Finite Group Databasebeta

← #117839

Subgroups — #117839

Order 512.

523 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17795C211yesmaximal, characteristic
2#17667C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4#17394C211yesmaximal, characteristic
5#8064C211yesmaximal, characteristic
6#8010C211yesmaximal, characteristic
7#7968C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#432C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15#1569—22no—
16#1569—22no—
17#1564—22no—
18#1534—22no—
19#1528—22no—
20#1528—22no—
21#1528—22no—
22#1528—22no—
23C2×#330C412yes—
24C2×#330C412yes—
25#1470—22no—
26#1470—22no—
27#1463—22no—
28#1299—22no—
29#1293—22no—
30#1287—22no—
31C22×M16—21no—
32C2×#125—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125C2×C412yes—
43C2×#125D412yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4Q811yescharacteristic
47C22×C4⋊C4Q811yescharacteristic
48C22×C42C2311yescharacteristic
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432D412yes—
60#432D412yes—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431D412yes—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73C2×C4⋊C8—21no—
74#407—21no—
75#407—21no—
76#407—21no—
77#407D412yes—
78C2×C22⋊C8—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×M16—21no—
85C4×M16D412yes—
86C4×M16D412yes—
87C2×#97C2×C412yes—
88C2×#97C2×C411yescharacteristic
89C2×#97C2×C411yescharacteristic
90C2×C4×C8—21no—
91#335—24no—
92#334—24no—
93#330—28no—
94#330—24no—
95#330—24no—
96#324—28no—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×Q811yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—44no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C22×C8—21no—
110C22×C8—21no—
111C22×C8—22no—
112#125—22no—
113#125—22no—
114#125—22no—
115#125—22no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—22no—
120#125—41no—
121#125—41no—
122#125—41no—
123#125—41no—
124#125—41no—
125#125—41no—
126#125—41no—
127#125—41no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4C4⋊C412yes—
151C2×C4⋊C4C4⋊C412yes—
152C2×C42C22×C411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184#97—22no—
185#97—21no—
186#97—21no—
187#97—22no—
188#97—22no—
189#97—22no—
190#97—41no—
191#97—41no—
192#97C22⋊C412yes—
193#97C22⋊C412yes—
194C4×C8—22no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—41no—
198C4×C8—41no—
199C4×C8—41no—
200C24C22⋊Q811yescharacteristic
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—81no—
210C22×C4—82no—
211C22×C4—82no—
212C22×C4C2×C4⋊C411yescharacteristic
213C22×C4C4×D411yescharacteristic
214C22×C4C4×D411yescharacteristic
215C22×C4#12011yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4C22⋊Q811yescharacteristic
220C22×C4C22⋊Q811yescharacteristic
221C22×C4C22⋊Q811yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12611yescharacteristic
229C22×C4#12711yescharacteristic
230M16—44no—
231M16—44no—
232M16—82no—
233M16—82no—
234M16—82no—
235M16—82no—
236C2×C8—24no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—82no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C42C2×C22⋊C411yescharacteristic
263C42#11711yescharacteristic
264C42C4×D411yescharacteristic
265C42C4×D411yescharacteristic
266C42#12011yescharacteristic
267C42#12011yescharacteristic
268C42#12111yescharacteristic
269C42#12111yescharacteristic
270C42#12111yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12311yescharacteristic
274C42#12411yescharacteristic
275C42#12411yescharacteristic
276C42#12411yescharacteristic
277C42#12611yescharacteristic
278C23—22no—
279C23—41no—
280C23—41no—
281C23#38511yescharacteristic
282C23#39611yescharacteristic
283C23#39911yescharacteristic
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
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—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4#38011yescharacteristic
311C2×C4#38511yescharacteristic
312C2×C4#38611yescharacteristic
313C2×C4#38811yescharacteristic
314C2×C4#38811yescharacteristic
315C2×C4#39011yescharacteristic
316C2×C4#39211yescharacteristic
317C2×C4#39311yescharacteristic
318C2×C4#39411yescharacteristic
319C2×C4#39411yescharacteristic
320C2×C4#39611yescharacteristic
321C2×C4#39711yescharacteristic
322C8—24no—
323C8—42no—
324C8—82no—
325C8—82no—
326C8—82no—
327C8—82no—
328C8—82no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—44no—
338C22#143911yescharacteristic
339C22#186112yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—82no—
353C4#207012yes—
354C2—22no—
355C2—41no—
356C2—41no—
357C2#1108011yescharacteristic
358C2#1111511yescharacteristic
359C2#1114011yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ 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
#177952
#176672
C2×#15282
#173942
#80642
#80102
#79682