Finite Group Databasebeta

← #117446

Subgroups — #117446

Order 512.

647 conjugacy classes of subgroups.

The subgroup lattice has 371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21994C211yesmaximal, characteristic
2C2×#1966C211yesmaximal, characteristic
3#17742C211yesmaximal, characteristic
4C2×#1556C211yesmaximal, characteristic
5#8087C211yesmaximal, characteristic
6#7994C211yesmaximal, characteristic
7#7990C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#432C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×#101—22no—
15C2×C4×M16C2211yescharacteristic
16#1966—22no—
17#1966—22no—
18#1950—22no—
19#1855—22no—
20#1849—21no—
21#1838—21no—
22#1556—22no—
23#1556—22no—
24#1556C414yes—
25#1549—22no—
26#1546—21no—
27#1546—21no—
28C2×#332—22no—
29#1302—22no—
30#1291—22no—
31#1290—22no—
32C23×Q8—21no—
33C22×M16—21no—
34C22×M16D412yes—
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⋊Q8—21no—
45C2×C4⋊Q8C2×C412yes—
46C2×C4⋊Q8D412yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4Q812yes—
49C22×C42C2311yescharacteristic
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#432C2×C412yes—
59#432C2×C412yes—
60#432D412yes—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66C2×#108—24no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423D411yescharacteristic
73#423D411yescharacteristic
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8D412yes—
78C2×#101—28no—
79C2×#101—48no—
80#407—21no—
81#407—21no—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16D412yes—
90C2×#97—21no—
91C2×#97—21no—
92C2×#97—21no—
93C2×C4×C8—21no—
94#341—24no—
95#332—24no—
96#332—24no—
97#332—28no—
98C22×Q8—22no—
99C22×Q8—22no—
100C22×Q8—44no—
101C22×Q8—44no—
102C22×Q8—41no—
103C22×Q8—41no—
104C22×Q8—41no—
105C22×Q8—41no—
106C23×C4—22no—
107C23×C4C2×D411yescharacteristic
108C23×C4C2×Q811yescharacteristic
109C23×C4#4111yescharacteristic
110C2×M16—24no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—21no—
115C2×M16—21no—
116C2×M16—42no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—44no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—41no—
123C22×C8—41no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—22no—
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4⋊Q8—41no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4C4⋊C414yes—
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
164#108—84no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—22no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8C22⋊C414yes—
179#101—416no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188#97—22no—
189#97—22no—
190#97—22no—
191#97—22no—
192#97—22no—
193#97—41no—
194#97—41no—
195#97—41no—
196C4×C8—22no—
197C4×C8—41no—
198C4×C8—41no—
199C4×C8—41no—
200C24C22⋊Q811yescharacteristic
201C2×Q8—44no—
202C2×Q8—48no—
203C2×Q8—44no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—84no—
209C2×Q8—84no—
210C2×Q8—82no—
211C2×Q8—82no—
212C2×Q8—82no—
213C2×Q8—82no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—48no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C2×C4⋊C411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4#12011yescharacteristic
226C22×C4#12011yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12411yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12411yescharacteristic
239C22×C4#12611yescharacteristic
240M16—24no—
241M16—44no—
242M16—42no—
243M16—44no—
244M16—42no—
245M16—44no—
246M16—42no—
247M16—82no—
248C2×C8—24no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—82no—
259C2×C8—82no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C42C2×C22⋊C411yescharacteristic
269C42#11711yescharacteristic
270C42C4×D411yescharacteristic
271C42C4×D411yescharacteristic
272C42#12011yescharacteristic
273C42#12111yescharacteristic
274C42#12111yescharacteristic
275C42#12111yescharacteristic
276C42#12111yescharacteristic
277C42#12111yescharacteristic
278C42#12311yescharacteristic
279C42#12311yescharacteristic
280C42#12311yescharacteristic
281C42#12311yescharacteristic
282C42#12611yescharacteristic
283C42#12711yescharacteristic
284C23—22no—
285C23—22no—
286C23—41no—
287C23#38511yescharacteristic
288C23#39311yescharacteristic
289C23#39611yescharacteristic
290Q8—84no—
291Q8—84no—
292Q8—84no—
293Q8—82no—
294Q8—82no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—84no—
317C2×C4—84no—
318C2×C4#38011yescharacteristic
319C2×C4#38511yescharacteristic
320C2×C4#38611yescharacteristic
321C2×C4#38811yescharacteristic
322C2×C4#38811yescharacteristic
323C2×C4#39011yescharacteristic
324C2×C4#39211yescharacteristic
325C2×C4#39411yescharacteristic
326C2×C4#39411yescharacteristic
327C2×C4#39611yescharacteristic
328C2×C4#39711yescharacteristic
329C2×C4#39911yescharacteristic
330C2×C4#45312yes—
331C2×C4#45412yes—
332C8—44no—
333C8—44no—
334C8—82no—
335C8—82no—
336C8—82no—
337C8—81no—
338C8—81no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#143911yescharacteristic
348C22#202712yes—
349C22#207012yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—84no—
360C4#188312yes—
361C4#200211yescharacteristic
362C4#200311yescharacteristic
363C4#208212yes—
364C2—22no—
365C2—22no—
366C2—41no—
367C2#1106311yescharacteristic
368C2#1113411yescharacteristic
369C2#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
#219942
C2×#19662
#177422
C2×#15562
#80872
#79942
#79902