Finite Group Databasebeta

← #16220

Subgroups — #16220

Order 256.

495 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1443C211yesmaximal, characteristic
2#1443C211yesmaximal, characteristic
3#1443C211yesmaximal, characteristic
4#1443C211yesmaximal, characteristic
5#1443C211yesmaximal, characteristic
6#1443C211yesmaximal, characteristic
7#1442C211yesmaximal, characteristic
8#1441C211yesmaximal, characteristic
9#1441C211yesmaximal, characteristic
10#1436C211yesmaximal, characteristic
11#1436C211yesmaximal, characteristic
12C4⋊#95C211yesmaximal, characteristic
13#1434C211yesmaximal, characteristic
14#1434C211yesmaximal, characteristic
15#1434C211yesmaximal, characteristic
16C22×C4⋊C4C2211yescharacteristic
17C22×C4⋊C4C2211yescharacteristic
18C22×C4⋊C4C2211yescharacteristic
19C22×C42C2211yescharacteristic
20C22×C42C2211yescharacteristic
21C2×#95C2211yescharacteristic
22C2×#95C2211yescharacteristic
23C2×#95C2211yescharacteristic
24C2×#95C2211yescharacteristic
25C2×#95C2211yescharacteristic
26C2×#95C2211yescharacteristic
27C2×#95C2211yescharacteristic
28C2×#95C2211yescharacteristic
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
51C23×C4C2311yescharacteristic
52C23×C4C2311yescharacteristic
53C23×C4C2311yescharacteristic
54C23×C4C2311yescharacteristic
55C23×C4C2311yescharacteristic
56C23×C4C2311yescharacteristic
57C23×C4C2311yescharacteristic
58C23×C4C2311yescharacteristic
59C23×C4C2311yescharacteristic
60C23×C4C2311yescharacteristic
61C23×C4C2311yescharacteristic
62C23×C4C2311yescharacteristic
63C23×C4C2311yescharacteristic
64C23×C4C2311yescharacteristic
65C23×C4C2311yescharacteristic
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4—41no—
75C2×C42—22no—
76C2×C42—22no—
77C2×C42—22no—
78C2×C42—22no—
79C2×C42—41no—
80C2×C42—41no—
81#95—22no—
82#95—22no—
83#95—22no—
84#95—22no—
85#95—22no—
86#95—22no—
87#95—22no—
88#95—22no—
89#95—22no—
90#95—22no—
91#95—22no—
92#95—22no—
93#95—22no—
94#95—22no—
95#95—22no—
96#95—22no—
97#95—22no—
98#95—41no—
99#95—41no—
100#95—41no—
101#95—41no—
102#95—41no—
103#95—41no—
104#95—41no—
105#95—41no—
106#95—41no—
107#95—41no—
108#95—41no—
109#95—41no—
110#95—41no—
111C24C2411yescharacteristic
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
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#4112yes—
209C22×C4#4112yes—
210C22×C4#4112yes—
211C22×C4#4112yes—
212C22×C4#4112yes—
213C22×C4#4112yes—
214C22×C4#4112yes—
215C22×C4#4112yes—
216C22×C4#4112yes—
217C4⋊C4—44no—
218C4⋊C4—44no—
219C4⋊C4—44no—
220C42—44no—
221C42—44no—
222C23C2×#4111yescharacteristic
223C23C2×#4111yescharacteristic
224C23C2×#4111yescharacteristic
225C23C2×#4111yescharacteristic
226C23C2×#4111yescharacteristic
227C23C2×#4111yescharacteristic
228C23C2×#4111yescharacteristic
229C23C2×#4111yescharacteristic
230C23C2×#4111yescharacteristic
231C23H(5,𝔽2)11yescharacteristic
232C23H(5,𝔽2)11yescharacteristic
233C23H(5,𝔽2)11yescharacteristic
234C232−1+411yescharacteristic
235C232−1+411yescharacteristic
236C232−1+411yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
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—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
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#12614yes—
342C22C2×#12611yescharacteristic
343C22#52911yescharacteristic
344C22#52911yescharacteristic
345C22#52911yescharacteristic
346C22#52911yescharacteristic
347C22#52911yescharacteristic
348C22#53811yescharacteristic
349C22#53911yescharacteristic
350C22#53911yescharacteristic
351C22#54011yescharacteristic
352C22#54111yescharacteristic
353C22#54111yescharacteristic
354C22#54211yescharacteristic
355C22#54211yescharacteristic
356C22#54211yescharacteristic
357C22#55111yescharacteristic
358C22#55111yescharacteristic
359C22#55111yescharacteristic
360C22#55211yescharacteristic
361C22#55211yescharacteristic
362C22#55211yescharacteristic
363C22#55211yescharacteristic
364C22#55211yescharacteristic
365C22#55311yescharacteristic
366C22#55311yescharacteristic
367C22#55311yescharacteristic
368C22#55311yescharacteristic
369C22#55311yescharacteristic
370C22#55511yescharacteristic
371C22#55611yescharacteristic
372C22#55611yescharacteristic
373C22#55611yescharacteristic
374C22#55611yescharacteristic
375C22#56211yescharacteristic
376C22#56311yescharacteristic
377C4—24no—
378C4—42no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4—42no—
383C4—42no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C2#249511yescharacteristic
393C2#251011yescharacteristic
394C2#251411yescharacteristic
395C2#251511yescharacteristic
396C2#253011yescharacteristic
397C2#253111yescharacteristic
398C2#253311yescharacteristic
399C2#259411yescharacteristic
400C2#259411yescharacteristic
401C2#274411yescharacteristic
402C2#274511yescharacteristic
403C2#275811yescharacteristic
404C2#277211yescharacteristic
405C2#279311yescharacteristic
406C2#280011yescharacteristic
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
#14432
#14422
#14412
#14362
C4⋊#952
#14342