Finite Group Databasebeta

← C2×#21447493 #29832805

Subgroups — C2×#21447493 #29832805

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840333C211yesmaximal, characteristic
2C2×#16839736C211yesmaximal, characteristic
3#21447493C218yesmaximal, direct product factor
4C2×#16839556C214yesmaximal, complemented
5C2×C61×#410C211yesmaximal, characteristic
6C23×Dic122C411yescharacteristic, complemented
7#16840333—22no—
8#16840333—22no—
9#16840333C414yescomplemented
10#16840333C2214yes—
11C2×#14519775C412yescomplemented
12C2×#14519764C2212yes—
13C2×#14519758—21no—
14C2×#14519758—21no—
15C2×#14519756—21no—
16C2×#14519756—21no—
17C2×#14519736—21no—
18C2×#14519736C411yescharacteristic, complemented
19#16839736—22no—
20#16839736C2214yes—
21C2×#14519692—21no—
22C2×#14519692C2212yes—
23#16839556C22116yescomplemented
24C22×#41×C61C2211yescharacteristic
25C2×#117×C61—21no—
26C61×#410—22no—
27C61×#410C2214yes—
28C2×#99×C61—21no—
29C2×#99×C61C2212yes—
30C22×Dic122—21no—
31C22×Dic122—22no—
32C22×Dic122—42no—
33C22×Dic122—41no—
34C22×Dic122—41no—
35C22×Dic122C2×C412yes—
36C22×Dic122C2×C414yescomplemented
37C23×Dic61—21no—
38#14519775—24no—
39#14519775C2×C418yescomplemented
40#14519764—22no—
41#14519764—22no—
42#14519764C2×C414yes—
43#14519764C2314yes—
44#14519758—24no—
45#14519758—24no—
46#14519758—24no—
47#14519758—24no—
48#14519756—24no—
49#14519756—24no—
50#14519756—24no—
51#14519756—24no—
52#14519736—22no—
53#14519736—24no—
54#14519736—42no—
55#14519736C2×C414yescomplemented
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—41no—
58C2×#11758196—22no—
59C2×#11758196—22no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C4×Dic61—41no—
65C2×C4×Dic61C2×C412yes—
66#14519692—24no—
67#14519692—22no—
68#14519692C2314yes—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61—42no—
72C2×#41×C61C2×C412yes—
73C2×#41×C61D412yes—
74C2×#41×C61D412yes—
75C2×#41×C61C2312yes—
76C22×Q8×C61C2×C411yescharacteristic
77C22×D4×C61D411yescharacteristic
78C22×D4×C61D411yescharacteristic
79C22×D4×C61C2311yescharacteristic
80C23×C4×C61C2×C411yescharacteristic
81C23×C4×C61D411yescharacteristic
82C23×C4×C61D411yescharacteristic
83#117×C61—24no—
84#117×C61—42no—
85C2×C4⋊C4×C61—41no—
86C2×C22⋊C4×C61—22no—
87C2×C42×C61—41no—
88#99×C61—24no—
89#99×C61—22no—
90#99×C61C2314yes—
91C24×C61C22⋊C411yescharacteristic
92C24×C61C2×D411yescharacteristic
93C24×C61C2×D411yescharacteristic
94#41×C61—42no—
95#41×C61—42no—
96#41×C61—42no—
97#41×C61—42no—
98#41×C61—42no—
99#41×C61—42no—
100#41×C61—42no—
101#41×C61—42no—
102C2×Q8×C61—41no—
103C2×Q8×C61—41no—
104C2×Q8×C61C22⋊C412yes—
105C2×Q8×C61C22×C412yes—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61C22⋊C412yes—
113C2×D4×C61C22⋊C412yes—
114C2×D4×C61C22×C411yescharacteristic
115C2×D4×C61C2×D412yes—
116C2×D4×C61C2×D411yescharacteristic
117C2×D4×C61C2×D412yes—
118C2×D4×C61C2×D411yescharacteristic
119C2×D4×C61C2411yescharacteristic
120C22×C4×C61—22no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—42no—
130C22×C4×C61C22⋊C412yes—
131C22×C4×C61C22⋊C411yescharacteristic
132C22×C4×C61C22⋊C411yescharacteristic
133C22×C4×C61C22⋊C412yes—
134C22×C4×C61C22⋊C412yes—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×Dic61—22no—
141C22×Dic61—24no—
142C22×Dic61—22no—
143C22×Dic61—42no—
144C22×Dic61—42no—
145C22×Dic61—42no—
146C2×Dic122—22no—
147C2×Dic122—24no—
148C2×Dic122—44no—
149C2×Dic122—44no—
150C2×Dic122—42no—
151C2×Dic122—41no—
152C2×Dic122—41no—
153C2×Dic122—42no—
154C2×Dic122—42no—
155C2×Dic122—44no—
156C2×Dic122—44no—
157C2×Dic122C22×C414yes—
158C4⋊C4×C61—44no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—42no—
161C42×C61—44no—
162C22⋊Dic61—24no—
163C22⋊Dic61—24no—
164C22⋊Dic61—24no—
165C22⋊Dic61—24no—
166C22⋊Dic61—24no—
167C22⋊Dic61—24no—
168C22⋊Dic61—42no—
169C4⋊Dic61—24no—
170C4⋊Dic61—44no—
171#11758196—28no—
172#11758196—28no—
173C4×Dic61—22no—
174C4×Dic61—44no—
175C4×Dic61C22×C414yes—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—21no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61C2×C22⋊C411yescharacteristic
186C23×C61C2×C22⋊C411yescharacteristic
187C23×C61C2×C22⋊C411yescharacteristic
188C23×C61C2×C22⋊C412yes—
189C23×C61C22×D411yescharacteristic
190C23×C61C22×D411yescharacteristic
191Q8×C61—42no—
192Q8×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—41no—
196D4×C61—41no—
197D4×C61—41no—
198D4×C61—42no—
199D4×C61—42no—
200D4×C61—41no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—44no—
220C2×C4×C61—84no—
221C2×C4×C61#9912yes—
222C2×C4×C61#9911yescharacteristic
223C2×C4×C61#9911yescharacteristic
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C412yes—
226C2×C4×C61C2×C22⋊C412yes—
227C2×C4×C61C2×C22⋊C412yes—
228C2×C4×C61C23×C411yescharacteristic
229C2×Dic61—24no—
230C2×Dic61—24no—
231C2×Dic61—48no—
232C2×Dic61—44no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—44no—
236C2×Dic61—84no—
237Dic122—44no—
238Dic122—44no—
239Dic122—44no—
240Dic122—44no—
241C2×#2129—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—42no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61C2×#9911yescharacteristic
260C22×C61C2×#9911yescharacteristic
261C22×C61C22×C22⋊C411yescharacteristic
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—22no—
265C4×C61—22no—
266C4×C61—84no—
267C4×C61C2×#9912yes—
268C4×C61C2×#9912yes—
269Dic61—44no—
270Dic61—44no—
271Dic61—84no—
272C2×#536—611no—
273C2×#410—611no—
274C2×#410D6111yescharacteristic
275#2129—618no—
276C2×#354—614no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—41no—
280C2×C61—41no—
281C2×C61—42no—
282C2×C61—41no—
283C2×C61—41no—
284C2×C61#212912yescomplemented
285C2×C61C22×#9911yescharacteristic
286C22×#41C2×D6111yescharacteristic
287C23×Q8—611no—
288#536—614no—
289#536—614no—
290#536—1222no—
291#536—1222no—
292C2×C4⋊Q8—612no—
293C2×#124—612no—
294C2×#123—1221no—
295C2×#123—1221no—
296C2×C22⋊Q8—1221no—
297C2×C22⋊Q8—1221no—
298C2×#117—21no—
299C2×#117—611no—
300C2×#117—1221no—
301#410—22no—
302#410—614no—
303#410—1222no—
304#410C2×D6114yes—
305C2×#99—21no—
306C2×#99—612no—
307C2×#99—1221no—
308C2×#99C2×D6112yes—
309#354—6116no—
310C61C2×#212911yescharacteristic, complemented, Sylow
311C2×#41—41no—
312C2×#41—41no—
313C2×#41—42no—
314C2×#41C4×D6112yes—
315C2×#41D24412yes—
316C2×#41C22⋊D6112yes—
317C2×#41C22×D6112yes—
318C22×Q8—612no—
319C22×Q8—614no—
320C22×Q8—1222no—
321C22×Q8—1221no—
322C22×Q8—2442no—
323C22×Q8—2441no—
324C22×Q8—2441no—
325C22×Q8C4×D6111yescharacteristic
326C22×D4D24411yescharacteristic
327C22×D4C22⋊D6111yescharacteristic
328C22×D4C22×D6111yescharacteristic
329C23×C4—1221no—
330C23×C4C4×D6111yescharacteristic
331C23×C4D24411yescharacteristic
332C23×C4C22⋊D6111yescharacteristic
333C4⋊Q8—618no—
334C4⋊Q8—1224no—
335#124—614no—
336#124—614no—
337#124—1222no—
338#124—1222no—
339#123—1224no—
340#123—1224no—
341#123—1224no—
342#123—1224no—
343C22⋊Q8—1224no—
344C22⋊Q8—1224no—
345C22⋊Q8—1224no—
346C22⋊Q8—1224no—
347#117—24no—
348#117—42no—
349#117—614no—
350#117—1222no—
351#117—1224no—
352#117—2442no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—2441no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1222no—
363C2×C42—41no—
364C2×C42—612no—
365C2×C42—2441no—
366#99—24no—
367#99—22no—
368#99—614no—
369#99—1222no—
370#99—1224no—
371#99C22×D6114yes—
372C24#1175819811yescharacteristic
373C24C2×D24411yescharacteristic
374C24C2×C22⋊D6111yescharacteristic
375#41—42no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381#41—42no—
382#41—42no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—614no—
386C2×Q8—1224no—
387C2×Q8—1222no—
388C2×Q8—2444no—
389C2×Q8—2444no—
390C2×Q8—2444no—
391C2×Q8—2444no—
392C2×Q8—2442no—
393C2×Q8—2442no—
394C2×Q8—2442no—
395C2×Q8—2441no—
396C2×Q8—2441no—
397C2×Q8#1175819812yes—
398C2×Q8C2×C4×D6112yes—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4#1175819812yes—
406C2×D4#1175819812yes—
407C2×D4C2×C4×D6111yescharacteristic
408C2×D4C2×D24412yes—
409C2×D4C2×D24411yescharacteristic
410C2×D4C2×C22⋊D6112yes—
411C2×D4C2×C22⋊D6111yescharacteristic
412C2×D4C23×D6111yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1224no—
426C22×C4—2442no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4#1175819811yescharacteristic
430C22×C4#1175819811yescharacteristic
431C22×C4#1175819812yes—
432C22×C4#1175819812yes—
433C22×C4#1175819812yes—
434C22×C4#1175819811yescharacteristic
435C22×C4C2×C4×D6111yescharacteristic
436C22×C4C2×C4×D6112yes—
437C22×C4C2×D24412yes—
438C22×C4C2×C22⋊D6112yes—
439C4⋊C4—44no—
440C4⋊C4—1228no—
441C4⋊C4—1228no—
442C4⋊C4—1224no—
443C4⋊C4—2444no—
444C22⋊C4—24no—
445C22⋊C4—42no—
446C22⋊C4—1224no—
447C22⋊C4—1224no—
448C22⋊C4—1224no—
449C22⋊C4—1224no—
450C22⋊C4—1224no—
451C22⋊C4—1224no—
452C22⋊C4—2442no—
453C42—44no—
454C42—614no—
455C42—1222no—
456C42—2444no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23C2×#1175819811yescharacteristic
467C23C2×#1175819811yescharacteristic
468C23C2×#1175819811yescharacteristic
469C23C2×#1175819812yes—
470C23C22×C22⋊D6111yescharacteristic
471C23C22×D24411yescharacteristic
472Q8—42no—
473Q8—42no—
474Q8—2444no—
475Q8—2444no—
476Q8—2444no—
477Q8—2444no—
478D4—42no—
479D4—42no—
480D4—41no—
481D4—42no—
482D4—41no—
483D4—42no—
484D4—41no—
485D4—41no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—44no—
505C2×C4—84no—
506C2×C4—1224no—
507C2×C4—1224no—
508C2×C4—4884no—
509C2×C4—2444no—
510C2×C4—2444no—
511C2×C4—2448no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4#1451969112yes—
515C2×C4#1451969111yescharacteristic
516C2×C4#1451969111yescharacteristic
517C2×C4C2×#1175819811yescharacteristic
518C2×C4C2×#1175819812yes—
519C2×C4C2×#1175819812yes—
520C2×C4C2×#1175819812yes—
521C2×C4C22×C4×D6111yescharacteristic
522C22—22no—
523C22—21no—
524C22—21no—
525C22—22no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—42no—
531C22—41no—
532C22—41no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22C2×#1451969111yescharacteristic
540C22C2×#1451969111yescharacteristic
541C22C22×#1175819811yescharacteristic
542C4—21no—
543C4—22no—
544C4—22no—
545C4—21no—
546C4—84no—
547C4—4884no—
548C4—2444no—
549C4—2444no—
550C4C2×#1451969112yes—
551C4C2×#1451969112yes—
552C2—21no—
553C2—21no—
554C2—41no—
555C2—41no—
556C2—42no—
557C2—41no—
558C2—41no—
559C2#2144749312yesdirect product factor
560C2C22×#1451969111yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC2×C4×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#410C2
socleC22×C61C2×#99
prime radicalC22×#41×C61C22
cosocleC2×D4×C61C24
hypercenterC2×#410D61
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #21447493C2direct (N × H)
4. C2×#16839556C2semidirect
6. C23×Dic122C4semidirect
9. #16840333C4semidirect
11. C2×#14519775C4semidirect
18. C2×#14519736C4semidirect
23. #16839556C22semidirect
36. C22×Dic122C2×C4semidirect
39. #14519775C2×C4semidirect
55. #14519736C2×C4semidirect
284. C2×C61#2129semidirect
310. C61C2×#2129semidirect
559. C2#21447493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403332
C2×#168397362
#214474932
C2×#168395562
C2×C61×#4102
C2×#212961