Finite Group Databasebeta

← #134343

Subgroups — #134343

Order 512.

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

normal subgroups only

This group has 606 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#14040C211yesmaximal, characteristic
2C2×#1326C212yesmaximal
3#8559C211yesmaximal, characteristic
4#8557C211yesmaximal, characteristic
5#7187C212yesmaximal
6C2×#385C2211yescharacteristic
7C2×C4×C22⋊C4C2211yescharacteristic
8C22×#95C411yescharacteristic
9#1797—21no—
10#1797—21no—
11C2×#323C2212yes—
12C2×#323C2212yes—
13#1445—21no—
14#1443—21no—
15#1436—21no—
16#1434—21no—
17C22⋊#95C411yescharacteristic
18C22⋊#95C411yescharacteristic
19C22⋊#95C411yescharacteristic
20C22⋊#95C2211yescharacteristic
21#1326—24no—
22#1280—21no—
23#1280—21no—
24C24×C4C2×C411yescharacteristic
25C24×C4C2×C411yescharacteristic
26C24×C4C2×C411yescharacteristic
27C22×C4⋊C4—21no—
28C22×C22⋊C4C2×C411yescharacteristic
29C22×C22⋊C4C2×C411yescharacteristic
30C22×C22⋊C4C2×C411yescharacteristic
31C22×C22⋊C4C2311yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42D411yescharacteristic
34C2×C4⋊C8—41no—
35C2×C4⋊C8—41no—
36C2×C22⋊C8—22no—
37C2×C22⋊C8—22no—
38#385—21no—
39#385—21no—
40#385D412yes—
41#385Q812yes—
42C4×C22⋊C4—41no—
43C4×C22⋊C4—41no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—41no—
56C2×#95—41no—
57C2×#95D411yescharacteristic
58C2×#95D411yescharacteristic
59#336—41no—
60#336—41no—
61#323—22no—
62#323—22no—
63#323—22no—
64#323—22no—
65C25C22×C411yescharacteristic
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—22no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—22no—
75C23×C4—41no—
76C23×C4—42no—
77C23×C4—42no—
78C23×C4—41no—
79C23×C4—41no—
80C23×C4—41no—
81C23×C4—41no—
82C23×C4—81no—
83C23×C4—81no—
84C23×C4—81no—
85C23×C4—81no—
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22⋊C411yescharacteristic
89C23×C4C22⋊C411yescharacteristic
90C23×C4C4⋊C412yes—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C22×C8—42no—
94C22×C8—42no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—81no—
98C2×C4⋊C4—81no—
99C2×C22⋊C4—22no—
100C2×C22⋊C4—22no—
101C2×C22⋊C4—21no—
102C2×C22⋊C4—22no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—22no—
105C2×C22⋊C4—41no—
106C2×C22⋊C4—41no—
107C2×C22⋊C4—41no—
108C2×C22⋊C4—41no—
109C2×C22⋊C4—41no—
110C2×C22⋊C4C4⋊C412yes—
111C2×C22⋊C4C2×D411yescharacteristic
112C2×C22⋊C4C2×Q811yescharacteristic
113C2×C22⋊C4#4111yescharacteristic
114C2×C22⋊C4#4111yescharacteristic
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—42no—
120C2×C42—81no—
121C4⋊C8—82no—
122C4⋊C8—82no—
123C22⋊C8—42no—
124C22⋊C8—42no—
125C22⋊C8—42no—
126C22⋊C8—42no—
127#95—22no—
128#95—22no—
129#95—41no—
130#95—41no—
131#95—42no—
132#95—42no—
133#95—42no—
134#95—42no—
135#95—41no—
136#95—41no—
137#95—81no—
138#95—81no—
139#95—81no—
140#95—81no—
141#95—81no—
142C24—21no—
143C24—21no—
144C24—21no—
145C24—21no—
146C24—41no—
147C24—41no—
148C24—41no—
149C24—41no—
150C24C2×C22⋊C411yescharacteristic
151C24C2×C4⋊C411yescharacteristic
152C24#11711yescharacteristic
153C24#13112yes—
154C24#13112yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
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—42no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—82no—
220C22×C4—82no—
221C22×C4—84no—
222C22×C4—84no—
223C22×C4—84no—
224C22×C4—84no—
225C22×C4—84no—
226C22×C4—82no—
227C22×C4—82no—
228C22×C4—82no—
229C22×C4—82no—
230C22×C4#9911yescharacteristic
231C22×C4#9911yescharacteristic
232C22×C4#10112yes—
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C2×C8—82no—
238C2×C8—82no—
239C2×C8—82no—
240C2×C8—82no—
241C2×C8—82no—
242C2×C8—82no—
243C4⋊C4—82no—
244C4⋊C4—82no—
245C22⋊C4—24no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—44no—
251C22⋊C4—42no—
252C22⋊C4—82no—
253C42—42no—
254C42—42no—
255C42—81no—
256C42—81no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—41no—
270C23—41no—
271C23—42no—
272C23—42no—
273C23—41no—
274C23—41no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23#38011yescharacteristic
288C23#40811yescharacteristic
289C23#40811yescharacteristic
290C23C2×#9911yescharacteristic
291C23#41011yescharacteristic
292C23C2×#10111yescharacteristic
293C23#41311yescharacteristic
294C23#42412yes—
295C23#43312yes—
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—22no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—84no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—84no—
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—84no—
349C2×C4—84no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—84no—
358C2×C4—84no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4#35212yes—
367C8—162no—
368C8—162no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—42no—
384C22—42no—
385C22—44no—
386C22—42no—
387C22—42no—
388C22—44no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22#146811yescharacteristic
398C22#147011yescharacteristic
399C22#147211yescharacteristic
400C22#147311yescharacteristic
401C22#179811yescharacteristic
402C22#179911yescharacteristic
403C22#180111yescharacteristic
404C22C2×#35211yescharacteristic
405C22#212011yescharacteristic
406C22#212111yescharacteristic
407C22#212211yescharacteristic
408C4—22no—
409C4—41no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—82no—
416C4—82no—
417C4—81no—
418C4—81no—
419C4—82no—
420C4—161no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—42no—
427C2#856211yescharacteristic
428C2#1154211yescharacteristic
429C2#1154311yescharacteristic
430C2#1157811yescharacteristic
431C2#1157911yescharacteristic
432C2#1279411yescharacteristic
433C2#1279511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutator, prime radicalC25C22×C4
Frattini, cosocleC22×C22⋊C4C23
LCSG ▷ C25 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#140402
C2×#13262
#85592
#85572
#71872