Finite Group Databasebeta

← #100646

Subgroups — #100646

Order 512.

489 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 489 conjugacy classes of subgroups — too many to draw. Only its 96 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#29757C211yesmaximal, characteristic
2#14470C211yesmaximal, characteristic
3#9912C211yesmaximal, characteristic
4#9884C211yesmaximal, characteristic
5#7576C211yesmaximal, characteristic
6#7039C211yesmaximal, characteristic
7#7024C211yesmaximal, characteristic
8C2×#484—21no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11#2083C412yescomplemented
12#2068—22no—
13#2043C412yescomplemented
14#1872—21no—
15#1797C2211yescharacteristic
16#1797C2211yescharacteristic
17C4×C22⋊C8C2211yescharacteristic
18#1445—21no—
19#1445—21no—
20#1442—21no—
21#1436—21no—
22#1436—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⋊C4D411yescharacteristic
36C22×C4⋊C4D411yescharacteristic
37C22×C42—21no—
38C22×C42C2311yescharacteristic
39#484—42no—
40#484—42no—
41C2×#107—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#103—22no—
45C2×#103—22no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389C2×C412yes—
56#389D412yes—
57#384C2×C411yescharacteristic
58#380—21no—
59#380—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—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95D411yescharacteristic
72C2×#95D411yescharacteristic
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75#340—22no—
76#336—21no—
77#336—21no—
78#336C2×C412yes—
79C22×Q8—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C22×C8—22no—
90C22×C8—41no—
91C22×C8—41no—
92C4⋊Q8—81no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C22⋊Q8—41no—
96C22⋊Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—81no—
115C2×C4⋊C4—81no—
116C2×C4⋊C4—81no—
117C2×C4⋊C4—81no—
118C2×C4⋊C4C22⋊C412yes—
119C2×C4⋊C4C22⋊C412yes—
120C2×C22⋊C4—41no—
121C2×C42—81no—
122C2×C42—81no—
123C2×C42—81no—
124C2×C42—81no—
125C2×C42C22×C411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129#107—44no—
130C4⋊C8—81no—
131C4⋊C8—81no—
132#103—44no—
133#103—82no—
134C22⋊C8—22no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C4×C8—81no—
141#95—22no—
142#95—22no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—41no—
147#95—41no—
148#95—42no—
149#95—42no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—81no—
157#95—81no—
158#95—81no—
159#95—81no—
160#95—81no—
161#95—81no—
162#95Q1612yes—
163C24#12011yescharacteristic
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—41no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4C2×Q1611yescharacteristic
227C22×C4#13511yescharacteristic
228C22×C4#13511yescharacteristic
229C22×C4#13511yescharacteristic
230C22×C4AGL(1,ℤ/8)11yescharacteristic
231C22×C4AGL(1,ℤ/8)11yescharacteristic
232C22×C4#13711yescharacteristic
233C22×C4#13711yescharacteristic
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—81no—
239C2×C8—81no—
240C2×C8—81no—
241C2×C8—81no—
242C2×C8—81no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—81no—
251C4⋊C4—82no—
252C4⋊C4—82no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—82no—
258C4⋊C4—82no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C22⋊C4—81no—
262C22⋊C4—81no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—84no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23#38611yescharacteristic
273C23#44911yescharacteristic
274C23#44911yescharacteristic
275C23#45111yescharacteristic
276C23#45211yescharacteristic
277C23#45511yescharacteristic
278C23#45611yescharacteristic
279Q8—82no—
280Q8—82no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
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#41611yescharacteristic
354C2×C4#41811yescharacteristic
355C2×C4C4×Q1611yescharacteristic
356C2×C4#44111yescharacteristic
357C2×C4#46211yescharacteristic
358C2×C4#46411yescharacteristic
359C2×C4#48211yescharacteristic
360C2×C4#48211yescharacteristic
361C8—82no—
362C8—82no—
363C8—161no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22#164011yescharacteristic
377C22#164411yescharacteristic
378C22#164811yescharacteristic
379C22#165211yescharacteristic
380C22#187511yescharacteristic
381C22#187811yescharacteristic
382C22#188211yescharacteristic
383C22#190411yescharacteristic
384C22#190611yescharacteristic
385C22#191211yescharacteristic
386C22#191311yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—82no—
399C4—82no—
400C4—82no—
401C4—161no—
402C4—161no—
403C4—161no—
404C4—161no—
405C2—21no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2#898611yescharacteristic
410C2#918111yescharacteristic
411C2#920611yescharacteristic
412C2#927611yescharacteristic
413C2#929811yescharacteristic
414C2#934111yescharacteristic
415C2#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
11. #2083C4semidirect
13. #2043C4semidirect

Maximal subgroups

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

subgroupindex
#297572
#144702
#99122
#98842
#75762
#70392
#70242