Finite Group Databasebeta

← C2×#25919 #6447735

Subgroups — C2×#25919 #6447735

Order 512.

3066 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic
2C2×#3139C212yesmaximal
3C2×#2546C211yesmaximal, characteristic
4#25919C2116yesmaximal, direct product factor
5C2×#2028C214yesmaximal
6C2×#1986C212yesmaximal
7C2×#1886C214yesmaximal
8C2×C4×#101C211yesmaximal, characteristic
9#3502—28no—
10#3502—24no—
11#3502C2218yes—
12C2×Q82—22no—
13C2×#557—22no—
14C2×#557—24no—
15C2×#544—22no—
16C2×#544C2212yes—
17C2×#533—22no—
18C2×#533C2212yes—
19C22×C4⋊Q8C2212yes—
20C22×C4⋊Q8C2211yescharacteristic
21C2×#519C2212yes—
22C22×C4×Q8C2211yescharacteristic
23#3139—28no—
24#3139C22116yes—
25C2×#491—24no—
26C2×#487—22no—
27C2×#487—22no—
28C2×#419C2218yes—
29C22×#101C2212yes—
30C2×C4×M16C2212yes—
31#2546—24no—
32#2546C2218yes—
33C2×#398—22no—
34C2×#391C2212yes—
35C2×#389—22no—
36C2×C4×C4⋊C4C2211yescharacteristic
37#2028C22132yes—
38#1986C22116yes—
39#1886C22132yes—
40C4×#101C2218yes—
41C2×#343C2212yes—
42C2×#339C2218yes—
43C23×Q8C2312yes—
44C23×Q8C2311yescharacteristic
45C22×M16C2314yes—
46Q82—216no—
47Q82—216no—
48#557—216no—
49#557—232no—
50#557—216no—
51#557—232no—
52#544—216no—
53#544—28no—
54#544—216no—
55#544—24no—
56#544C2318yes—
57#533—216no—
58#533—216no—
59#533—24no—
60#533—24no—
61#533D418yes—
62#533C2318yes—
63C2×C4⋊Q8—22no—
64C2×C4⋊Q8—22no—
65C2×C4⋊Q8—28no—
66C2×C4⋊Q8—24no—
67C2×C4⋊Q8—24no—
68C2×C4⋊Q8—216no—
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—24no—
73C2×C4⋊Q8D412yes—
74C2×C4⋊Q8D412yes—
75C2×C4⋊Q8C2314yes—
76C2×C4⋊Q8C2318yes—
77C2×#125—24no—
78C2×#125—28no—
79C2×#125—24no—
80C2×#125D414yes—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—24no—
83C2×C22⋊Q8—22no—
84#519—24no—
85#519—28no—
86#519C2318yes—
87C2×C4×Q8—24no—
88C2×C4×Q8—24no—
89C2×C4×Q8—24no—
90C2×C4×Q8—24no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—24no—
94C2×C4×Q8—22no—
95C2×C4×Q8—22no—
96C2×C4×Q8D414yes—
97C2×C4×Q8C2314yes—
98C2×#117—24no—
99C2×#117C2314yes—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4D412yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C42D412yes—
107C22×C42C2312yes—
108C22×C42C2311yescharacteristic
109#491—232no—
110#487—216no—
111#487—216no—
112#419—216no—
113#419C23132yes—
114C2×#103—28no—
115C2×#103—28no—
116C2×#101—28no—
117C2×#101C2318yes—
118C4×M16—24no—
119C4×M16C2318yes—
120C2×#97—22no—
121C2×C4×C8—22no—
122#398—216no—
123#391—24no—
124#391C2318yes—
125#389—216no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4C2314yes—
128C2×#95—21no—
129C2×#95—24no—
130#343C2318yes—
131#339C23132yes—
132C22×Q8—24no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—22no—
137C22×Q8—22no—
138C22×Q8—24no—
139C22×Q8—24no—
140C22×Q8—24no—
141C22×Q8—28no—
142C22×Q8—28no—
143C22×Q8C2×D412yes—
144C22×Q8#4118yes—
145C22×Q8C2414yes—
146C22×Q8C2412yes—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C23×C4C2×D412yes—
152C23×C4C2×D411yescharacteristic
153C23×C4C2411yescharacteristic
154C2×M16—24no—
155C2×M16—28no—
156C2×M16—28no—
157C2×M16C2418yes—
158C22×C8—24no—
159C4⋊Q8—216no—
160C4⋊Q8—216no—
161C4⋊Q8—264no—
162C4⋊Q8—216no—
163C4⋊Q8—216no—
164C4⋊Q8—232no—
165C4⋊Q8—24no—
166C4⋊Q8—24no—
167C4⋊Q8—28no—
168C4⋊Q8—28no—
169C4⋊Q8—416no—
170C4⋊Q8—44no—
171C4⋊Q8—44no—
172C4⋊Q8C2×D418yes—
173C4⋊Q8C2×D418yes—
174#125—232no—
175#125—264no—
176#125—216no—
177#125—216no—
178#125—28no—
179#125C2×D4116yes—
180C22⋊Q8—216no—
181C22⋊Q8—28no—
182C22⋊Q8—28no—
183C22⋊Q8—28no—
184C22⋊Q8—216no—
185C22⋊Q8—28no—
186C4×Q8—216no—
187C4×Q8—216no—
188C4×Q8—232no—
189C4×Q8—232no—
190C4×Q8—216no—
191C4×Q8—216no—
192C4×Q8—28no—
193C4×Q8—28no—
194C4×Q8—28no—
195C4×Q8—28no—
196C4×Q8—28no—
197C4×Q8—28no—
198C4×Q8—28no—
199C4×Q8—28no—
200#117—216no—
201#117—216no—
202#117—24no—
203#117—24no—
204#117C2×D418yes—
205#117C2418yes—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—216no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—42no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—416no—
229C2×C4⋊C4C2×D418yes—
230C2×C4⋊C4C2×D412yes—
231C2×C4⋊C4C2×D414yes—
232C2×C4⋊C4C2×D414yes—
233C2×C4⋊C4C2412yes—
234C2×C22⋊C4—24no—
235C2×C42—28no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—24no—
239C2×C42—24no—
240C2×C42—28no—
241C2×C42—22no—
242C2×C42C2×D418yes—
243C2×C42C2×D412yes—
244C2×C42C2×D412yes—
245C2×C42C2×D412yes—
246C2×C42C2×D414yes—
247C2×C42C2414yes—
248C2×C42C2412yes—
249#103—232no—
250#103—232no—
251#101—216no—
252#97—28no—
253C4×C8—28no—
254#95—24no—
255#95—216no—
256C24C22×D411yescharacteristic
257C2×Q8—216no—
258C2×Q8—24no—
259C2×Q8—28no—
260C2×Q8—28no—
261C2×Q8—24no—
262C2×Q8—216no—
263C2×Q8—216no—
264C2×Q8—24no—
265C2×Q8—24no—
266C2×Q8—28no—
267C2×Q8—28no—
268C2×Q8—28no—
269C2×Q8—44no—
270C2×Q8—44no—
271C2×Q8—44no—
272C2×Q8—48no—
273C2×Q8—416no—
274C2×Q8—416no—
275C2×Q8—84no—
276C2×Q8—88no—
277C2×Q8#12418yes—
278C2×Q8C2×#4118yes—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—28no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—42no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4#12012yes—
299C22×C4#12011yescharacteristic
300C22×C4#12012yes—
301C22×C4#12012yes—
302C22×C4#12011yescharacteristic
303C22×C4#12418yes—
304C22×C4C22×D412yes—
305C22×C4C22×D414yes—
306C22×C4C22×D414yes—
307C22×C4C22×D412yes—
308C22×C4C22×D411yescharacteristic
309C22×C4C22×D412yes—
310C22×C4C22×D412yes—
311C22×C4C2×#4114yes—
312C22×C42−1+414yes—
313C22×C4C2511yescharacteristic
314M16—28no—
315M16—28no—
316M16—48no—
317C2×C8—28no—
318C2×C8—48no—
319C4⋊C4—216no—
320C4⋊C4—216no—
321C4⋊C4—216no—
322C4⋊C4—216no—
323C4⋊C4—232no—
324C4⋊C4—216no—
325C4⋊C4—24no—
326C4⋊C4—216no—
327C4⋊C4—28no—
328C4⋊C4—28no—
329C4⋊C4—216no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—44no—
334C4⋊C4—48no—
335C4⋊C4—44no—
336C4⋊C4—432no—
337C4⋊C4C22×D418yes—
338C4⋊C4C22×D418yes—
339C22⋊C4—28no—
340C22⋊C4—28no—
341C42—232no—
342C42—28no—
343C42—28no—
344C42—28no—
345C42—28no—
346C42—28no—
347C42—44no—
348C42#12014yes—
349C42#12014yes—
350C42C22×D414yes—
351C42C22×D414yes—
352C23—22no—
353C23—22no—
354C23C2×#12011yescharacteristic
355C23C2×#12011yescharacteristic
356C23C2×#12412yes—
357C23#53612yes—
358C23C23×D411yescharacteristic
359Q8—216no—
360Q8—216no—
361Q8—416no—
362Q8—416no—
363Q8—88no—
364Q8—816no—
365Q8—88no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—28no—
369C2×C4—28no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—28no—
375C2×C4—28no—
376C2×C4—28no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—416no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—48no—
384C2×C4—44no—
385C2×C4—48no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—84no—
392C2×C4—84no—
393C2×C4#45614yes—
394C2×C4C2×#12012yes—
395C2×C4C2×#12014yes—
396C2×C4C2×#12012yes—
397C2×C4C2×#12012yes—
398C2×C4C2×#12418yes—
399C2×C4C2×#12412yes—
400C2×C4#53612yes—
401C2×C4#54818yes—
402C2×C4#54818yes—
403C2×C4C23×D412yes—
404C2×C4C22×#4112yes—
405C2×C4C2×2−1+412yes—
406C8—48no—
407C22—24no—
408C22—24no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22#243612yes—
414C22#243612yes—
415C22C2×#45612yes—
416C22#302212yes—
417C22C22×#12011yescharacteristic
418C22C22×#12411yescharacteristic
419C22C2×#53611yescharacteristic
420C4—28no—
421C4—22no—
422C4—24no—
423C4—48no—
424C4—48no—
425C4—44no—
426C4—48no—
427C4—84no—
428C4#243614yes—
429C4C2×#45614yes—
430C4C2×#54814yes—
431C2—21no—
432C2—21no—
433C2—22no—
434C2#2591914yesdirect product factor
435C2C2×#243611yescharacteristic
436C2C22×#45611yescharacteristic
437C2C2×#302211yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #25919C2direct (N × H)
434. C2#25919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#31392
C2×#25462
#259192
C2×#20282
C2×#19862
C2×#18862
C2×C4×#1012