Finite Group Databasebeta

← #117913

Subgroups — #117913

Order 512.

624 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21337C211yesmaximal, characteristic
2C2×#1567C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic
5C4⋊#338C211yesmaximal, characteristic
6#8001C211yesmaximal, characteristic
7C2×#1278C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1998—22no—
16#1997—21no—
17#1997—21no—
18#1742—22no—
19C2×#338—22no—
20#1567—22no—
21#1567—22no—
22C2×#335—22no—
23#1550—22no—
24#1549—21no—
25#1548—21no—
26#1542—22no—
27#1493—22no—
28#1493—21no—
29#1493—21no—
30C2×Q8⋊C8C414yes—
31#1292—22no—
32#1278—21no—
33#1278—21no—
34C22×M16—21no—
35C22×M16—21no—
36C22×M16—21no—
37C22×M16D412yes—
38C23×C8—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47C2×C4⋊Q8D411yescharacteristic
48C2×C4⋊Q8D411yescharacteristic
49C2×#125—21no—
50C2×C22⋊Q8—21no—
51C2×C22⋊Q8Q812yes—
52C2×C4×Q8—21no—
53C2×C4×Q8C2×C412yes—
54C2×#117—21no—
55C22×C42C2311yescharacteristic
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423D412yes—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8C2×C412yes—
77C2×C4⋊C8D412yes—
78C2×C4⋊C8D412yes—
79C2×C22⋊C8—21no—
80C4×M16—21no—
81C4×M16—21no—
82C4×M16—21no—
83C4×M16—21no—
84C2×#97—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8C2×C412yes—
91C2×C4×C8D412yes—
92C2×C4×C8D411yescharacteristic
93C2×C4×C8D411yescharacteristic
94#343—24no—
95#343—24no—
96#338—44no—
97#335—28no—
98#333—24no—
99#332—24no—
100Q8⋊C8—24no—
101Q8⋊C8—24no—
102C22×Q8—21no—
103C22×Q8C4⋊C412yes—
104C23×C4C2×D411yescharacteristic
105C23×C4C2×Q811yescharacteristic
106C23×C4#4111yescharacteristic
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—22no—
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—22no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—42no—
119C2×M16—42no—
120C2×M16—42no—
121C2×M16—42no—
122C2×M16—42no—
123C2×M16—42no—
124C2×M16Q1614yes—
125C22×C8—21no—
126C22×C8—22no—
127C22×C8—21no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—44no—
134C22×C8—41no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140C4⋊Q8—21no—
141C4⋊Q8—21no—
142C4⋊Q8—21no—
143#125—41no—
144#125—41no—
145#125—41no—
146#125—41no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—41no—
152C22⋊Q8—41no—
153C22⋊Q8—41no—
154C22⋊Q8—41no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C4×Q8—41no—
163#117—41no—
164#117—41no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C4⋊C412yes—
173C2×C22⋊C4—22no—
174C2×C42—22no—
175C2×C42C22×C411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×D411yescharacteristic
179C2×C42C2×D411yescharacteristic
180C2×C42C2×D411yescharacteristic
181C2×C42C2×D411yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C2×C42#4111yescharacteristic
185C2×C42#4111yescharacteristic
186C2×C42#4111yescharacteristic
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193C4⋊C8—22no—
194C4⋊C8—22no—
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C22⋊C8—41no—
202C22⋊C8—41no—
203#97—41no—
204#97—41no—
205C4×C8—22no—
206C4×C8—22no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—41no—
210C4×C8—41no—
211C4×C8—41no—
212C4×C8—41no—
213C4×C8C22⋊C412yes—
214C4×C8C22⋊C412yes—
215C24C22⋊Q811yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—82no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4C2×C4⋊C411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4C4×D411yescharacteristic
229C22×C4#12011yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12311yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12611yescharacteristic
243C22×C4#12711yescharacteristic
244C22×C4C2×Q1612yes—
245C22×C4#13512yes—
246C22×C4AGL(1,ℤ/8)12yes—
247C22×C4#13712yes—
248M16—24no—
249M16—24no—
250M16—42no—
251M16—42no—
252M16—44no—
253M16—82no—
254M16—82no—
255M16—81no—
256M16—81no—
257M16—81no—
258M16—81no—
259M16—81no—
260M16—81no—
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—24no—
265C2×C8—44no—
266C2×C8—44no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—44no—
275C2×C8—44no—
276C2×C8—82no—
277C2×C8—82no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C42—42no—
293C42—42no—
294C42C2×C22⋊C411yescharacteristic
295C42#11711yescharacteristic
296C42C4×D411yescharacteristic
297C42C4×D411yescharacteristic
298C42#12011yescharacteristic
299C42#12011yescharacteristic
300C42#12111yescharacteristic
301C42#12111yescharacteristic
302C42#12111yescharacteristic
303C42#12111yescharacteristic
304C42#12111yescharacteristic
305C42#12311yescharacteristic
306C42#12411yescharacteristic
307C42#12411yescharacteristic
308C42#12411yescharacteristic
309C42#12611yescharacteristic
310C23—41no—
311C23—41no—
312C23#38511yescharacteristic
313C23#39611yescharacteristic
314C23#39911yescharacteristic
315C23#47712yes—
316C23#47912yes—
317Q8—44no—
318Q8—82no—
319Q8—82no—
320Q8—82no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4#38011yescharacteristic
338C2×C4#38511yescharacteristic
339C2×C4#38611yescharacteristic
340C2×C4#38811yescharacteristic
341C2×C4#38811yescharacteristic
342C2×C4#39011yescharacteristic
343C2×C4#39211yescharacteristic
344C2×C4#39311yescharacteristic
345C2×C4#39411yescharacteristic
346C2×C4#39411yescharacteristic
347C2×C4#39611yescharacteristic
348C2×C4#39711yescharacteristic
349C2×C4C4×Q1612yes—
350C2×C4#44012yes—
351C2×C4#44912yes—
352C2×C4#45112yes—
353C2×C4#46212yes—
354C2×C4#46312yes—
355C2×C4#46712yes—
356C2×C4#46812yes—
357C2×C4#48412yes—
358C2×C4#48512yes—
359C2×C4#49411yescharacteristic
360C2×C4#49511yescharacteristic
361C2×C4#49611yescharacteristic
362C2×C4#49711yescharacteristic
363C8—24no—
364C8—42no—
365C8—44no—
366C8—82no—
367C8—82no—
368C8—82no—
369C8—82no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22#143911yescharacteristic
379C22#186312yes—
380C22#206812yes—
381C22#209511yescharacteristic
382C22#209711yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4#181312yes—
392C4#192812yes—
393C4#196911yescharacteristic
394C4#197311yescharacteristic
395C4#201211yescharacteristic
396C4#201611yescharacteristic
397C4#203612yes—
398C4#205012yes—
399C2—22no—
400C2—21no—
401C2—21no—
402C2—22no—
403C2#1108211yescharacteristic
404C2#1109911yescharacteristic
405C2#1112411yescharacteristic
subgroupG/H
centerC2×C4#388
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#213372
C2×#15672
#177082
C2×#14932
C4⋊#3382
#80012
C2×#12782