Finite Group Databasebeta

← #99529

Subgroups — #99529

Order 512.

446 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22825C211yesmaximal, characteristic
2C4×#475C211yesmaximal, characteristic
3#9870C211yesmaximal, characteristic
4#9673C211yesmaximal, characteristic
5C4×Q8⋊C8C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#475C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1988C411yescharacteristic
12#1984—21no—
13#1948C411yescharacteristic
14#1919—21no—
15#1917—22no—
16#1865—21no—
17#1842C2211yescharacteristic
18#1831—21no—
19#1803C411yescharacteristic
20C4×#106—21no—
21#1770—21no—
22#1767—21no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C42×C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—22no—
32#1279—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#475—22no—
39#475—22no—
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8C2×C411yescharacteristic
46C2×C4⋊C8C2×C411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D412yes—
50C2×#103—21no—
51C2×#103—21no—
52C2×#97—22no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59#391—21no—
60#389—21no—
61#389—21no—
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4C2×C411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C4×C4⋊C4D411yescharacteristic
71C43—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—22no—
79#336—22no—
80#336—21no—
81#336—21no—
82#336—21no—
83Q8⋊C8—24no—
84Q8⋊C8—42no—
85Q8⋊C8—42no—
86C22×Q8—21no—
87C22×Q8C22⋊C411yescharacteristic
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—22no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—21no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8M1612yes—
99C4×Q8—22no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8—21no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
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—21no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—41no—
132C2×C42C22×C411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42#4111yescharacteristic
138C2×C42#4111yescharacteristic
139#106—24no—
140#106—42no—
141C4⋊C8—22no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—42no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—41no—
153C4⋊C8—41no—
154C4⋊C8M1612yes—
155C4⋊C8SD1612yes—
156#103—24no—
157#103—42no—
158#97—82no—
159C4×C8—22no—
160C4×C8—22no—
161C4×C8—22no—
162C4×C8—41no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—41no—
167C4×C8—41no—
168C4×C8—41no—
169C4×C8—41no—
170C4×C8—41no—
171#95—21no—
172#95—21no—
173#95—21no—
174#95—41no—
175#95—41no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8#10412yes—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4C2×C22⋊C411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4C4×D411yescharacteristic
197C22×C4#12011yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4#12311yescharacteristic
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—42no—
216C2×C8—41no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—41no—
220C2×C8—81no—
221C2×C8—81no—
222C4⋊C4—22no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—42no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—81no—
261C42—81no—
262C42—81no—
263C42C2×M1611yescharacteristic
264C42C2×M1611yescharacteristic
265C42#13111yescharacteristic
266C42#13111yescharacteristic
267C42C2×SD1611yescharacteristic
268C42#13511yescharacteristic
269C42#13511yescharacteristic
270C42#13511yescharacteristic
271C42AGL(1,ℤ/8)11yescharacteristic
272C42#13711yescharacteristic
273C42#13711yescharacteristic
274C42#13711yescharacteristic
275C23#38611yescharacteristic
276Q8—22no—
277Q8—22no—
278Q8—41no—
279Q8—41no—
280Q8—42no—
281Q8—42no—
282Q8—81no—
283Q8—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4#40711yescharacteristic
312C2×C4#40811yescharacteristic
313C2×C4#41611yescharacteristic
314C2×C4#41911yescharacteristic
315C2×C4C2×#10411yescharacteristic
316C2×C4#42111yescharacteristic
317C2×C4#43511yescharacteristic
318C2×C4#43511yescharacteristic
319C2×C4#43611yescharacteristic
320C2×C4#43611yescharacteristic
321C2×C4C4×SD1611yescharacteristic
322C2×C4#44011yescharacteristic
323C2×C4#44311yescharacteristic
324C2×C4#44411yescharacteristic
325C2×C4#44811yescharacteristic
326C2×C4#44911yescharacteristic
327C2×C4#45211yescharacteristic
328C2×C4#45211yescharacteristic
329C2×C4#45511yescharacteristic
330C2×C4#45611yescharacteristic
331C2×C4#46011yescharacteristic
332C2×C4#46411yescharacteristic
333C2×C4#48511yescharacteristic
334C2×C4#48511yescharacteristic
335C8—44no—
336C8—42no—
337C8—42no—
338C8—82no—
339C8—82no—
340C8—81no—
341C8—81no—
342C22#187011yescharacteristic
343C22#187111yescharacteristic
344C22#187311yescharacteristic
345C22#187611yescharacteristic
346C22#188011yescharacteristic
347C22#188111yescharacteristic
348C22#188211yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—42no—
357C4—81no—
358C4—81no—
359C4—82no—
360C4—81no—
361C4—161no—
362C4#148811yescharacteristic
363C4#149111yescharacteristic
364C4#149411yescharacteristic
365C4#149711yescharacteristic
366C4#158211yescharacteristic
367C4#158511yescharacteristic
368C4#159011yescharacteristic
369C4#159211yescharacteristic
370C4#164011yescharacteristic
371C4#164311yescharacteristic
372C4#165011yescharacteristic
373C4#165311yescharacteristic
374C2#894111yescharacteristic
375C2#895211yescharacteristic
376C2#895511yescharacteristic
377C2#897211yescharacteristic
378C2#898211yescharacteristic
379C2#899211yescharacteristic
380C2#899411yescharacteristic
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
#228252
C4×#4752
#98702
#96732
C4×Q8⋊C82
#70312
#70152