Finite Group Databasebeta

← #101138

Subgroups — #101138

Order 512.

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

normal subgroups only

This group has 666 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#21822C211yesmaximal, characteristic
2#14880C211yesmaximal, characteristic
3#10763C211yesmaximal, characteristic
4#7610C212yesmaximal
5#7037C212yesmaximal
6C22×C4×Q8C2211yescharacteristic
7C2×#432—21no—
8C22×#101—21no—
9C2×#398C411yescharacteristic
10C2×#398C411yescharacteristic
11C2×#395—21no—
12C2×#389C2211yescharacteristic
13#1985—24no—
14#1817—21no—
15#1817C2212yes—
16C2×#343—21no—
17#1728C2212yes—
18#1441—21no—
19#1441C411yescharacteristic
20#1441C411yescharacteristic
21#1436—21no—
22#1436—21no—
23#1434C2211yescharacteristic
24#1271—24no—
25C23×Q8D411yescharacteristic
26C22×M16—22no—
27C2×C4×Q8—22no—
28C2×C4×Q8—22no—
29C2×C4×Q8—42no—
30C2×C4×Q8—42no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C22×C42C2311yescharacteristic
42#432—42no—
43#432—42no—
44C2×C4⋊C8—22no—
45C2×#101—24no—
46C2×#101—42no—
47C2×#101—42no—
48C2×C22⋊C8—22no—
49C2×#97—22no—
50#398—42no—
51#398—42no—
52#395—44no—
53#389—22no—
54#389—22no—
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×#95C2×C411yescharacteristic
65C2×#95C2×C411yescharacteristic
66#343—42no—
67#336—24no—
68#336—22no—
69#336—22no—
70#336—22no—
71#336D414yes—
72C22×Q8—22no—
73C22×Q8—22no—
74C22×Q8—22no—
75C22×Q8—21no—
76C22×Q8—22no—
77C22×Q8—21no—
78C22×Q8—41no—
79C22×Q8—41no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—21no—
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22×C411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C2×M16—24no—
92C2×M16—42no—
93C2×M16—42no—
94C2×M16—42no—
95C2×M16—42no—
96C2×M16—42no—
97C22×C8—24no—
98C22×C8—42no—
99C4×Q8—44no—
100C4×Q8—44no—
101C4×Q8—48no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—41no—
126C2×C42—22no—
127C2×C42—22no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—41no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42—41no—
136C2×C42C2×D412yes—
137C2×C42#4112yes—
138C4⋊C8—44no—
139#101—48no—
140C22⋊C8—42no—
141C22⋊C8—42no—
142#97—44no—
143#95—24no—
144#95—41no—
145#95—41no—
146#95—42no—
147#95—42no—
148#95—42no—
149#95—42no—
150#95—42no—
151#95—42no—
152#95—41no—
153#95—41no—
154#95—42no—
155C24C2×C22⋊C411yescharacteristic
156C2×Q8—24no—
157C2×Q8—24no—
158C2×Q8—44no—
159C2×Q8—44no—
160C2×Q8—44no—
161C2×Q8—44no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
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×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4#9912yes—
228C22×C4#9912yes—
229C22×C4#10412yes—
230C22×C4C4×D412yes—
231C22×C4#12011yescharacteristic
232C22×C4#12112yes—
233C22×C4#12311yescharacteristic
234C22×C4AGL(1,ℤ/8)12yes—
235C22×C4AGL(1,ℤ/8)11yescharacteristic
236C22×C4#13711yescharacteristic
237M16—44no—
238M16—44no—
239M16—82no—
240M16—82no—
241C2×C8—44no—
242C2×C8—44no—
243C2×C8—44no—
244C2×C8—44no—
245C2×C8—82no—
246C2×C8—82no—
247C4⋊C4—24no—
248C4⋊C4—44no—
249C4⋊C4—44no—
250C4⋊C4—44no—
251C4⋊C4—42no—
252C4⋊C4—82no—
253C4⋊C4—84no—
254C4⋊C4—84no—
255C4⋊C4—82no—
256C4⋊C4—82no—
257C42—22no—
258C42—22no—
259C42—24no—
260C42—42no—
261C42—42no—
262C42—42no—
263C42—42no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#38611yescharacteristic
269C23C2×#9911yescharacteristic
270C23C2×#9911yescharacteristic
271C23#41711yescharacteristic
272C23#41811yescharacteristic
273C23C2×#10411yescharacteristic
274C23#42111yescharacteristic
275Q8—48no—
276Q8—48no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
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—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
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#45612yes—
350C2×C4#46812yes—
351C2×C4#46912yes—
352C8—84no—
353C8—84no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22#150411yescharacteristic
367C22#150711yescharacteristic
368C22#151011yescharacteristic
369C22#151311yescharacteristic
370C22#187111yescharacteristic
371C22#188611yescharacteristic
372C22#189111yescharacteristic
373C22#189511yescharacteristic
374C22#189811yescharacteristic
375C22#191211yescharacteristic
376C22#191511yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—42no—
383C4—42no—
384C4—41no—
385C4—82no—
386C4—82no—
387C4—82no—
388C4—81no—
389C4—161no—
390C2—21no—
391C2—21no—
392C2—21no—
393C2—21no—
394C2#903011yescharacteristic
395C2#911711yescharacteristic
396C2#919011yescharacteristic
397C2#940211yescharacteristic
398C2#946211yescharacteristic
399C2#949011yescharacteristic
400C2#951311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#218222
#148802
#107632
#76102
#70372