Finite Group Databasebeta

← #118367

Subgroups — #118367

Order 512.

548 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17817C211yesmaximal, characteristic
2#17749C211yesmaximal, characteristic
3C2×#1550C211yesmaximal, characteristic
4#17385C211yesmaximal, characteristic
5#8129C211yesmaximal, characteristic
6C2×#1301C211yesmaximal, characteristic
7#7935C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15#1574—22no—
16#1573—22no—
17#1567—21no—
18#1566—21no—
19#1559—22no—
20#1550—22no—
21#1550—21no—
22#1550—21no—
23#1550—22no—
24#1548—21no—
25#1546—21no—
26C2×#333—21no—
27C2×#332—21no—
28#1472C414yes—
29#1470—22no—
30#1461—22no—
31#1309—22no—
32#1301—22no—
33#1283—22no—
34C22×M16—21no—
35C22×M16—21no—
36C23×C8—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45C2×C4⋊Q8D411yescharacteristic
46C2×C4⋊Q8D411yescharacteristic
47C2×#125—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8C2×C412yes—
50C2×C4×Q8—21no—
51C2×C4×Q8Q812yes—
52C2×#117—21no—
53C22×C42C2311yescharacteristic
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431D412yes—
65#431D412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423D411yescharacteristic
74#423D411yescharacteristic
75#423D412yes—
76#423D412yes—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8—21no—
84C2×C4⋊C8—21no—
85C2×C4⋊C8—21no—
86C2×C4⋊C8—21no—
87C2×C4⋊C8D412yes—
88#407—21no—
89#407C2×C412yes—
90C2×C22⋊C8C2×C412yes—
91C4×M16—21no—
92C4×M16—21no—
93C2×C4×C8—21no—
94#335—24no—
95#334—24no—
96#333—24no—
97#333—22no—
98#333—22no—
99#332—24no—
100#332—22no—
101#332—22no—
102#324—28no—
103C22×Q8—21no—
104C22×Q8C4⋊C412yes—
105C23×C4C22×C411yescharacteristic
106C23×C4#4111yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—21no—
109C2×M16—21no—
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—81no—
116C2×M16—82no—
117C2×M16—81no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—81no—
125C22×C8—81no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134#125—41no—
135#125—41no—
136#125—41no—
137#125—41no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C22⋊Q8—41no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154#117—41no—
155#117—41no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4C4⋊C412yes—
164C2×C22⋊C4—22no—
165C2×C42—22no—
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×Q811yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—22no—
185C4⋊C8—21no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—41no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—41no—
202C22⋊C8—41no—
203C22⋊C8C22⋊C414yes—
204#97—41no—
205#97—41no—
206C4×C8—22no—
207C4×C8—22no—
208C4×C8—41no—
209C4×C8—41no—
210C24#11711yescharacteristic
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8—82no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—81no—
229C22×C4C2×C22⋊C411yescharacteristic
230C22×C4C2×C4⋊C411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12411yescharacteristic
244C22×C4#12411yescharacteristic
245C22×C4#12611yescharacteristic
246C22×C4#12611yescharacteristic
247M16—42no—
248M16—42no—
249M16—81no—
250M16—82no—
251M16—81no—
252M16—82no—
253M16—82no—
254M16—82no—
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—82no—
263C2×C8—82no—
264C2×C8—82no—
265C2×C8—82no—
266C2×C8—81no—
267C2×C8—81no—
268C2×C8—82no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—42no—
284C42—42no—
285C42#12011yescharacteristic
286C42#12011yescharacteristic
287C42#12011yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42C22⋊Q811yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42#12311yescharacteristic
297C42#12311yescharacteristic
298C42#12311yescharacteristic
299C42#12411yescharacteristic
300C42#12711yescharacteristic
301C23—21no—
302C23—21no—
303C23—22no—
304C23—41no—
305C23#38011yescharacteristic
306C23#38811yescharacteristic
307C23#38811yescharacteristic
308Q8—82no—
309Q8—82no—
310Q8—81no—
311Q8—81no—
312Q8—81no—
313Q8—81no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4#38511yescharacteristic
343C2×C4#38511yescharacteristic
344C2×C4#38611yescharacteristic
345C2×C4#39011yescharacteristic
346C2×C4#39211yescharacteristic
347C2×C4#39311yescharacteristic
348C2×C4#39411yescharacteristic
349C2×C4#39411yescharacteristic
350C2×C4#39611yescharacteristic
351C2×C4#39611yescharacteristic
352C2×C4#39711yescharacteristic
353C2×C4#39911yescharacteristic
354C2×C4#47111yescharacteristic
355C2×C4#47111yescharacteristic
356C2×C4#47112yes—
357C2×C4#47211yescharacteristic
358C2×C4#47311yescharacteristic
359C2×C4#47312yes—
360C8—44no—
361C8—82no—
362C8—82no—
363C8—82no—
364C8—82no—
365C8—81no—
366C8—81no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#143911yescharacteristic
377C22#181511yescharacteristic
378C22#181611yescharacteristic
379C22#193012yes—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—82no—
389C4—82no—
390C4#201911yescharacteristic
391C4#202011yescharacteristic
392C4#205111yescharacteristic
393C4#205111yescharacteristic
394C4#205211yescharacteristic
395C4#205211yescharacteristic
396C4#206412yes—
397C2—21no—
398C2—21no—
399C2—22no—
400C2—41no—
401C2#1109011yescharacteristic
402C2#1110511yescharacteristic
403C2#1114511yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C23×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
#178172
#177492
C2×#15502
#173852
#81292
C2×#13012
#79352