Finite Group Databasebeta

← #117130

Subgroups — #117130

Order 512.

692 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1990C211yesmaximal, characteristic
2C2×#1837C211yesmaximal, characteristic
3C2×#1549C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5#8043C211yesmaximal, characteristic
6#8043C211yesmaximal, characteristic
7#7849C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14C2×#384C2211yescharacteristic
15#1990—22no—
16#1990C414yes—
17#1837—22no—
18#1837—22no—
19C2×#341—22no—
20C2×#340—22no—
21#1549—22no—
22#1549—22no—
23#1548—22no—
24#1548—22no—
25C2×#333—22no—
26C2×#332—22no—
27#1296—22no—
28#1296—22no—
29#1273—22no—
30C23×Q8—21no—
31C22×M16—21no—
32C22×M16—21no—
33C23×C8D412yes—
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⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8C2×C412yes—
44C2×C4⋊Q8D412yes—
45C2×C4⋊Q8Q812yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C42C2311yescharacteristic
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
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#423D412yes—
67#423D412yes—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8D412yes—
73C2×C4⋊C8D412yes—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C4×C8—21no—
77C2×C4×C8—21no—
78C2×C4×C8—21no—
79C2×C4×C8—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82C2×C4×C8C2×C412yes—
83C2×C4×C8D412yes—
84#384—21no—
85#384—21no—
86#384—21no—
87#384C2×C412yes—
88#341—28no—
89#340—28no—
90#333—28no—
91#332—28no—
92C22×Q8—22no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—82no—
99C22×Q8—82no—
100C23×C4—41no—
101C23×C4—41no—
102C23×C4C2×D411yescharacteristic
103C23×C4#4111yescharacteristic
104C23×C4#4111yescharacteristic
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—41no—
108C2×M16—41no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16—42no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8C22⋊C414yes—
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—22no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4⋊Q8C4⋊C414yes—
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—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4—82no—
162C2×C42C22×C411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×Q811yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—22no—
194C4×C8—41no—
195C4×C8—41no—
196C4×C8—41no—
197C4×C8—41no—
198C24#12411yescharacteristic
199C2×Q8—24no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—84no—
204C2×Q8—84no—
205C2×Q8—84no—
206C2×Q8—84no—
207C2×Q8—82no—
208C2×Q8—82no—
209C2×Q8—82no—
210C2×Q8—82no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—82no—
220C22×C4—82no—
221C22×C4—82no—
222C22×C4—82no—
223C22×C4—82no—
224C22×C4C2×C22⋊C411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4#12011yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12411yescharacteristic
239C22×C4#12611yescharacteristic
240C22×C4#12611yescharacteristic
241C22×C4#12711yescharacteristic
242C22×C4#13512yes—
243C22×C4#13512yes—
244C22×C4#13712yes—
245C22×C4#13712yes—
246M16—44no—
247M16—44no—
248M16—82no—
249M16—82no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—81no—
266C2×C8—81no—
267C2×C8—81no—
268C2×C8—81no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—44no—
278C4⋊C4—82no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C42C2×C4⋊C411yescharacteristic
285C42#11711yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×D411yescharacteristic
288C42#12011yescharacteristic
289C42#12011yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42#12111yescharacteristic
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42C22⋊Q811yescharacteristic
297C42C22⋊Q811yescharacteristic
298C42#12311yescharacteristic
299C42#12311yescharacteristic
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#39011yescharacteristic
305C23#39311yescharacteristic
306C23#39711yescharacteristic
307C23#48812yes—
308C23#49112yes—
309Q8—84no—
310Q8—84no—
311Q8—84no—
312Q8—84no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—44no—
326C2×C4—84no—
327C2×C4—84no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—164no—
334C2×C4#38011yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38511yescharacteristic
337C2×C4#38611yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#39211yescharacteristic
341C2×C4#39411yescharacteristic
342C2×C4#39411yescharacteristic
343C2×C4#39611yescharacteristic
344C2×C4#39611yescharacteristic
345C2×C4#39911yescharacteristic
346C2×C4#41612yes—
347C2×C4#41912yes—
348C2×C4#45212yes—
349C2×C4#45212yes—
350C2×C4#46412yes—
351C2×C4#46412yes—
352C2×C4#47112yes—
353C2×C4#47112yes—
354C2×C4#47212yes—
355C2×C4#47312yes—
356C2×C4#47912yes—
357C2×C4#47912yes—
358C2×C4#48512yes—
359C2×C4#48512yes—
360C2×C4#49511yescharacteristic
361C2×C4#49511yescharacteristic
362C2×C4#49711yescharacteristic
363C2×C4#49711yescharacteristic
364C8—44no—
365C8—82no—
366C8—82no—
367C8—82no—
368C8—82no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#143911yescharacteristic
378C22#195811yescharacteristic
379C22#196011yescharacteristic
380C22#197711yescharacteristic
381C22#197711yescharacteristic
382C22#197811yescharacteristic
383C22#197911yescharacteristic
384C22#202612yes—
385C22#207412yes—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—84no—
391C4—162no—
392C4#180512yes—
393C4#187312yes—
394C4#201511yescharacteristic
395C4#201511yescharacteristic
396C4#205112yes—
397C4#205212yes—
398C4#206312yes—
399C4#206412yes—
400C4#209711yescharacteristic
401C4#209711yescharacteristic
402C2—22no—
403C2—22no—
404C2#976911yescharacteristic
405C2#977011yescharacteristic
406C2#977611yescharacteristic
407C2#977811yescharacteristic
408C2#1105211yescharacteristic
409C2#1112711yescharacteristic
410C2#1112811yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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×#19902
C2×#18372
C2×#15492
C2×#15482
#80432
#78492