Finite Group Databasebeta

← C61×#8712 #29512145

Subgroups — C61×#8712 #29512145

Order 15616.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#380C211yesmaximal, characteristic
2C61×#1779C211yesmaximal, characteristic
3C61×C22⋊#95C211yesmaximal, characteristic
4C61×#1294C214yesmaximal, complemented
5C24×C4×C61C2211yescharacteristic
6C22×C4⋊C4×C61C411yescharacteristic, complemented
7C22×C4⋊C4×C61C411yescharacteristic, complemented
8C22×C22⋊C4×C61—21no—
9C22×C22⋊C4×C61—21no—
10C2×C22⋊C8×C61—21no—
11C2×C22⋊C8×C61—21no—
12C2×C22⋊C8×C61C2212yes—
13C61×#380—21no—
14C61×#380—21no—
15C61×#380C412yescomplemented
16C61×#380C2212yes—
17C2×#95×C61—21no—
18C2×#95×C61—21no—
19C2×#95×C61C2212yes—
20C25×C61D411yescharacteristic
21C23×C4×C61—24no—
22C23×C4×C61—21no—
23C23×C4×C61—21no—
24C23×C4×C61—22no—
25C23×C4×C61—42no—
26C23×C4×C61—42no—
27C23×C4×C61C2×C411yescharacteristic
28C23×C4×C61C2×C411yescharacteristic
29C23×C4×C61D411yescharacteristic
30C23×C4×C61D411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C23×C4×C61C2311yescharacteristic
33C22×C8×C61—22no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—42no—
37C2×C4⋊C4×C61—42no—
38C2×C4⋊C4×C61C2×C412yes—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C22⋊C4×C61—24no—
41C2×C22⋊C4×C61—22no—
42C2×C22⋊C4×C61—22no—
43C2×C22⋊C4×C61—42no—
44C2×C22⋊C4×C61—42no—
45C2×C22⋊C4×C61—42no—
46C2×C22⋊C4×C61—42no—
47C22⋊C8×C61—24no—
48C22⋊C8×C61—42no—
49C22⋊C8×C61—42no—
50#95×C61—22no—
51#95×C61—22no—
52#95×C61—24no—
53#95×C61—42no—
54C24×C61—22no—
55C24×C61—22no—
56C24×C61—22no—
57C24×C61—22no—
58C24×C61—41no—
59C24×C61—41no—
60C24×C61C22⋊C411yescharacteristic
61C24×C61C22⋊C411yescharacteristic
62C24×C61D812yes—
63C24×C61SD1612yes—
64C24×C61C2×D411yescharacteristic
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—24no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—416no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4114yes—
103C2×C8×C61—42no—
104C2×C8×C61—42no—
105C2×C8×C61—42no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61—42no—
108C4⋊C4×C61—42no—
109C4⋊C4×C61—42no—
110C22⋊C4×C61—48no—
111C22⋊C4×C61—44no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—42no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—24no—
123C23×C61—24no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—24no—
131C23×C61—24no—
132C23×C61—42no—
133C23×C61—42no—
134C23×C61—44no—
135C23×C61—44no—
136C23×C61—44no—
137C23×C61—44no—
138C23×C61#9912yes—
139C23×C61#10212yes—
140C23×C61#10212yes—
141C23×C61#10412yes—
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61#12312yes—
144C23×C61C2×D811yescharacteristic
145C23×C61C2×SD1611yescharacteristic
146C23×C61#13712yes—
147C2×C4×C61—28no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—44no—
158C2×C4×C61—44no—
159C2×C4×C61—44no—
160C2×C4×C61—44no—
161C2×C4×C61—44no—
162C2×C4×C61—44no—
163C2×C4×C61—44no—
164C2×C4×C61—44no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—82no—
172C2×C4×C61—82no—
173C2×C4×C61—82no—
174C2×C4×C61—84no—
175C2×C4×C61—84no—
176C2×C4×C61—82no—
177C2×C4×C61#9912yes—
178C2×C4×C61#11712yes—
179C2×C4×C61#12312yes—
180C8×C61—82no—
181#8712C6111yesmaximal, characteristic, direct product factor, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—48no—
200C22×C61—48no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61#32714yes—
206C22×C61#38111yescharacteristic
207C22×C61C2×#9911yescharacteristic
208C22×C61C2×#9911yescharacteristic
209C22×C61C2×#10211yescharacteristic
210C22×C61#41911yescharacteristic
211C22×C61C2×#10411yescharacteristic
212C22×C61#42111yescharacteristic
213C22×C61#48012yes—
214C22×C61#48312yes—
215C4×C61—22no—
216C4×C61—22no—
217C4×C61—22no—
218C4×C61—41no—
219C4×C61—84no—
220C4×C61—82no—
221C4×C61—82no—
222C2×#380C2×C6111yescharacteristic
223#1779C2×C6111yescharacteristic
224C22⋊#95C2×C6111yescharacteristic
225#1294C2×C6114yescomplemented
226C2×C61—22no—
227C2×C61—24no—
228C2×C61—22no—
229C2×C61—42no—
230C2×C61C2×#32711yescharacteristic
231C2×C61#150811yescharacteristic
232C2×C61#151111yescharacteristic
233C2×C61#151911yescharacteristic
234C2×C61#181911yescharacteristic
235C2×C61#182311yescharacteristic
236C2×C61#182611yescharacteristic
237C24×C4C22×C6111yescharacteristic
238C22×C4⋊C4C4×C6111yescharacteristic, complemented
239C22×C4⋊C4C4×C6111yescharacteristic, complemented
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C2×C22⋊C8—21no—
243C2×C22⋊C8—21no—
244C2×C22⋊C8C22×C6112yes—
245#380—21no—
246#380—21no—
247#380C4×C6112yescomplemented
248#380C22×C6112yes—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95C22×C6112yes—
252C61#871211yescharacteristic, direct product factor, Sylow
253C25D4×C6111yescharacteristic
254C23×C4—24no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—22no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4C2×C4×C6111yescharacteristic
261C23×C4C2×C4×C6111yescharacteristic
262C23×C4D4×C6111yescharacteristic
263C23×C4D4×C6111yescharacteristic
264C23×C4D4×C6111yescharacteristic
265C23×C4C23×C6111yescharacteristic
266C22×C8—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4C2×C4×C6112yes—
272C2×C4⋊C4C2×C4×C6112yes—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C22⋊C8—24no—
281C22⋊C8—42no—
282C22⋊C8—42no—
283#95—22no—
284#95—22no—
285#95—24no—
286#95—42no—
287C24—22no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—41no—
292C24—41no—
293C24C22⋊C4×C6111yescharacteristic
294C24C22⋊C4×C6111yescharacteristic
295C24D8×C6112yes—
296C24SD16×C6112yes—
297C24C2×D4×C6111yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—416no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4C22⋊C4×C6111yescharacteristic
332C22×C4C22⋊C4×C6111yescharacteristic
333C22×C4C22×C4×C6111yescharacteristic
334C22×C4C2×D4×C6111yescharacteristic
335C22×C4#41×C6114yes—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C22⋊C4—48no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—24no—
356C23—24no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—24no—
364C23—24no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#99×C6112yes—
372C23#102×C6112yes—
373C23#102×C6112yes—
374C23#104×C6112yes—
375C23C2×C22⋊C4×C6111yescharacteristic
376C23#123×C6112yes—
377C23C2×D8×C6111yescharacteristic
378C23C2×SD16×C6111yescharacteristic
379C23#137×C6112yes—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—82no—
410C2×C4#99×C6112yes—
411C2×C4#117×C6112yes—
412C2×C4#123×C6112yes—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22C61×#32714yes—
438C22C61×#38111yescharacteristic
439C22C2×#99×C6111yescharacteristic
440C22C2×#99×C6111yescharacteristic
441C22C2×#102×C6111yescharacteristic
442C22C61×#41911yescharacteristic
443C22C2×#104×C6111yescharacteristic
444C22C61×#42111yescharacteristic
445C22C61×#48012yes—
446C22C61×#48312yes—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—84no—
452C4—82no—
453C4—82no—
454C2—22no—
455C2—24no—
456C2—22no—
457C2—42no—
458C2C2×C61×#32711yescharacteristic
459C2C61×#150811yescharacteristic
460C2C61×#151111yescharacteristic
461C2C61×#151911yescharacteristic
462C2C61×#181911yescharacteristic
463C2C61×#182311yescharacteristic
464C2C61×#182611yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC25×C61D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1294C2semidirect
6. C22×C4⋊C4×C61C4semidirect
7. C22×C4⋊C4×C61C4semidirect
15. C61×#380C4semidirect
181. #8712C61direct (N × H)
225. #1294C2×C61semidirect
238. C22×C4⋊C4C4×C61semidirect
239. C22×C4⋊C4C4×C61semidirect
247. #380C4×C61semidirect
252. C61#8712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3802
C61×#17792
C61×C22⋊#952
C61×#12942
#871261