Finite Group Databasebeta

← #119171

Subgroups — #119171

Order 512.

516 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17718C211yesmaximal, characteristic
2C2×#1531C211yesmaximal, characteristic
3#17464C211yesmaximal, characteristic
4#8090C211yesmaximal, characteristic
5#8088C211yesmaximal, characteristic
6#7933C211yesmaximal, characteristic
7C2×#1275C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C22×#97C2211yescharacteristic
15#1554—22no—
16#1548C412yes—
17#1546C412yes—
18#1542—22no—
19#1531—22no—
20#1531—22no—
21C2×#330—22no—
22#1485—22no—
23#1481—22no—
24#1479—22no—
25#1302—22no—
26#1302—22no—
27#1283—22no—
28#1275—22no—
29C23×C8—21no—
30#533—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533D412yes—
37#533D412yes—
38C2×C4⋊Q8C2×C411yescharacteristic
39C2×C4⋊Q8C2×C411yescharacteristic
40C2×#125—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C2×#117—21no—
46C22×C42C2311yescharacteristic
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431C2×C412yes—
65#431D412yes—
66#431D412yes—
67#423—21no—
68#423C2×C412yes—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72#407—21no—
73#407—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C4×M16—21no—
78C4×M16—21no—
79C2×#97—21no—
80C2×#97—21no—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97—21no—
84C2×#97D412yes—
85C2×#97D412yes—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88#333—24no—
89#332—24no—
90#330—28no—
91Q8⋊C8—28no—
92C22×Q8—21no—
93C22×Q8—21no—
94C23×C4#4111yescharacteristic
95C23×C4#4111yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—22no—
98C2×M16—41no—
99C22×C8—24no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—42no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113C4⋊Q8C22⋊C412yes—
114C4⋊Q8C22⋊C412yes—
115#125—22no—
116#125—22no—
117#125—41no—
118#125—41no—
119C22⋊Q8—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C22⋊Q8—41no—
124C22⋊Q8—41no—
125C22⋊Q8—41no—
126C22⋊Q8—41no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C4×Q8—41no—
135#117—22no—
136#117—22no—
137#117—41no—
138#117—41no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C42—41no—
147C2×C42C22×C411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—41no—
173C22⋊C8—41no—
174C22⋊C8—41no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179#97—22no—
180#97—22no—
181#97—22no—
182#97—22no—
183#97—41no—
184#97—41no—
185#97—41no—
186#97—41no—
187C4×C8—22no—
188C4×C8—22no—
189C4×C8—22no—
190C4×C8—41no—
191C4×C8—41no—
192C4×C8—41no—
193C24#12611yescharacteristic
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—82no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—81no—
207C22×C4#11711yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12311yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12411yescharacteristic
222C22×C4#12411yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4#12611yescharacteristic
225M16—42no—
226M16—42no—
227M16—82no—
228C2×C8—24no—
229C2×C8—44no—
230C2×C8—44no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—82no—
239C2×C8—82no—
240C2×C8—82no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42—42no—
256C42—42no—
257C42C2×C22⋊C411yescharacteristic
258C42#11711yescharacteristic
259C42C4×D411yescharacteristic
260C42C4×D411yescharacteristic
261C42#12011yescharacteristic
262C42#12011yescharacteristic
263C42#12111yescharacteristic
264C42#12111yescharacteristic
265C42#12111yescharacteristic
266C42#12111yescharacteristic
267C42#12111yescharacteristic
268C42#12311yescharacteristic
269C42#12311yescharacteristic
270C42#12311yescharacteristic
271C42#12411yescharacteristic
272C42#12611yescharacteristic
273C23—22no—
274C23—22no—
275C23—41no—
276C23#38811yescharacteristic
277C23#39711yescharacteristic
278C23#39711yescharacteristic
279Q8—44no—
280Q8—82no—
281Q8—82no—
282Q8—81no—
283Q8—81no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
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—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4#38111yescharacteristic
308C2×C4#38611yescharacteristic
309C2×C4#38611yescharacteristic
310C2×C4#38811yescharacteristic
311C2×C4#38811yescharacteristic
312C2×C4#38811yescharacteristic
313C2×C4#39411yescharacteristic
314C2×C4#39411yescharacteristic
315C2×C4#39411yescharacteristic
316C2×C4#39411yescharacteristic
317C2×C4#39711yescharacteristic
318C2×C4#39711yescharacteristic
319C2×C4#44312yes—
320C2×C4#44412yes—
321C8—44no—
322C8—82no—
323C8—82no—
324C8—82no—
325C8—82no—
326C8—82no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—44no—
335C22#144011yescharacteristic
336C22#192912yes—
337C22#208212yes—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4#187612yes—
351C4#193711yescharacteristic
352C4#193811yescharacteristic
353C2—22no—
354C2—22no—
355C2—41no—
356C2#1115911yescharacteristic
357C2#1118211yescharacteristic
358C2#1119111yescharacteristic
subgroupG/H
center, socleC22#1440
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
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
#177182
C2×#15312
#174642
#80902
#80882
#79332
C2×#12752