Finite Group Databasebeta

← #101298

Subgroups — #101298

Order 512.

497 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 94 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#23747C211yesmaximal, characteristic
2#14487C211yesmaximal, characteristic
3#8717C211yesmaximal, characteristic
4#8717C211yesmaximal, characteristic
5#7593C211yesmaximal, characteristic
6#7037C211yesmaximal, characteristic
7#7037C211yesmaximal, characteristic
8C2×#389C2211yescharacteristic
9C2×#387—21no—
10#2285C2211yescharacteristic
11#2101—22no—
12#2100C412yescomplemented
13#2099C412yescomplemented
14#1817C2211yescharacteristic
15#1817C2211yescharacteristic
16#1736—21no—
17#1736—21no—
18#1728C2211yescharacteristic
19#1442—21no—
20#1441—21no—
21#1441—21no—
22#1436—21no—
23C4⋊#95—21no—
24#1434C2211yescharacteristic
25#1434C2211yescharacteristic
26#1294—21no—
27#1294—21no—
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⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C42—21no—
39C22×C42C2311yescharacteristic
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42#389—21no—
43#389—21no—
44#389C2×C412yes—
45#389D412yes—
46#387—42no—
47#387—42no—
48#384C2×C411yescharacteristic
49#384C2×C411yescharacteristic
50#382—21no—
51#380—21no—
52#380—21no—
53C4×C4⋊C4—21no—
54C4×C4⋊C4—21no—
55C2×#95—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×#95D411yescharacteristic
66C2×#95D411yescharacteristic
67C2×#95D411yescharacteristic
68C2×#95D411yescharacteristic
69#340—22no—
70#340—22no—
71#340—22no—
72#340—22no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336C2×C412yes—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C2×M16—41no—
89C2×M16—41no—
90C2×M16—41no—
91C2×M16—41no—
92C2×M16—41no—
93C2×M16—41no—
94C22×C8—22no—
95C22×C8—41no—
96C22×C8—41no—
97#117—42no—
98#117—42no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—81no—
117C2×C4⋊C4—81no—
118C2×C4⋊C4—81no—
119C2×C4⋊C4—81no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4C22⋊C412yes—
122C2×C4⋊C4C22⋊C412yes—
123C2×C4⋊C4SD1612yes—
124C2×C4⋊C4Q1612yes—
125C2×C22⋊C4—41no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—42no—
129C2×C42—42no—
130C2×C42—41no—
131C2×C42—81no—
132C2×C42C22×C411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140#95—22no—
141#95—22no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—42no—
147#95—42no—
148#95—42no—
149#95—42no—
150#95—42no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95—81no—
158#95—81no—
159C24#12011yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4C2×SD1611yescharacteristic
223C22×C4C2×Q1611yescharacteristic
224C22×C4AGL(1,ℤ/8)11yescharacteristic
225C22×C4#13711yescharacteristic
226M16—81no—
227M16—81no—
228M16—81no—
229M16—81no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—81no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—81no—
246C4⋊C4—82no—
247C4⋊C4—82no—
248C4⋊C4—81no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—84no—
253C4⋊C4—84no—
254C4⋊C4#10314yes—
255C22⋊C4—81no—
256C22⋊C4—81no—
257C42—41no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42—82no—
262C42—84no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23#38611yescharacteristic
268C23#45011yescharacteristic
269C23#45111yescharacteristic
270C23#45411yescharacteristic
271C23#45411yescharacteristic
272C23#45811yescharacteristic
273C23#45811yescharacteristic
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—24no—
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—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
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×C4C2×#10311yescharacteristic
351C2×C4#41711yescharacteristic
352C2×C4#48311yescharacteristic
353C2×C4#48411yescharacteristic
354C8—82no—
355C8—161no—
356C8—161no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22#161611yescharacteristic
370C22#161611yescharacteristic
371C22#161711yescharacteristic
372C22#161711yescharacteristic
373C22#187211yescharacteristic
374C22#188811yescharacteristic
375C22#189011yescharacteristic
376C22#190411yescharacteristic
377C22#190511yescharacteristic
378C22#190611yescharacteristic
379C22#190611yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—44no—
389C4—82no—
390C4—82no—
391C4—82no—
392C4—161no—
393C4—161no—
394C4—161no—
395C4—161no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2#902311yescharacteristic
401C2#917511yescharacteristic
402C2#917611yescharacteristic
403C2#943011yescharacteristic
404C2#944211yescharacteristic
405C2#952511yescharacteristic
406C2#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
12. #2100C4semidirect
13. #2099C4semidirect

Maximal subgroups

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

subgroupindex
#237472
#144872
#87172
#75932
#70372