Finite Group Databasebeta

← #101436

Subgroups — #101436

Order 512.

504 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#27613C211yesmaximal, characteristic
2#14280C211yesmaximal, characteristic
3#11359C211yesmaximal, characteristic
4#8717C211yesmaximal, characteristic
5#7610C211yesmaximal, characteristic
6#7037C211yesmaximal, characteristic
7#7017C211yesmaximal, characteristic
8C2×#389C2211yescharacteristic
9C2×#387—21no—
10#2285C2211yescharacteristic
11#2100C412yescomplemented
12#2084C412yescomplemented
13#1919—22no—
14#1853—21no—
15#1823—21no—
16#1817C2211yescharacteristic
17#1817C2211yescharacteristic
18C2×#339—21no—
19C2×#339—21no—
20#1728C2211yescharacteristic
21#1445—21no—
22#1443—21no—
23#1442—21no—
24#1441—21no—
25#1436—21no—
26#1434C2211yescharacteristic
27C4×#95C2211yescharacteristic
28#1294—21no—
29#1294—21no—
30#1271—22no—
31C22×M16—21no—
32C2×#117—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4D411yescharacteristic
36C22×C4⋊C4D411yescharacteristic
37C22×C42D411yescharacteristic
38C22×C42D411yescharacteristic
39C22×C42C2311yescharacteristic
40C2×#106—22no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43#389—21no—
44#389—21no—
45#389C2×C412yes—
46#389D412yes—
47#387—42no—
48#387—42no—
49#384C2×C411yescharacteristic
50#384C2×C411yescharacteristic
51#382—21no—
52#380—21no—
53#380—21no—
54C4×C4⋊C4—21no—
55C4×C4⋊C4—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95D411yescharacteristic
69C2×#95D411yescharacteristic
70#340—22no—
71#340—22no—
72#340—22no—
73#339—42no—
74#339—42no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336C2×C412yes—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C2×M16—22no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C22×C8—22no—
97C22×C8—41no—
98C22×C8—41no—
99#117—41no—
100#117—41no—
101#117—41no—
102#117—41no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
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—21no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—81no—
122C2×C4⋊C4—81no—
123C2×C4⋊C4C22⋊C412yes—
124C2×C4⋊C4C22⋊C412yes—
125C2×C22⋊C4—41no—
126C2×C42—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42SD1612yes—
137C2×C42C22×C411yescharacteristic
138C2×C42C2×D411yescharacteristic
139C2×C42#4111yescharacteristic
140C2×C42#4111yescharacteristic
141#106—44no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146#95—22no—
147#95—22no—
148#95—41no—
149#95—41no—
150#95—42no—
151#95—42no—
152#95—42no—
153#95—42no—
154#95—42no—
155#95—42no—
156#95—42no—
157#95—42no—
158#95—41no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—81no—
163#95—81no—
164C24#12011yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4C2×SD1611yescharacteristic
228C22×C4#13511yescharacteristic
229C22×C4AGL(1,ℤ/8)11yescharacteristic
230C22×C4#13711yescharacteristic
231M16—42no—
232M16—42no—
233M16—81no—
234M16—81no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—81no—
240C2×C8—81no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—84no—
262C22⋊C4—81no—
263C22⋊C4—81no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—42no—
269C42—42no—
270C42—81no—
271C42—81no—
272C42—81no—
273C42—81no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#38611yescharacteristic
279C23#45011yescharacteristic
280C23#45211yescharacteristic
281C23#45311yescharacteristic
282C23#45411yescharacteristic
283C23#45811yescharacteristic
284C23#45811yescharacteristic
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4#42112yes—
361C2×C4C4×SD1611yescharacteristic
362C2×C4#44011yescharacteristic
363C2×C4#46111yescharacteristic
364C2×C4#46311yescharacteristic
365C8—82no—
366C8—82no—
367C8—161no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22#161311yescharacteristic
381C22#161511yescharacteristic
382C22#161611yescharacteristic
383C22#161811yescharacteristic
384C22#187711yescharacteristic
385C22#188311yescharacteristic
386C22#189011yescharacteristic
387C22#189711yescharacteristic
388C22#190511yescharacteristic
389C22#190611yescharacteristic
390C22#191211yescharacteristic
391C4—22no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—82no—
400C4—82no—
401C4—82no—
402C4—82no—
403C4—161no—
404C4—161no—
405C4—161no—
406C4—161no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2#904511yescharacteristic
412C2#923511yescharacteristic
413C2#929611yescharacteristic
414C2#933011yescharacteristic
415C2#938211yescharacteristic
416C2#948211yescharacteristic
417C2#952611yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ 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
11. #2100C4semidirect
12. #2084C4semidirect

Maximal subgroups

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

subgroupindex
#276132
#142802
#113592
#87172
#76102
#70372
#70172