Finite Group Databasebeta

← C2×#9190 #197363

Subgroups — C2×#9190 #197363

Order 512.

1160 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2983C211yesmaximal, characteristic
2C2×#2634C211yesmaximal, characteristic
3C2×C4×#101C211yesmaximal, characteristic
4C2×#1528C212yesmaximal
5#9190C218yesmaximal, direct product factor
6C2×#1288C212yesmaximal
7C22×#125C2211yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9#2983—24no—
10#2983—22no—
11#2983C2214yes—
12C2×#446—24no—
13C2×#432—21no—
14C2×#432C2212yes—
15C2×#431—21no—
16C22×#101—21no—
17C2×C4×M16C2212yes—
18#2634—22no—
19#2634—22no—
20#2634C414yes—
21#2634C2214yes—
22C2×#400—21no—
23C2×#400C411yescharacteristic
24C2×#400C411yescharacteristic
25C2×#398C411yescharacteristic
26C2×#398C411yescharacteristic
27C2×#395—21no—
28C2×#387—21no—
29C2×#387—21no—
30C2×#383C2211yescharacteristic
31C4×#101—22no—
32C4×#101C2214yes—
33C2×#343—21no—
34#1528—24no—
35#1528C2218yes—
36C2×#330—24no—
37#1288C2218yes—
38C23×Q8D411yescharacteristic
39C22×M16—22no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—22no—
43C2×#125—22no—
44C2×#125—22no—
45C2×#125—22no—
46C2×#125C2×C412yes—
47C2×#125C2312yes—
48C2×C4×Q8—22no—
49C2×C4×Q8—22no—
50C2×C4×Q8—22no—
51C2×C4×Q8—22no—
52C2×C4×Q8C2×C412yes—
53C2×C4×Q8D412yes—
54C2×C4×Q8D412yes—
55C2×C4×Q8C2312yes—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4C2×C411yescharacteristic
64C22×C4⋊C4D411yescharacteristic
65C22×C42D411yescharacteristic
66C22×C42D411yescharacteristic
67C22×C42C2311yescharacteristic
68#446—216no—
69#446—216no—
70#432—24no—
71#432—24no—
72#432—22no—
73#432—22no—
74#432D414yes—
75#432C2314yes—
76#431—24no—
77#431—24no—
78C2×C4⋊C8—22no—
79C2×C4⋊C8—22no—
80C2×C4⋊C8—22no—
81C2×#101—28no—
82C2×#101—24no—
83C2×C22⋊C8—22no—
84C4×M16—22no—
85C4×M16—22no—
86C4×M16—22no—
87C4×M16C2314yes—
88C2×#97—22no—
89C2×#97—22no—
90C2×#97D414yes—
91C2×C4×C8—22no—
92C2×C4×C8—22no—
93#400—22no—
94#400—22no—
95#400—24no—
96#400—24no—
97#400C2×C414yes—
98#400C2×C414yes—
99#398—22no—
100#398—22no—
101#398C2×C414yes—
102#398C2×C414yes—
103#395—24no—
104#395—24no—
105#387—24no—
106#387—24no—
107#387—24no—
108#387—24no—
109#383—21no—
110#383—21no—
111#383C2×C412yes—
112#383C2312yes—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95C2×C411yescharacteristic
122C2×#95C2×C411yescharacteristic
123#343—24no—
124#330—216no—
125C22×Q8—24no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—42no—
129C22×Q8C22⋊C412yes—
130C22×Q8C2×D412yes—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22×C411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C2×M16—28no—
143C2×M16—24no—
144C2×M16—44no—
145C2×M16—42no—
146C22×C8—24no—
147C22×C8—42no—
148#125—24no—
149#125—24no—
150#125—24no—
151#125—24no—
152#125—42no—
153#125—42no—
154#125—42no—
155#125—42no—
156C4×Q8—24no—
157C4×Q8—24no—
158C4×Q8—24no—
159C4×Q8—24no—
160C4×Q8—24no—
161C4×Q8—24no—
162C4×Q8—24no—
163C4×Q8—24no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4C22⋊C412yes—
191C2×C4⋊C4C22⋊C412yes—
192C2×C4⋊C4C22⋊C412yes—
193C2×C4⋊C4C22×C412yes—
194C2×C4⋊C4C22×C412yes—
195C2×C4⋊C4C22×C412yes—
196C2×C4⋊C4C22×C412yes—
197C2×C4⋊C4C2×D412yes—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42C22⋊C412yes—
207C2×C42C22⋊C412yes—
208C2×C42C22×C411yescharacteristic
209C2×C42C2×D412yes—
210C2×C42C2×D412yes—
211C2×C42C2×D412yes—
212C2×C42C2×D412yes—
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42#4112yes—
216C2×C42#4112yes—
217C2×C42C2411yescharacteristic
218C4⋊C8—28no—
219C4⋊C8—28no—
220C4⋊C8—24no—
221C4⋊C8—24no—
222#101—216no—
223C22⋊C8—24no—
224C22⋊C8—24no—
225#97—28no—
226#97—24no—
227#97—24no—
228#97—42no—
229#97C2×D418yes—
230C4×C8—28no—
231C4×C8—24no—
232C4×C8—42no—
233#95—22no—
234#95—22no—
235#95—24no—
236#95—24no—
237#95—24no—
238#95—24no—
239#95—24no—
240#95—24no—
241#95—21no—
242#95—21no—
243#95—22no—
244#95—22no—
245#95C22×C412yes—
246#95C22×C412yes—
247C24C2×C22⋊C411yescharacteristic
248C2×Q8—24no—
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—48no—
255C2×Q8—48no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4#10414yes—
291C22×C4C2×C22⋊C412yes—
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C412yes—
296C22×C4C2×C22⋊C411yescharacteristic
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C4×D412yes—
299C22×C4C4×D412yes—
300C22×C4#12011yescharacteristic
301C22×C4#12011yescharacteristic
302C22×C4#12112yes—
303C22×C4#12112yes—
304C22×C4#12311yescharacteristic
305C22×C4#12311yescharacteristic
306C22×C4C23×C411yescharacteristic
307C22×C4C22×D411yescharacteristic
308C22×C4C22×D411yescharacteristic
309M16—28no—
310M16—48no—
311M16—44no—
312C2×C8—28no—
313C2×C8—48no—
314C2×C8—48no—
315C2×C8—44no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—48no—
325C4⋊C4—42no—
326C4⋊C4—44no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—48no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42C4×D412yes—
343C42C4×D412yes—
344C42#12012yes—
345C42#12112yes—
346C42#12112yes—
347C42#12312yes—
348C42C22×D412yes—
349C42C2×#4112yes—
350C23—22no—
351C23—22no—
352C23#38611yescharacteristic
353C23#38611yescharacteristic
354C23C2×#10412yes—
355C23#42112yes—
356C23C22×C22⋊C411yescharacteristic
357Q8—48no—
358Q8—48no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—84no—
404C2×C4—84no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4#38611yescharacteristic
410C2×C4#38611yescharacteristic
411C2×C4#38612yes—
412C2×C4#38612yes—
413C2×C4C2×#10414yes—
414C2×C4C2×C4×D412yes—
415C2×C4C2×#12011yescharacteristic
416C2×C4C2×#12112yes—
417C2×C4C2×#12311yescharacteristic
418C8—48no—
419C8—48no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—24no—
426C22#187112yes—
427C22#187112yes—
428C22#191212yes—
429C22#191512yes—
430C22C2×#38611yescharacteristic
431C22C22×#10411yescharacteristic
432C22C2×#42111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—22no—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—24no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—82no—
446C4—82no—
447C4—82no—
448C4—82no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2#919014yesdirect product factor
453C2C2×#187111yescharacteristic
454C2C2×#191211yescharacteristic
455C2C2×#191511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #9190C2direct (N × H)
452. C2#9190direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29832
C2×#26342
C2×C4×#1012
C2×#15282
#91902
C2×#12882