Finite Group Databasebeta

← #103264

Subgroups — #103264

Order 512.

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

normal subgroups only

This group has 581 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#33108C211yesmaximal, characteristic
2#29967C211yesmaximal, characteristic
3#15194C211yesmaximal, characteristic
4#9884C211yesmaximal, characteristic
5#8706C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C2×#483—21no—
9#2857C2211yescharacteristic
10C2×#389—21no—
11C2×#389C2211yescharacteristic
12C2×C4×C4⋊C4C2211yescharacteristic
13#2099—21no—
14#2088—22no—
15#2058—21no—
16#1981—21no—
17#1948—21no—
18#1927—22no—
19#1872—21no—
20#1853—21no—
21#1824—21no—
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24C4×C22⋊C8C2211yescharacteristic
25#1445—21no—
26#1444—21no—
27#1441—22no—
28C4⋊#95—21no—
29C4⋊#95C2211yescharacteristic
30#1294—22no—
31#1279—22no—
32#1271—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C22⋊Q8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—22no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C4⋊C4D411yescharacteristic
42C22×C42—21no—
43C22×C42C2311yescharacteristic
44#483—42no—
45#483—42no—
46C2×#106—22no—
47C2×#106—22no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8D412yes—
50C2×#103—22no—
51C2×#103—22no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C4×C8—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—42no—
64#389—42no—
65#384D411yescharacteristic
66#380—21no—
67#380—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C2×#95—22no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95D412yes—
79#340—22no—
80#340—22no—
81#340—22no—
82#340—22no—
83#336—21no—
84#336—21no—
85#336D412yes—
86C22×Q8—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—22no—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C22×C8—22no—
96C22×C8—22no—
97C22×C8—41no—
98C4⋊Q8—42no—
99C22⋊Q8—41no—
100C22⋊Q8—41no—
101C22⋊Q8—41no—
102C22⋊Q8—41no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
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—21no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—44no—
129C2×C4⋊C4—44no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—82no—
134C2×C4⋊C4—82no—
135C2×C4⋊C4SD1612yes—
136C2×C4⋊C4SD1612yes—
137C2×C22⋊C4—41no—
138C2×C42—42no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149#106—44no—
150#106—82no—
151C4⋊C8—42no—
152C4⋊C8—42no—
153#103—44no—
154#103—44no—
155C22⋊C8—22no—
156C22⋊C8—41no—
157C22⋊C8—41no—
158C22⋊C8—41no—
159C22⋊C8—41no—
160C22⋊C8—41no—
161C4×C8—42no—
162#95—42no—
163#95—44no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—41no—
170#95—41no—
171#95—41no—
172#95—82no—
173#95—82no—
174C24#12011yescharacteristic
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8—41no—
178C2×Q8—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4#12011yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12711yescharacteristic
226C22×C4C2×SD1611yescharacteristic
227C22×C4C2×SD1611yescharacteristic
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—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—81no—
242C2×C8—81no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—82no—
266C4⋊C4—82no—
267C4⋊C4—88no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C42—22no—
273C42—22no—
274C42—41no—
275C42—41no—
276C42—81no—
277C42—81no—
278C42—81no—
279C42—81no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#39211yescharacteristic
285C23#44811yescharacteristic
286C23#44911yescharacteristic
287C23#45011yescharacteristic
288C23#45211yescharacteristic
289C23#45511yescharacteristic
290C23#45611yescharacteristic
291Q8—82no—
292Q8—82no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—82no—
332C2×C4—82no—
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—82no—
342C2×C4—82no—
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#44811yescharacteristic
353C2×C4#44911yescharacteristic
354C2×C4#45011yescharacteristic
355C2×C4#45211yescharacteristic
356C2×C4#45612yes—
357C2×C4#45812yes—
358C2×C4#46511yescharacteristic
359C2×C4#46511yescharacteristic
360C2×C4#46811yescharacteristic
361C2×C4#46811yescharacteristic
362C8—82no—
363C8—82no—
364C8—82no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#164211yescharacteristic
378C22#164311yescharacteristic
379C22#165011yescharacteristic
380C22#165111yescharacteristic
381C22#200011yescharacteristic
382C22#200011yescharacteristic
383C22#200511yescharacteristic
384C22#200711yescharacteristic
385C22#200811yescharacteristic
386C22#201011yescharacteristic
387C22#202211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—84no—
397C4—82no—
398C4—82no—
399C4—82no—
400C4—161no—
401C4—161no—
402C4—161no—
403C4#160912yes—
404C4#161112yes—
405C2—21no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2#992711yescharacteristic
410C2#993611yescharacteristic
411C2#1000011yescharacteristic
412C2#1001111yescharacteristic
413C2#1023211yescharacteristic
414C2#1024511yescharacteristic
415C2#1032311yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ 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
#331082
#299672
#151942
#98842
#87062
#75762
#70392