Finite Group Databasebeta

← #134535

Subgroups — #134535

Order 512.

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

normal subgroups only

This group has 536 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#14223C211yesmaximal, characteristic
2C2×#1346C212yesmaximal
3#10847C211yesmaximal, characteristic
4#8560C211yesmaximal, characteristic
5#7251C212yesmaximal
6C2×#423—21no—
7C2×#398C2211yescharacteristic
8C2×#387—21no—
9C2×C4×C4⋊C4C411yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1797—21no—
12C2×#343—21no—
13C2×#343C2212yes—
14C2×#324C2212yes—
15#1445C411yescharacteristic
16#1442C411yescharacteristic
17#1441C2211yescharacteristic
18#1436—21no—
19#1434—21no—
20#1434—21no—
21#1434C411yescharacteristic
22#1346—24no—
23#1280—21no—
24C22×M16—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4D411yescharacteristic
29C22×C4⋊C4C2311yescharacteristic
30C22×C42—21no—
31C22×C42C2×C411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42D411yescharacteristic
34#423—24no—
35#423—42no—
36C2×C4⋊C8—41no—
37C2×C4⋊C8—41no—
38C2×C4⋊C8—41no—
39C2×C22⋊C8—22no—
40#398—21no—
41#398—21no—
42#398D412yes—
43#398Q812yes—
44#387—42no—
45#387—42no—
46C4×C4⋊C4—41no—
47C4×C4⋊C4—41no—
48C4×C4⋊C4—41no—
49C4×C4⋊C4—41no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95C2×C411yescharacteristic
61C2×#95C2×C411yescharacteristic
62C2×#95C2×C411yescharacteristic
63C2×#95D411yescharacteristic
64#343—22no—
65#343—22no—
66#343—42no—
67#336—41no—
68#324—22no—
69#324—22no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22⋊C411yescharacteristic
78C23×C4C22×C411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C2×M16—24no—
82C2×M16—42no—
83C2×M16—42no—
84C2×M16—42no—
85C2×M16—42no—
86C2×M16—42no—
87C22×C8—42no—
88C22×C8—42no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4C4⋊C412yes—
105C2×C4⋊C4D812yes—
106C2×C4⋊C4SD1612yes—
107C2×C4⋊C4C2×D411yescharacteristic
108C2×C4⋊C4C2×Q811yescharacteristic
109C2×C4⋊C4#4111yescharacteristic
110C2×C4⋊C4#4111yescharacteristic
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—22no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—42no—
125C4⋊C8—44no—
126C4⋊C8—44no—
127C4⋊C8—82no—
128C22⋊C8—42no—
129C22⋊C8—42no—
130#95—21no—
131#95—22no—
132#95—22no—
133#95—41no—
134#95—41no—
135#95—41no—
136#95—42no—
137#95—42no—
138#95—42no—
139#95—41no—
140#95—41no—
141#95—42no—
142#95—42no—
143#95—42no—
144#95—42no—
145#95—41no—
146#95—41no—
147#95C4⋊C412yes—
148C24C2×C22⋊C411yescharacteristic
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
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#9911yescharacteristic
206C22×C4#9911yescharacteristic
207C22×C4#10212yes—
208C22×C4#10212yes—
209C22×C4#10412yes—
210C22×C4C2×C4⋊C411yescharacteristic
211C22×C4#11711yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C2×D811yescharacteristic
217C22×C4C2×SD1611yescharacteristic
218C22×C4AGL(1,ℤ/8)11yescharacteristic
219C22×C4#13711yescharacteristic
220M16—44no—
221M16—44no—
222M16—82no—
223M16—82no—
224C2×C8—44no—
225C2×C8—82no—
226C2×C8—82no—
227C2×C8—82no—
228C2×C8—82no—
229C2×C8—82no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C42—22no—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—42no—
249C42—42no—
250C42—42no—
251C42—81no—
252C42—84no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#38011yescharacteristic
258C23C2×#9911yescharacteristic
259C23#41011yescharacteristic
260C23C2×#10211yescharacteristic
261C23#41711yescharacteristic
262C23C2×#10411yescharacteristic
263C23#42111yescharacteristic
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—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
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#35212yes—
341C2×C4#45911yescharacteristic
342C2×C4#46111yescharacteristic
343C2×C4#47411yescharacteristic
344C2×C4#47611yescharacteristic
345C8—84no—
346C8—162no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#150211yescharacteristic
360C22#150411yescharacteristic
361C22#151211yescharacteristic
362C22#151911yescharacteristic
363C22#179911yescharacteristic
364C22#180211yescharacteristic
365C22#180611yescharacteristic
366C22C2×#35211yescharacteristic
367C22#212011yescharacteristic
368C22#213311yescharacteristic
369C22#213511yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—82no—
384C4—82no—
385C4—82no—
386C4—161no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2—21no—
391C2#857711yescharacteristic
392C2#1176311yescharacteristic
393C2#1176411yescharacteristic
394C2#1187911yescharacteristic
395C2#1188111yescharacteristic
396C2#1279411yescharacteristic
397C2#1280411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#142232
C2×#13462
#108472
#85602
#72512