Finite Group Databasebeta

← C2×#21460690 #30596770

Subgroups — C2×#21460690 #30596770

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840734C211yesmaximal, characteristic
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21460690C214yesmaximal, direct product factor
4C2×#16839724C211yesmaximal, characteristic
5C22×#11758217—21no—
6C22×D61⋊C8C412yes—
7#16840734—21no—
8#16840734—21no—
9#16840734C412yes—
10#16840734C2212yes—
11C2×#14519834—21no—
12C2×#14519834—21no—
13C2×#14519834C412yes—
14D61⋊(C22⋊C8)—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)C412yes—
17D61⋊(C22⋊C8)C2212yes—
18C2×C22⋊#92420—21no—
19C23×C4×D61C2211yescharacteristic
20C22×#11758189—21no—
21#16839724—21no—
22#16839724—21no—
23#16839724C412yes—
24#16839724C2212yes—
25C2×C22⋊#92418C411yescharacteristic
26C2×#14519689—21no—
27C2×C22⋊C8×C61C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—44no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—44no—
33C2×D61⋊C8C2×C414yes—
34C22×#92420—22no—
35C22×#92420—22no—
36#14519834—22no—
37#14519834—22no—
38#14519834—22no—
39#14519834—22no—
40#14519834—22no—
41#14519834C2×C414yes—
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44C24×D61Q811yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758189—22no—
60C2×#11758189—22no—
61C2×#11758189—44no—
62C22×#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C412yes—
65#14519689—22no—
66#14519689—22no—
67C23×C4×C61C2×C411yescharacteristic
68C22×C8×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61C2×C412yes—
71C24×C61C4⋊C411yescharacteristic
72C23×D61—24no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C4⋊C411yescharacteristic
76C23×D61C4⋊C411yescharacteristic
77C23×D61C4⋊C411yescharacteristic
78C23×D61C4⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C2×Q811yescharacteristic
81C22×C4×C61—42no—
82C22×C4×C61C4211yescharacteristic
83C22×C4×C61C4211yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C4⋊C411yescharacteristic
87C22×C4×C61C22×C411yescharacteristic
88C22×Dic61—24no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C4⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×C4×D61—24no—
96C2×C4×D61—24no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61C4211yescharacteristic
108C2×C4×D61C4211yescharacteristic
109C2×C4×D61C22⋊C411yescharacteristic
110C2×C4×D61C22⋊C411yescharacteristic
111C2×C4×D61C22⋊C411yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C4⋊C411yescharacteristic
116C2×C4×D61C4⋊C411yescharacteristic
117C2×C4×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C22×C411yescharacteristic
120C2×C4×D61C22×C411yescharacteristic
121C2×C4×D61C2×D411yescharacteristic
122C2×C4×D61C2×D411yescharacteristic
123#11758217—44no—
124#11758217—44no—
125C2×#92420—24no—
126C2×#92420—24no—
127C2×#92420—44no—
128C2×#92420—44no—
129D61⋊C8—44no—
130D61⋊C8—44no—
131C2×C8×C61—22no—
132C2×C8×C61—42no—
133C2×#92418—22no—
134C2×#92418—42no—
135#11758189—44no—
136#11758189—44no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61#9511yescharacteristic
141C23×C61#9511yescharacteristic
142C23×C61C2×C4⋊C411yescharacteristic
143C22×D61—22no—
144C22×D61—22no—
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—416no—
161C22×D61#9511yescharacteristic
162C22×D61#9511yescharacteristic
163C22×D61#10814yes—
164C22×D61C2×C4⋊C411yescharacteristic
165C22×D61C2×C4⋊C411yescharacteristic
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61#9511yescharacteristic
173C2×C4×C61#9511yescharacteristic
174C2×C4×C61C2×C4211yescharacteristic
175C2×C4×C61C2×C22⋊C411yescharacteristic
176C2×Dic61—22no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61#9511yescharacteristic
182C2×Dic61#9511yescharacteristic
183C2×Dic61#9914yes—
184C2×Dic61C2×C22⋊C411yescharacteristic
185C2×Dic61C2×C22⋊C411yescharacteristic
186C4×D61—22no—
187C4×D61—22no—
188C4×D61—22no—
189C4×D61—22no—
190C4×D61—22no—
191C4×D61—22no—
192C4×D61—22no—
193C4×D61—22no—
194C4×D61—41no—
195C4×D61—41no—
196C4×D61—41no—
197C4×D61—41no—
198C4×D61—41no—
199C4×D61—41no—
200C4×D61—41no—
201C4×D61—41no—
202#92420—44no—
203#92420—44no—
204C8×C61—42no—
205#92418—42no—
206C2×#1293—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—44no—
214C22×C61#33812yes—
215C22×C61#34112yes—
216C22×C61#34212yes—
217C22×C61C2×#9511yescharacteristic
218C2×D61—28no—
219C2×D61—21no—
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—21no—
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—44no—
230C2×D61—44no—
231C2×D61—44no—
232C2×D61—44no—
233C2×D61—44no—
234C2×D61#34112yes—
235C2×D61C2×#10812yes—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240Dic61—21no—
241Dic61—21no—
242Dic61#34212yes—
243Dic61C2×#9912yes—
244C2×#407—611no—
245C2×#407—611no—
246C22×C22⋊C8—611no—
247#1293—614no—
248C2×C61—41no—
249C2×C61—41no—
250C2×C61#129314yescomplemented
251C2×C61C2×#33811yescharacteristic
252C2×C61C2×#34111yescharacteristic
253C2×C61C2×#34211yescharacteristic
254D61—22no—
255D61—22no—
256D61—41no—
257D61—41no—
258C24×C4—611no—
259C22×M16—1221no—
260C22×M16—1221no—
261C23×C8—612no—
262#407—612no—
263#407—612no—
264#407—612no—
265#407—612no—
266#407—1221no—
267#407—1221no—
268#407—1221no—
269#407—1221no—
270C2×C22⋊C8—612no—
271C2×C22⋊C8—611no—
272C2×C22⋊C8—612no—
273C2×C22⋊C8—612no—
274C2×C22⋊C8—1221no—
275C2×C22⋊C8—1221no—
276C2×C22⋊C8—1221no—
277C2×C22⋊C8—1221no—
278C2×C22⋊C8—1221no—
279C2×C22⋊C8—1221no—
280C2×C22⋊C8#692311yescharacteristic
281C61C2×#129311yescharacteristic, complemented, Sylow
282C25—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—611no—
287C23×C4—611no—
288C23×C4—611no—
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C23×C4—611no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—2444no—
297C23×C4C2×#692311yescharacteristic
298C2×M16—1222no—
299C2×M16—1222no—
300C2×M16—1222no—
301C2×M16—1222no—
302C2×M16—2444no—
303C2×M16—2444no—
304C22×C8—21no—
305C22×C8—614no—
306C22×C8—1222no—
307C22×C8—1222no—
308C22×C8—1222no—
309C22×C8—1221no—
310C22×C8—2444no—
311C22⋊C8—21no—
312C22⋊C8—614no—
313C22⋊C8—612no—
314C22⋊C8—1222no—
315C22⋊C8—1222no—
316C22⋊C8—1222no—
317C22⋊C8—1222no—
318C22⋊C8—1222no—
319C22⋊C8—1222no—
320C22⋊C8—1222no—
321C22⋊C8—1222no—
322C22⋊C8—1222no—
323C22⋊C8—1221no—
324C22⋊C8C2×#692312yes—
325C24—611no—
326C24—611no—
327C24—611no—
328C24—611no—
329C24—611no—
330C24—611no—
331C24—1224no—
332C24—2442no—
333C24—2442no—
334C24C4⋊#692311yescharacteristic
335C22×C4—42no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—1224no—
359C22×C4—1224no—
360C22×C4—1224no—
361C22×C4—2442no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4C4×#692311yescharacteristic
372C22×C4C4×#692311yescharacteristic
373C22×C4C4⋊#692311yescharacteristic
374C22×C4C22⋊#692311yescharacteristic
375C22×C4C22⋊#692311yescharacteristic
376C22×C4C22×#692311yescharacteristic
377M16—2444no—
378M16—2444no—
379M16—2444no—
380M16—2444no—
381C2×C8—22no—
382C2×C8—42no—
383C2×C8—1224no—
384C2×C8—1224no—
385C2×C8—1222no—
386C2×C8—2442no—
387C2×C8—2444no—
388C2×C8—2444no—
389C2×C8—2444no—
390C2×C8—2444no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—614no—
395C23—611no—
396C23—611no—
397C23—611no—
398C23—611no—
399C23—1222no—
400C23—1222no—
401C23—1222no—
402C23—1222no—
403C23—1222no—
404C23—1222no—
405C23—1222no—
406C23—1222no—
407C23—1222no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23—2441no—
416C23—24416no—
417C23(C2×#6923)⋊C411yescharacteristic
418C23(C2×#6923)⋊C411yescharacteristic
419C23C2×C4⋊#692311yescharacteristic
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—614no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—1222no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4(C2×#6923)⋊C411yescharacteristic
453C2×C4(C2×#6923)⋊C411yescharacteristic
454C2×C4C2×C4×#692311yescharacteristic
455C2×C4C2×C22⋊#692311yescharacteristic
456C8—42no—
457C8—2442no—
458C8—2444no—
459C8—2444no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—44no—
467C22—612no—
468C22—612no—
469C22—1221no—
470C22—1221no—
471C22—1228no—
472C22—1221no—
473C22—1221no—
474C22—1221no—
475C22—1221no—
476C22—1221no—
477C22—1221no—
478C22—1221no—
479C22—1221no—
480C22—2444no—
481C22—2444no—
482C22—2444no—
483C22—2444no—
484C22—2444no—
485C22#1684063112yes—
486C22#1684063712yes—
487C22#1684063912yes—
488C22C2×(C2×#6923)⋊C411yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—612no—
494C4—612no—
495C4—1221no—
496C4—1221no—
497C2—41no—
498C2—41no—
499C2—1222no—
500C2—1222no—
501C2—2441no—
502C2—2441no—
503C2#2146069014yesdirect product factor
504C2C2×#1684063111yescharacteristic
505C2C2×#1684063711yescharacteristic
506C2C2×#1684063911yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61C2×#1293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460690C2direct (N × H)
250. C2×C61#1293semidirect
281. C61C2×#1293semidirect
503. C2#21460690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407342
C2×D61⋊(C22⋊C8)2
#214606902
C2×#168397242
C2×#129361