Finite Group Databasebeta

← C61×#9174 #29512607

Subgroups — C61×#9174 #29512607

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3038C211yesmaximal, characteristic
2C61×#2925C211yesmaximal, characteristic, complemented
3C61×#1545C211yesmaximal, characteristic, complemented
4C2×C61×#331C211yesmaximal, characteristic, complemented
5C61×#1477C211yesmaximal, characteristic, complemented
6C61×#1301C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C61—21no—
9C2×#127×C61C2211yescharacteristic
10C4×#41×C61C2211yescharacteristic
11C61×#460—21no—
12C61×#460C412yes—
13C61×#459—21no—
14C61×#459C412yes—
15C61×#433—22no—
16C61×#432—21no—
17C61×#431—21no—
18C61×#431C2211yescharacteristic
19C61×#423C2211yescharacteristic
20C61×#423C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C61×#418—21no—
24C61×#408—21no—
25C61×#405—21no—
26C61×#331—21no—
27C61×#331—21no—
28C61×#331—22no—
29C61×Q8⋊C8—21no—
30C61×D4⋊C8—21no—
31C2×#41×C61D411yescharacteristic
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—21no—
35AGL(1,ℤ/8)×C61—42no—
36AGL(1,ℤ/8)×C61—42no—
37C2×SD16×C61—22no—
38C2×D8×C61—22no—
39C2×M16×C61—21no—
40C2×M16×C61—21no—
41C22×C8×C61—21no—
42C22×C8×C61—21no—
43#127×C61—21no—
44#127×C61—21no—
45#127×C61—21no—
46#127×C61C2×C412yes—
47C4×Q8×C61C2×C411yescharacteristic
48C4×Q8×C61D411yescharacteristic
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4×D4×C61D411yescharacteristic
53#117×C61—21no—
54#117×C61D411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61C2×C412yes—
64C4⋊C8×C61D411yescharacteristic
65C4⋊C8×C61D411yescharacteristic
66C4⋊C8×C61D412yes—
67#102×C61—22no—
68#102×C61—22no—
69C22⋊C8×C61—22no—
70C22⋊C8×C61—22no—
71C22⋊C8×C61—21no—
72#97×C61—22no—
73C4×C8×C61—22no—
74C4×C8×C61—21no—
75C24×C61—41no—
76#41×C61—21no—
77#41×C61—21no—
78#41×C61—21no—
79#41×C61—21no—
80C2×Q8×C61C22⋊C411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—22no—
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—81no—
93C2×D4×C61—81no—
94C2×D4×C61—82no—
95C2×D4×C61C22⋊C411yescharacteristic
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×C4×C61#4111yescharacteristic
102SD16×C61—44no—
103D8×C61—44no—
104M16×C61—41no—
105M16×C61—41no—
106M16×C61—41no—
107M16×C61—41no—
108C2×C8×C61—22no—
109C2×C8×C61—21no—
110C2×C8×C61—22no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—81no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C411yescharacteristic
120C4⋊C4×C61C22⋊C411yescharacteristic
121C22⋊C4×C61—21no—
122C22⋊C4×C61—21no—
123C22⋊C4×C61—21no—
124C42×C61—21no—
125C42×C61—21no—
126C42×C61—21no—
127C42×C61C22×C411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C23×C61—21no—
132C23×C61—42no—
133C23×C61—82no—
134C23×C61—82no—
135C23×C61—81no—
136C23×C61—81no—
137C23×C61#12311yescharacteristic
138Q8×C61—21no—
139Q8×C61—21no—
140D4×C61—21no—
141D4×C61—21no—
142D4×C61—41no—
143D4×C61—41no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—82no—
147D4×C61—82no—
148D4×C61—82no—
149D4×C61—81no—
150D4×C61—81no—
151D4×C61—81no—
152D4×C61—81no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61C2×C22⋊C411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C8×C61—42no—
175C8×C61—41no—
176C8×C61—41no—
177C8×C61—42no—
178C8×C61—81no—
179C8×C61—81no—
180#9174C6111yesmaximal, characteristic, direct product factor, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—82no—
187C22×C61—82no—
188C22×C61—82no—
189C22×C61—162no—
190C22×C61—162no—
191C22×C61#38611yescharacteristic
192C22×C61#48211yescharacteristic
193C22×C61#48211yescharacteristic
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61#41611yescharacteristic
201C4×C61#41811yescharacteristic
202C4×C61#44911yescharacteristic
203C4×C61#44911yescharacteristic
204C4×C61#47111yescharacteristic
205C4×C61#47211yescharacteristic
206#3038C2×C6111yescharacteristic
207#2925C2×C6111yescharacteristic, complemented
208#1545C2×C6111yescharacteristic, complemented
209C2×#331C2×C6111yescharacteristic, complemented
210#1477C2×C6111yescharacteristic, complemented
211#1301C2×C6111yescharacteristic, complemented
212#1292C2×C6111yescharacteristic, complemented
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—81no—
216C2×C61—162no—
217C2×C61#187511yescharacteristic
218C2×C61#190311yescharacteristic
219C2×C61#190711yescharacteristic
220C2×AGL(1,ℤ/8)—21no—
221C2×#127C22×C6111yescharacteristic
222C4×#41C22×C6111yescharacteristic
223#460—21no—
224#460C4×C6112yes—
225#459—21no—
226#459C4×C6112yes—
227#433—22no—
228#432—21no—
229#431—21no—
230#431C22×C6111yescharacteristic
231#423C22×C6111yescharacteristic
232#423C22×C6111yescharacteristic
233C2×C4⋊C8C22×C6111yescharacteristic
234C2×C4⋊C8C22×C6111yescharacteristic
235#418—21no—
236#408—21no—
237#405—21no—
238#331—21no—
239#331—21no—
240#331—22no—
241Q8⋊C8—21no—
242D4⋊C8—21no—
243C61#917411yescharacteristic, direct product factor, Sylow
244C2×#41D4×C6111yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248AGL(1,ℤ/8)—42no—
249AGL(1,ℤ/8)—42no—
250C2×SD16—22no—
251C2×D8—22no—
252C2×M16—21no—
253C2×M16—21no—
254C22×C8—21no—
255C22×C8—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2×C4×C6112yes—
260C4×Q8C2×C4×C6111yescharacteristic
261C4×Q8D4×C6111yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C2×C4×C6111yescharacteristic
265C4×D4D4×C6111yescharacteristic
266#117—21no—
267#117D4×C6111yescharacteristic
268C2×C42—21no—
269C2×C42C23×C6111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C6112yes—
277C4⋊C8D4×C6111yescharacteristic
278C4⋊C8D4×C6111yescharacteristic
279C4⋊C8D4×C6112yes—
280#102—22no—
281#102—22no—
282C22⋊C8—22no—
283C22⋊C8—22no—
284C22⋊C8—21no—
285#97—22no—
286C4×C8—22no—
287C4×C8—21no—
288C24—41no—
289#41—21no—
290#41—21no—
291#41—21no—
292#41—21no—
293C2×Q8C22⋊C4×C6111yescharacteristic
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—81no—
306C2×D4—81no—
307C2×D4—82no—
308C2×D4C22⋊C4×C6111yescharacteristic
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4C2×D4×C6111yescharacteristic
313C22×C4#41×C6111yescharacteristic
314C22×C4#41×C6111yescharacteristic
315SD16—44no—
316D8—44no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321C2×C8—22no—
322C2×C8—21no—
323C2×C8—22no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—81no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4C22⋊C4×C6111yescharacteristic
333C4⋊C4C22⋊C4×C6111yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C42—21no—
338C42—21no—
339C42—21no—
340C42C22×C4×C6111yescharacteristic
341C42C2×D4×C6111yescharacteristic
342C42C2×D4×C6111yescharacteristic
343C42C2×D4×C6111yescharacteristic
344C23—21no—
345C23—42no—
346C23—82no—
347C23—82no—
348C23—81no—
349C23—81no—
350C23#123×C6111yescharacteristic
351Q8—21no—
352Q8—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4C2×C22⋊C4×C6111yescharacteristic
378C2×C4C4×D4×C6111yescharacteristic
379C2×C4C4×D4×C6111yescharacteristic
380C2×C4#120×C6111yescharacteristic
381C2×C4#121×C6111yescharacteristic
382C2×C4#121×C6111yescharacteristic
383C2×C4#135×C6111yescharacteristic
384C2×C4#135×C6111yescharacteristic
385C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
386C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
387C8—42no—
388C8—41no—
389C8—41no—
390C8—42no—
391C8—81no—
392C8—81no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—162no—
402C22—162no—
403C22C61×#38611yescharacteristic
404C22C61×#48211yescharacteristic
405C22C61×#48211yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4C61×#41611yescharacteristic
413C4C61×#41811yescharacteristic
414C4C61×#44911yescharacteristic
415C4C61×#44911yescharacteristic
416C4C61×#47111yescharacteristic
417C4C61×#47211yescharacteristic
418C2—21no—
419C2—21no—
420C2—81no—
421C2—162no—
422C2C61×#187511yescharacteristic
423C2C61×#190311yescharacteristic
424C2C61×#190711yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3038C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2925C2semidirect
3. C61×#1545C2semidirect
4. C2×C61×#331C2semidirect
5. C61×#1477C2semidirect
6. C61×#1301C2semidirect
7. C61×#1292C2semidirect
180. #9174C61direct (N × H)
207. #2925C2×C61semidirect
208. #1545C2×C61semidirect
209. C2×#331C2×C61semidirect
210. #1477C2×C61semidirect
211. #1301C2×C61semidirect
212. #1292C2×C61semidirect
243. C61#9174direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30382
C61×#29252
C61×#15452
C2×C61×#3312
C61×#14772
C61×#13012
C61×#12922
#917461