Finite Group Databasebeta

← C2×#11326 #358439

Subgroups — C2×#11326 #358439

Order 512.

2130 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#108C212yesmaximal
2C22×#423C211yesmaximal, characteristic
3C22×#341C212yesmaximal
4C2×#1728C211yesmaximal, characteristic
5C22×#336C211yesmaximal, characteristic
6#11326C218yesmaximal, direct product factor
7C23×M16C2211yescharacteristic
8C23×M16C2212yes—
9C23×M16C2211yescharacteristic
10C24×C8C2212yes—
11C23×C42C2211yescharacteristic
12C22×#108—28no—
13C22×#108—28no—
14C22×#108—28no—
15C22×#108C2218yes—
16C2×#423—22no—
17C2×#423—28no—
18C2×#423C2214yes—
19C22×C4⋊C8—22no—
20C2×#341—28no—
21C2×#341C2218yes—
22#1728—22no—
23#1728C2214yes—
24C2×#336—22no—
25C2×#336C412yes—
26C2×#336C414yes—
27C2×#336C412yes—
28C2×#336C2214yes—
29C24×C4Q812yes—
30C24×C4C2311yescharacteristic
31C22×M16—24no—
32C22×M16—22no—
33C22×M16—21no—
34C22×M16—21no—
35C22×M16—22no—
36C22×M16—22no—
37C22×M16—24no—
38C22×M16—24no—
39C22×M16—24no—
40C22×M16—24no—
41C22×M16—24no—
42C22×M16—24no—
43C22×M16—24no—
44C22×M16—24no—
45C22×M16D418yes—
46C22×M16D414yes—
47C22×M16Q814yes—
48C22×M16C2314yes—
49C22×M16C2312yes—
50C22×M16C2312yes—
51C23×C8—24no—
52C23×C8—24no—
53C23×C8—24no—
54C23×C8—24no—
55C23×C8—22no—
56C23×C8—21no—
57C23×C8—21no—
58C23×C8C2×C414yes—
59C23×C8C2×C414yes—
60C23×C8D418yes—
61C23×C8Q818yes—
62C23×C8C2314yes—
63C22×C42—24no—
64C22×C42—24no—
65C22×C42C2×C411yescharacteristic
66C22×C42C2×C412yes—
67C22×C42C2×C411yescharacteristic
68C22×C42D412yes—
69C22×C42D412yes—
70C22×C42Q812yes—
71C22×C42C2312yes—
72C2×#108—264no—
73C2×#108—216no—
74C2×#108—216no—
75C2×#108—216no—
76#423—216no—
77#423—216no—
78C2×C4⋊C8—216no—
79C2×C4⋊C8—28no—
80#341—216no—
81#336—28no—
82#336C2×C418yes—
83#336C2×C418yes—
84C25C2×Q811yescharacteristic
85C23×C4—28no—
86C23×C4—28no—
87C23×C4—44no—
88C23×C4C4⋊C412yes—
89C23×C4C4⋊C414yes—
90C23×C4C4⋊C412yes—
91C23×C4C22×C411yescharacteristic
92C23×C4C22×C411yescharacteristic
93C23×C4C2×D414yes—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D412yes—
96C23×C4C2×D414yes—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×Q814yes—
99C23×C4C2×Q811yescharacteristic
100C23×C4C2×Q814yes—
101C23×C4C2×Q812yes—
102C23×C4#4112yes—
103C23×C4#4114yes—
104C23×C4#4112yes—
105C23×C4C2411yescharacteristic
106C2×M16—28no—
107C2×M16—24no—
108C2×M16—24no—
109C2×M16—24no—
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—216no—
113C2×M16—216no—
114C2×M16—216no—
115C2×M16—216no—
116C2×M16—24no—
117C2×M16—24no—
118C2×M16—24no—
119C2×M16—24no—
120C2×M16—24no—
121C2×M16—24no—
122C2×M16—24no—
123C2×M16—24no—
124C2×M16—42no—
125C2×M16—48no—
126C2×M16—44no—
127C2×M16—48no—
128C2×M16—48no—
129C2×M16—42no—
130C2×M16—48no—
131C2×M16—44no—
132C2×M16—42no—
133C2×M16—42no—
134C2×M16C2×D418yes—
135C2×M16C2×D414yes—
136C2×M16C2×Q814yes—
137C22×C8—28no—
138C22×C8—28no—
139C22×C8—28no—
140C22×C8—28no—
141C22×C8—216no—
142C22×C8—216no—
143C22×C8—216no—
144C22×C8—216no—
145C22×C8—24no—
146C22×C8—24no—
147C22×C8—24no—
148C22×C8—24no—
149C22×C8—28no—
150C22×C8—24no—
151C22×C8—24no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—24no—
155C22×C8—42no—
156C22×C8—44no—
157C22×C8—42no—
158C22×C8—44no—
159C22×C8—42no—
160C22×C8—42no—
161C22×C8C4⋊C4116yes—
162C22×C8C4⋊C4116yes—
163C22×C8C22×C418yes—
164C22×C8C2×D418yes—
165C22×C8C2×Q818yes—
166C2×C42—24no—
167C2×C42—28no—
168C2×C42—24no—
169C2×C42—24no—
170C2×C42—24no—
171C2×C42—28no—
172C2×C42—24no—
173C2×C42—24no—
174C2×C42—24no—
175C2×C42—24no—
176C2×C42C4⋊C412yes—
177C2×C42C4⋊C414yes—
178C2×C42C4⋊C412yes—
179C2×C42C22×C412yes—
180C2×C42C22×C412yes—
181C2×C42C2×D414yes—
182#108—264no—
183C4⋊C8—232no—
184C24—24no—
185C24—24no—
186C24C2×C4⋊C411yescharacteristic
187C24C2×C4⋊C411yescharacteristic
188C24C22⋊Q814yes—
189C24#12512yes—
190C24C4⋊Q814yes—
191C24C4⋊Q812yes—
192C24C22×Q811yescharacteristic
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—28no—
196C22×C4—28no—
197C22×C4—24no—
198C22×C4—24no—
199C22×C4—24no—
200C22×C4—28no—
201C22×C4—28no—
202C22×C4—44no—
203C22×C4—44no—
204C22×C4—432no—
205C22×C4#10818yescomplemented
206C22×C4C2×C4⋊C414yes—
207C22×C4C2×C4⋊C414yes—
208C22×C4C2×C4⋊C414yes—
209C22×C4C2×C4⋊C414yes—
210C22×C4C2×C4⋊C411yescharacteristic
211C22×C4C2×C4⋊C411yescharacteristic
212C22×C4C4×D412yes—
213C22×C4C4×D412yes—
214C22×C4C4×D414yes—
215C22×C4C4×D414yes—
216C22×C4C4×Q812yes—
217C22×C4C4×Q812yes—
218C22×C4#12018yes—
219C22×C4#12012yes—
220C22×C4#12012yes—
221C22×C4#12118yes—
222C22×C4#12112yes—
223C22×C4#12112yes—
224C22×C4C22⋊Q818yes—
225C22×C4C22⋊Q818yes—
226C22×C4C22⋊Q818yes—
227C22×C4C22⋊Q812yes—
228C22×C4C22⋊Q812yes—
229C22×C4C22⋊Q814yes—
230C22×C4#12318yes—
231C22×C4#12312yes—
232C22×C4#12312yes—
233C22×C4#12518yes—
234C22×C4#12512yes—
235C22×C4#12712yes—
236C22×C4#12712yes—
237C22×C4C4⋊Q812yes—
238C22×C4C4⋊Q812yes—
239C22×C4C4⋊Q818yes—
240C22×C4C4⋊Q814yes—
241C22×C4C4⋊Q812yes—
242C22×C4C23×C411yescharacteristic
243C22×C4C22×D412yes—
244C22×C4C22×D411yescharacteristic
245C22×C4C22×D412yes—
246C22×C4C22×D411yescharacteristic
247C22×C4C22×Q812yes—
248C22×C4C22×Q811yescharacteristic
249C22×C4C2×#4111yescharacteristic
250C22×C4C2×#4112yes—
251C22×C4C2×#4111yescharacteristic
252M16—28no—
253M16—28no—
254M16—28no—
255M16—28no—
256M16—44no—
257M16—44no—
258M16—44no—
259M16—44no—
260M16—416no—
261M16—48no—
262M16—48no—
263C2×C8—28no—
264C2×C8—28no—
265C2×C8—28no—
266C2×C8—28no—
267C2×C8—28no—
268C2×C8—28no—
269C2×C8—232no—
270C2×C8—232no—
271C2×C8—28no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—42no—
275C2×C8—44no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—44no—
279C2×C8—42no—
280C2×C8—416no—
281C2×C8—48no—
282C2×C8—48no—
283C2×C8C2×C4⋊C4116yes—
284C42—24no—
285C42—24no—
286C42—24no—
287C42—24no—
288C42—24no—
289C42—28no—
290C42—24no—
291C23—28no—
292C23—28no—
293C23—216no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—28no—
299C23—28no—
300C23#38412yes—
301C23#38412yes—
302C23#38512yes—
303C23#38512yes—
304C23#38912yes—
305C23#38912yes—
306C23#39518yes—
307C23#39818yes—
308C23C2×#10814yes—
309C23#43014yes—
310C23C22×C4⋊C411yescharacteristic
311C23C2×C22⋊Q812yes—
312C23C2×#12511yescharacteristic
313C23C2×C4⋊Q811yescharacteristic
314C23C2×C4⋊Q812yes—
315C2×C4—216no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—416no—
322C2×C4—416no—
323C2×C4—48no—
324C2×C4#38412yes—
325C2×C4#38412yes—
326C2×C4#38512yes—
327C2×C4#38512yes—
328C2×C4#38518yes—
329C2×C4#38518yes—
330C2×C4#38912yes—
331C2×C4#38912yes—
332C2×C4#38918yes—
333C2×C4#38918yes—
334C2×C4#39214yes—
335C2×C4#39214yes—
336C2×C4#39514yes—
337C2×C4#39514yes—
338C2×C4#39518yes—
339C2×C4#39814yes—
340C2×C4#39814yes—
341C2×C4#39818yes—
342C2×C4#39914yes—
343C2×C4#39914yes—
344C2×C4C2×#10818yescomplemented
345C2×C4C22×C4⋊C412yes—
346C2×C4C2×C4×D411yescharacteristic
347C2×C4C2×C4×D412yes—
348C2×C4C2×C4×Q811yescharacteristic
349C2×C4C2×#12011yescharacteristic
350C2×C4C2×#12012yes—
351C2×C4C2×#12111yescharacteristic
352C2×C4C2×#12112yes—
353C2×C4C2×C22⋊Q811yescharacteristic
354C2×C4C2×C22⋊Q812yes—
355C2×C4C2×C22⋊Q812yes—
356C2×C4C2×C22⋊Q812yes—
357C2×C4C2×#12311yescharacteristic
358C2×C4C2×#12312yes—
359C2×C4C2×#12512yes—
360C2×C4C2×#12711yescharacteristic
361C2×C4C2×C4⋊Q811yescharacteristic
362C2×C4C2×C4⋊Q812yes—
363C8—216no—
364C8—48no—
365C8—44no—
366C8—44no—
367C22—216no—
368C22—216no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—24no—
374C22—24no—
375C22—22no—
376C22—22no—
377C22—24no—
378C22#144414yes—
379C22#144414yes—
380C22#184814yes—
381C22#184914yes—
382C22#185518yes—
383C22#195018yes—
384C22C2×#38411yescharacteristic
385C22C2×#38511yescharacteristic
386C22C2×#38911yescharacteristic
387C22C2×#39512yes—
388C22C2×#39812yes—
389C22C22×#10812yes—
390C22C2×#43012yes—
391C4—28no—
392C4—44no—
393C4#144414yes—
394C4#144414yes—
395C4C2×#38512yes—
396C4C2×#38912yes—
397C4C2×#39211yescharacteristic
398C4C2×#39511yescharacteristic
399C4C2×#39811yescharacteristic
400C4C2×#39911yescharacteristic
401C2—22no—
402C2—22no—
403C2—24no—
404C2#1132618yesdirect product factor
405C2C2×#144411yescharacteristic
406C2C2×#184811yescharacteristic
407C2C2×#184911yescharacteristic
408C2C2×#185512yes—
409C2C2×#195012yes—
subgroupG/H
centerC23×C4C2×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC24C2×C4⋊C4
prime radicalC25C2×Q8
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #11326C2direct (N × H)
205. C22×C4#108semidirect
344. C2×C4C2×#108semidirect
404. C2#11326direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1082
C22×#4232
C22×#3412
C2×#17282
C22×#3362
#113262