Finite Group Databasebeta

← #117606

Subgroups — #117606

Order 512.

638 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21820C211yesmaximal, characteristic
2#20735C211yesmaximal, characteristic
3#17818C211yesmaximal, characteristic
4C2×#1491C211yesmaximal, characteristic
5#8073C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7926C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2283C2211yescharacteristic
15#1985—22no—
16#1984—22no—
17#1823C411yescharacteristic
18#1823C411yescharacteristic
19#1817—22no—
20#1805—22no—
21#1787C411yescharacteristic
22#1787C411yescharacteristic
23C4×#103—22no—
24#1573—22no—
25#1573—22no—
26#1568—22no—
27#1491—22no—
28#1491—22no—
29C2×Q8⋊C8—22no—
30#1300—22no—
31#1283—22no—
32#1282—22no—
33C23×Q8C2×C411yescharacteristic
34C22×M16—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×Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8D412yes—
46C2×C4×Q8Q812yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C42—21no—
50C22×C42C2311yescharacteristic
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8D412yes—
69C2×C4⋊C8D412yes—
70C2×C4⋊C8D412yes—
71C2×#103—22no—
72C2×#103—22no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8C2×C411yescharacteristic
76C2×C22⋊C8C2×C411yescharacteristic
77C2×C22⋊C8D412yes—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16—21no—
81C4×M16D412yes—
82C2×#97—21no—
83C2×#97—21no—
84C2×#97—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8D412yes—
88#383—21no—
89#382—21no—
90#381—21no—
91#380C2×C411yescharacteristic
92#380C2×C411yescharacteristic
93C4×C4⋊C4—21no—
94C4×C22⋊C4—21no—
95#376—21no—
96#340—22no—
97#340—22no—
98#336—28no—
99#335—24no—
100#334—24no—
101Q8⋊C8—28no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—44no—
108C22×Q8C4⋊C412yes—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4C22×C411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C23×C4#4111yescharacteristic
114C2×M16—24no—
115C2×M16—22no—
116C2×M16—42no—
117C2×M16—41no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—41no—
122C22×C8C22⋊C412yes—
123C22×C8C22⋊C412yes—
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—41no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136C4×Q8—41no—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4C4⋊C412yes—
154C2×C22⋊C4—21no—
155C2×C22⋊C4—21no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—41no—
159C2×C42—41no—
160C2×C42—41no—
161C2×C42—41no—
162C2×C42—41no—
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
174C2×C42#4111yescharacteristic
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183#103—44no—
184#103—44no—
185C22⋊C8—21no—
186C22⋊C8—21no—
187C22⋊C8—21no—
188C22⋊C8—21no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195#97—22no—
196#97—41no—
197#97—41no—
198#97—41no—
199#97—41no—
200#97—41no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—22no—
204C4×C8—41no—
205C4×C8—41no—
206C4×C8—41no—
207#95—21no—
208#95—21no—
209#95—41no—
210#95—41no—
211#95—41no—
212C24C4×D411yescharacteristic
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8—24no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8—44no—
223C2×Q8—44no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—44no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4C2×C22⋊C411yescharacteristic
242C22×C4C2×C4⋊C411yescharacteristic
243C22×C4#11711yescharacteristic
244C22×C4C4×D411yescharacteristic
245C22×C4C4×D411yescharacteristic
246C22×C4C4×D411yescharacteristic
247C22×C4#12011yescharacteristic
248C22×C4#12111yescharacteristic
249C22×C4#12111yescharacteristic
250C22×C4#12111yescharacteristic
251C22×C4C22⋊Q811yescharacteristic
252C22×C4C22⋊Q811yescharacteristic
253C22×C4#12311yescharacteristic
254C22×C4#12311yescharacteristic
255C22×C4#12411yescharacteristic
256C22×C4#12411yescharacteristic
257C22×C4#12611yescharacteristic
258C22×C4#12711yescharacteristic
259M16—24no—
260M16—44no—
261M16—42no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—44no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—44no—
269C2×C8—44no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—42no—
287C42—42no—
288C42—42no—
289C42—42no—
290C42—82no—
291C42#12011yescharacteristic
292C42#12011yescharacteristic
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42C22⋊Q811yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42#12311yescharacteristic
303C42#12311yescharacteristic
304C42#12311yescharacteristic
305C42#12411yescharacteristic
306C42#12611yescharacteristic
307C23—41no—
308C23—41no—
309C23#38511yescharacteristic
310C23#38811yescharacteristic
311C23#39011yescharacteristic
312C23#44312yes—
313C23#44412yes—
314Q8—24no—
315Q8—24no—
316Q8—42no—
317Q8—42no—
318Q8—44no—
319Q8—44no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4#38011yescharacteristic
357C2×C4#38511yescharacteristic
358C2×C4#38611yescharacteristic
359C2×C4#38811yescharacteristic
360C2×C4#39211yescharacteristic
361C2×C4#39311yescharacteristic
362C2×C4#39411yescharacteristic
363C2×C4#39411yescharacteristic
364C2×C4#39611yescharacteristic
365C2×C4#39611yescharacteristic
366C2×C4#39711yescharacteristic
367C2×C4#39911yescharacteristic
368C8—44no—
369C8—42no—
370C8—42no—
371C8—82no—
372C8—82no—
373C8—82no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22#143911yescharacteristic
383C22#186612yes—
384C22#192912yes—
385C22#197411yescharacteristic
386C22#197511yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—82no—
399C4—161no—
400C4—161no—
401C4#189112yes—
402C4#200912yes—
403C2—21no—
404C2—21no—
405C2—22no—
406C2—22no—
407C2#1107111yescharacteristic
408C2#1112511yescharacteristic
409C2#1113011yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ 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
#218202
#207352
#178182
C2×#14912
#80732
#79322
#79262