Finite Group Databasebeta

← #121142

Subgroups — #121142

Order 512.

460 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10858C211yesmaximal, characteristic
2#10855C211yesmaximal, characteristic
3#8095C211yesmaximal, characteristic
4#8026C211yesmaximal, characteristic
5#8001C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7918C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#382C2211yescharacteristic
15C2×#344—21no—
16C2×#344—21no—
17C2×#343—21no—
18C2×#343—21no—
19#1303—22no—
20#1294C414yes—
21#1292—22no—
22#1286—22no—
23#1281—22no—
24C22×M16—21no—
25C22×M16—21no—
26C22×M16D411yescharacteristic
27C22×M16D411yescharacteristic
28C2×#117—21no—
29C22×C4⋊C4—21no—
30C22×C42C2311yescharacteristic
31#431—21no—
32#431—21no—
33#431—21no—
34#431—21no—
35#431—21no—
36#431—21no—
37#431—21no—
38#431D412yes—
39#423—21no—
40#423—21no—
41#423—21no—
42#423—21no—
43#423—21no—
44#423—21no—
45#423—21no—
46#423D412yes—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8Q812yes—
53C2×C22⋊C8—21no—
54C2×C22⋊C8C2×C412yes—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16—21no—
58C4×M16—21no—
59C2×#97—21no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62C2×C4×C8—21no—
63#384—21no—
64#382—21no—
65#382—21no—
66#382—21no—
67#382—21no—
68#382—21no—
69#380—21no—
70#380C2×C412yes—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C2×#95—21no—
74C2×#95C2×C412yes—
75#344—42no—
76#344—42no—
77#343—42no—
78#343—42no—
79C23×C4—22no—
80C23×C4C22×C411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4#4111yescharacteristic
83C2×M16—21no—
84C2×M16—21no—
85C2×M16—21no—
86C2×M16—21no—
87C2×M16—21no—
88C2×M16—21no—
89C2×M16—21no—
90C2×M16—21no—
91C2×M16—21no—
92C2×M16—21no—
93C2×M16—22no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—41no—
97C2×M16—41no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16SD1612yes—
106C2×M16Q1612yes—
107C22×C8—21no—
108C22×C8—21no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—41no—
112C22×C8—41no—
113#117—41no—
114#117—41no—
115#117—41no—
116#117—41no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C22⋊C4—22no—
127C2×C42—41no—
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×Q811yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133C2×C42#4111yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137C2×C42#4111yescharacteristic
138C2×C42#4111yescharacteristic
139C2×C42#4111yescharacteristic
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154C22⋊C8—22no—
155C22⋊C8—41no—
156#97—41no—
157#97—41no—
158C4×C8—22no—
159C4×C8—41no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—41no—
163C4×C8—41no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—41no—
168#95—41no—
169#95—41no—
170C24C4×D411yescharacteristic
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—81no—
176C22×C4—81no—
177C22×C4—82no—
178C22×C4—82no—
179C22×C4#11711yescharacteristic
180C22×C4#11711yescharacteristic
181C22×C4#11711yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4C4×D411yescharacteristic
184C22×C4C4×Q811yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4C22⋊Q811yescharacteristic
188C22×C4#12311yescharacteristic
189C22×C4#12311yescharacteristic
190C22×C4#12311yescharacteristic
191C22×C4#12411yescharacteristic
192C22×C4#12411yescharacteristic
193C22×C4#12511yescharacteristic
194C22×C4#12611yescharacteristic
195C22×C4#12611yescharacteristic
196C22×C4#12611yescharacteristic
197C22×C4C2×SD1611yescharacteristic
198C22×C4C2×Q1611yescharacteristic
199C22×C4#13511yescharacteristic
200C22×C4#13511yescharacteristic
201C22×C4AGL(1,ℤ/8)11yescharacteristic
202C22×C4AGL(1,ℤ/8)11yescharacteristic
203C22×C4AGL(1,ℤ/8)11yescharacteristic
204C22×C4#13711yescharacteristic
205M16—22no—
206M16—22no—
207M16—22no—
208M16—22no—
209M16—41no—
210M16—41no—
211M16—41no—
212M16—41no—
213M16—42no—
214M16—42no—
215M16—81no—
216M16—81no—
217M16—81no—
218M16—81no—
219M16—81no—
220M16—81no—
221C2×C8—22no—
222C2×C8—22no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—82no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—82no—
237C4⋊C4—82no—
238C4⋊C4—82no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—81no—
248C42—81no—
249C42#12111yescharacteristic
250C42C22⋊Q811yescharacteristic
251C42C22⋊Q811yescharacteristic
252C42#12311yescharacteristic
253C42#12311yescharacteristic
254C42#12311yescharacteristic
255C42#12411yescharacteristic
256C42#12511yescharacteristic
257C42#12511yescharacteristic
258C42#12611yescharacteristic
259C42#12611yescharacteristic
260C42#12611yescharacteristic
261C42#12611yescharacteristic
262C42#12611yescharacteristic
263C42#12611yescharacteristic
264C42#12611yescharacteristic
265C23—41no—
266C23—41no—
267C23#38711yescharacteristic
268C23#38811yescharacteristic
269C23#38811yescharacteristic
270C23C4×SD1611yescharacteristic
271C23C4×Q1611yescharacteristic
272C23#44011yescharacteristic
273C23#44211yescharacteristic
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—162no—
293C2×C4—162no—
294C2×C4#38311yescharacteristic
295C2×C4#38711yescharacteristic
296C2×C4#38711yescharacteristic
297C2×C4#38811yescharacteristic
298C2×C4#39611yescharacteristic
299C2×C4#39711yescharacteristic
300C2×C4#39711yescharacteristic
301C2×C4#39711yescharacteristic
302C2×C4#40011yescharacteristic
303C2×C4#40011yescharacteristic
304C2×C4#40011yescharacteristic
305C2×C4#40111yescharacteristic
306C2×C4#46011yescharacteristic
307C2×C4#46211yescharacteristic
308C2×C4#46311yescharacteristic
309C2×C4#46311yescharacteristic
310C2×C4#46511yescharacteristic
311C2×C4#46711yescharacteristic
312C2×C4#46811yescharacteristic
313C2×C4#46911yescharacteristic
314C2×C4#47611yescharacteristic
315C2×C4#47711yescharacteristic
316C2×C4#47811yescharacteristic
317C2×C4#47911yescharacteristic
318C2×C4#48111yescharacteristic
319C2×C4#48211yescharacteristic
320C2×C4#48211yescharacteristic
321C2×C4#48211yescharacteristic
322C2×C4#48311yescharacteristic
323C2×C4#48411yescharacteristic
324C2×C4#48411yescharacteristic
325C2×C4#48511yescharacteristic
326C2×C4#48711yescharacteristic
327C2×C4#48811yescharacteristic
328C2×C4#48911yescharacteristic
329C2×C4#49011yescharacteristic
330C8—42no—
331C8—42no—
332C8—82no—
333C8—82no—
334C8—82no—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22#144311yescharacteristic
347C22#192011yescharacteristic
348C22#192111yescharacteristic
349C22#192611yescharacteristic
350C22#192811yescharacteristic
351C22#193311yescharacteristic
352C22#193611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—162no—
362C4—162no—
363C4#206511yescharacteristic
364C4#206811yescharacteristic
365C4#207211yescharacteristic
366C4#207311yescharacteristic
367C4#207611yescharacteristic
368C4#207711yescharacteristic
369C4#210011yescharacteristic
370C4#210111yescharacteristic
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2—21no—
377C2#1131011yescharacteristic
378C2#1131611yescharacteristic
379C2#1131911yescharacteristic
subgroupG/H
center, socleC22#1443
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#108582
#108552
#80952
#80262
#80012
C2×#12862
#79182