Finite Group Databasebeta

← C2×#11792 #481650

Subgroups — C2×#11792 #481650

Order 512.

992 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2581C211yesmaximal, characteristic
2C2×C4×#101C211yesmaximal, characteristic
3C2×#1467C211yesmaximal, characteristic
4#11792C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal
6C2×#1353C212yesmaximal
7C22×C4×Q8C411yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C22×#101—21no—
11C2×C4×M16—21no—
12#2581—22no—
13#2581—22no—
14#2581C414yes—
15#2581C2214yes—
16C2×#400C411yescharacteristic
17C2×#400C2211yescharacteristic
18C2×#395C411yescharacteristic
19C2×#395C2211yescharacteristic
20C2×#391—21no—
21C2×#389—21no—
22C2×#387—21no—
23C2×#387—21no—
24C2×#382C411yescharacteristic
25C4×#101—22no—
26C4×#101C2214yes—
27C2×#343C2212yes—
28#1467—22no—
29#1467C2214yes—
30C2×#324—21no—
31C2×#324C2212yes—
32#1354C2218yes—
33#1353C2218yes—
34C23×Q8C2×C411yescharacteristic
35C23×Q8D411yescharacteristic
36C22×M16—22no—
37C2×C4×Q8—22no—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8—42no—
41C2×C4×Q8—42no—
42C2×C4×Q8—41no—
43C2×C4×Q8—41no—
44C2×C4×Q8C2×C414yes—
45C2×C4×Q8C2×C412yes—
46C2×C4×Q8D412yes—
47C2×C4×Q8D412yes—
48C2×C4×Q8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C42—21no—
58C22×C42C2×C411yescharacteristic
59C22×C42D411yescharacteristic
60C22×C42D411yescharacteristic
61#432—24no—
62#432—42no—
63C2×C4⋊C8—41no—
64C2×#101—28no—
65C2×#101—24no—
66C2×C22⋊C8—22no—
67C4×M16—24no—
68C4×M16—42no—
69C2×#97—41no—
70C2×#97—41no—
71C2×C4×C8—41no—
72#400—22no—
73#400—21no—
74#400—21no—
75#400C2×C412yes—
76#400C2×C414yes—
77#400C2312yes—
78#395—22no—
79#395—21no—
80#395—21no—
81#395C2×C412yes—
82#395C2×C414yes—
83#395C2312yes—
84#391—24no—
85#391—24no—
86#389—24no—
87#389—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#382—22no—
93#382C2×C414yes—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—24no—
106#324—22no—
107#324C2314yes—
108C22×Q8—24no—
109C22×Q8—21no—
110C22×Q8—24no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—44no—
114C22×Q8—41no—
115C22×Q8—41no—
116C22×Q8C22⋊C412yes—
117C22×Q8C22×C412yes—
118C22×Q8C2×D412yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4C22⋊C411yescharacteristic
124C23×C4C22⋊C411yescharacteristic
125C23×C4C22⋊C411yescharacteristic
126C23×C4C22⋊C411yescharacteristic
127C23×C4C22×C411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C2×M16—28no—
131C2×M16—24no—
132C2×M16—42no—
133C2×M16—44no—
134C22×C8—42no—
135C22×C8—42no—
136C4×Q8—42no—
137C4×Q8—42no—
138C4×Q8—42no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—42no—
143C4×Q8—42no—
144C4×Q8—44no—
145C4×Q8—44no—
146C4×Q8—44no—
147C4×Q8—44no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4C22⋊C412yes—
169C2×C4⋊C4C22⋊C412yes—
170C2×C4⋊C4C22×C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C411yescharacteristic
173C2×C4⋊C4C2×D412yes—
174C2×C4⋊C4C2×D411yescharacteristic
175C2×C4⋊C4C2×D411yescharacteristic
176C2×C4⋊C4C2411yescharacteristic
177C2×C42—22no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—22no—
184C2×C42—21no—
185C2×C42—22no—
186C2×C42—24no—
187C2×C42—42no—
188C2×C42—42no—
189C2×C42C22⋊C412yes—
190C2×C42C22⋊C412yes—
191C2×C42C22⋊C412yes—
192C2×C42C22×C412yes—
193C2×C42C2×D412yes—
194C2×C42C2×D412yes—
195C4⋊C8—44no—
196#101—216no—
197C22⋊C8—24no—
198C22⋊C8—42no—
199#97—44no—
200#97—44no—
201C4×C8—44no—
202#95—24no—
203#95—22no—
204#95—24no—
205#95—24no—
206#95—22no—
207#95—24no—
208#95—22no—
209#95—21no—
210#95—21no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95C22×C412yes—
215#95C22×C412yes—
216C24C2×C22⋊C411yescharacteristic
217C2×Q8—24no—
218C2×Q8—24no—
219C2×Q8—24no—
220C2×Q8—24no—
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—48no—
224C2×Q8—48no—
225C2×Q8—44no—
226C2×Q8—42no—
227C2×Q8—44no—
228C2×Q8—42no—
229C2×Q8—48no—
230C2×Q8—44no—
231C2×Q8—44no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—44no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4#9911yescharacteristic
270C22×C4#9911yescharacteristic
271C22×C4#9912yes—
272C22×C4#10414yes—
273C22×C4C2×C22⋊C412yes—
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C412yes—
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C2×C22⋊C412yes—
279C22×C4C2×C22⋊C412yes—
280C22×C4#13714yes—
281C22×C4C23×C411yescharacteristic
282C22×C4C22×D411yescharacteristic
283C22×C4C22×D411yescharacteristic
284M16—28no—
285M16—48no—
286M16—44no—
287C2×C8—44no—
288C2×C8—48no—
289C2×C8—44no—
290C2×C8—84no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—42no—
300C4⋊C4—48no—
301C4⋊C4—44no—
302C4⋊C4—44no—
303C4⋊C4—42no—
304C4⋊C4—44no—
305C4⋊C4—44no—
306C4⋊C4—48no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—48no—
320C23—22no—
321C23—22no—
322C23C2×#9911yescharacteristic
323C23C2×#9911yescharacteristic
324C23#41912yes—
325C23C2×#10412yes—
326C23C22×C22⋊C411yescharacteristic
327Q8—48no—
328Q8—48no—
329Q8—44no—
330Q8—44no—
331Q8—48no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—84no—
381C2×C4—84no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4C2×#9912yes—
385C2×C4C2×#9912yes—
386C2×C4#41912yes—
387C2×C4C2×#10414yes—
388C2×C4C2×#13712yes—
389C8—48no—
390C8—84no—
391C22—24no—
392C22—24no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22#150812yes—
398C22#150812yes—
399C22#212012yes—
400C22#213312yes—
401C22C22×#9911yescharacteristic
402C22C2×#41911yescharacteristic
403C22C22×#10411yescharacteristic
404C4—22no—
405C4—22no—
406C4—22no—
407C4—22no—
408C4—24no—
409C4—41no—
410C4—44no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—42no—
415C4—42no—
416C4—82no—
417C4—82no—
418C4—82no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2#1179214yesdirect product factor
423C2C2×#150811yescharacteristic
424C2C2×#212011yescharacteristic
425C2C2×#213311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11792C2direct (N × H)
422. C2#11792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25812
C2×C4×#1012
C2×#14672
#117922
C2×#13542
C2×#13532