Finite Group Databasebeta

← #117690

Subgroups — #117690

Order 512.

575 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21829C211yesmaximal, characteristic
2#17822C211yesmaximal, characteristic
3C2×#1556C211yesmaximal, characteristic
4C2×#1546C211yesmaximal, characteristic
5#8058C211yesmaximal, characteristic
6#7990C211yesmaximal, characteristic
7#7864C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#432C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×#423C2211yescharacteristic
15#1997—22no—
16#1997C414yes—
17#1821—22no—
18#1573—22no—
19#1571—21no—
20#1570—21no—
21#1569—22no—
22#1556—22no—
23#1556—22no—
24#1546—22no—
25#1546—22no—
26C2×#332—22no—
27C2×#332—21no—
28C2×#332—21no—
29#1298—22no—
30#1290—22no—
31#1275—22no—
32C23×Q8—21no—
33C22×M16—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4⋊Q8—21no—
39C2×C4⋊Q8—21no—
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8C2×C412yes—
45C2×C4⋊Q8D412yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4Q812yes—
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#432—21no—
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—
73#423—21no—
74#423C2×C412yes—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8D411yescharacteristic
79C2×C4⋊C8D411yescharacteristic
80C2×C4⋊C8D412yes—
81#407—21no—
82#407D412yes—
83C2×C22⋊C8—21no—
84C2×C22⋊C8—21no—
85C2×C22⋊C8—21no—
86C4×M16C2×C412yes—
87C4×M16D412yes—
88C2×#97—21no—
89C2×#97—21no—
90C2×C4×C8—21no—
91#343—28no—
92#335—24no—
93#334—24no—
94#332—28no—
95#332—24no—
96#332—24no—
97C22×Q8—22no—
98C22×Q8—22no—
99C22×Q8—41no—
100C22×Q8—41no—
101C22×Q8—41no—
102C22×Q8—41no—
103C22×Q8—82no—
104C22×Q8—82no—
105C23×C4—22no—
106C23×C4C2×D411yescharacteristic
107C23×C4C2×Q811yescharacteristic
108C23×C4#4111yescharacteristic
109C2×M16—22no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—82no—
113C2×M16C22⋊C414yes—
114C22×C8—21no—
115C22×C8—21no—
116C22×C8—22no—
117C22×C8—41no—
118C22×C8—41no—
119C4⋊Q8—22no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—41no—
128C4⋊Q8—41no—
129C4⋊Q8—41no—
130C4⋊Q8—41no—
131C4⋊Q8—41no—
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4C4⋊C414yes—
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—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—22no—
168C4⋊C8—21no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
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—
184C22⋊C8—41no—
185#97—22no—
186#97—22no—
187#97—22no—
188#97—41no—
189#97—41no—
190#97—41no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—22no—
194C4×C8—41no—
195C24C22⋊Q811yescharacteristic
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—84no—
201C2×Q8—82no—
202C2×Q8—82no—
203C2×Q8—84no—
204C2×Q8—84no—
205C2×Q8—82no—
206C2×Q8—82no—
207C2×Q8—82no—
208C2×Q8—82no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—84no—
217C22×C4C2×C22⋊C411yescharacteristic
218C22×C4C2×C4⋊C411yescharacteristic
219C22×C4#11711yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4#12611yescharacteristic
234C22×C4#12611yescharacteristic
235M16—44no—
236M16—44no—
237M16—82no—
238M16—82no—
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—82no—
249C2×C8—82no—
250C2×C8—82no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C42C4×D411yescharacteristic
260C42C4×D411yescharacteristic
261C42C4×D411yescharacteristic
262C42C4×D411yescharacteristic
263C42#12011yescharacteristic
264C42#12011yescharacteristic
265C42#12011yescharacteristic
266C42#12311yescharacteristic
267C42#12311yescharacteristic
268C42#12311yescharacteristic
269C42#12311yescharacteristic
270C42#12311yescharacteristic
271C42#12411yescharacteristic
272C42#12411yescharacteristic
273C42#12411yescharacteristic
274C42#12711yescharacteristic
275C23—22no—
276C23—22no—
277C23—41no—
278C23#38011yescharacteristic
279C23#39611yescharacteristic
280C23#39611yescharacteristic
281Q8—84no—
282Q8—84no—
283Q8—84no—
284Q8—82no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—44no—
306C2×C4—84no—
307C2×C4—84no—
308C2×C4—84no—
309C2×C4#38511yescharacteristic
310C2×C4#38511yescharacteristic
311C2×C4#38611yescharacteristic
312C2×C4#38811yescharacteristic
313C2×C4#38811yescharacteristic
314C2×C4#39011yescharacteristic
315C2×C4#39211yescharacteristic
316C2×C4#39311yescharacteristic
317C2×C4#39411yescharacteristic
318C2×C4#39411yescharacteristic
319C2×C4#39711yescharacteristic
320C2×C4#39911yescharacteristic
321C2×C4#47112yes—
322C2×C4#47212yes—
323C8—44no—
324C8—82no—
325C8—82no—
326C8—82no—
327C8—81no—
328C8—82no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—44no—
338C22#143911yescharacteristic
339C22#206312yes—
340C22#207012yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—84no—
351C4#190912yes—
352C4#193112yes—
353C4#201811yescharacteristic
354C4#201911yescharacteristic
355C2—22no—
356C2—22no—
357C2—41no—
358C2#1107411yescharacteristic
359C2#1114011yescharacteristic
360C2#1114411yescharacteristic
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
#218292
#178222
C2×#15562
C2×#15462
#80582
#79902
#78642