Finite Group Databasebeta

← #117337

Subgroups — #117337

Order 512.

590 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21799C211yesmaximal, characteristic
2#17808C211yesmaximal, characteristic
3#17742C211yesmaximal, characteristic
4C2×#1549C211yesmaximal, characteristic
5#8078C211yesmaximal, characteristic
6#8061C211yesmaximal, characteristic
7#8006C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×#423C2211yescharacteristic
15#1966—22no—
16#1966—22no—
17#1784—22no—
18#1574—22no—
19#1572—22no—
20#1565—22no—
21#1556C414yes—
22#1549—22no—
23#1549—22no—
24#1549—22no—
25#1546—22no—
26C2×#332—22no—
27#1301—22no—
28#1299—22no—
29#1293—22no—
30C23×Q8—21no—
31C22×M16—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—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⋊Q8C2×C412yes—
43C2×C4⋊Q8D412yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4Q812yes—
46C22×C42C2311yescharacteristic
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432C2×C412yes—
54#432C2×C412yes—
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#431—21no—
65#431—21no—
66#431D412yes—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423D412yes—
73#423D412yes—
74#423D412yes—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8D412yes—
78C2×#101—28no—
79#407—21no—
80#407—21no—
81#407—21no—
82#407D412yes—
83C2×C22⋊C8—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C2×C4×C8—21no—
89#335—24no—
90#334—24no—
91#332—28no—
92#332—28no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—41no—
99C22×Q8—84no—
100C23×C4—22no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×Q811yescharacteristic
103C23×C4#4111yescharacteristic
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—82no—
111C22×C8—22no—
112C22×C8—41no—
113C4⋊Q8—22no—
114C4⋊Q8—22no—
115C4⋊Q8—22no—
116C4⋊Q8—22no—
117C4⋊Q8—22no—
118C4⋊Q8—22no—
119C4⋊Q8—22no—
120C4⋊Q8—22no—
121C4⋊Q8—41no—
122C4⋊Q8—41no—
123C4⋊Q8—41no—
124C4⋊Q8—41no—
125C4⋊Q8—41no—
126C4⋊Q8—41no—
127C4⋊Q8—41no—
128C4⋊Q8—41no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C4⋊C414yes—
141C2×C42C22×C411yescharacteristic
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—41no—
162C4⋊C8—41no—
163C4⋊C8—41no—
164C4⋊C8—41no—
165C4⋊C8—41no—
166C4⋊C8C22⋊C414yes—
167#101—88no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—41no—
174C22⋊C8—41no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178#97—22no—
179#97—22no—
180#97—41no—
181#97—41no—
182C4×C8—22no—
183C4×C8—41no—
184C4×C8—41no—
185C4×C8—41no—
186C4×C8—41no—
187C4×C8—41no—
188C24C22⋊Q811yescharacteristic
189C2×Q8—48no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—84no—
195C2×Q8—84no—
196C2×Q8—84no—
197C2×Q8—84no—
198C2×Q8—84no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—24no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—84no—
207C22×C4C2×C4⋊C411yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4#12011yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4C22⋊Q811yescharacteristic
218C22×C4C22⋊Q811yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12311yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4#12711yescharacteristic
225M16—42no—
226M16—42no—
227M16—44no—
228M16—44no—
229M16—82no—
230M16—82no—
231M16—82no—
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—82no—
239C2×C8—82no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C42C2×C22⋊C411yescharacteristic
249C42#11711yescharacteristic
250C42C4×D411yescharacteristic
251C42C4×D411yescharacteristic
252C42#12011yescharacteristic
253C42#12011yescharacteristic
254C42#12111yescharacteristic
255C42#12111yescharacteristic
256C42#12111yescharacteristic
257C42#12111yescharacteristic
258C42#12111yescharacteristic
259C42#12311yescharacteristic
260C42#12411yescharacteristic
261C42#12411yescharacteristic
262C42#12411yescharacteristic
263C42#12611yescharacteristic
264C23—22no—
265C23—41no—
266C23—41no—
267C23#38511yescharacteristic
268C23#39611yescharacteristic
269C23#39911yescharacteristic
270Q8—84no—
271Q8—84no—
272Q8—84no—
273Q8—84no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—48no—
294C2×C4—44no—
295C2×C4—84no—
296C2×C4—84no—
297C2×C4#38011yescharacteristic
298C2×C4#38511yescharacteristic
299C2×C4#38611yescharacteristic
300C2×C4#38811yescharacteristic
301C2×C4#38811yescharacteristic
302C2×C4#39011yescharacteristic
303C2×C4#39211yescharacteristic
304C2×C4#39311yescharacteristic
305C2×C4#39411yescharacteristic
306C2×C4#39411yescharacteristic
307C2×C4#39611yescharacteristic
308C2×C4#39711yescharacteristic
309C2×C4#47112yes—
310C2×C4#47312yes—
311C8—44no—
312C8—82no—
313C8—82no—
314C8—82no—
315C8—82no—
316C8—82no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—44no—
326C22#143911yescharacteristic
327C22#206412yes—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—84no—
337C4#190812yes—
338C4#200812yes—
339C4#204611yescharacteristic
340C4#204711yescharacteristic
341C4#207012yes—
342C2—22no—
343C2—41no—
344C2—41no—
345C2#1106211yescharacteristic
346C2#1112911yescharacteristic
347C2#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
#217992
#178082
#177422
C2×#15492
#80782
#80612
#80062