Finite Group Databasebeta

← #99520

Subgroups — #99520

Order 512.

470 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22722C211yesmaximal, characteristic
2C4×#477C211yesmaximal, characteristic
3#9864C211yesmaximal, characteristic
4#9637C211yesmaximal, characteristic
5C4×Q8⋊C8C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#477C411yescharacteristic
9C2×#446—21no—
10C4×C4⋊Q8C2211yescharacteristic
11C42×Q8C2211yescharacteristic
12#1987C411yescharacteristic
13#1947C411yescharacteristic
14#1940—22no—
15#1939—21no—
16#1921—21no—
17#1863—21no—
18#1842—21no—
19#1842C2211yescharacteristic
20#1803C411yescharacteristic
21C4×#107—21no—
22#1767—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—22no—
29C2×Q8⋊C8—21no—
30#1279—21no—
31#1279—21no—
32#1279—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#477—22no—
39#477—22no—
40#446—42no—
41#446—42no—
42C2×#107—21no—
43C2×#107—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—22no—
49C2×C4⋊C8C2×C411yescharacteristic
50C2×C4⋊C8C2×C411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×C4⋊C8D411yescharacteristic
53C2×C4⋊C8D412yes—
54C2×#103—21no—
55C2×#103—21no—
56C2×#97—22no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62C2×C4×C8—21no—
63#391—21no—
64#389—21no—
65#389—21no—
66#384C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4C2×C411yescharacteristic
73C4×C4⋊C4D411yescharacteristic
74C4×C4⋊C4D411yescharacteristic
75C43—21no—
76C43C2311yescharacteristic
77#340—21no—
78#340—21no—
79#340—21no—
80#340—21no—
81#336—22no—
82#336—21no—
83#336—21no—
84#336—21no—
85Q8⋊C8—24no—
86Q8⋊C8—44no—
87C22×Q8—21no—
88C22×Q8C22⋊C411yescharacteristic
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—22no—
94C22×C8—41no—
95C22×C8—41no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8—21no—
99C4⋊Q8M1612yes—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—22no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8—41no—
108C4×Q8—42no—
109C4×Q8—42no—
110C4×Q8SD1612yes—
111C4×Q8Q1612yes—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—41no—
131C2×C42C22×C411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42#4111yescharacteristic
137C2×C42#4111yescharacteristic
138#107—24no—
139#107—42no—
140C4⋊C8—22no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—42no—
148C4⋊C8—41no—
149C4⋊C8—44no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—41no—
154C4⋊C8—82no—
155C4⋊C8M1612yes—
156C4⋊C8Q1612yes—
157#103—24no—
158#103—42no—
159#97—44no—
160C4×C8—22no—
161C4×C8—22no—
162C4×C8—22no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—41no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8—41no—
170C4×C8—41no—
171C4×C8—41no—
172#95—21no—
173#95—21no—
174#95—21no—
175#95—41no—
176#95—41no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8#10312yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4C2×C22⋊C411yescharacteristic
194C22×C4C4×D411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12311yescharacteristic
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—42no—
215C2×C8—41no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—41no—
219C2×C8—81no—
220C2×C8—81no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—22no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—82no—
240C4⋊C4#10312yes—
241C4⋊C4#10412yes—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—22no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—42no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42—41no—
258C42—81no—
259C42—81no—
260C42—81no—
261C42C2×M1611yescharacteristic
262C42C2×M1611yescharacteristic
263C42#13111yescharacteristic
264C42#13111yescharacteristic
265C42C2×SD1611yescharacteristic
266C42C2×Q1611yescharacteristic
267C42C2×Q1611yescharacteristic
268C42#13511yescharacteristic
269C42AGL(1,ℤ/8)11yescharacteristic
270C42#13711yescharacteristic
271C42#13711yescharacteristic
272C42#13711yescharacteristic
273C23#38611yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—44no—
277Q8—41no—
278Q8—41no—
279Q8—82no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4#40711yescharacteristic
308C2×C4#40811yescharacteristic
309C2×C4C2×#10311yescharacteristic
310C2×C4#41711yescharacteristic
311C2×C4C2×#10411yescharacteristic
312C2×C4#42111yescharacteristic
313C2×C4#43511yescharacteristic
314C2×C4#43511yescharacteristic
315C2×C4#43611yescharacteristic
316C2×C4#43611yescharacteristic
317C2×C4C4×Q1611yescharacteristic
318C2×C4#44111yescharacteristic
319C2×C4#44311yescharacteristic
320C2×C4#44411yescharacteristic
321C2×C4#45011yescharacteristic
322C2×C4#45111yescharacteristic
323C2×C4#45111yescharacteristic
324C2×C4#45211yescharacteristic
325C2×C4#45311yescharacteristic
326C2×C4#45411yescharacteristic
327C2×C4#46211yescharacteristic
328C2×C4#46411yescharacteristic
329C2×C4#48311yescharacteristic
330C2×C4#48411yescharacteristic
331C8—44no—
332C8—42no—
333C8—42no—
334C8—82no—
335C8—81no—
336C8—82no—
337C8—81no—
338C22#187011yescharacteristic
339C22#187111yescharacteristic
340C22#187211yescharacteristic
341C22#187611yescharacteristic
342C22#187811yescharacteristic
343C22#188111yescharacteristic
344C22#188311yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—42no—
353C4—42no—
354C4—42no—
355C4—81no—
356C4—82no—
357C4—161no—
358C4#148711yescharacteristic
359C4#148911yescharacteristic
360C4#149311yescharacteristic
361C4#149511yescharacteristic
362C4#158411yescharacteristic
363C4#158711yescharacteristic
364C4#159111yescharacteristic
365C4#159311yescharacteristic
366C4#163111yescharacteristic
367C4#163311yescharacteristic
368C4#163611yescharacteristic
369C4#163711yescharacteristic
370C2#894211yescharacteristic
371C2#895011yescharacteristic
372C2#895611yescharacteristic
373C2#896911yescharacteristic
374C2#897511yescharacteristic
375C2#899011yescharacteristic
376C2#899311yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#227222
C4×#4772
#98642
#96372
C4×Q8⋊C82
#70312
#70152