Finite Group Databasebeta

← C2×#3554 #62746

Subgroups — C2×#3554 #62746

Order 256.

3591 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554C2132yesmaximal, direct product factor
2C2×#562C214yesmaximal, complemented
3C2×#559C212yesmaximal, complemented
4C2×#559C211yesmaximal, characteristic, complemented
5C2×#557C211yesmaximal, characteristic, complemented
6C2×#554C212yesmaximal, complemented
7C2×#550C211yesmaximal, characteristic, complemented
8C2×D4×Q8C211yesmaximal, characteristic, complemented
9C2×#548C212yesmaximal, complemented
10C2×#547C212yesmaximal, complemented
11C2×#542C212yesmaximal, complemented
12C2×#542C212yesmaximal, complemented
13C2×#540C212yesmaximal, complemented
14C2×#539C214yesmaximal, complemented
15C2×#536C212yesmaximal, complemented
16C2×#533C211yesmaximal, characteristic, complemented
17C2×#532C211yesmaximal, characteristic, complemented
18C2×#529C211yesmaximal, characteristic, complemented
19C22×#41C2212yes—
20C22×#41C2212yes—
21C23×Q8C2212yes—
22#562C22164yescomplemented
23#559C22132yescomplemented
24#559C22116yescomplemented
25#557C22116yescomplemented
26#554C22132yescomplemented
27#550C22116yescomplemented
28D4×Q8C22116yescomplemented
29#548C22132yescomplemented
30#547C22132yescomplemented
31#542C22132yescomplemented
32#542C22132yescomplemented
33#540C22132yescomplemented
34#539C22164yescomplemented
35#536C22132yescomplemented
36#533C22116yescomplemented
37#532C22116yescomplemented
38C2×C4⋊Q8C2211yescharacteristic
39C2×C4⋊Q8C2211yescharacteristic
40C2×C4⋊Q8C2211yescharacteristic
41C2×C4⋊Q8C2212yes—
42C2×C4⋊Q8C2212yes—
43C2×#127C2211yescharacteristic
44C2×#127C2212yes—
45#529C22116yescomplemented
46C2×#126C2212yes—
47C2×#126C2214yes—
48C2×#125C2211yescharacteristic
49C2×#125C2212yes—
50C2×#125C2214yes—
51C2×#125C2212yes—
52C2×#124C2211yescharacteristic
53C2×#124C2212yes—
54C2×#124C2212yes—
55C2×#124C2214yes—
56C2×#124C2212yes—
57C2×#124C2214yes—
58C2×#123C2212yes—
59C2×#123C2214yes—
60C2×#123C2214yes—
61C2×#123C2214yes—
62C2×#123C2214yes—
63C2×#123C2214yes—
64C2×#123C2214yes—
65C2×C22⋊Q8C2211yescharacteristic
66C2×C22⋊Q8C2211yescharacteristic
67C2×C22⋊Q8C2211yescharacteristic
68C2×C22⋊Q8C2212yes—
69C2×C22⋊Q8C2214yes—
70C2×C22⋊Q8C2214yes—
71C2×C22⋊Q8C2214yes—
72C2×C22⋊Q8C2214yes—
73C2×C22⋊Q8C2212yes—
74C2×C22⋊Q8C2214yes—
75C2×#121C2211yescharacteristic
76C2×#121C2212yes—
77C2×#121C2212yes—
78C2×#121C2214yes—
79C2×#121C2214yes—
80C2×#121C2214yes—
81C2×#121C2212yes—
82C2×C4×Q8C2211yescharacteristic
83C2×C4×Q8C2211yescharacteristic
84C2×C4×Q8C2211yescharacteristic
85C2×C4×Q8C2212yes—
86C2×C4×Q8C2212yes—
87C2×C4×Q8C2212yes—
88C2×C4×D4C2212yes—
89C2×C4×D4C2211yescharacteristic
90C2×C4×D4C2212yes—
91C2×C4×D4C2212yes—
92C2×C4×D4C2214yes—
93C2×C4×D4C2212yes—
94C2×C4×D4C2212yes—
95C2×C4×D4C2212yes—
96C2×C4×D4C2212yes—
97C2×#117C2212yes—
98C2×#117C2212yes—
99C22×C4⋊C4C2214yes—
100C22×C42C2211yescharacteristic
101C2×#41—48no—
102C2×#41—48no—
103C2×#41C23116yes—
104C2×#41C23116yes—
105C22×Q8—48no—
106C22×Q8C2311yescharacteristic
107C22×Q8C2311yescharacteristic
108C22×Q8C2312yes—
109C22×Q8C2311yescharacteristic
110C22×Q8C2312yes—
111C22×Q8C2314yes—
112C22×Q8C23116yes—
113C22×D4C2311yescharacteristic
114C22×D4C2312yes—
115C22×D4C2312yes—
116C22×D4C2312yes—
117C22×D4C2312yes—
118C22×D4C2314yes—
119C22×D4C2314yes—
120C22×D4C2314yes—
121C23×C4C2311yescharacteristic
122C23×C4C2312yes—
123C23×C4C2311yescharacteristic
124C23×C4C2314yes—
125C23×C4C2314yes—
126C23×C4C2314yes—
127C23×C4C2314yes—
128C23×C4C2311yescharacteristic
129C4⋊Q8C2318yes—
130C4⋊Q8C2318yes—
131C4⋊Q8C2318yes—
132C4⋊Q8C23116yes—
133C4⋊Q8C23116yes—
134#127C2318yes—
135#127C23116yes—
136#126C23116yes—
137#126C23132yes—
138#125C2318yes—
139#125C23116yes—
140#125C23132yes—
141#125C23116yes—
142#124C2318yes—
143#124C23116yes—
144#124C23116yes—
145#124C23132yes—
146#124C23116yes—
147#124C23132yes—
148#123C23116yes—
149#123C23132yes—
150#123C23132yes—
151#123C23132yes—
152#123C23132yes—
153#123C23132yes—
154#123C23132yes—
155C22⋊Q8C2318yes—
156C22⋊Q8C2318yes—
157C22⋊Q8C2318yes—
158C22⋊Q8C23116yes—
159C22⋊Q8C23132yes—
160C22⋊Q8C23132yes—
161C22⋊Q8C23132yes—
162C22⋊Q8C23132yes—
163C22⋊Q8C23116yes—
164C22⋊Q8C23132yes—
165#121C2318yes—
166#121C23116yes—
167#121C23116yes—
168#121C23132yes—
169#121C23132yes—
170#121C23132yes—
171#121C23116yes—
172C4×Q8C2318yes—
173C4×Q8C2318yes—
174C4×Q8C2318yes—
175C4×Q8C23116yes—
176C4×Q8C23116yes—
177C4×Q8C23116yes—
178C4×D4C23116yes—
179C4×D4C2318yes—
180C4×D4C23116yes—
181C4×D4C23116yes—
182C4×D4C23132yes—
183C4×D4C23116yes—
184C4×D4C23116yes—
185C4×D4C23116yes—
186C4×D4C23116yes—
187#117C23116yes—
188#117C23116yes—
189C2×C4⋊C4C2312yes—
190C2×C4⋊C4C2312yes—
191C2×C4⋊C4C2314yes—
192C2×C4⋊C4C2314yes—
193C2×C4⋊C4C23132yes—
194C2×C4⋊C4C2312yes—
195C2×C4⋊C4C2312yes—
196C2×C4⋊C4C2312yes—
197C2×C4⋊C4C2312yes—
198C2×C4⋊C4C2311yescharacteristic
199C2×C4⋊C4C2311yescharacteristic
200C2×C4⋊C4C2312yes—
201C2×C4⋊C4C2312yes—
202C2×C4⋊C4C2311yescharacteristic
203C2×C4⋊C4C2312yes—
204C2×C4⋊C4C2311yescharacteristic
205C2×C4⋊C4C2312yes—
206C2×C4⋊C4C2314yes—
207C2×C4⋊C4C2312yes—
208C2×C4⋊C4C2312yes—
209C2×C4⋊C4C2314yes—
210C2×C4⋊C4C2312yes—
211C2×C22⋊C4C2312yes—
212C2×C22⋊C4C2312yes—
213C2×C22⋊C4C2312yes—
214C2×C22⋊C4C2312yes—
215C2×C22⋊C4C2312yes—
216C2×C22⋊C4C2312yes—
217C2×C22⋊C4C2314yes—
218C2×C22⋊C4C2314yes—
219C2×C22⋊C4C2314yes—
220C2×C22⋊C4C2314yes—
221C2×C22⋊C4C2314yes—
222C2×C22⋊C4C2312yes—
223C2×C22⋊C4C2314yes—
224C2×C22⋊C4C2314yes—
225C2×C42C2311yescharacteristic
226C2×C42C2312yes—
227C2×C42C2312yes—
228C2×C42C2312yes—
229C2×C42C2311yescharacteristic
230C2×C42C2311yescharacteristic
231C2×C42C2311yescharacteristic
232C2×C42C2314yes—
233C2×C42C2318yes—
234C24C2412yes—
235C24C2411yescharacteristic
236C24C2414yes—
237#41—432no—
238#41—432no—
239C2×Q8—24no—
240C2×Q8—28no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—48no—
244C2×Q8—44no—
245C2×Q8—432no—
246C2×Q8C2414yes—
247C2×Q8C2414yes—
248C2×Q8C2418yes—
249C2×Q8C2414yes—
250C2×Q8C2418yes—
251C2×Q8C24116yes—
252C2×D4—28no—
253C2×D4—24no—
254C2×D4—28no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—48no—
258C2×D4—48no—
259C2×D4—48no—
260C2×D4C2414yes—
261C2×D4C2418yes—
262C2×D4C2418yes—
263C2×D4C2418yes—
264C2×D4C2418yes—
265C2×D4C24116yes—
266C2×D4C24116yes—
267C2×D4C24116yes—
268C22×C4—28no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—48no—
272C22×C4—42no—
273C22×C4—48no—
274C22×C4—48no—
275C22×C4—48no—
276C22×C4C2414yes—
277C22×C4C2414yes—
278C22×C4C2418yes—
279C22×C4C2412yes—
280C22×C4C2412yes—
281C22×C4C2411yescharacteristic
282C22×C4C2411yescharacteristic
283C22×C4C2411yescharacteristic
284C22×C4C2411yescharacteristic
285C22×C4C2412yes—
286C22×C4C2412yes—
287C22×C4C2412yes—
288C22×C4C2414yes—
289C22×C4C2412yes—
290C22×C4C2412yes—
291C22×C4C2414yes—
292C22×C4C24116yes—
293C22×C4C24116yes—
294C22×C4C24116yes—
295C22×C4C24116yes—
296C22×C4C2411yescharacteristic
297C22×C4C2411yescharacteristic
298C4⋊C4C2418yes—
299C4⋊C4C2418yes—
300C4⋊C4C24116yes—
301C4⋊C4C24116yes—
302C4⋊C4C2418yes—
303C4⋊C4C2418yes—
304C4⋊C4C2418yes—
305C4⋊C4C2418yes—
306C4⋊C4C2414yes—
307C4⋊C4C2414yes—
308C4⋊C4C2418yes—
309C4⋊C4C2418yes—
310C4⋊C4C2414yes—
311C4⋊C4C2418yes—
312C4⋊C4C2414yes—
313C4⋊C4C2418yes—
314C4⋊C4C24116yes—
315C4⋊C4C2418yes—
316C4⋊C4C2418yes—
317C4⋊C4C24116yes—
318C4⋊C4C2418yes—
319C22⋊C4C2418yes—
320C22⋊C4C2418yes—
321C22⋊C4C2418yes—
322C22⋊C4C2418yes—
323C22⋊C4C2418yes—
324C22⋊C4C2418yes—
325C22⋊C4C24116yes—
326C22⋊C4C24116yes—
327C22⋊C4C24116yes—
328C22⋊C4C24116yes—
329C22⋊C4C24116yes—
330C22⋊C4C2418yes—
331C22⋊C4C24116yes—
332C22⋊C4C24116yes—
333C42C2414yes—
334C42C2414yes—
335C42C2414yes—
336C42C2414yes—
337C42C2418yes—
338C42C2418yes—
339C42C2418yes—
340C42C24116yes—
341C23—24no—
342C23—22no—
343C23—28no—
344C23—22no—
345C23—24no—
346C23—28no—
347C23—22no—
348C23—28no—
349C23—24no—
350C23C2514yes—
351C23C2512yes—
352C23C2518yes—
353C23C2511yescharacteristic
354Q8—28no—
355Q8—216no—
356Q8—28no—
357Q8—28no—
358Q8—416no—
359Q8—48no—
360D4—216no—
361D4—28no—
362D4—216no—
363D4—48no—
364D4—48no—
365D4—416no—
366D4—416no—
367D4—416no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—216no—
381C2×C4—28no—
382C2×C4—28no—
383C2×C4—416no—
384C2×C4—44no—
385C2×C4—416no—
386C2×C4—416no—
387C2×C4—416no—
388C2×C4H(5,𝔽2)14yes—
389C2×C42−1+414yes—
390C2×C4C2514yes—
391C2×C4C2514yes—
392C2×C4C2512yes—
393C2×C4C2512yes—
394C2×C4C2512yes—
395C2×C4C2512yes—
396C2×C4C2514yes—
397C2×C4C2514yes—
398C2×C4C2514yes—
399C2×C4C2518yes—
400C2×C4C2514yes—
401C2×C4C2514yes—
402C2×C4C2512yes—
403C2×C4C2512yes—
404C22—24no—
405C22—22no—
406C22—28no—
407C22—22no—
408C22—24no—
409C22—28no—
410C22—22no—
411C22—28no—
412C22—24no—
413C22—48no—
414C22—44no—
415C22—416no—
416C22C2×H(5,𝔽2)12yes—
417C22C2×2−1+412yes—
418C22#58512yes—
419C22C2611yescharacteristic
420C4—22no—
421C4—24no—
422C4—24no—
423C4—28no—
424C4—24no—
425C4—22no—
426C4—24no—
427C4—24no—
428C4—24no—
429C4—22no—
430C4—22no—
431C4—24no—
432C4C2×H(5,𝔽2)14yes—
433C4C2×2−1+414yes—
434C2—44no—
435C2—42no—
436C2—48no—
437C2#355414yesdirect product factor
438C2C22×H(5,𝔽2)11yescharacteristic
439C2C22×2−1+411yescharacteristic
440C2C2×#58511yescharacteristic
subgroupG/H
center, socleC23C25
commutator, Frattini, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3554C2direct (N × H)
2. C2×#562C2semidirect
3. C2×#559C2semidirect
4. C2×#559C2semidirect
5. C2×#557C2semidirect
6. C2×#554C2semidirect
7. C2×#550C2semidirect
8. C2×D4×Q8C2semidirect
9. C2×#548C2semidirect
10. C2×#547C2semidirect
11. C2×#542C2semidirect
12. C2×#542C2semidirect
13. C2×#540C2semidirect
14. C2×#539C2semidirect
15. C2×#536C2semidirect
16. C2×#533C2semidirect
17. C2×#532C2semidirect
18. C2×#529C2semidirect
22. #562C22semidirect
23. #559C22semidirect
24. #559C22semidirect
25. #557C22semidirect
26. #554C22semidirect
27. #550C22semidirect
28. D4×Q8C22semidirect
29. #548C22semidirect
30. #547C22semidirect
31. #542C22semidirect
32. #542C22semidirect
33. #540C22semidirect
34. #539C22semidirect
35. #536C22semidirect
36. #533C22semidirect
37. #532C22semidirect
45. #529C22semidirect
437. C2#3554direct (N × H)

Maximal subgroups

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

subgroupindex
#35542
C2×#5622
C2×#5592
C2×#5572
C2×#5542
C2×#5502
C2×D4×Q82
C2×#5482
C2×#5472
C2×#5422
C2×#5402
C2×#5392
C2×#5362
C2×#5332
C2×#5322
C2×#5292