Finite Group Databasebeta

← #100644

Subgroups — #100644

Order 512.

539 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29756C211yesmaximal, characteristic
2#14439C211yesmaximal, characteristic
3#9912C211yesmaximal, characteristic
4#9884C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7039C211yesmaximal, characteristic
7#7024C211yesmaximal, characteristic
8C2×#483—21no—
9#2857C2211yescharacteristic
10C2×#389—21no—
11C2×#389C2211yescharacteristic
12C2×#387—21no—
13#2084C412yescomplemented
14#2066—22no—
15#2043C412yescomplemented
16#1872—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20#1442—21no—
21#1441—21no—
22#1441—21no—
23#1436—21no—
24C4⋊#95C2211yescharacteristic
25#1434C2211yescharacteristic
26#1294—21no—
27#1294—21no—
28#1294—21no—
29#1294—21no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41#483—42no—
42#483—42no—
43C2×#106—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×#103—22no—
47C2×#103—22no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—42no—
58#389—42no—
59#389C2×C412yes—
60#389D412yes—
61#387—42no—
62#387—42no—
63#384C2×C411yescharacteristic
64#380—21no—
65#380—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95D411yescharacteristic
76C2×#95D411yescharacteristic
77C2×#95D411yescharacteristic
78C2×#95D411yescharacteristic
79#340—22no—
80#336—21no—
81#336—21no—
82#336C2×C412yes—
83C22×Q8—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C22×C8—22no—
94C22×C8—41no—
95C22×C8—41no—
96C4⋊Q8—81no—
97C22⋊Q8—41no—
98C22⋊Q8—41no—
99C22⋊Q8—41no—
100C22⋊Q8—41no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—81no—
125C2×C4⋊C4—81no—
126C2×C4⋊C4—81no—
127C2×C4⋊C4—81no—
128C2×C4⋊C4C22⋊C412yes—
129C2×C4⋊C4C22⋊C412yes—
130C2×C4⋊C4D812yes—
131C2×C4⋊C4SD1612yes—
132C2×C22⋊C4—41no—
133C2×C42—42no—
134C2×C42—42no—
135C2×C42—81no—
136C2×C42—81no—
137C2×C42C22×C411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141#106—44no—
142C4⋊C8—81no—
143C4⋊C8—81no—
144#103—44no—
145#103—82no—
146C22⋊C8—22no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C4×C8—81no—
153#95—22no—
154#95—22no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—41no—
159#95—41no—
160#95—42no—
161#95—42no—
162#95—42no—
163#95—42no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—41no—
170#95—81no—
171#95—81no—
172#95SD1612yes—
173C24#12011yescharacteristic
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—41no—
177C2×Q8—41no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
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—41no—
217C22×C4—41no—
218C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4C2×D811yescharacteristic
237C22×C4C2×SD1611yescharacteristic
238C22×C4C2×SD1611yescharacteristic
239C22×C4#13511yescharacteristic
240C22×C4AGL(1,ℤ/8)11yescharacteristic
241C22×C4AGL(1,ℤ/8)11yescharacteristic
242C22×C4#13711yescharacteristic
243C22×C4#13711yescharacteristic
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—81no—
252C2×C8—81no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—82no—
269C4⋊C4—82no—
270C4⋊C4—84no—
271C4⋊C4—84no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4#10214yes—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C42—84no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23#38611yescharacteristic
287C23#44711yescharacteristic
288C23#44811yescharacteristic
289C23#45011yescharacteristic
290C23#45211yescharacteristic
291C23#45511yescharacteristic
292C23#45611yescharacteristic
293Q8—82no—
294Q8—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
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×C4C2×#10211yescharacteristic
368C2×C4#41711yescharacteristic
369C2×C4C4×SD1611yescharacteristic
370C2×C4#44011yescharacteristic
371C2×C4#46111yescharacteristic
372C2×C4#46311yescharacteristic
373C2×C4#48011yescharacteristic
374C2×C4#48111yescharacteristic
375C8—82no—
376C8—82no—
377C8—161no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22#163911yescharacteristic
391C22#164311yescharacteristic
392C22#164711yescharacteristic
393C22#165111yescharacteristic
394C22#187411yescharacteristic
395C22#187711yescharacteristic
396C22#188211yescharacteristic
397C22#190511yescharacteristic
398C22#190611yescharacteristic
399C22#191211yescharacteristic
400C22#191311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—44no—
410C4—41no—
411C4—41no—
412C4—82no—
413C4—82no—
414C4—82no—
415C4—161no—
416C4—161no—
417C4—161no—
418C4—161no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2#898511yescharacteristic
424C2#918011yescharacteristic
425C2#920411yescharacteristic
426C2#927511yescharacteristic
427C2#929611yescharacteristic
428C2#934211yescharacteristic
429C2#938011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
13. #2084C4semidirect
15. #2043C4semidirect

Maximal subgroups

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

subgroupindex
#297562
#144392
#99122
#98842
#75732
#70392
#70242