Finite Group Databasebeta

← #98717

Subgroups — #98717

Order 512.

546 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 116 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#59870C211yesmaximal, characteristic
2#9874C211yesmaximal, characteristic
3#8591C211yesmaximal, characteristic
4#8590C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7591C211yesmaximal, characteristic
7#7590C211yesmaximal, characteristic
8#2805—22no—
9#2581—22no—
10#2571—21no—
11#2568C412yes—
12#2567—21no—
13#2511—22no—
14#2509—22no—
15#2365—21no—
16#2355—21no—
17Q8×C4⋊C4C412yes—
18C4×C4⋊Q8C2211yescharacteristic
19C4×C4⋊Q8C2211yescharacteristic
20C4×C4⋊Q8C2211yescharacteristic
21#1842C2211yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1744C2211yescharacteristic
25C2×#333—21no—
26C2×#332—21no—
27#1296—21no—
28#1296—21no—
29#1279—22no—
30#1272—22no—
31#1271—22no—
32#1271—22no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—22no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8C2×C412yes—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4×C8—21no—
46#400—24no—
47#400—24no—
48#400—24no—
49#395—24no—
50#391—22no—
51#391—22no—
52#391—22no—
53#391—21no—
54#391—21no—
55#391D412yes—
56#389—22no—
57#389—22no—
58#389—22no—
59#389—24no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389D412yes—
65#389D412yes—
66#387—24no—
67#387—24no—
68#387—24no—
69#384—22no—
70#384C2×C411yescharacteristic
71#384D411yescharacteristic
72#384D411yescharacteristic
73#382—22no—
74#382—22no—
75C4×C4⋊C4—22no—
76C4×C4⋊C4—22no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4C2×C412yes—
82C4×C4⋊C4D412yes—
83C43C2311yescharacteristic
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336—21no—
89#336—21no—
90#333—42no—
91#332—42no—
92C22×Q8—21no—
93C22×Q8—21no—
94C22×Q8C22⋊C412yes—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C4⋊Q8—21no—
100C4⋊Q8—21no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—42no—
106C4⋊Q8SD1612yes—
107C4⋊Q8Q1612yes—
108C4×Q8—44no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
113C4×Q8—82no—
114C4×Q8—84no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—24no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4C22⋊C412yes—
131C2×C4⋊C4C22⋊C412yes—
132C2×C4⋊C4C22⋊C412yes—
133C2×C4⋊C4C22⋊C412yes—
134C2×C4⋊C4C22⋊C412yes—
135C2×C42—22no—
136C2×C42—22no—
137C2×C42—22no—
138C2×C42—24no—
139C2×C42C22×C411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C4⋊C8—42no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4×C8—22no—
156C4×C8—41no—
157#95—24no—
158#95—24no—
159#95—24no—
160#95—24no—
161#95—24no—
162#95—22no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×Q8—22no—
169C2×Q8—42no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—42no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—81no—
178C2×Q8—81no—
179C2×Q8#10314yes—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C2×C22⋊C411yescharacteristic
187C22×C4C2×C22⋊C411yescharacteristic
188C22×C4C2×C22⋊C411yescharacteristic
189C22×C4#12011yescharacteristic
190C22×C4#12011yescharacteristic
191C22×C4#12011yescharacteristic
192C22×C4#12011yescharacteristic
193C2×C8—42no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C2×C8—81no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—44no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—82no—
231C4⋊C4—84no—
232C4⋊C4—84no—
233C42—22no—
234C42—21no—
235C42—21no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—44no—
240C42—44no—
241C42—42no—
242C42—42no—
243C42—84no—
244C42C2×SD1611yescharacteristic
245C42C2×Q1611yescharacteristic
246C42#13511yescharacteristic
247C42#13511yescharacteristic
248C42AGL(1,ℤ/8)11yescharacteristic
249C42#13711yescharacteristic
250C42#13711yescharacteristic
251C42#13711yescharacteristic
252C23#37911yescharacteristic
253Q8—44no—
254Q8—44no—
255Q8—82no—
256Q8—82no—
257Q8—82no—
258Q8—82no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4#41312yes—
291C2×C4C2×#10311yescharacteristic
292C2×C4#41611yescharacteristic
293C2×C4#41711yescharacteristic
294C2×C4#41911yescharacteristic
295C2×C4#44811yescharacteristic
296C2×C4#44811yescharacteristic
297C2×C4#44911yescharacteristic
298C2×C4#44911yescharacteristic
299C2×C4#45111yescharacteristic
300C2×C4#45111yescharacteristic
301C2×C4#45211yescharacteristic
302C2×C4#45211yescharacteristic
303C2×C4#45411yescharacteristic
304C2×C4#45611yescharacteristic
305C8—82no—
306C8—161no—
307C8—161no—
308C8—161no—
309C22#178511yescharacteristic
310C22#178711yescharacteristic
311C22#178811yescharacteristic
312C22#179311yescharacteristic
313C22#179411yescharacteristic
314C22#179511yescharacteristic
315C22#179611yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—44no—
327C4—82no—
328C4—82no—
329C4—82no—
330C4—82no—
331C4—82no—
332C4#162611yescharacteristic
333C4#163611yescharacteristic
334C4#164811yescharacteristic
335C4#165311yescharacteristic
336C2#839411yescharacteristic
337C2#839511yescharacteristic
338C2#843311yescharacteristic
339C2#843411yescharacteristic
340C2#844811yescharacteristic
341C2#846111yescharacteristic
342C2#849611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#379
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#598702
#98742
#85912
#85902
#76522
#75912
#75902