Finite Group Databasebeta

← #110545

Subgroups — #110545

Order 512.

687 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1966C211yesmaximal, characteristic
2#17746C211yesmaximal, characteristic
3C2×#1548C211yesmaximal, characteristic
4#17327C211yesmaximal, characteristic
5#8065C211yesmaximal, characteristic
6#8004C211yesmaximal, characteristic
7#7938C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×#101C414yes—
15C2×C4×M16C2211yescharacteristic
16#1966—22no—
17#1966—21no—
18#1966—21no—
19#1558C414yes—
20#1548—22no—
21#1548—21no—
22#1548—21no—
23#1548—22no—
24#1548—22no—
25C2×#333C414yes—
26#1453—22no—
27#1451—21no—
28#1451—21no—
29C8×M16—21no—
30C8×M16—21no—
31#1299—22no—
32#1292—22no—
33#1283—22no—
34C23×Q8C2×C412yes—
35C22×M16—21no—
36C22×M16C2×C412yes—
37C22×M16C2×C412yes—
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⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8C2×C412yes—
49C2×C4⋊Q8C2×C412yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432C2×C412yes—
56#432C2×C412yes—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431D412yes—
63#431D411yescharacteristic
64#431D411yescharacteristic
65#431D412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—21no—
75#423D412yes—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8C2×C412yes—
80C2×C4⋊C8C2×C412yes—
81C2×#101—24no—
82C2×#101—24no—
83C2×#101—48no—
84#407—21no—
85#407—21no—
86C2×C22⋊C8—21no—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16—21no—
90C4×M16—21no—
91C4×M16D412yes—
92C4×M16D411yescharacteristic
93C4×M16D411yescharacteristic
94C2×#97—21no—
95C2×C4×C8—21no—
96C2×C4×C8—21no—
97#333—24no—
98#333—24no—
99#333—28no—
100#322—22no—
101#322—22no—
102#322—22no—
103C82—22no—
104C22×Q8—22no—
105C22×Q8—22no—
106C22×Q8—22no—
107C22×Q8—22no—
108C22×Q8—22no—
109C22×Q8—44no—
110C22×Q8—44no—
111C22×Q8C4214yes—
112C23×C4—22no—
113C23×C4C22×C411yescharacteristic
114C23×C4#4111yescharacteristic
115C23×C4#4111yescharacteristic
116C2×M16—22no—
117C2×M16—22no—
118C2×M16—24no—
119C2×M16—22no—
120C2×M16—22no—
121C2×M16—42no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C2×M16—44no—
126C2×M16—82no—
127C2×M16C22⋊C412yes—
128C2×M16C22⋊C412yes—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—22no—
141C4⋊Q8—41no—
142C4⋊Q8—41no—
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4⋊Q8—41no—
146C4⋊Q8—41no—
147C4⋊Q8—41no—
148C4⋊Q8—41no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C42C22×C411yescharacteristic
162C2×C42C22×C411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8C22⋊C412yes—
186C4⋊C8C22⋊C412yes—
187C4⋊C8C22⋊C414yes—
188#101—48no—
189#101—48no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—21no—
193C22⋊C8—21no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197#97—22no—
198#97—22no—
199#97—22no—
200#97—21no—
201#97—21no—
202C4×C8—21no—
203C4×C8—21no—
204C4×C8—22no—
205C4×C8—21no—
206C4×C8—21no—
207C4×C8—22no—
208C4×C8—22no—
209C4×C8—41no—
210C24#11711yescharacteristic
211C2×Q8—24no—
212C2×Q8—24no—
213C2×Q8—48no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—44no—
217C2×Q8—44no—
218C2×Q8—84no—
219C2×Q8—84no—
220C2×Q8—82no—
221C2×Q8—82no—
222C2×Q8—82no—
223C2×Q8—82no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—48no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4C2×C4211yescharacteristic
234C22×C4C2×C22⋊C411yescharacteristic
235C22×C4C4×D411yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4C4×D411yescharacteristic
240C22×C4C4×D411yescharacteristic
241C22×C4C4×D411yescharacteristic
242C22×C4C4×D411yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4#12311yescharacteristic
246C22×C4#12311yescharacteristic
247C22×C4#12411yescharacteristic
248C22×C4#12411yescharacteristic
249C22×C4#12611yescharacteristic
250C22×C4#12611yescharacteristic
251M16—22no—
252M16—22no—
253M16—22no—
254M16—44no—
255M16—42no—
256M16—42no—
257M16—44no—
258M16—82no—
259M16—82no—
260M16—82no—
261M16—82no—
262M16#10014yes—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—24no—
268C2×C8—44no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—82no—
273C2×C8—82no—
274C2×C8—82no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C42C2×C22⋊C411yescharacteristic
284C42C2×C22⋊C411yescharacteristic
285C42#11711yescharacteristic
286C42#11711yescharacteristic
287C42C4×D411yescharacteristic
288C42C4×D411yescharacteristic
289C42C4×D411yescharacteristic
290C42C4×D411yescharacteristic
291C42#12011yescharacteristic
292C42#12111yescharacteristic
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42#12111yescharacteristic
296C42#12311yescharacteristic
297C42#12411yescharacteristic
298C42#12711yescharacteristic
299C23—22no—
300C23—22no—
301C23—41no—
302C23C4×C22⋊C411yescharacteristic
303C23#38811yescharacteristic
304C23#38811yescharacteristic
305Q8—84no—
306Q8—84no—
307Q8—84no—
308Q8—82no—
309Q8—82no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—48no—
332C2×C4—84no—
333C2×C4—84no—
334C2×C4C4×C22⋊C411yescharacteristic
335C2×C4C4×C22⋊C411yescharacteristic
336C2×C4#38611yescharacteristic
337C2×C4#38611yescharacteristic
338C2×C4#38611yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#38811yescharacteristic
341C2×C4#38811yescharacteristic
342C2×C4#38811yescharacteristic
343C2×C4#39011yescharacteristic
344C2×C4#39011yescharacteristic
345C2×C4#39011yescharacteristic
346C2×C4C2×#10012yes—
347C2×C4#41312yes—
348C2×C4#47112yes—
349C2×C4#47312yes—
350C8—24no—
351C8—42no—
352C8—42no—
353C8—42no—
354C8—44no—
355C8—82no—
356C8—82no—
357C8—82no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22#143711yescharacteristic
367C22C4×#10012yes—
368C22#193012yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—84no—
377C4#190012yes—
378C4#190212yes—
379C4#190812yes—
380C4#196511yescharacteristic
381C4#196711yescharacteristic
382C4#197711yescharacteristic
383C4#197911yescharacteristic
384C2—22no—
385C2—22no—
386C2—41no—
387C2#1094211yescharacteristic
388C2#1095211yescharacteristic
389C2#1096211yescharacteristic
subgroupG/H
center, socleC22#1437
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C22×C4 ▷ 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
C2×#19662
#177462
C2×#15482
#173272
#80652
#80042
#79382