Finite Group Databasebeta

← C2×#21461100 #30610068

Subgroups — C2×#21461100 #30610068

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic, complemented
2C2×#16840779C211yesmaximal, characteristic, complemented
3#21461100C218yesmaximal, direct product factor
4C2×#16840607C212yesmaximal, complemented
5C2×#16840605C212yesmaximal
6C22×#14519770C211yesmaximal, characteristic
7#16840783—22no—
8#16840783C2214yescomplemented
9#16840779—22no—
10#16840779C2214yescomplemented
11C2×#14519844—21no—
12C2×C4⋊#92420—21no—
13C2×C22⋊#92420C2212yes—
14C2×C22⋊#92420C2212yes—
15C2×#14519832—21no—
16C2×C4×#92420—21no—
17#16840607C2218yescomplemented
18#16840605C2218yes—
19C2×#14519770—21no—
20C2×#14519770—21no—
21C2×#14519770—21no—
22C2×#14519770—21no—
23C2×#14519770—22no—
24C2×#14519770—22no—
25C2×#14519770C414yes—
26C2×#14519770C2214yes—
27C22×C4⋊Dic61C2211yescharacteristic
28C22×#11758196C411yescharacteristic
29C22×#11758196C411yescharacteristic
30C22×C22⋊Dic61C411yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C22⋊C4×C61C411yescharacteristic
34C22×#92420—22no—
35C22×#92420—22no—
36#14519844—24no—
37C4⋊#92420—24no—
38C22⋊#92420—22no—
39C22⋊#92420—22no—
40C22⋊#92420C2314yes—
41C22⋊#92420C2314yes—
42#14519832—24no—
43C4×#92420—24no—
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2311yescharacteristic
48#14519770—24no—
49#14519770—24no—
50#14519770—24no—
51#14519770—24no—
52#14519770—24no—
53#14519770—24no—
54#14519770—24no—
55#14519770—24no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61C2×C412yes—
61C2×C4⋊Dic61C2312yes—
62C2×#11758196—21no—
63C2×#11758196—21no—
64C2×#11758196—22no—
65C2×#11758196—22no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196C2×C414yes—
69C2×#11758196C2×C414yes—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61C2×C414yes—
78C2×C22⋊Dic61C2×C412yes—
79C2×C22⋊Dic61C2312yes—
80C2×C4×Dic61C2×C412yes—
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D412yes—
86C2×C4×Dic61D412yes—
87C2×C4×Dic61C2312yes—
88C25×C61C2×C411yescharacteristic
89C23×C4×C61C2×C411yescharacteristic
90C23×C4×C61C2×C411yescharacteristic
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61C2×C414yes—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61—24no—
98C24×C61—42no—
99C24×C61—42no—
100C24×C61C22×C411yescharacteristic
101C24×C61C22×C412yes—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—24no—
105C22×C4×C61—42no—
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22⋊C412yes—
109C22×C4×C61C22×C412yes—
110C22×C4×C61C22×C412yes—
111C22×Dic61—24no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—42no—
117C22×Dic61—42no—
118C22×Dic61—42no—
119C22×Dic61C22⋊C412yes—
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22×C412yes—
123C22×Dic61C22×C412yes—
124C22×Dic61C22×C412yes—
125C22×Dic61C22×C411yescharacteristic
126C22×Dic61C2×D411yescharacteristic
127C22×Dic61C2×D411yescharacteristic
128C22×Dic61C2×D411yescharacteristic
129C22×Dic61C2×D411yescharacteristic
130C22×Dic61C2411yescharacteristic
131C2×#92420—24no—
132C2×#92420—24no—
133C2×#92420—44no—
134C2×#92420—44no—
135C22⋊C4×C61—24no—
136C22⋊C4×C61—24no—
137C22⋊Dic61—22no—
138C22⋊Dic61—22no—
139C22⋊Dic61—24no—
140C22⋊Dic61—24no—
141C22⋊Dic61—22no—
142C22⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—22no—
147#11758196—24no—
148#11758196—24no—
149#11758196—24no—
150#11758196—24no—
151C4×Dic61C22⋊C412yes—
152C4×Dic61C22⋊C412yes—
153C4×Dic61C22⋊C412yes—
154C4×Dic61C22⋊C412yes—
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D412yes—
157C4×Dic61C2×D412yes—
158C4×Dic61C2×D412yes—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—24no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61—88no—
172C23×C61C2×C22⋊C411yescharacteristic
173C23×C61C2×C22⋊C411yescharacteristic
174C23×C61#13114yes—
175C23×C61C23×C411yescharacteristic
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—24no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61C2×C22⋊C412yes—
185C2×C4×C61C2×C22⋊C412yes—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61C2×C22⋊C411yescharacteristic
205C2×Dic61C2×C22⋊C411yescharacteristic
206C2×Dic61C2×C22⋊C412yes—
207C2×Dic61C2×C22⋊C412yes—
208C2×Dic61C22×D411yescharacteristic
209C2×Dic61C22×D411yescharacteristic
210#92420—44no—
211#92420—44no—
212C2×#1473—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—28no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—42no—
221C22×C61—84no—
222C22×C61—84no—
223C22×C61—84no—
224C22×C61#40812yes—
225C22×C61#40812yes—
226C22×C61#41012yes—
227C22×C61#41312yes—
228C22×C61C22×C22⋊C411yescharacteristic
229C22×C61C2×#13112yes—
230C4×C61—22no—
231C4×C61—22no—
232C4×C61—42no—
233Dic61—22no—
234Dic61—22no—
235Dic61—21no—
236Dic61—21no—
237Dic61—21no—
238Dic61—21no—
239Dic61—42no—
240Dic61—42no—
241C22×#126—611no—
242C2×#432—611no—
243C2×#431—611no—
244#1473—618no—
245C2×#324—612no—
246C2×#323—612no—
247C2×C61—22no—
248C2×C61—22no—
249C2×C61—82no—
250C2×C61#147314yescomplemented
251C2×C61C2×#40811yescharacteristic
252C2×C61C2×#41011yescharacteristic
253C2×C61C2×#41311yescharacteristic
254C2×#126—614no—
255C2×#126—614no—
256C2×#126—1221no—
257C2×#126—1221no—
258C2×#126—1221no—
259C2×#126—1221no—
260C2×#126—1222no—
261C2×#126—1222no—
262C22×C4⋊C4—611no—
263C22×C4⋊C4—611no—
264C22×C4⋊C4—611no—
265C22×C22⋊C4—611no—
266C22×C22⋊C4—611no—
267C22×C22⋊C4#692311yescharacteristic
268C22×C42—611no—
269#432—614no—
270#432—1222no—
271#431—614no—
272#431—1222no—
273C2×C4⋊C8—1221no—
274C2×C4⋊C8—1221no—
275C2×C22⋊C8—612no—
276C2×C22⋊C8—612no—
277C2×#97—1221no—
278C2×C4×C8—1221no—
279#324—618no—
280#323—618no—
281C61C2×#147311yescharacteristic, complemented, Sylow
282C25C2×#692311yescharacteristic
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—611no—
287C23×C4C2×#692311yescharacteristic
288C23×C4C2×#692311yescharacteristic
289C22×C8—1222no—
290C22×C8—1222no—
291#126—1224no—
292#126—1224no—
293#126—1224no—
294#126—1224no—
295#126—1224no—
296#126—1224no—
297#126—1224no—
298#126—1224no—
299C2×C4⋊C4—612no—
300C2×C4⋊C4—614no—
301C2×C4⋊C4—614no—
302C2×C4⋊C4—612no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—612no—
317C2×C22⋊C4—614no—
318C2×C22⋊C4—612no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1221no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4C2×#692314yes—
327C2×C42—611no—
328C2×C42—611no—
329C2×C42—611no—
330C2×C42—611no—
331C2×C42—612no—
332C2×C42—612no—
333C2×C42—612no—
334C2×C42—612no—
335C4⋊C8—1224no—
336C4⋊C8—1224no—
337C22⋊C8—614no—
338C22⋊C8—614no—
339C22⋊C8—1222no—
340C22⋊C8—1222no—
341#97—1224no—
342C4×C8—1224no—
343C24—21no—
344C24—21no—
345C24—24no—
346C24—42no—
347C24—42no—
348C24C22×#692311yescharacteristic
349C24C22×#692312yes—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—42no—
354C22×C4—612no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—612no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—1224no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4C22⋊#692311yescharacteristic
375C22×C4C22⋊#692311yescharacteristic
376C22×C4C22⋊#692312yes—
377C22×C4C22×#692312yes—
378C22×C4C22×#692312yes—
379C2×C8—1224no—
380C2×C8—1224no—
381C2×C8—2444no—
382C2×C8—2444no—
383C4⋊C4—1224no—
384C4⋊C4—1224no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1222no—
389C4⋊C4—1224no—
390C4⋊C4—1224no—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—1224no—
394C22⋊C4—1224no—
395C22⋊C4—1222no—
396C22⋊C4—1222no—
397C22⋊C4—1222no—
398C22⋊C4—1222no—
399C42—612no—
400C42—612no—
401C42—612no—
402C42—612no—
403C42—612no—
404C42—612no—
405C42—612no—
406C42—612no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—24no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—88no—
420C23C2×C22⋊#692311yescharacteristic
421C23C2×C22⋊#692311yescharacteristic
422C23#1451986414yes—
423C23C23×#692311yescharacteristic
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—1224no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1224no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4C2×C22⋊#692312yes—
457C2×C4C2×C22⋊#692312yes—
458C8—2444no—
459C8—2444no—
460C22—28no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—84no—
470C22—84no—
471C22#1684073612yes—
472C22#1684073612yes—
473C22#1684074112yes—
474C22#1684074912yes—
475C22C22×C22⋊#692311yescharacteristic
476C22C2×#1451986412yes—
477C4—22no—
478C4—22no—
479C4—42no—
480C4—1222no—
481C4—1222no—
482C4—1221no—
483C4—1221no—
484C4—1221no—
485C4—1221no—
486C4—2442no—
487C4—2442no—
488C2—22no—
489C2—22no—
490C2—82no—
491C2#2146110014yesdirect product factor
492C2C2×#1684073611yescharacteristic
493C2C2×#1684074111yescharacteristic
494C2C2×#1684074911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1473
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840783C2semidirect
2. C2×#16840779C2semidirect
3. #21461100C2direct (N × H)
4. C2×#16840607C2semidirect
8. #16840783C22semidirect
10. #16840779C22semidirect
17. #16840607C22semidirect
250. C2×C61#1473semidirect
281. C61C2×#1473semidirect
491. C2#21461100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407832
C2×#168407792
#214611002
C2×#168406072
C2×#168406052
C22×#145197702
C2×#147361