Finite Group Databasebeta

← C61×#9497 #29512930

Subgroups — C61×#9497 #29512930

Order 15616.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2403C211yesmaximal, characteristic
2C61×#2309C211yesmaximal, characteristic, complemented
3C61×#1781C212yesmaximal, complemented
4C61×#1781C211yesmaximal, characteristic, complemented
5C61×#1304C212yesmaximal, complemented
6C23×D4×C61C2211yescharacteristic
7C23×D4×C61C2211yescharacteristic
8C2×#120×C61—21no—
9C2×#120×C61C412yescomplemented
10C2×#117×C61—21no—
11C2×#99×C61—22no—
12C2×#99×C61—24no—
13C61×#392—22no—
14C61×#390—24no—
15C61×#386—21no—
16C61×#386C412yescomplemented
17C61×#379—21no—
18C61×#379C2212yes—
19C61×#379C2211yescharacteristic
20C61×#379C2212yes—
21C25×C61C2×C411yescharacteristic
22C25×C61D411yescharacteristic
23C25×C61C2311yescharacteristic
24C22×D4×C61—21no—
25C22×D4×C61—22no—
26C22×D4×C61—22no—
27C22×D4×C61—22no—
28C22×D4×C61—21no—
29C22×D4×C61—22no—
30C22×D4×C61—22no—
31C22×D4×C61—44no—
32C22×D4×C61—44no—
33C22×D4×C61C2×C412yes—
34C22×D4×C61D412yes—
35C23×C4×C61C2×C411yescharacteristic
36C23×C4×C61D411yescharacteristic
37#120×C61—44no—
38#120×C61—44no—
39#117×C61—44no—
40C2×C4⋊C4×C61—22no—
41C2×C22⋊C4×C61—22no—
42C2×C22⋊C4×C61—22no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—22no—
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61—22no—
47C2×C22⋊C4×C61—22no—
48C2×C22⋊C4×C61—22no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61C2×C412yes—
53C2×C22⋊C4×C61D414yescomplemented
54C2×C42×C61—22no—
55#99×C61—48no—
56#99×C61—44no—
57#95×C61—22no—
58C24×C61—21no—
59C24×C61—21no—
60C24×C61—22no—
61C24×C61—21no—
62C24×C61—42no—
63C24×C61—42no—
64C24×C61—42no—
65C24×C61—42no—
66C24×C61—42no—
67C24×C61—42no—
68C24×C61—81no—
69C24×C61—81no—
70C24×C61—81no—
71C24×C61C22⋊C412yes—
72C24×C61C22×C411yescharacteristic
73C24×C61C2×D411yescharacteristic
74C24×C61C2×D411yescharacteristic
75C24×C61C2×D412yes—
76C24×C61#4112yes—
77C2×D4×C61—28no—
78C2×D4×C61—24no—
79C2×D4×C61—24no—
80C2×D4×C61—24no—
81C2×D4×C61—24no—
82C2×D4×C61—24no—
83C2×D4×C61—42no—
84C2×D4×C61—42no—
85C2×D4×C61—44no—
86C2×D4×C61—44no—
87C2×D4×C61—48no—
88C2×D4×C61—42no—
89C2×D4×C61—44no—
90C2×D4×C61—42no—
91C2×D4×C61—44no—
92C2×D4×C61—42no—
93C2×D4×C61—44no—
94C2×D4×C61—41no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—44no—
98C2×D4×C61—44no—
99C2×D4×C61—82no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—24no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—24no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C22⋊C412yes—
110C4⋊C4×C61—44no—
111C22⋊C4×C61—44no—
112C22⋊C4×C61—44no—
113C22⋊C4×C61—42no—
114C22⋊C4×C61—44no—
115C22⋊C4×C61—44no—
116C22⋊C4×C61—42no—
117C22⋊C4×C61—44no—
118C22⋊C4×C61—44no—
119C22⋊C4×C61—82no—
120C22⋊C4×C61—82no—
121C22⋊C4×C61—81no—
122C22⋊C4×C61—82no—
123C22⋊C4×C61—82no—
124C42×C61—44no—
125C23×C61—22no—
126C23×C61—22no—
127C23×C61—22no—
128C23×C61—22no—
129C23×C61—24no—
130C23×C61—22no—
131C23×C61—24no—
132C23×C61—22no—
133C23×C61—22no—
134C23×C61—22no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—42no—
139C23×C61—41no—
140C23×C61—42no—
141C23×C61—41no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—42no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—41no—
149C23×C61—42no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—42no—
153C23×C61—41no—
154C23×C61—42no—
155C23×C61—42no—
156C23×C61—81no—
157C23×C61—81no—
158C23×C61—82no—
159C23×C61—82no—
160C23×C61—88no—
161C23×C61—88no—
162C23×C61—88no—
163C23×C61C2×C22⋊C411yescharacteristic
164C23×C61C4×D412yes—
165C23×C61#12011yescharacteristic
166C23×C61#12112yes—
167C23×C61#12311yescharacteristic
168D4×C61—48no—
169D4×C61—48no—
170D4×C61—48no—
171D4×C61—44no—
172D4×C61—44no—
173D4×C61—88no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—41no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61—44no—
185C2×C4×C61—42no—
186C2×C4×C61—44no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—44no—
190C2×C4×C61—82no—
191C2×C4×C61—82no—
192C2×C4×C61—82no—
193C2×C4×C61#9914yescomplemented
194#9497C6111yesmaximal, characteristic, direct product factor, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—21no—
208C22×C61—44no—
209C22×C61—44no—
210C22×C61—44no—
211C22×C61—44no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61—84no—
217C22×C61—82no—
218C22×C61—82no—
219C22×C61—84no—
220C22×C61—82no—
221C22×C61—84no—
222C22×C61—84no—
223C22×C61—84no—
224C22×C61—84no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61#38611yescharacteristic
228C22×C61C2×#9912yes—
229C22×C61B(4,𝔽2)12yes—
230C4×C61—24no—
231C4×C61—42no—
232C4×C61—84no—
233C4×C61—82no—
234C4×C61—162no—
235#2403C2×C6111yescharacteristic
236#2309C2×C6111yescharacteristic, complemented
237#1781C2×C6112yescomplemented
238#1781C2×C6111yescharacteristic, complemented
239#1304C2×C6112yescomplemented
240C2×C61—22no—
241C2×C61—22no—
242C2×C61—42no—
243C2×C61—42no—
244C2×C61—41no—
245C2×C61—82no—
246C2×C61—82no—
247C2×C61#188911yescharacteristic
248C2×C61#189811yescharacteristic
249C2×C61#191311yescharacteristic
250C23×D4C22×C6111yescharacteristic
251C23×D4C22×C6111yescharacteristic
252C2×#120—21no—
253C2×#120C4×C6112yescomplemented
254C2×#117—21no—
255C2×#99—22no—
256C2×#99—24no—
257#392—22no—
258#390—24no—
259#386—21no—
260#386C4×C6112yescomplemented
261#379—21no—
262#379C22×C6112yes—
263#379C22×C6111yescharacteristic
264#379C22×C6112yes—
265C61#949711yescharacteristic, direct product factor, Sylow
266C25C2×C4×C6111yescharacteristic
267C25D4×C6111yescharacteristic
268C25C23×C6111yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C6112yes—
279C22×D4D4×C6112yes—
280C23×C4C2×C4×C6111yescharacteristic
281C23×C4D4×C6111yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C6112yes—
298C2×C22⋊C4D4×C6114yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C6112yes—
317C24C22×C4×C6111yescharacteristic
318C24C2×D4×C6111yescharacteristic
319C24C2×D4×C6111yescharacteristic
320C24C2×D4×C6112yes—
321C24#41×C6112yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C6112yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C6111yescharacteristic
409C23C4×D4×C6112yes—
410C23#120×C6111yescharacteristic
411C23#121×C6112yes—
412C23#123×C6111yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C6114yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22C61×#38611yescharacteristic
472C22C2×#99×C6112yes—
473C22C61×B(4,𝔽2)12yes—
474C4—24no—
475C4—42no—
476C4—84no—
477C4—82no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C61×#188911yescharacteristic
487C2C61×#189811yescharacteristic
488C2C61×#191311yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC24C22×C4×C61
Frattini, cosocleC25C23×C61
prime radicalC61×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2309C2semidirect
3. C61×#1781C2semidirect
4. C61×#1781C2semidirect
5. C61×#1304C2semidirect
9. C2×#120×C61C4semidirect
16. C61×#386C4semidirect
53. C2×C22⋊C4×C61D4semidirect
193. C2×C4×C61#99semidirect
194. #9497C61direct (N × H)
236. #2309C2×C61semidirect
237. #1781C2×C61semidirect
238. #1781C2×C61semidirect
239. #1304C2×C61semidirect
253. C2×#120C4×C61semidirect
260. #386C4×C61semidirect
265. C61#9497direct (N × H)
298. C2×C22⋊C4D4×C61semidirect
438. C2×C4#99×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#24032
C61×#23092
C61×#17812
C61×#13042
#949761