Finite Group Databasebeta

← #15076

Subgroups — #15076

Order 256.

619 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387C211yesmaximal, characteristic
2C2×#387C211yesmaximal, characteristic
3C2×#383C211yesmaximal, characteristic
4C2×C4×C4⋊C4C211yesmaximal, characteristic
5#1444C211yesmaximal, characteristic
6#1443C211yesmaximal, characteristic
7#1443C211yesmaximal, characteristic
8#1442C211yesmaximal, characteristic
9#1442C211yesmaximal, characteristic
10#1442C211yesmaximal, characteristic
11#1441C211yesmaximal, characteristic
12#1441C211yesmaximal, characteristic
13#1436C211yesmaximal, characteristic
14#1436C211yesmaximal, characteristic
15#1434C211yesmaximal, characteristic
16C22×C4⋊C4C2211yescharacteristic
17C22×C4⋊C4C2211yescharacteristic
18C22×C4⋊C4C2211yescharacteristic
19C22×C4⋊C4C2211yescharacteristic
20C22×C4⋊C4C2211yescharacteristic
21C22×C4⋊C4C2211yescharacteristic
22C22×C42C2211yescharacteristic
23C22×C42C2211yescharacteristic
24C22×C42C2211yescharacteristic
25#387—24no—
26#387—24no—
27#383—24no—
28C4×C4⋊C4—24no—
29C2×#95C2211yescharacteristic
30C2×#95C2211yescharacteristic
31C2×#95C2211yescharacteristic
32C2×#95C2211yescharacteristic
33C2×#95C2211yescharacteristic
34C2×#95C2211yescharacteristic
35C2×#95C2211yescharacteristic
36C2×#95C2211yescharacteristic
37C2×#95C2211yescharacteristic
38C2×#95C2211yescharacteristic
39C2×#95C2211yescharacteristic
40C2×#95C2211yescharacteristic
41C2×#95C2211yescharacteristic
42C2×#95C2211yescharacteristic
43C2×#95C2211yescharacteristic
44C2×#95C2211yescharacteristic
45C2×#95C2211yescharacteristic
46C2×#95C2211yescharacteristic
47C2×#95C2211yescharacteristic
48C2×#95C2211yescharacteristic
49C2×#95C2211yescharacteristic
50C2×#95C2211yescharacteristic
51C2×#95C2211yescharacteristic
52C2×#95C2211yescharacteristic
53C2×#95C2211yescharacteristic
54C2×#95C2211yescharacteristic
55C23×C4C2311yescharacteristic
56C23×C4C2311yescharacteristic
57C23×C4C2311yescharacteristic
58C23×C4C2311yescharacteristic
59C23×C4C2311yescharacteristic
60C23×C4C2311yescharacteristic
61C23×C4C2311yescharacteristic
62C23×C4C2311yescharacteristic
63C23×C4C2311yescharacteristic
64C23×C4C2311yescharacteristic
65C23×C4C2311yescharacteristic
66C23×C4C2311yescharacteristic
67C23×C4C2311yescharacteristic
68C23×C4C2311yescharacteristic
69C23×C4C2311yescharacteristic
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C42—22no—
89C2×C42—22no—
90C2×C42—22no—
91C2×C42—22no—
92C2×C42—22no—
93C2×C42—22no—
94C2×C42—22no—
95C2×C42—22no—
96C2×C42D414yes—
97#95—22no—
98#95—22no—
99#95—22no—
100#95—22no—
101#95—22no—
102#95—22no—
103#95—22no—
104#95—22no—
105#95—22no—
106#95—22no—
107#95—22no—
108#95—22no—
109#95—22no—
110#95—22no—
111#95—22no—
112#95—22no—
113#95—22no—
114#95—22no—
115#95—22no—
116#95—22no—
117#95—22no—
118#95—22no—
119#95—22no—
120#95—22no—
121#95—22no—
122#95D414yes—
123C24C2411yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
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—21no—
164C22×C4—21no—
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—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—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C2×D412yes—
215C22×C4C2×D412yes—
216C22×C4C2×D412yes—
217C22×C4C2×D412yes—
218C22×C4C2×D412yes—
219C22×C4C2×D412yes—
220C22×C4#4112yes—
221C22×C4#4112yes—
222C22×C4#4112yes—
223C22×C4#4112yes—
224C22×C4#4112yes—
225C22×C4#4112yes—
226C22×C4#4112yes—
227C22×C4#4112yes—
228C22×C4#4112yes—
229C4⋊C4—28no—
230C4⋊C4—28no—
231C4⋊C4—28no—
232C4⋊C4—28no—
233C4⋊C4—44no—
234C4⋊C4—44no—
235C42—28no—
236C42—28no—
237C42—44no—
238C23C22×D411yescharacteristic
239C23C22×D411yescharacteristic
240C23C2×#4111yescharacteristic
241C23C2×#4111yescharacteristic
242C23C2×#4111yescharacteristic
243C23C2×#4111yescharacteristic
244C23C2×#4111yescharacteristic
245C23C2×#4111yescharacteristic
246C23C2×#4111yescharacteristic
247C23C2×#4111yescharacteristic
248C23C2×#4111yescharacteristic
249C232−1+411yescharacteristic
250C232−1+411yescharacteristic
251C232−1+411yescharacteristic
252C232−1+411yescharacteristic
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
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—41no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4#12114yes—
357C2×C4#12614yes—
358C22C2×#12111yescharacteristic
359C22#52511yescharacteristic
360C22#52511yescharacteristic
361C22#52511yescharacteristic
362C22#52511yescharacteristic
363C22#52511yescharacteristic
364C22C2×#12611yescharacteristic
365C22#52911yescharacteristic
366C22#52911yescharacteristic
367C22#52911yescharacteristic
368C22#52911yescharacteristic
369C22#52911yescharacteristic
370C22#53211yescharacteristic
371C22#53611yescharacteristic
372C22#53611yescharacteristic
373C22#54111yescharacteristic
374C22#54111yescharacteristic
375C22#54111yescharacteristic
376C22#54111yescharacteristic
377C22#54711yescharacteristic
378C22#54711yescharacteristic
379C22#54711yescharacteristic
380C22#54811yescharacteristic
381C22#55211yescharacteristic
382C22#55211yescharacteristic
383C22#55211yescharacteristic
384C22#55211yescharacteristic
385C22#55211yescharacteristic
386C22#55211yescharacteristic
387C22#55211yescharacteristic
388C22#55611yescharacteristic
389C22#55611yescharacteristic
390C22#55611yescharacteristic
391C22#55611yescharacteristic
392C22#55611yescharacteristic
393C4—24no—
394C4—24no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—42no—
399C4—42no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—81no—
408C2#239211yescharacteristic
409C2#241311yescharacteristic
410C2#241511yescharacteristic
411C2#246911yescharacteristic
412C2#247811yescharacteristic
413C2#249611yescharacteristic
414C2#251411yescharacteristic
415C2#251911yescharacteristic
416C2#252411yescharacteristic
417C2#252411yescharacteristic
418C2#253311yescharacteristic
419C2#259911yescharacteristic
420C2#259911yescharacteristic
421C2#263411yescharacteristic
422C2#285211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#3872
C2×#3832
C2×C4×C4⋊C42
#14442
#14432
#14422
#14412
#14362
#14342