8—82no—
267C2×C8—82no—
268C2×C8—82no—
269C2×C8—82no—
270C2×C8—82no—
271C2×C8—82no—
272C2×C8—82no—
273C4⋊C4—24no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—48no—
280C4⋊C4—42no—
281C4⋊C4—44no—
282C4⋊C4—44no—
283C42—24no—
284C42—24no—
285C42—42no—
286C42—42no—
287C42—44no—
288C42—44no—
289C42—42no—
290C42—42no—
291C42—42no—
292C42—42no—
293C42—42no—
294C42—42no—
295C23#37911yescharacteristic
296C23#40811yescharacteristic
297C23#40811yescharacteristic
298C23#41011yescharacteristic
299C23#41011yescharacteristic
300C23#41311yescharacteristic
301C23#41311yescharacteristic
302C23C2×#10311yescharacteristic
303C23#41611yescharacteristic
304C23#41711yescharacteristic
305C23#41911yescharacteristic
306C23C2×#10411yescharacteristic
307C23C2×#10411yescharacteristic
308C23#42111yescharacteristic
309C23#42111yescharacteristic
310Q8—84no—
311Q8—84no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4#40812yes—
393C2×C4#40812yes—
394C2×C4#44812yes—
395C2×C4#44912yes—
396C2×C4#45112yes—
397C2×C4#45212yes—
398C8—84no—
399C8—84no—
400C22#147311yescharacteristic
401C22#147311yescharacteristic
402C22#147311yescharacteristic
403C22#147311yescharacteristic
404C22#148111yescharacteristic
405C22#148211yescharacteristic
406C22#148311yescharacteristic
407C22#148511yescharacteristic
408C22#149311yescharacteristic
409C22#149411yescharacteristic
410C22#149511yescharacteristic
411C22#149711yescharacteristic
412C22#150011yescharacteristic
413C22#150311yescharacteristic
414C22#150611yescharacteristic
415C22#150911yescharacteristic
416C22#151211yescharacteristic
417C22#151511yescharacteristic
418C22#151811yescharacteristic
419C22#152111yescharacteristic
420C22#152411yescharacteristic
421C22#152911yescharacteristic
422C22#153211yescharacteristic
423C22#153511yescharacteristic
424C22#154211yescharacteristic
425C22#155011yescharacteristic
426C22#155411yescharacteristic
427C22#155911yescharacteristic
428C22#178011yescharacteristic
429C22#178211yescharacteristic
430C22#178511yescharacteristic
431C22#178711yescharacteristic
432C22#178811yescharacteristic
433C22#178911yescharacteristic
434C22#178911yescharacteristic
435C4—22no—
436C4—22no—
437C4—22no—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C4—82no—
448C4—82no—
449C2#766911yescharacteristic
450C2#767311yescharacteristic
451C2#768911yescharacteristic
452C2#769311yescharacteristic
453C2#770911yescharacteristic
454C2#771311yescharacteristic
455C2#772911yescharacteristic
456C2#773311yescharacteristic
457C2#830911yescharacteristic
458C2#831411yescharacteristic
459C2#831511yescharacteristic
460C2#833011yescharacteristic
461C2#833311yescharacteristic
462C2#833611yescharacteristic
463C2#834311yescharacteristic
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
C2×#28632
#107952
C2×#12722
C2×#12712