Finite Group Databasebeta

← #117197

Subgroups — #117197

Order 512.

646 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21969C211yesmaximal, characteristic
2C2×#1988C211yesmaximal, characteristic
3#17746C211yesmaximal, characteristic
4#17742C211yesmaximal, characteristic
5#8098C211yesmaximal, characteristic
6#7950C211yesmaximal, characteristic
7#7935C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1988—22no—
16#1988C414yes—
17#1950—22no—
18#1950—22no—
19#1810—22no—
20C2×#340—22no—
21#1558—22no—
22#1556—22no—
23#1549—22no—
24#1548—22no—
25#1548—22no—
26#1546—22no—
27#1303—22no—
28#1285—22no—
29#1283—22no—
30C23×Q8—21no—
31C23×C8D412yes—
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⋊Q8C2×C412yes—
42C2×C4⋊Q8D412yes—
43C2×C4⋊Q8Q812yes—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C42—21no—
48C22×C42C2311yescharacteristic
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432D412yes—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65C2×#108—24no—
66#423—21no—
67#423D412yes—
68#423D412yes—
69#423D412yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8C2×C412yes—
75C2×C4⋊C8D412yes—
76#407—21no—
77#407—21no—
78#407—21no—
79#407—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4C2×C412yes—
88C2×#95—21no—
89#341—24no—
90#340—28no—
91#333—28no—
92#332—28no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—22no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—41no—
99C22×Q8—82no—
100C22×Q8—82no—
101C23×C4—41no—
102C23×C4—41no—
103C23×C4C2×D411yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—41no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—44no—
113C22×C8C22⋊C414yes—
114C4⋊Q8—22no—
115C4⋊Q8—22no—
116C4⋊Q8—22no—
117C4⋊Q8—22no—
118C4⋊Q8—22no—
119C4⋊Q8—22no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—41no—
124C4⋊Q8—41no—
125C4⋊Q8—41no—
126C4⋊Q8—41no—
127C4⋊Q8—41no—
128C4⋊Q8—41no—
129C4⋊Q8C4⋊C414yes—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—42no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C42—22no—
147C2×C42—41no—
148C2×C42—82no—
149C2×C42C22×C411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×Q811yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161#108—84no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—41no—
174C22⋊C8—22no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182#97—22no—
183#97—41no—
184#97—41no—
185#97—41no—
186C4×C8—41no—
187C4×C8—41no—
188C4×C8—41no—
189C4×C8—41no—
190#95—22no—
191#95—41no—
192C24#12411yescharacteristic
193C2×Q8—24no—
194C2×Q8—42no—
195C2×Q8—42no—
196C2×Q8—42no—
197C2×Q8—84no—
198C2×Q8—84no—
199C2×Q8—84no—
200C2×Q8—84no—
201C2×Q8—82no—
202C2×Q8—82no—
203C2×Q8—82no—
204C2×Q8—82no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—82no—
216C22×C4—82no—
217C22×C4—82no—
218C22×C4—82no—
219C22×C4C2×C22⋊C411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4#12011yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12411yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4#12611yescharacteristic
236C22×C4#12711yescharacteristic
237M16—42no—
238M16—42no—
239M16—42no—
240M16—42no—
241M16—42no—
242M16—42no—
243M16—82no—
244C2×C8—24no—
245C2×C8—44no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—82no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C42—82no—
264C42—82no—
265C42C2×C4⋊C411yescharacteristic
266C42#11711yescharacteristic
267C42C4×D411yescharacteristic
268C42C4×D411yescharacteristic
269C42#12011yescharacteristic
270C42#12011yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12111yescharacteristic
274C42#12111yescharacteristic
275C42#12111yescharacteristic
276C42C22⋊Q811yescharacteristic
277C42C22⋊Q811yescharacteristic
278C42C22⋊Q811yescharacteristic
279C42#12311yescharacteristic
280C42#12311yescharacteristic
281C23—22no—
282C23—21no—
283C23—21no—
284C23—22no—
285C23#39011yescharacteristic
286C23#39311yescharacteristic
287C23#39711yescharacteristic
288Q8—84no—
289Q8—84no—
290Q8—84no—
291Q8—84no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—88no—
314C2×C4—82no—
315C2×C4—84no—
316C2×C4—84no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4#38011yescharacteristic
321C2×C4#38511yescharacteristic
322C2×C4#38511yescharacteristic
323C2×C4#38611yescharacteristic
324C2×C4#38811yescharacteristic
325C2×C4#38811yescharacteristic
326C2×C4#39211yescharacteristic
327C2×C4#39411yescharacteristic
328C2×C4#39411yescharacteristic
329C2×C4#39611yescharacteristic
330C2×C4#39611yescharacteristic
331C2×C4#39911yescharacteristic
332C2×C4#45512yes—
333C2×C4#45612yes—
334C2×C4#47112yes—
335C2×C4#47212yes—
336C8—44no—
337C8—82no—
338C8—82no—
339C8—82no—
340C8—82no—
341C22—24no—
342C22—24no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#143911yescharacteristic
350C22#197711yescharacteristic
351C22#197811yescharacteristic
352C22#202812yes—
353C22#208212yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—84no—
363C4—84no—
364C4#188511yescharacteristic
365C4#188611yescharacteristic
366C4#200712yes—
367C4#205112yes—
368C4#206312yes—
369C2—21no—
370C2—22no—
371C2—21no—
372C2—22no—
373C2#1105511yescharacteristic
374C2#1112711yescharacteristic
375C2#1113411yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
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
#219692
C2×#19882
#177462
#177422
#80982
#79502
#79352