Finite Group Databasebeta

← C61×#8978 #29512411

Subgroups — C61×#8978 #29512411

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#460C211yesmaximal, characteristic
2C61×#2355C211yesmaximal, characteristic, complemented
3C61×#1982C211yesmaximal, characteristic
4C61×#1957C211yesmaximal, characteristic
5C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
6C61×#1296C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C61—21no—
9C2×#127×C61C2211yescharacteristic
10C2×C4×Q8×C61C2211yescharacteristic
11C61×#460—22no—
12C61×#460C414yescomplemented
13C2×C4⋊C8×C61C2211yescharacteristic
14C2×C4⋊C8×C61C2211yescharacteristic
15C2×#102×C61—21no—
16C2×#102×C61—22no—
17C2×#102×C61—21no—
18C2×#102×C61—21no—
19C2×C4×C8×C61C2211yescharacteristic
20C61×#391—21no—
21C61×#387—22no—
22C61×#384C2211yescharacteristic
23C61×#382—21no—
24C4×C4⋊C4×C61—21no—
25C4×C4⋊C4×C61—21no—
26C4×C4⋊C4×C61C2211yescharacteristic
27C61×Q8⋊C8—22no—
28C22×Q8×C61D411yescharacteristic
29C22×D4×C61—21no—
30C22×D4×C61—21no—
31C22×D4×C61—21no—
32C2×SD16×C61—24no—
33C2×SD16×C61—42no—
34C2×SD16×C61—42no—
35C22×C8×C61—21no—
36C22×C8×C61—21no—
37C22×C8×C61—21no—
38#127×C61—21no—
39#127×C61—21no—
40#127×C61—21no—
41#127×C61C2×C412yes—
42C4×Q8×C61—21no—
43C4×Q8×C61—21no—
44C4×Q8×C61C2×C412yes—
45C4×Q8×C61D412yes—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61D412yes—
53C2×C42×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61—22no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61C2×C412yes—
61#102×C61—24no—
62#102×C61—42no—
63#102×C61—44no—
64#102×C61—42no—
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67#95×C61—22no—
68#95×C61—22no—
69#95×C61—22no—
70#95×C61—21no—
71C24×C61—41no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61C22⋊C412yes—
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—42no—
82C2×D4×C61—42no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
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—41no—
93C2×D4×C61—41no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—22no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102SD16×C61—48no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—42no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61C22⋊C412yes—
124C4⋊C4×C61SD1612yescomplemented
125C42×C61—22no—
126C42×C61—22no—
127C42×C61—41no—
128C42×C61—41no—
129C42×C61—82no—
130C42×C61C22×C411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C42×C61#4111yescharacteristic
134C23×C61—42no—
135C23×C61—81no—
136C23×C61—81no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61#12011yescharacteristic
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146D4×C61—44no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—42no—
150D4×C61—42no—
151D4×C61—82no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—81no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61C4×D411yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12311yescharacteristic
179C2×C4×C61C2×SD1611yescharacteristic
180C2×C4×C61#13511yescharacteristic
181C2×C4×C61#13511yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C61#13711yescharacteristic
187C8×C61—42no—
188C8×C61—42no—
189C8×C61—81no—
190#8978C6111yesmaximal, characteristic, direct product factor, Sylow
191C22×C61—82no—
192C22×C61—82no—
193C22×C61—82no—
194C22×C61—161no—
195C22×C61—161no—
196C22×C61—161no—
197C22×C61—161no—
198C22×C61#38611yescharacteristic
199C22×C61#44811yescharacteristic
200C22×C61#44911yescharacteristic
201C22×C61#44911yescharacteristic
202C22×C61#44911yescharacteristic
203C22×C61#45311yescharacteristic
204C22×C61#45411yescharacteristic
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—42no—
208C4×C61—42no—
209C4×C61—42no—
210C4×C61—82no—
211C4×C61—81no—
212C4×C61#41611yescharacteristic
213C4×C61#41811yescharacteristic
214C4×C61C4×SD1611yescharacteristic
215C4×C61#44011yescharacteristic
216C4×C61#46011yescharacteristic
217C4×C61#46411yescharacteristic
218C4×C61#48211yescharacteristic
219C4×C61#48211yescharacteristic
220C2×#460C2×C6111yescharacteristic
221#2355C2×C6111yescharacteristic, complemented
222#1982C2×C6111yescharacteristic
223#1957C2×C6111yescharacteristic
224C2×Q8⋊C8C2×C6111yescharacteristic, complemented
225#1296C2×C6111yescharacteristic, complemented
226#1279C2×C6111yescharacteristic, complemented
227C2×C61—162no—
228C2×C61#162011yescharacteristic
229C2×C61#162211yescharacteristic
230C2×C61#162611yescharacteristic
231C2×C61#162811yescharacteristic
232C2×C61#187511yescharacteristic
233C2×C61#188011yescharacteristic
234C2×C61#188311yescharacteristic
235C22×SD16—21no—
236C2×#127C22×C6111yescharacteristic
237C2×C4×Q8C22×C6111yescharacteristic
238#460—22no—
239#460C4×C6114yescomplemented
240C2×C4⋊C8C22×C6111yescharacteristic
241C2×C4⋊C8C22×C6111yescharacteristic
242C2×#102—21no—
243C2×#102—22no—
244C2×#102—21no—
245C2×#102—21no—
246C2×C4×C8C22×C6111yescharacteristic
247#391—21no—
248#387—22no—
249#384C22×C6111yescharacteristic
250#382—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C6111yescharacteristic
254Q8⋊C8—22no—
255C61#897811yescharacteristic, direct product factor, Sylow
256C22×Q8D4×C6111yescharacteristic
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C2×SD16—24no—
261C2×SD16—42no—
262C2×SD16—42no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266#127—21no—
267#127—21no—
268#127—21no—
269#127C2×C4×C6112yes—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8C2×C4×C6112yes—
273C4×Q8D4×C6112yes—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C6111yescharacteristic
278C2×C4⋊C4D4×C6111yescharacteristic
279C2×C4⋊C4D4×C6111yescharacteristic
280C2×C4⋊C4D4×C6112yes—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—22no—
284C2×C42C23×C6111yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8C2×C4×C6112yes—
289#102—24no—
290#102—42no—
291#102—44no—
292#102—42no—
293C4×C8—21no—
294C4×C8—21no—
295#95—22no—
296#95—22no—
297#95—22no—
298#95—21no—
299C24—41no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8C22⋊C4×C6112yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4C2×D4×C6111yescharacteristic
328C22×C4C2×D4×C6111yescharacteristic
329C22×C4C2×D4×C6111yescharacteristic
330SD16—48no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4C22⋊C4×C6112yes—
352C4⋊C4SD16×C6112yescomplemented
353C42—22no—
354C42—22no—
355C42—41no—
356C42—41no—
357C42—82no—
358C42C22×C4×C6111yescharacteristic
359C42C2×D4×C6111yescharacteristic
360C42#41×C6111yescharacteristic
361C42#41×C6111yescharacteristic
362C23—42no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—81no—
369C23#120×C6111yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—44no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—82no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4C2×C22⋊C4×C6111yescharacteristic
402C2×C4C4×D4×C6111yescharacteristic
403C2×C4C4×D4×C6111yescharacteristic
404C2×C4#121×C6111yescharacteristic
405C2×C4#121×C6111yescharacteristic
406C2×C4#123×C6111yescharacteristic
407C2×C4C2×SD16×C6111yescharacteristic
408C2×C4#135×C6111yescharacteristic
409C2×C4#135×C6111yescharacteristic
410C2×C4#135×C6111yescharacteristic
411C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
412C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
413C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
414C2×C4#137×C6111yescharacteristic
415C8—42no—
416C8—42no—
417C8—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—161no—
422C22—161no—
423C22—161no—
424C22—161no—
425C22C61×#38611yescharacteristic
426C22C61×#44811yescharacteristic
427C22C61×#44911yescharacteristic
428C22C61×#44911yescharacteristic
429C22C61×#44911yescharacteristic
430C22C61×#45311yescharacteristic
431C22C61×#45411yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4C61×#41611yescharacteristic
440C4C61×#41811yescharacteristic
441C4C4×SD16×C6111yescharacteristic
442C4C61×#44011yescharacteristic
443C4C61×#46011yescharacteristic
444C4C61×#46411yescharacteristic
445C4C61×#48211yescharacteristic
446C4C61×#48211yescharacteristic
447C2—162no—
448C2C61×#162011yescharacteristic
449C2C61×#162211yescharacteristic
450C2C61×#162611yescharacteristic
451C2C61×#162811yescharacteristic
452C2C61×#187511yescharacteristic
453C2C61×#188011yescharacteristic
454C2C61×#188311yescharacteristic
subgroupG/H
center, socleC23×C61#120
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC2×#127×C61C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2355C2semidirect
5. C2×C61×Q8⋊C8C2semidirect
6. C61×#1296C2semidirect
7. C61×#1279C2semidirect
12. C61×#460C4semidirect
124. C4⋊C4×C61SD16semidirect
190. #8978C61direct (N × H)
221. #2355C2×C61semidirect
224. C2×Q8⋊C8C2×C61semidirect
225. #1296C2×C61semidirect
226. #1279C2×C61semidirect
239. #460C4×C61semidirect
255. C61#8978direct (N × H)
352. C4⋊C4SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4602
C61×#23552
C61×#19822
C61×#19572
C2×C61×Q8⋊C82
C61×#12962
C61×#12792
#897861