Finite Group Databasebeta

← #35958

Subgroups — #35958

Order 256.

756 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2666C212yesmaximal
2#2660C211yesmaximal, characteristic
3#2612C212yesmaximal
4#2605C212yesmaximal
5#2586C212yesmaximal
6#2585C212yesmaximal
7#2582C211yesmaximal, characteristic
8#2581C211yesmaximal, characteristic
9#2571C211yesmaximal, characteristic
10#2570C211yesmaximal, characteristic
11#2568C211yesmaximal, characteristic
12#2565C211yesmaximal, characteristic
13#2520C212yesmaximal
14#2520C212yesmaximal
15#2402C212yesmaximal
16#2399C211yesmaximal, characteristic
17#2370C211yesmaximal, characteristic
18#2369C211yesmaximal, characteristic
19#2356C211yesmaximal, characteristic
20#2355C211yesmaximal, characteristic
21#2355C211yesmaximal, characteristic
22#2355C211yesmaximal, characteristic
23#2276C211yesmaximal, characteristic
24C2×C4⋊Q8C2211yescharacteristic
25C2×#125C2211yescharacteristic
26C2×C4×Q8C2211yescharacteristic
27C2×C4×Q8C2211yescharacteristic
28C2×C4×Q8C2211yescharacteristic
29C2×C4×Q8C2211yescharacteristic
30C2×C4×Q8C2211yescharacteristic
31#400C2212yes—
32#400C2212yes—
33#400C2212yes—
34#400C2212yes—
35#400C2212yes—
36#400C2212yes—
37#398C2212yes—
38#398C2212yes—
39#398C2212yes—
40#398C2212yes—
41#398C2212yes—
42#398C2211yescharacteristic
43#398C2212yes—
44#398C2211yescharacteristic
45#398C2211yescharacteristic
46#398C2211yescharacteristic
47#398C2212yes—
48#395C2212yes—
49#395C2211yescharacteristic
50#395C2212yes—
51#395C2211yescharacteristic
52#395C2212yes—
53#395C2211yescharacteristic
54#395C2211yescharacteristic
55#391C2211yescharacteristic
56#391C2211yescharacteristic
57#391C2211yescharacteristic
58#391C2211yescharacteristic
59#391C2212yes—
60#391C2212yes—
61#391C2212yes—
62#391C2212yes—
63#391C2212yes—
64#391C2212yes—
65#391C2212yes—
66#389C2211yescharacteristic
67#389C2211yescharacteristic
68#389C2211yescharacteristic
69#389C2211yescharacteristic
70#389C2212yes—
71#389C2212yes—
72#389C2212yes—
73#389C2212yes—
74#387C2212yes—
75#387C2212yes—
76#387C2212yes—
77#387C2212yes—
78#387C2212yes—
79#387C2212yes—
80#387C2212yes—
81#387C2212yes—
82#387C2212yes—
83#387C2212yes—
84#387C2212yes—
85#387C2212yes—
86#387C2212yes—
87#387C2212yes—
88#387C2212yes—
89#387C2212yes—
90#384C2211yescharacteristic
91#384C2211yescharacteristic
92#384C2211yescharacteristic
93#383C2212yes—
94#382C2211yescharacteristic
95#382C2211yescharacteristic
96#382C2211yescharacteristic
97#382C2211yescharacteristic
98#382C2212yes—
99#382C2211yescharacteristic
100#382C2212yes—
101C4×C4⋊C4C2211yescharacteristic
102C4×C4⋊C4C2211yescharacteristic
103C4×C4⋊C4C2211yescharacteristic
104C4×C4⋊C4C2211yescharacteristic
105C4×C4⋊C4C2211yescharacteristic
106C4×C4⋊C4C2212yes—
107C4×C4⋊C4C2212yes—
108C4×C4⋊C4C2212yes—
109C4×C4⋊C4C2212yes—
110C4×C4⋊C4C2212yes—
111C4×C4⋊C4C2211yescharacteristic
112C4×C4⋊C4C2211yescharacteristic
113C4×C4⋊C4C2211yescharacteristic
114C4×C4⋊C4C2211yescharacteristic
115C4×C4⋊C4C2211yescharacteristic
116C4×C4⋊C4C2212yes—
117C4×C4⋊C4C2211yescharacteristic
118C4×C4⋊C4C2212yes—
119C4×C4⋊C4C2212yes—
120#376C2212yes—
121#376C2212yes—
122#376C2211yescharacteristic
123C22×Q8C2311yescharacteristic
124C22×Q8C2311yescharacteristic
125C22×Q8C2311yescharacteristic
126C22×Q8C2312yes—
127C4⋊Q8—24no—
128#125—24no—
129C4×Q8—24no—
130C4×Q8—24no—
131C4×Q8—24no—
132C4×Q8—24no—
133C4×Q8Q818yescomplemented
134C2×C4⋊C4C2311yescharacteristic
135C2×C4⋊C4C2311yescharacteristic
136C2×C4⋊C4C2311yescharacteristic
137C2×C4⋊C4C2312yes—
138C2×C4⋊C4C2311yescharacteristic
139C2×C4⋊C4C2312yes—
140C2×C4⋊C4C2311yescharacteristic
141C2×C4⋊C4C2311yescharacteristic
142C2×C4⋊C4C2311yescharacteristic
143C2×C4⋊C4C2311yescharacteristic
144C2×C4⋊C4C2311yescharacteristic
145C2×C4⋊C4C2311yescharacteristic
146C2×C4⋊C4C2312yes—
147C2×C4⋊C4C2312yes—
148C2×C4⋊C4C2311yescharacteristic
149C2×C4⋊C4C2311yescharacteristic
150C2×C4⋊C4C2312yes—
151C2×C4⋊C4C2311yescharacteristic
152C2×C4⋊C4C2311yescharacteristic
153C2×C4⋊C4C2312yes—
154C2×C4⋊C4C2311yescharacteristic
155C2×C4⋊C4C2311yescharacteristic
156C2×C4⋊C4C2312yes—
157C2×C4⋊C4C2312yes—
158C2×C4⋊C4C2311yescharacteristic
159C2×C4⋊C4C2311yescharacteristic
160C2×C4⋊C4C2312yes—
161C2×C4⋊C4C2311yescharacteristic
162C2×C4⋊C4C2311yescharacteristic
163C2×C4⋊C4C2312yes—
164C2×C4⋊C4C2312yes—
165C2×C4⋊C4C2312yes—
166C2×C4⋊C4C2312yes—
167C2×C4⋊C4C2312yes—
168C2×C4⋊C4C2312yes—
169C2×C4⋊C4C2311yescharacteristic
170C2×C4⋊C4C2312yes—
171C2×C42C2312yes—
172C2×C42C2312yes—
173C2×C42C2311yescharacteristic
174C2×C42C2311yescharacteristic
175C2×C42C2311yescharacteristic
176C2×C42C2311yescharacteristic
177C2×C42C2312yes—
178C2×C42C2312yes—
179C2×C42C2312yes—
180C2×C42C2312yes—
181C2×C42C2312yes—
182C2×C42C2312yes—
183C2×C42C2312yes—
184C2×C42C2312yes—
185C2×C42C2311yescharacteristic
186C2×C42C2311yescharacteristic
187C2×C42C2311yescharacteristic
188#95C2311yescharacteristic
189#95C2311yescharacteristic
190#95C2312yes—
191#95C2312yes—
192#95C2311yescharacteristic
193#95C2311yescharacteristic
194#95C2311yescharacteristic
195#95C2312yes—
196#95C2312yes—
197#95C2312yes—
198#95C2312yes—
199#95C2311yescharacteristic
200#95C2312yes—
201#95C2312yes—
202#95C2312yes—
203#95C2312yes—
204#95C2312yes—
205#95C2312yes—
206#95C2312yes—
207#95C2311yescharacteristic
208#95C2312yes—
209#95C2312yes—
210#95C2311yescharacteristic
211#95C2311yescharacteristic
212#95C2312yes—
213#95C2311yescharacteristic
214#95C2311yescharacteristic
215#95C2312yes—
216#95C2312yes—
217#95C2311yescharacteristic
218#95C2312yes—
219#95C2312yes—
220#95C2312yes—
221#95C2312yes—
222#95C2312yes—
223#95C2312yes—
224#95C2312yes—
225#95C2312yes—
226#95C2312yes—
227#95C2312yes—
228#95C2312yes—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8C2×Q814yes—
241C22×C4C2411yescharacteristic
242C22×C4C2411yescharacteristic
243C22×C4C2412yes—
244C22×C4C2411yescharacteristic
245C22×C4C2412yes—
246C22×C4C2411yescharacteristic
247C22×C4C2411yescharacteristic
248C22×C4C2412yes—
249C22×C4C2412yes—
250C22×C4C2411yescharacteristic
251C22×C4C2412yes—
252C22×C4C2411yescharacteristic
253C22×C4C2412yes—
254C22×C4C2411yescharacteristic
255C22×C4C2412yes—
256C22×C4C2412yes—
257C22×C4C2411yescharacteristic
258C22×C4C2411yescharacteristic
259C22×C4C2411yescharacteristic
260C22×C4C2411yescharacteristic
261C22×C4C2411yescharacteristic
262C22×C4C2411yescharacteristic
263C22×C4C2411yescharacteristic
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—24no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4C2×Q818yes—
300C4⋊C4C2×Q814yes—
301C42—24no—
302C42—24no—
303C42—22no—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—42no—
308C42—42no—
309C42—42no—
310C42—42no—
311C42—42no—
312C42—42no—
313C42—42no—
314C42C2×Q818yes—
315C42C2×Q814yes—
316C42#4114yes—
317C42#4114yes—
318C23C2511yescharacteristic
319Q8—28no—
320Q8—44no—
321Q8—44no—
322Q8—84no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4C22×Q812yes—
381C2×C4C22×Q814yes—
382C2×C4C22×Q812yes—
383C2×C4C22×Q814yes—
384C2×C4C22×Q812yes—
385C2×C4C2×#4112yes—
386C2×C4C2×#4112yes—
387C2×C4C2×#4112yes—
388C2×C4C2×#4112yes—
389C2×C4C2×#4112yes—
390C2×C4C2×#4112yes—
391C2×C42−1+412yes—
392C22C23×Q811yescharacteristic
393C22C22×#4111yescharacteristic
394C22C22×#4111yescharacteristic
395C22C2×2−1+411yescharacteristic
396C22#58511yescharacteristic
397C22#58511yescharacteristic
398C22#58511yescharacteristic
399C4—24no—
400C4—22no—
401C4—22no—
402C4—22no—
403C4—22no—
404C4—24no—
405C4—22no—
406C4—22no—
407C4—22no—
408C4—42no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—42no—
417C4—42no—
418C4—42no—
419C4—42no—
420C4—42no—
421C4#53314yes—
422C2C2×#53311yescharacteristic
423C2#349311yescharacteristic
424C2#349511yescharacteristic
425C2#350211yescharacteristic
426C2#350411yescharacteristic
427C2#350711yescharacteristic
428C2#351011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
133. C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#26662
#26602
#26122
#26052
#25862
#25852
#25822
#25812
#25712
#25702
#25682
#25652
#25202
#24022
#23992
#23702
#23692
#23562
#23552
#22762