Finite Group Databasebeta

← #100625

Subgroups — #100625

Order 512.

493 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 493 conjugacy classes of subgroups — too many to draw. Only its 96 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#29968C211yesmaximal, characteristic
2#14443C211yesmaximal, characteristic
3#9911C211yesmaximal, characteristic
4#9679C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7039C211yesmaximal, characteristic
7#7024C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10C2×#387—21no—
11#2100C412yescomplemented
12#2088—22no—
13#2058C412yescomplemented
14#1853—21no—
15#1823—21no—
16#1797C2211yescharacteristic
17#1797C2211yescharacteristic
18C4×C22⋊C8C2211yescharacteristic
19C2×#328—21no—
20C2×#328—21no—
21#1445—21no—
22#1443—21no—
23#1441—21no—
24#1436—21no—
25C4⋊#95C2211yescharacteristic
26#1434—21no—
27#1434C2211yescharacteristic
28#1294—21no—
29#1294—21no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4D411yescharacteristic
36C22×C4⋊C4D411yescharacteristic
37C22×C42—21no—
38C22×C42C2311yescharacteristic
39C2×#106—22no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C4×C8—21no—
46#391—21no—
47#389—21no—
48#389—21no—
49#389—21no—
50#389—21no—
51#389C2×C412yes—
52#389D412yes—
53#387—42no—
54#387—42no—
55#384C2×C411yescharacteristic
56#380—21no—
57#380—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×#95—21no—
69C2×#95D411yescharacteristic
70C2×#95D411yescharacteristic
71C2×#95D411yescharacteristic
72C2×#95D411yescharacteristic
73#340—22no—
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336C2×C412yes—
79#328—42no—
80#328—42no—
81C22×Q8—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C22×C8—22no—
92C22×C8—41no—
93C22×C8—41no—
94C4⋊Q8—81no—
95C22⋊Q8—41no—
96C22⋊Q8—41no—
97C22⋊Q8—41no—
98C22⋊Q8—41no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
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—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4—81no—
122C2×C4⋊C4C22⋊C412yes—
123C2×C4⋊C4C22⋊C412yes—
124C2×C22⋊C4—41no—
125C2×C42—42no—
126C2×C42—42no—
127C2×C42—81no—
128C2×C42—81no—
129C2×C42C22×C411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133#106—82no—
134C4⋊C8—81no—
135C4⋊C8—81no—
136C22⋊C8—22no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C4×C8—81no—
143#95—22no—
144#95—22no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—41no—
149#95—41no—
150#95—42no—
151#95—42no—
152#95—42no—
153#95—42no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—41no—
160#95—81no—
161#95—81no—
162#95—81no—
163#95—81no—
164#95SD1612yes—
165C24#12011yescharacteristic
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—81no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4—41no—
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×C4—41no—
222C22×C4C2×C22⋊C411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4C2×SD1611yescharacteristic
229C22×C4#13511yescharacteristic
230C22×C4#13511yescharacteristic
231C22×C4#13511yescharacteristic
232C22×C4AGL(1,ℤ/8)11yescharacteristic
233C22×C4#13711yescharacteristic
234C22×C4#13711yescharacteristic
235C22×C4#13711yescharacteristic
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—81no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—82no—
264C4⋊C4—82no—
265C22⋊C4—81no—
266C22⋊C4—81no—
267C42—41no—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—84no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#38611yescharacteristic
277C23#45011yescharacteristic
278C23#45211yescharacteristic
279C23#45211yescharacteristic
280C23#45211yescharacteristic
281C23#45311yescharacteristic
282C23#45411yescharacteristic
283Q8—161no—
284Q8—161no—
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—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
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—81no—
320C2×C4—81no—
321C2×C4—81no—
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#41611yescharacteristic
358C2×C4#41911yescharacteristic
359C2×C4C4×SD1611yescharacteristic
360C2×C4#44011yescharacteristic
361C2×C4#46111yescharacteristic
362C2×C4#46311yescharacteristic
363C2×C4#48511yescharacteristic
364C2×C4#48511yescharacteristic
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#163111yescharacteristic
381C22#163411yescharacteristic
382C22#163511yescharacteristic
383C22#163811yescharacteristic
384C22#187311yescharacteristic
385C22#187711yescharacteristic
386C22#188311yescharacteristic
387C22#190511yescharacteristic
388C22#190611yescharacteristic
389C22#191211yescharacteristic
390C22#191311yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—82no—
402C4—82no—
403C4—82no—
404C4—82no—
405C4—161no—
406C4—161no—
407C4—161no—
408C4—161no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2—21no—
413C2#897611yescharacteristic
414C2#917811yescharacteristic
415C2#920211yescharacteristic
416C2#927511yescharacteristic
417C2#929611yescharacteristic
418C2#934411yescharacteristic
419C2#938211yescharacteristic
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
13. #2058C4semidirect

Maximal subgroups

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

subgroupindex
#299682
#144432
#99112
#96792
#75732
#70392
#70242