Finite Group Databasebeta

← #93031

Subgroups — #93031

Order 512.

498 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1314C211yesmaximal, characteristic
2#11096C211yesmaximal, characteristic
3C2×#1289C211yesmaximal, characteristic
4C22×#107C411yescharacteristic, complemented
5C22×C22⋊C8C2211yescharacteristic
6C2×#380—21no—
7C2×#380—21no—
8C2×C22⋊C16—21no—
9C2×#340—21no—
10C2×#340C411yescharacteristic, complemented
11#1314—21no—
12#1314C412yescomplemented
13#1289—21no—
14#1289C412yescomplemented
15C24×C4D411yescharacteristic
16C23×C8C2×C411yescharacteristic
17C23×C8D411yescharacteristic
18C22×C4⋊C4—21no—
19C22×C4⋊C4—21no—
20C22×C4⋊C4—41no—
21C22×C22⋊C4—41no—
22C22×C22⋊C4—41no—
23C22×C16—41no—
24C2×#107—41no—
25C2×#107—42no—
26C2×C22⋊C8—41no—
27C2×C22⋊C8—41no—
28C2×C22⋊C8C2×C411yescharacteristic
29C2×C22⋊C8C2×C411yescharacteristic
30C2×C22⋊C8D411yescharacteristic
31C2×C22⋊C8Q811yescharacteristic
32#380—22no—
33#380—22no—
34#380—42no—
35#380—42no—
36#380—41no—
37#380—41no—
38C2×#95—22no—
39C2×#95—41no—
40C22⋊C16—22no—
41C22⋊C16—41no—
42#340—42no—
43#340—41no—
44C25D811yescharacteristic
45C23×C4—21no—
46C23×C4—21no—
47C23×C4—21no—
48C23×C4—21no—
49C23×C4—41no—
50C23×C4—41no—
51C23×C4—41no—
52C23×C4—41no—
53C23×C4—42no—
54C23×C4—41no—
55C23×C4—41no—
56C23×C4C22⋊C411yescharacteristic
57C23×C4C22⋊C411yescharacteristic
58C23×C4C4⋊C411yescharacteristic
59C23×C4SD1611yescharacteristic
60C23×C4SD1611yescharacteristic
61C23×C4Q1611yescharacteristic
62C22×C8—21no—
63C22×C8—21no—
64C22×C8—21no—
65C22×C8—21no—
66C22×C8—41no—
67C22×C8—41no—
68C22×C8—41no—
69C22×C8—41no—
70C22×C8C4211yescharacteristic
71C22×C8C22⋊C411yescharacteristic
72C22×C8C4⋊C411yescharacteristic
73C22×C8C4⋊C411yescharacteristic
74C2×C4⋊C4—22no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—42no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—81no—
89C2×C4⋊C4—81no—
90C2×C4⋊C4—81no—
91C2×C4⋊C4—81no—
92C2×C22⋊C4—42no—
93C2×C22⋊C4—44no—
94C2×C22⋊C4—42no—
95C2×C22⋊C4—81no—
96C2×C22⋊C4—81no—
97C2×C22⋊C4—82no—
98C2×C22⋊C4—81no—
99C2×C22⋊C4—81no—
100C2×C22⋊C4—81no—
101C2×C22⋊C4—81no—
102C2×C16—42no—
103C2×C16—81no—
104C2×C16—81no—
105#107—42no—
106#107—42no—
107C22⋊C8—41no—
108C22⋊C8—41no—
109C22⋊C8—41no—
110C22⋊C8—41no—
111#95—24no—
112#95—42no—
113#95—44no—
114C24—21no—
115C24—21no—
116C24—21no—
117C24—21no—
118C24—41no—
119C24—41no—
120C24—41no—
121C24—41no—
122C24#10211yescharacteristic
123C24#10211yescharacteristic
124C24#10711yescharacteristic
125C24D1611yescharacteristic
126C24SD3211yescharacteristic
127C24SD3211yescharacteristic
128C24Q3211yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—44no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—81no—
161C22×C4—81no—
162C22×C4—81no—
163C22×C4—81no—
164C22×C4—81no—
165C22×C4—81no—
166C22×C4—81no—
167C22×C4—81no—
168C22×C4—82no—
169C22×C4—82no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4—81no—
174C22×C4—82no—
175C22×C4—82no—
176C22×C4—82no—
177C22×C4—82no—
178C22×C4—81no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4#9511yescharacteristic
185C22×C4#9911yescharacteristic
186C22×C4#9911yescharacteristic
187C22×C4#10311yescharacteristic
188C22×C4#10311yescharacteristic
189C22×C4#10411yescharacteristic
190C22×C4#10411yescharacteristic
191C22×C4#10611yescharacteristic
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—81no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C4⋊C4—81no—
218C22⋊C4—82no—
219C22⋊C4—82no—
220C22⋊C4—82no—
221C22⋊C4—84no—
222C22⋊C4—84no—
223C22⋊C4—82no—
224C16—82no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23#32711yescharacteristic
264C23#32711yescharacteristic
265C23#34011yescharacteristic
266C23#35711yescharacteristic
267C23#35711yescharacteristic
268C23#35811yescharacteristic
269C23#35811yescharacteristic
270C23#36011yescharacteristic
271C23#36011yescharacteristic
272C23#36611yescharacteristic
273C23#36711yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—84no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—84no—
310C2×C4—84no—
311C2×C4—82no—
312C2×C4—161no—
313C2×C4—161no—
314C2×C4—161no—
315C2×C4—161no—
316C2×C4—161no—
317C2×C4—162no—
318C2×C4—162no—
319C2×C4—162no—
320C2×C4—162no—
321C2×C4—161no—
322C2×C4—161no—
323C2×C4—161no—
324C2×C4#32811yescharacteristic
325C2×C4#32811yescharacteristic
326C2×C4#33911yescharacteristic
327C2×C4#34211yescharacteristic
328C2×C4AΣL(1,𝔽16)11yescharacteristic
329C2×C4#35211yescharacteristic
330C2×C4#35311yescharacteristic
331C2×C4#35411yescharacteristic
332C8—41no—
333C8—41no—
334C8—41no—
335C8—41no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22#129411yescharacteristic
375C22#133911yescharacteristic
376C22#134011yescharacteristic
377C22#134311yescharacteristic
378C22#134411yescharacteristic
379C22#134711yescharacteristic
380C22#134711yescharacteristic
381C22#134811yescharacteristic
382C22#134811yescharacteristic
383C22#138011yescharacteristic
384C22#138611yescharacteristic
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—162no—
390C4—164no—
391C4—162no—
392C4#135111yescharacteristic
393C4#135211yescharacteristic
394C4#139011yescharacteristic
395C4#139311yescharacteristic
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—41no—
403C2—41no—
404C2#707611yescharacteristic
405C2#707711yescharacteristic
406C2#707811yescharacteristic
407C2#707911yescharacteristic
408C2#725011yescharacteristic
409C2#725411yescharacteristic
410C2#725811yescharacteristic
subgroupG/H
center, socleC23#327
commutatorC22×C8C42
Frattini, cosocleC22×C22⋊C8C22
prime radicalC25D8
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C22×C22⋊C8 ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#107C4semidirect
10. C2×#340C4semidirect
12. #1314C4semidirect
14. #1289C4semidirect

Maximal subgroups

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

subgroupindex
C2×#13142
#110962
C2×#12892