Finite Group Databasebeta

← C2×#44982 #7669515

Subgroups — C2×#44982 #7669515

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2802C214yesmaximal
2C2×#2726C214yesmaximal
3#44982C2132yesmaximal, direct product factor
4C2×#2552C212yesmaximal
5C2×#2584C212yesmaximal
6C2×#2584C214yesmaximal
7C2×#2507C212yesmaximal
8C2×#2506C212yesmaximal
9C2×#2462C214yesmaximal
10C2×#2399C211yesmaximal, characteristic
11C2×#2370C212yesmaximal
12C2×Q8×C4⋊C4C212yesmaximal
13C2×#2330C211yesmaximal, characteristic
14C2×#2330C211yesmaximal, characteristic
15C22×#125C2211yescharacteristic
16C22×#125C2214yes—
17C22×#125C2214yes—
18C22×#125C2211yescharacteristic
19C22×C4×Q8C2212yes—
20C22×C4×Q8C2214yes—
21#2802C22164yes—
22#2726C22164yes—
23#2584C22132yes—
24#2584C22164yes—
25#2552C22132yes—
26#2507C22132yes—
27#2506C22132yes—
28#2462C22164yes—
29#2399C22116yes—
30C2×#400C2214yes—
31C2×#398C2212yes—
32C2×#398C2214yes—
33C2×#398C2214yes—
34C2×#398C2214yes—
35C2×#398C2214yes—
36C2×#398C2214yes—
37C2×#398C2214yes—
38C2×#398C2212yes—
39C2×#395C2214yes—
40C2×#395C2212yes—
41C2×#395C2212yes—
42#2370C22132yes—
43Q8×C4⋊C4C22132yes—
44#2330C22116yes—
45#2330C22116yes—
46C2×#389C2214yes—
47C2×#389C2214yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2214yes—
51C2×#389C2214yes—
52C2×#389C2214yes—
53C2×#389C2214yes—
54C2×#389C2214yes—
55C2×#389C2214yes—
56C2×#389C2214yes—
57C2×#389C2212yes—
58C2×#389C2212yes—
59C2×#389C2212yes—
60C2×#389C2212yes—
61C2×#389C2214yes—
62C2×#387C2214yes—
63C2×#387C2214yes—
64C2×#387C2214yes—
65C2×#387C2214yes—
66C2×#387C2214yes—
67C2×#387C2214yes—
68C2×#384C2211yescharacteristic
69C2×#384C2211yescharacteristic
70C2×#384C2212yes—
71C2×#384C2212yes—
72C2×C4×C4⋊C4C2212yes—
73C2×C4×C4⋊C4C2212yes—
74C2×C4×C4⋊C4C2212yes—
75C2×C4×C4⋊C4C2212yes—
76C2×C4×C4⋊C4C2214yes—
77C2×C4×C4⋊C4C2212yes—
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×#376C2211yescharacteristic
81C23×Q8C2312yes—
82C2×#125—28no—
83C2×#125—416no—
84C2×#125—416no—
85C2×#125Q8116yescomplemented
86C2×#125C2318yes—
87C2×#125C23132yes—
88C2×#125C23132yes—
89C2×#125C2318yes—
90C2×C4×Q8—216no—
91C2×C4×Q8—416no—
92C2×C4×Q8C23116yes—
93C2×C4×Q8C23132yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2312yes—
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2314yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C42C2314yes—
120C22×C42C2312yes—
121C22×C42C2312yes—
122C22×C42C2311yescharacteristic
123C22×C42C2314yes—
124C22×C42C2314yes—
125C22×C42C2314yes—
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128#400C23132yes—
129#398C23132yes—
130#398C23132yes—
131#398C23132yes—
132#398C23116yes—
133#398C23116yes—
134#398C23132yes—
135#398C23132yes—
136#398C23132yes—
137#395C23116yes—
138#395C23132yes—
139#395C23116yes—
140#389C23132yes—
141#389C23132yes—
142#389C23132yes—
143#389C23132yes—
144#389C23132yes—
145#389C23116yes—
146#389C23116yes—
147#389C23132yes—
148#389C23132yes—
149#389C23116yes—
150#389C23116yes—
151#389C23132yes—
152#389C23116yes—
153#389C23116yes—
154#389C23132yes—
155#389C23132yes—
156#387C23132yes—
157#387C23132yes—
158#387C23132yes—
159#387C23132yes—
160#387C23132yes—
161#387C23132yes—
162#384C2318yes—
163#384C2318yes—
164#384C23116yes—
165#384C23116yes—
166C4×C4⋊C4C23116yes—
167C4×C4⋊C4C23132yes—
168C4×C4⋊C4C23116yes—
169C4×C4⋊C4C23116yes—
170C4×C4⋊C4C23116yes—
171C4×C4⋊C4C23116yes—
172C4×C4⋊C4C2318yes—
173C4×C4⋊C4C2318yes—
174#376C2318yes—
175C2×#95C2312yes—
176C2×#95C2311yescharacteristic
177C2×#95C2311yescharacteristic
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2311yescharacteristic
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C22×Q8—28no—
194C22×Q8—28no—
195C22×Q8—28no—
196C22×Q8C2418yes—
197C23×C4C2414yes—
198C23×C4C2411yescharacteristic
199C23×C4C2412yes—
200C23×C4C2412yes—
201C23×C4C2414yes—
202C23×C4C2414yes—
203C23×C4C2411yescharacteristic
204C23×C4C2414yes—
205C23×C4C2412yes—
206C23×C4C2412yes—
207C23×C4C2412yes—
208C23×C4C2412yes—
209C23×C4C2411yescharacteristic
210#125—232no—
211#125—464no—
212#125—464no—
213#125C2×Q8164yescomplemented
214C4×Q8—264no—
215C4×Q8—464no—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—28no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—216no—
220C2×C4⋊C4—28no—
221C2×C4⋊C4—216no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—216no—
224C2×C4⋊C4—28no—
225C2×C4⋊C4—216no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—28no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—48no—
231C2×C4⋊C4—48no—
232C2×C4⋊C4—48no—
233C2×C4⋊C4—48no—
234C2×C4⋊C4—48no—
235C2×C4⋊C4—48no—
236C2×C4⋊C4—48no—
237C2×C4⋊C4—48no—
238C2×C4⋊C4—48no—
239C2×C4⋊C4C2×Q8132yes—
240C2×C4⋊C4C2×Q8116yes—
241C2×C4⋊C4C24116yes—
242C2×C4⋊C4C2418yes—
243C2×C4⋊C4C2418yes—
244C2×C4⋊C4C2418yes—
245C2×C4⋊C4C2418yes—
246C2×C4⋊C4C2418yes—
247C2×C4⋊C4C24116yes—
248C2×C4⋊C4C2418yes—
249C2×C4⋊C4C24116yes—
250C2×C4⋊C4C2418yes—
251C2×C4⋊C4C2418yes—
252C2×C4⋊C4C2418yes—
253C2×C4⋊C4C24116yes—
254C2×C4⋊C4C2418yes—
255C2×C4⋊C4C24116yes—
256C2×C4⋊C4C24116yes—
257C2×C4⋊C4C24116yes—
258C2×C4⋊C4C24116yes—
259C2×C4⋊C4C24116yes—
260C2×C4⋊C4C24116yes—
261C2×C4⋊C4C24116yes—
262C2×C4⋊C4C24116yes—
263C2×C4⋊C4C24116yes—
264C2×C4⋊C4C2418yes—
265C2×C4⋊C4C24116yes—
266C2×C42—28no—
267C2×C42—28no—
268C2×C42—216no—
269C2×C42—24no—
270C2×C42—48no—
271C2×C42—48no—
272C2×C42—48no—
273C2×C42C2×Q818yes—
274C2×C42#4118yes—
275C2×C42C24116yes—
276C2×C42C2418yes—
277C2×C42C2418yes—
278C2×C42C2414yes—
279C2×C42C24116yes—
280C2×C42C24116yes—
281C2×C42C24116yes—
282C2×C42C2414yes—
283C2×C42C2414yes—
284#95C2418yes—
285#95C2418yes—
286#95C2418yes—
287#95C2414yes—
288#95C24116yes—
289#95C24116yes—
290#95C24116yes—
291#95C2418yes—
292#95C24116yes—
293#95C24116yes—
294#95C2414yes—
295#95C2414yes—
296#95C2414yes—
297#95C24116yes—
298#95C24116yes—
299#95C24116yes—
300#95C24116yes—
301#95C24116yes—
302C24C2511yescharacteristic
303C2×Q8—264no—
304C2×Q8—216no—
305C2×Q8—216no—
306C2×Q8—216no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—28no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—28no—
322C22×C4—28no—
323C22×C4—28no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—28no—
333C22×C4—28no—
334C22×C4—28no—
335C22×C4—24no—
336C22×C4C22×Q818yes—
337C22×C4C22×Q8116yes—
338C22×C4C22×Q814yes—
339C22×C4C2×#4118yes—
340C22×C4C2×#4114yes—
341C22×C4H(5,𝔽2)18yes—
342C22×C42−1+418yes—
343C22×C42−1+414yes—
344C22×C4C2512yes—
345C22×C4C2514yes—
346C22×C4C2514yes—
347C22×C4C2518yes—
348C22×C4C2518yes—
349C22×C4C2518yes—
350C22×C4C2512yes—
351C22×C4C2518yes—
352C22×C4C2514yes—
353C22×C4C2514yes—
354C22×C4C2514yes—
355C22×C4C2514yes—
356C22×C4C2512yes—
357C4⋊C4—216no—
358C4⋊C4—216no—
359C4⋊C4—216no—
360C4⋊C4—232no—
361C4⋊C4—216no—
362C4⋊C4—232no—
363C4⋊C4—216no—
364C4⋊C4—232no—
365C4⋊C4—216no—
366C4⋊C4—232no—
367C4⋊C4—216no—
368C4⋊C4—216no—
369C4⋊C4—216no—
370C4⋊C4—216no—
371C4⋊C4—416no—
372C4⋊C4—416no—
373C4⋊C4—416no—
374C4⋊C4—416no—
375C4⋊C4—416no—
376C4⋊C4—416no—
377C4⋊C4—416no—
378C4⋊C4—416no—
379C4⋊C4—416no—
380C4⋊C4C22×Q8164yes—
381C4⋊C4C22×Q8132yes—
382C42—216no—
383C42—216no—
384C42—232no—
385C42—28no—
386C42—416no—
387C42—416no—
388C42—416no—
389C42C22×Q8116yes—
390C42C2×#41116yes—
391C23C23×Q812yes—
392C23C22×#4112yes—
393C23C2×H(5,𝔽2)14yes—
394C23C2×2−1+412yes—
395C23C2×2−1+414yes—
396C23C2611yescharacteristic
397Q8—264no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—28no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—216no—
409C2×C4—216no—
410C2×C4—216no—
411C2×C4—232no—
412C2×C4—216no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—28no—
416C2×C4—28no—
417C2×C4—28no—
418C2×C4—28no—
419C2×C4—28no—
420C2×C4—28no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—28no—
427C2×C4—28no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—28no—
432C2×C4—48no—
433C2×C4—48no—
434C2×C4—416no—
435C2×C4—416no—
436C2×C4—416no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4#557116yes—
440C2×C4C23×Q818yes—
441C2×C4C23×Q8116yes—
442C2×C4C23×Q814yes—
443C2×C4C22×#4118yes—
444C2×C4C22×#4114yes—
445C2×C4C2×H(5,𝔽2)18yes—
446C2×C4C2×2−1+418yes—
447C2×C4C2×2−1+414yes—
448C22C2×#55714yes—
449C22#349218yes—
450C22#350318yes—
451C22#354814yes—
452C22#355614yes—
453C22C24×Q811yescharacteristic
454C22C23×#4111yescharacteristic
455C22C22×H(5,𝔽2)12yes—
456C22C22×2−1+411yescharacteristic
457C22C22×2−1+412yes—
458C4—28no—
459C4—28no—
460C4—28no—
461C4—216no—
462C4—28no—
463C4—48no—
464C4—48no—
465C4—42no—
466C4—42no—
467C4—44no—
468C4—44no—
469C4—48no—
470C4C2×#55718yes—
471C2#4498218yesdirect product factor
472C2C22×#55711yescharacteristic
473C2C2×#354811yescharacteristic
474C2C2×#355611yescharacteristic
475C2C2×#349212yes—
476C2C2×#350312yes—
subgroupG/H
center, socle, prime radicalC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #44982C2direct (N × H)
85. C2×#125Q8semidirect
213. #125C2×Q8semidirect
471. C2#44982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28022
C2×#27262
#449822
C2×#25522
C2×#25842
C2×#25072
C2×#25062
C2×#24622
C2×#23992
C2×#23702
C2×Q8×C4⋊C42
C2×#23302