Finite Group Databasebeta

← #117644

Subgroups — #117644

Order 512.

623 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
1#20727C211yesmaximal, characteristic
2#17822C211yesmaximal, characteristic
3C2×#1491C211yesmaximal, characteristic
4C2×#1487C211yesmaximal, characteristic
5#8060C211yesmaximal, characteristic
6#7938C211yesmaximal, characteristic
7#7921C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15#1821C412yes—
16#1801—22no—
17#1784C412yes—
18C4×#101—22no—
19#1573—22no—
20#1571—21no—
21#1570—21no—
22#1569—22no—
23#1491—22no—
24#1491—22no—
25#1487—22no—
26#1487—22no—
27C2×Q8⋊C8—22no—
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30#1299—22no—
31#1283—22no—
32#1281—22no—
33C23×Q8C2×C411yescharacteristic
34C22×M16—21no—
35C22×M16—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×Q8—21no—
46C2×C4×Q8D412yes—
47C2×C4×Q8Q812yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C42—21no—
51C22×C42C2311yescharacteristic
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431D412yes—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423D412yes—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8D411yescharacteristic
77C2×C4⋊C8D411yescharacteristic
78C2×C4⋊C8D412yes—
79C2×#101—24no—
80#407C2×C412yes—
81#407C2×C412yes—
82C2×C22⋊C8—21no—
83C2×C22⋊C8—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16D412yes—
89C4×M16D412yes—
90C2×#97—21no—
91C2×#97—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94#343—24no—
95#335—24no—
96#334—24no—
97Q8⋊C8—28no—
98Q8⋊C8—24no—
99Q8⋊C8—24no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—44no—
106C22×Q8C4⋊C412yes—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4C22×C411yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—44no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—82no—
119C2×M16C22⋊C414yes—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—22no—
123C22×C8—41no—
124C22×C8—41no—
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×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C4⋊C412yes—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—41no—
156C2×C42—41no—
157C2×C42—41no—
158C2×C42—41no—
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×Q811yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C4⋊C8—22no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—22no—
176C4⋊C8—21no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185#101—48no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194#97—22no—
195#97—22no—
196#97—41no—
197#97—41no—
198#97—41no—
199#97—41no—
200C4×C8—22no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—41no—
204C4×C8—41no—
205C4×C8—41no—
206C24#11711yescharacteristic
207C2×Q8—24no—
208C2×Q8—24no—
209C2×Q8—24no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—44no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—44no—
217C2×Q8—44no—
218C2×Q8—41no—
219C2×Q8—41no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—44no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—82no—
232C22×C4C2×C22⋊C411yescharacteristic
233C22×C4C2×C4⋊C411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4C4×D411yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12111yescharacteristic
242C22×C4C22⋊Q811yescharacteristic
243C22×C4C22⋊Q811yescharacteristic
244C22×C4#12311yescharacteristic
245C22×C4#12311yescharacteristic
246C22×C4#12411yescharacteristic
247C22×C4#12411yescharacteristic
248C22×C4#12611yescharacteristic
249C22×C4#12611yescharacteristic
250M16—24no—
251M16—42no—
252M16—44no—
253M16—44no—
254M16—44no—
255M16—82no—
256M16—82no—
257C2×C8—24no—
258C2×C8—44no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—82no—
268C2×C8—82no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C42—42no—
278C42—42no—
279C42—42no—
280C42—42no—
281C42#12011yescharacteristic
282C42#12011yescharacteristic
283C42#12011yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12311yescharacteristic
295C42#12411yescharacteristic
296C42#12711yescharacteristic
297C23—22no—
298C23—22no—
299C23—41no—
300C23#38011yescharacteristic
301C23#38811yescharacteristic
302C23#38811yescharacteristic
303Q8—24no—
304Q8—24no—
305Q8—44no—
306Q8—42no—
307Q8—42no—
308Q8—44no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—24no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4#38511yescharacteristic
338C2×C4#38511yescharacteristic
339C2×C4#38611yescharacteristic
340C2×C4#39011yescharacteristic
341C2×C4#39211yescharacteristic
342C2×C4#39311yescharacteristic
343C2×C4#39411yescharacteristic
344C2×C4#39411yescharacteristic
345C2×C4#39611yescharacteristic
346C2×C4#39611yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#39911yescharacteristic
349C2×C4#47112yes—
350C2×C4#47312yes—
351C8—44no—
352C8—44no—
353C8—82no—
354C8—82no—
355C8—81no—
356C8—82no—
357C8—81no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22#143911yescharacteristic
367C22#193012yes—
368C22#193212yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—82no—
380C4#189112yes—
381C4#201911yescharacteristic
382C4#202011yescharacteristic
383C4#206412yes—
384C2—22no—
385C2—22no—
386C2—41no—
387C2#1107111yescharacteristic
388C2#1114511yescharacteristic
389C2#1114611yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#117
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
#207272
#178222
C2×#14912
C2×#14872
#80602
#79382
#79212