Finite Group Databasebeta

← #99889

Subgroups — #99889

Order 512.

477 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625C211yesmaximal, characteristic
2C2×#1921C211yesmaximal, characteristic
3#9879C211yesmaximal, characteristic
4#8707C211yesmaximal, characteristic
5#7576C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×#107C411yescharacteristic
9C2×#389C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1939—21no—
12#1921—21no—
13#1921—21no—
14#1921—21no—
15#1921—21no—
16#1916—22no—
17#1797—21no—
18#1797C2211yescharacteristic
19#1797C2211yescharacteristic
20C8×C4⋊C4—21no—
21C4×C22⋊C8—21no—
22C4×C22⋊C8C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24C2×#340C411yescharacteristic
25C2×#340C411yescharacteristic
26C2×#340C411yescharacteristic
27C2×#336C2211yescharacteristic
28#1280—21no—
29#1280—21no—
30#1279—21no—
31#1279—21no—
32#1271—22no—
33C23×C8C2×C411yescharacteristic
34C23×C8C2×C411yescharacteristic
35C22×C4⋊C4—21no—
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42C2×#107—21no—
43C2×#107—21no—
44C2×#107—22no—
45C2×#107C814yescomplemented
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—22no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8D411yescharacteristic
53C2×C22⋊C8D411yescharacteristic
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—22no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4D411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C2×#95—21no—
68C2×#95—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#336—22no—
76#336—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D412yes—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4C22×C411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4#4111yescharacteristic
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—22no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8C2×C812yes—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—82no—
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C2×C812yes—
128C2×C4⋊C4C2×C812yes—
129C2×C4⋊C4M1612yes—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42—82no—
137C2×C42C2×D411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42#4111yescharacteristic
141#107—24no—
142#107—24no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—82no—
148C22⋊C8—21no—
149C22⋊C8—22no—
150C22⋊C8—21no—
151C22⋊C8—21no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—41no—
157C22⋊C8Q1612yes—
158C4×C8—41no—
159C4×C8—41no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—82no—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—41no—
168#95—41no—
169C24C4×D411yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—81no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4C2×C22⋊C411yescharacteristic
203C22×C4C4×D411yescharacteristic
204C22×C4#12011yescharacteristic
205C22×C4#12111yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12311yescharacteristic
208C22×C4C22×C811yescharacteristic
209C22×C4C2×M1611yescharacteristic
210C22×C4#13111yescharacteristic
211C22×C4#13111yescharacteristic
212C22×C4C2×Q1611yescharacteristic
213C22×C4#13511yescharacteristic
214C22×C4#13711yescharacteristic
215C22×C4#13711yescharacteristic
216C2×C8—22no—
217C2×C8—22no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—42no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—42no—
224C2×C8—41no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—42no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C2×C8—81no—
240C2×C8—81no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—82no—
257C4⋊C4—82no—
258C4⋊C4C22⋊C812yes—
259C4⋊C4C22⋊C812yes—
260C4⋊C4#10112yes—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—41no—
266C42—41no—
267C42—42no—
268C42—42no—
269C42—81no—
270C42—81no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#38611yescharacteristic
276C23C8×D411yescharacteristic
277C23#43511yescharacteristic
278C23C4×Q1611yescharacteristic
279C23#44111yescharacteristic
280C23#44311yescharacteristic
281C23#44411yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—161no—
333C2×C4—161no—
334C2×C4C2×C22⋊C811yescharacteristic
335C2×C4#40811yescharacteristic
336C2×C4#41011yescharacteristic
337C2×C4#41011yescharacteristic
338C2×C4C2×#10111yescharacteristic
339C2×C4#41311yescharacteristic
340C2×C4C8×D411yescharacteristic
341C2×C4#43511yescharacteristic
342C2×C4#45111yescharacteristic
343C2×C4#45211yescharacteristic
344C2×C4#46211yescharacteristic
345C2×C4#46411yescharacteristic
346C8—42no—
347C8—42no—
348C8—81no—
349C8—82no—
350C8—82no—
351C8—81no—
352C8—161no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22C8×Q1611yescharacteristic
366C22#157911yescharacteristic
367C22#158411yescharacteristic
368C22#158711yescharacteristic
369C22#186911yescharacteristic
370C22#187611yescharacteristic
371C22#187811yescharacteristic
372C22#189911yescharacteristic
373C22#190111yescharacteristic
374C22#190311yescharacteristic
375C22#190411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—42no—
385C4—42no—
386C4—42no—
387C4—81no—
388C4—82no—
389C4—161no—
390C4#145811yescharacteristic
391C4#146111yescharacteristic
392C4#147011yescharacteristic
393C4#147311yescharacteristic
394C2—21no—
395C2—21no—
396C2—21no—
397C2—21no—
398C2#894611yescharacteristic
399C2#908211yescharacteristic
400C2#908911yescharacteristic
401C2#924211yescharacteristic
402C2#924511yescharacteristic
403C2#925011yescharacteristic
404C2#925711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
45. C2×#107C8semidirect

Maximal subgroups

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

subgroupindex
#226252
C2×#19212
#98792
#87072
#75762
#70202
#70162