Finite Group Databasebeta

← C2×#21444759 #29652191

Subgroups — C2×#21444759 #29652191

Order 15616.

1372 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839912C212yesmaximal
2C2×#16839679C211yesmaximal, characteristic
3#21444759C218yesmaximal, direct product factor
4C2×#16839499C212yesmaximal, complemented
5C2×#16839488C211yesmaximal, characteristic, complemented
6C2×C61×#544C211yesmaximal, characteristic, complemented
7C23×D244C2211yescharacteristic
8C22×#11758201—22no—
9C22×#11758198—21no—
10C22×#11758198—21no—
11#16839912—24no—
12#16839912C2218yes—
13C2×#14519697—22no—
14C2×C22⋊#92418C2212yes—
15#16839679—22no—
16#16839679C2214yes—
17C2×#14519684C2211yescharacteristic
18#16839499C2218yescomplemented
19#16839488C2214yescomplemented
20C61×#544—24no—
21C61×#544—22no—
22C61×#544C2214yescomplemented
23C2×C4⋊Q8×C61—22no—
24C2×#125×C61—22no—
25C2×C22⋊Q8×C61—21no—
26C2×C22⋊Q8×C61C2212yes—
27C2×#117×C61—21no—
28C22×C4⋊C4×C61C2211yescharacteristic
29C24×D61—21no—
30C22×D244—22no—
31C22×D244—22no—
32C22×D244—21no—
33C22×D244—44no—
34C22×D244C2312yes—
35C23×Dic61—21no—
36C2×#11758201—28no—
37C2×#11758201—48no—
38C22×#92418—22no—
39C2×#11758198—24no—
40C2×#11758198—24no—
41C2×#11758198—44no—
42C2×#11758198—44no—
43#14519697—28no—
44C22⋊#92418—22no—
45C22⋊#92418C2314yes—
46#14519684—21no—
47#14519684C2312yes—
48C22×Q8×C61—21no—
49C22×Q8×C61D412yes—
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C4⋊Q8×C61—28no—
54C4⋊Q8×C61—28no—
55#125×C61—28no—
56#125×C61—28no—
57C22⋊Q8×C61—24no—
58C22⋊Q8×C61—22no—
59C22⋊Q8×C61—22no—
60C22⋊Q8×C61—24no—
61C22⋊Q8×C61D414yes—
62C22⋊Q8×C61C2314yes—
63#117×C61—24no—
64#117×C61—24no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—22no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—22no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61D412yes—
73C2×C4⋊C4×C61D412yes—
74C2×C4⋊C4×C61C2312yes—
75C2×C22⋊C4×C61—22no—
76C2×C42×C61—22no—
77C24×C61C2×D411yescharacteristic
78C23×D61—24no—
79C23×D61—22no—
80C23×D61—42no—
81C23×D61—42no—
82C23×D61—42no—
83C23×D61—41no—
84C23×D61—41no—
85C23×D61—42no—
86C23×D61—42no—
87C2×Q8×C61—24no—
88C2×Q8×C61—22no—
89C2×Q8×C61—44no—
90C2×Q8×C61—82no—
91C2×Q8×C61C2×D414yes—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—42no—
100C22×C4×C61—42no—
101C22×C4×C61SD1614yescomplemented
102C22×C4×C61C2×D412yes—
103C22×C4×C61C2×D412yes—
104C22×C4×C61C2×D412yes—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D412yes—
107C22×C4×C61C2411yescharacteristic
108C22×Dic61—22no—
109C22×Dic61—42no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C2×D244—28no—
113C2×D244—24no—
114C2×D244—44no—
115C2×D244—48no—
116C2×D244—44no—
117C2×D244—44no—
118C2×D244—42no—
119C4⋊C4×C61—24no—
120C4⋊C4×C61—24no—
121C4⋊C4×C61—24no—
122C4⋊C4×C61—28no—
123C4⋊C4×C61—24no—
124C4⋊C4×C61—24no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—24no—
127C4⋊C4×C61—24no—
128C4⋊C4×C61C2×D414yes—
129C22⋊C4×C61—24no—
130C22⋊C4×C61—24no—
131C42×C61—28no—
132#11758201—416no—
133#11758198—48no—
134#11758198—48no—
135C2×#92418—24no—
136C2×#92418—44no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61#12011yescharacteristic
140C23×C61#12011yescharacteristic
141C23×C61C2×SD1612yes—
142C23×C61#13712yes—
143C23×C61C22×D411yescharacteristic
144C22×D61—24no—
145C22×D61—42no—
146C22×D61—44no—
147C22×D61—48no—
148C22×D61—48no—
149C22×D61—42no—
150C22×D61—42no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—42no—
154C22×D61—44no—
155C22×D61—84no—
156C22×D61—84no—
157C22×D61—82no—
158C22×D61—82no—
159C22×D61—82no—
160C22×D61—82no—
161Q8×C61—44no—
162Q8×C61—82no—
163Q8×C61—84no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—24no—
167C2×C4×C61—24no—
168C2×C4×C61—24no—
169C2×C4×C61—24no—
170C2×C4×C61—24no—
171C2×C4×C61—22no—
172C2×C4×C61—42no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—44no—
176C2×C4×C61—42no—
177C2×C4×C61—44no—
178C2×C4×C61—42no—
179C2×C4×C61—81no—
180C2×C4×C61#12012yes—
181C2×C4×C61C2×SD1614yescomplemented
182C2×C4×C61C22×D412yes—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—84no—
187D244—28no—
188D244—44no—
189D244—48no—
190#92418—44no—
191C2×#1599—611nomaximal, Sylow
192C22×C61—24no—
193C22×C61—24no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61#44812yes—
199C22×C61#44812yes—
200C22×C61#45412yes—
201C22×C61B(4,𝔽2)12yes—
202C22×C61C2×#12011yescharacteristic
203C22×C61C22×SD1611yescharacteristic
204C22×C61C2×#13711yescharacteristic
205C2×D61—44no—
206C2×D61—44no—
207C2×D61—44no—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—88no—
211C2×D61—88no—
212C2×D61—82no—
213C2×D61—82no—
214C4×C61—24no—
215C4×C61—22no—
216C4×C61—22no—
217C4×C61—44no—
218C4×C61—42no—
219C4×C61—44no—
220Dic61—82no—
221C2×#544D6111yescharacteristic, complemented
222C2×#450—612no—
223C2×#394—611no—
224#1599—618no—
225C2×#328—612no—
226C2×#324—611no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—22no—
230C2×C61#159914yescomplemented
231C2×C61C2×#44811yescharacteristic
232C2×C61C2×#45411yescharacteristic
233C2×C61C2×B(4,𝔽2)11yescharacteristic
234D61—84no—
235C23×D4—611no—
236C22×SD16—1222no—
237#544—24no—
238#544—22no—
239#544C2×D6114yescomplemented
240C2×C4⋊Q8—22no—
241C2×#125—22no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8C2×D6112yes—
244C2×#117—21no—
245C22×C4⋊C4C2×D6111yescharacteristic
246C22×C22⋊C4—1221no—
247C22×C22⋊C4—1221no—
248#450—618no—
249#450—1224no—
250C2×#102—1222no—
251C2×C22⋊C8—612no—
252#394—614no—
253#394—1222no—
254C2×#95—611no—
255#328—618no—
256#324—614no—
257C61C2×#159911yescharacteristic, complemented, Sylow
258C25—1221no—
259C22×Q8—21no—
260C22×Q8C22⋊D6112yes—
261C22×D4—612no—
262C22×D4—1222no—
263C22×D4—1222no—
264C22×D4—1221no—
265C22×D4—2444no—
266C23×C4—1221no—
267C23×C4C22⋊D6111yescharacteristic
268C23×C4C22⋊D6111yescharacteristic
269C23×C4C22×D6111yescharacteristic
270C2×SD16—1228no—
271C2×SD16—2448no—
272C22×C8—1222no—
273C4⋊Q8—28no—
274C4⋊Q8—28no—
275#125—28no—
276#125—28no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8C22⋊D6114yes—
282C22⋊Q8C22×D6114yes—
283#117—24no—
284#117—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4C22⋊D6112yes—
293C2×C4⋊C4C22⋊D6112yes—
294C2×C4⋊C4C22×D6112yes—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—1224no—
297C2×C22⋊C4—1224no—
298C2×C22⋊C4—2444no—
299C2×C22⋊C4—2444no—
300C2×C42—22no—
301#102—1228no—
302C22⋊C8—614no—
303C22⋊C8—1222no—
304#95—612no—
305#95—1221no—
306C24—1224no—
307C24—1222no—
308C24—2442no—
309C24—2442no—
310C24—2442no—
311C24—2442no—
312C24—2441no—
313C24—2441no—
314C24—2442no—
315C24C2×C22⋊D6111yescharacteristic
316C2×Q8—24no—
317C2×Q8—22no—
318C2×Q8—44no—
319C2×Q8—82no—
320C2×Q8C2×C22⋊D6114yes—
321C2×D4—1228no—
322C2×D4—1224no—
323C2×D4—2444no—
324C2×D4—2444no—
325C2×D4—2448no—
326C2×D4—2444no—
327C2×D4—2442no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—1222no—
338C22×C4—2442no—
339C22×C4—2442no—
340C22×C4—2442no—
341C22×C4#1175820114yescomplemented
342C22×C4C2×C22⋊D6112yes—
343C22×C4C2×C22⋊D6112yes—
344C22×C4C2×C22⋊D6112yes—
345C22×C4C2×C22⋊D6112yes—
346C22×C4C2×C22⋊D6111yescharacteristic
347C22×C4C23×D6111yescharacteristic
348SD16—24416no—
349C2×C8—1224no—
350C2×C8—2444no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—24no—
354C4⋊C4—28no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4C2×C22⋊D6114yes—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—2448no—
364C22⋊C4—2448no—
365C42—28no—
366C23—22no—
367C23—22no—
368C23—1224no—
369C23—4882no—
370C23—4884no—
371C23—4884no—
372C23—4882no—
373C23—4882no—
374C23—4882no—
375C23—2442no—
376C23—2444no—
377C23—2442no—
378C23—2442no—
379C23—2448no—
380C23—2448no—
381C23—2444no—
382C23—2442no—
383C23—2442no—
384C23—2442no—
385C23#1451974611yescharacteristic
386C23#1451974611yescharacteristic
387C23C2×#1175820112yes—
388C23#1451980812yes—
389C23C22×C22⋊D6111yescharacteristic
390Q8—44no—
391Q8—82no—
392Q8—84no—
393D4—1228no—
394D4—2444no—
395D4—2448no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—81no—
412C2×C4—4884no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4#1451974612yes—
417C2×C4C2×#1175820114yescomplemented
418C2×C4C22×C22⋊D6112yes—
419C8—2444no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—24no—
426C22—4882no—
427C22—4888no—
428C22—4882no—
429C22—4882no—
430C22—4888no—
431C22—4882no—
432C22—2444no—
433C22—2444no—
434C22—2444no—
435C22#1683990112yes—
436C22#1683990112yes—
437C22#1683993512yes—
438C22#1683994912yes—
439C22C2×#1451974611yescharacteristic
440C22C22×#1175820111yescharacteristic
441C22C2×#1451980811yescharacteristic
442C4—22no—
443C4—22no—
444C4—24no—
445C4—44no—
446C4—42no—
447C4—44no—
448C4—4882no—
449C2—21no—
450C2—22no—
451C2—21no—
452C2—4884no—
453C2#2144475914yesdirect product factor
454C2C2×#1683990111yescharacteristic
455C2C2×#1683993511yescharacteristic
456C2C2×#1683994911yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#544C2
socleC23×C61#120
prime radicalC23×D244C22
hypercenterC2×#544D61
hypocenterC61C2×#1599
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #21444759C2direct (N × H)
4. C2×#16839499C2semidirect
5. C2×#16839488C2semidirect
6. C2×C61×#544C2semidirect
18. #16839499C22semidirect
19. #16839488C22semidirect
22. C61×#544C22semidirect
101. C22×C4×C61SD16semidirect
181. C2×C4×C61C2×SD16semidirect
221. C2×#544D61semidirect
230. C2×C61#1599semidirect
239. #544C2×D61semidirect
257. C61C2×#1599semidirect
341. C22×C4#11758201semidirect
417. C2×C4C2×#11758201semidirect
453. C2#21444759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399122
C2×#168396792
#214447592
C2×#168394992
C2×#168394882
C2×C61×#5442
C2×#159961