Finite Group Databasebeta

← #103268

Subgroups — #103268

Order 512.

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

normal subgroups only

This group has 545 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#33109C211yesmaximal, characteristic
2#29967C211yesmaximal, characteristic
3#15200C211yesmaximal, characteristic
4#9884C211yesmaximal, characteristic
5#8707C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C2×#484—21no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12#2099—21no—
13#2088—22no—
14#2058—21no—
15#1981—21no—
16#1947—21no—
17#1928—22no—
18#1872—21no—
19#1853—21no—
20#1824—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24#1445—21no—
25#1442—22no—
26#1442—21no—
27C4⋊#95—21no—
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—21no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C42—21no—
42C22×C42C2311yescharacteristic
43#484—42no—
44#484—42no—
45C2×#107—22no—
46C2×#106—22no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D412yes—
49C2×#103—22no—
50C2×#103—22no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C4×C8—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#384D411yescharacteristic
63#380—21no—
64#380—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95D412yes—
77#340—22no—
78#340—22no—
79#340—22no—
80#340—22no—
81#336—21no—
82#336—21no—
83#336D412yes—
84C22×Q8—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—22no—
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—41no—
96C4⋊Q8—42no—
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—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—21no—
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—42no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—82no—
130C2×C4⋊C4SD1612yes—
131C2×C4⋊C4Q1612yes—
132C2×C22⋊C4—41no—
133C2×C42—42no—
134C2×C42—42no—
135C2×C42—42no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142#107—44no—
143#106—82no—
144C4⋊C8—42no—
145C4⋊C8—42no—
146#103—44no—
147#103—44no—
148C22⋊C8—22no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C4×C8—42no—
155#95—42no—
156#95—44no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165#95—82no—
166#95—82no—
167#95—82no—
168C24#12011yescharacteristic
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—41no—
172C2×Q8—41no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—42no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—42no—
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—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4#12011yescharacteristic
215C22×C4#12011yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4#12711yescharacteristic
220C22×C4C2×SD1611yescharacteristic
221C22×C4C2×Q1611yescharacteristic
222C22×C4#13511yescharacteristic
223C22×C4#13511yescharacteristic
224C22×C4AGL(1,ℤ/8)11yescharacteristic
225C22×C4#13711yescharacteristic
226C22×C4#13711yescharacteristic
227C22×C4#13711yescharacteristic
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—81no—
236C2×C8—81no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—82no—
258C4⋊C4—82no—
259C4⋊C4—82no—
260C4⋊C4—82no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C22⋊C4—81no—
264C22⋊C4—81no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C42—82no—
270C42—82no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#39211yescharacteristic
276C23#44811yescharacteristic
277C23#44911yescharacteristic
278C23#45111yescharacteristic
279C23#45211yescharacteristic
280C23#45511yescharacteristic
281C23#45611yescharacteristic
282Q8—82no—
283Q8—82no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—82no—
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—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
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#45011yescharacteristic
344C2×C4#45111yescharacteristic
345C2×C4#45211yescharacteristic
346C2×C4#45211yescharacteristic
347C2×C4#45412yes—
348C2×C4#45812yes—
349C2×C4#46511yescharacteristic
350C2×C4#46711yescharacteristic
351C2×C4#46811yescharacteristic
352C2×C4#47011yescharacteristic
353C8—82no—
354C8—82no—
355C8—82no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22#164011yescharacteristic
369C22#164511yescharacteristic
370C22#164811yescharacteristic
371C22#165311yescharacteristic
372C22#200011yescharacteristic
373C22#200111yescharacteristic
374C22#200311yescharacteristic
375C22#200711yescharacteristic
376C22#200811yescharacteristic
377C22#201011yescharacteristic
378C22#202211yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—82no—
388C4—82no—
389C4—82no—
390C4—162no—
391C4—161no—
392C4—161no—
393C4—161no—
394C4#161512yes—
395C4#161712yes—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2#992911yescharacteristic
401C2#993611yescharacteristic
402C2#1000211yescharacteristic
403C2#1000911yescharacteristic
404C2#1023411yescharacteristic
405C2#1024111yescharacteristic
406C2#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
#331092
#299672
#152002
#98842
#87072
#75762
#70392