Finite Group Databasebeta

← C61×#9031 #29512464

Subgroups — C61×#9031 #29512464

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2973C211yesmaximal, characteristic, complemented
2C61×#2397C211yesmaximal, characteristic
3C4×#100×C61C211yesmaximal, characteristic, complemented
4C61×#1490C212yesmaximal, complemented
5C61×#1300C212yesmaximal, complemented
6C2×C4×D4×C61—21no—
7C2×C4×D4×C61—21no—
8C2×C4×D4×C61C2211yescharacteristic
9C2×C4×D4×C61C2211yescharacteristic
10C61×#435—24no—
11C61×#432C2212yes—
12C2×#100×C61—21no—
13C61×#407—21no—
14C2×C22⋊C8×C61—21no—
15C4×M16×C61C2212yes—
16C61×#399—21no—
17C61×#399C411yescharacteristic
18C61×#399C411yescharacteristic
19C61×#392—21no—
20C61×#392C411yescharacteristic
21C61×#392C411yescharacteristic
22C61×#376C2211yescharacteristic
23C61×#343—21no—
24C61×D4⋊C8—24no—
25C22×D4×C61—21no—
26C22×D4×C61—21no—
27C22×D4×C61C2×C411yescharacteristic
28C22×D4×C61D411yescharacteristic
29C23×C4×C61—21no—
30C23×C4×C61D411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C2×M16×C61—22no—
33C2×M16×C61—22no—
34C22×C8×C61—22no—
35C4×D4×C61—22no—
36C4×D4×C61—22no—
37C4×D4×C61—22no—
38C4×D4×C61—22no—
39C4×D4×C61—44no—
40C4×D4×C61—44no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61D414yescomplemented
55#100×C61—24no—
56C22⋊C8×C61—22no—
57C22⋊C8×C61—22no—
58C22⋊C8×C61—22no—
59#97×C61—22no—
60#97×C61—22no—
61C4×C8×C61—22no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C22⋊C411yescharacteristic
67C24×C61C22⋊C411yescharacteristic
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—41no—
72C2×D4×C61—42no—
73C2×D4×C61—42no—
74C2×D4×C61—42no—
75C2×D4×C61—42no—
76C2×D4×C61—42no—
77C2×D4×C61—42no—
78C2×D4×C61—42no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97M16×C61—24no—
98M16×C61—42no—
99M16×C61—82no—
100C2×C8×C61—24no—
101C2×C8×C61—42no—
102C2×C8×C61—82no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—42no—
106C4⋊C4×C61—42no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—22no—
109C22⋊C4×C61—42no—
110C22⋊C4×C61—42no—
111C22⋊C4×C61—42no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—42no—
114C42×C61—24no—
115C42×C61C2×D412yes—
116C42×C61#4112yes—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61#10412yes—
134C23×C61C2×C22⋊C411yescharacteristic
135D4×C61—24no—
136D4×C61—44no—
137D4×C61—42no—
138D4×C61—48no—
139D4×C61—48no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—82no—
162C2×C4×C61—82no—
163C2×C4×C61C4×D412yes—
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12112yes—
166C2×C4×C61#12311yescharacteristic
167C8×C61—44no—
168C8×C61—44no—
169#9031C6111yesmaximal, characteristic, direct product factor, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—22no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—42no—
182C22×C61—41no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61#38611yescharacteristic
190C22×C61C2×#10411yescharacteristic
191C22×C61#42111yescharacteristic
192C4×C61—22no—
193C4×C61—21no—
194C4×C61—22no—
195C4×C61—42no—
196C4×C61—42no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—81no—
200C4×C61#45312yes—
201#2973C2×C6111yescharacteristic, complemented
202#2397C2×C6111yescharacteristic
203C4×#100C2×C6111yescharacteristic, complemented
204#1490C2×C6112yescomplemented
205#1300C2×C6112yescomplemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—42no—
209C2×C61—81no—
210C2×C61—82no—
211C2×C61#187111yescharacteristic
212C2×C61#188711yescharacteristic
213C2×C61#189111yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4—21no—
216C2×C4×D4C22×C6111yescharacteristic
217C2×C4×D4C22×C6111yescharacteristic
218#435—24no—
219#432C22×C6112yes—
220C2×#100—21no—
221#407—21no—
222C2×C22⋊C8—21no—
223C4×M16C22×C6112yes—
224#399—21no—
225#399C4×C6111yescharacteristic
226#399C4×C6111yescharacteristic
227#392—21no—
228#392C4×C6111yescharacteristic
229#392C4×C6111yescharacteristic
230#376C22×C6111yescharacteristic
231#343—21no—
232D4⋊C8—24no—
233C61#903111yescharacteristic, direct product factor, Sylow
234C22×D4—21no—
235C22×D4—21no—
236C22×D4C2×C4×C6111yescharacteristic
237C22×D4D4×C6111yescharacteristic
238C23×C4—21no—
239C23×C4D4×C6111yescharacteristic
240C23×C4D4×C6111yescharacteristic
241C2×M16—22no—
242C2×M16—22no—
243C22×C8—22no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—22no—
247C4×D4—22no—
248C4×D4—44no—
249C4×D4—44no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C6111yescharacteristic
253C2×C4⋊C4D4×C6111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4C2×C4×C6111yescharacteristic
260C2×C22⋊C4C2×C4×C6111yescharacteristic
261C2×C42—21no—
262C2×C42C23×C6111yescharacteristic
263C4⋊C8D4×C6114yescomplemented
264#100—24no—
265C22⋊C8—22no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268#97—22no—
269#97—22no—
270C4×C8—22no—
271#95—21no—
272#95C2×C4×C6111yescharacteristic
273#95C2×C4×C6111yescharacteristic
274C24—21no—
275C24C22⋊C4×C6111yescharacteristic
276C24C22⋊C4×C6111yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C22⋊C4×C6111yescharacteristic
302C22×C4C22⋊C4×C6111yescharacteristic
303C22×C4C22×C4×C6111yescharacteristic
304C22×C4C2×D4×C6111yescharacteristic
305C22×C4C2×D4×C6111yescharacteristic
306M16—24no—
307M16—42no—
308M16—82no—
309C2×C8—24no—
310C2×C8—42no—
311C2×C8—82no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C42—24no—
324C42C2×D4×C6112yes—
325C42#41×C6112yes—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#104×C6112yes—
343C23C2×C22⋊C4×C6111yescharacteristic
344D4—24no—
345D4—44no—
346D4—42no—
347D4—48no—
348D4—48no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4C4×D4×C6112yes—
373C2×C4#120×C6111yescharacteristic
374C2×C4#121×C6112yes—
375C2×C4#123×C6111yescharacteristic
376C8—44no—
377C8—44no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C61×#38611yescharacteristic
398C22C2×#104×C6111yescharacteristic
399C22C61×#42111yescharacteristic
400C4—22no—
401C4—21no—
402C4—22no—
403C4—42no—
404C4—42no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4C61×#45312yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—82no—
414C2C61×#187111yescharacteristic
415C2C61×#188711yescharacteristic
416C2C61×#189111yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#386
prime radicalC61×#2397C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2973C2semidirect
3. C4×#100×C61C2semidirect
4. C61×#1490C2semidirect
5. C61×#1300C2semidirect
54. C4⋊C8×C61D4semidirect
169. #9031C61direct (N × H)
201. #2973C2×C61semidirect
203. C4×#100C2×C61semidirect
204. #1490C2×C61semidirect
205. #1300C2×C61semidirect
233. C61#9031direct (N × H)
263. C4⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#29732
C61×#23972
C4×#100×C612
C61×#14902
C61×#13002
#903161