Finite Group Databasebeta

← C61×#9053 #29512486

Subgroups — C61×#9053 #29512486

Order 15616.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3169C211yesmaximal, characteristic
2C61×#2935C211yesmaximal, characteristic, complemented
3C61×#1980C211yesmaximal, characteristic, complemented
4C61×#1502C211yesmaximal, characteristic, complemented
5C61×#1480C211yesmaximal, characteristic, complemented
6C61×#1279C211yesmaximal, characteristic, complemented
7C61×#1278C211yesmaximal, characteristic, complemented
8C2×#131×C61—21no—
9C61×#532C2211yescharacteristic
10C61×#532C2211yescharacteristic
11C61×#500C411yescharacteristic, complemented
12C61×#493C411yescharacteristic, complemented
13C61×#486C411yescharacteristic, complemented
14C61×#486C411yescharacteristic, complemented
15C61×#466—22no—
16C4×D8×C61—22no—
17C61×#436—21no—
18C61×#435—22no—
19C8×D4×C61—21no—
20C61×#431C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×#104×C61—21no—
23C2×#104×C61—21no—
24C61×#408—21no—
25C4×M16×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#327—22no—
29C61×D4⋊C8—21no—
30C61×D4⋊C8—21no—
31C2×#41×C61—21no—
32C2×#41×C61—21no—
33C2×D8×C61—22no—
34#131×C61—42no—
35#131×C61—42no—
36C2×M16×C61—22no—
37C2×M16×C61D411yescharacteristic
38C2×M16×C61D411yescharacteristic
39C22×C8×C61—22no—
40C22×C8×C61—21no—
41C22×C8×C61—21no—
42C4⋊Q8×C61C2×C411yescharacteristic
43C4⋊Q8×C61C2×C411yescharacteristic
44#127×C61C2×C411yescharacteristic
45#127×C61C2×C411yescharacteristic
46#124×C61—21no—
47#124×C61—21no—
48#121×C61—21no—
49#121×C61—21no—
50#121×C61—21no—
51#121×C61D412yes—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61D412yes—
56C2×C4⋊C4×C61—21no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59#107×C61—22no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61D411yescharacteristic
63C4⋊C8×C61D411yescharacteristic
64#104×C61—42no—
65#104×C61—42no—
66#102×C61—22no—
67#102×C61—22no—
68C22⋊C8×C61—22no—
69C22⋊C8×C61—22no—
70C22⋊C8×C61—21no—
71#97×C61—21no—
72C4×C8×C61—21no—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C4×C8×C61C2×C411yescharacteristic
76C4×C8×C61C2×C411yescharacteristic
77#95×C61—21no—
78#41×C61—41no—
79#41×C61—41no—
80#41×C61—41no—
81#41×C61—41no—
82#41×C61—41no—
83#41×C61—41no—
84#41×C61—41no—
85#41×C61—41no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×D4×C61—22no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—41no—
95C2×D4×C61C22⋊C412yes—
96C22×C4×C61—22no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102D8×C61—44no—
103M16×C61—21no—
104M16×C61—21no—
105M16×C61—21no—
106M16×C61—44no—
107M16×C61D812yescomplemented
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—42no—
115C2×C8×C61—44no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—22no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61C22⋊C412yes—
125C22⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C42×C61—41no—
130C42×C61—41no—
131C42×C61C22×C411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61#4111yescharacteristic
135C23×C61—22no—
136C23×C61—41no—
137C23×C61#12111yescharacteristic
138Q8×C61—41no—
139Q8×C61—41no—
140Q8×C61—41no—
141Q8×C61—41no—
142D4×C61—42no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—41no—
147D4×C61—41no—
148D4×C61—41no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153D4×C61—41no—
154D4×C61—81no—
155D4×C61—81no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—22no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C2×C4×C61C2×D811yescharacteristic
175C2×C4×C61#13511yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C8×C61—22no—
179C8×C61—22no—
180C8×C61—41no—
181C8×C61—41no—
182C8×C61—41no—
183C8×C61—41no—
184C8×C61—81no—
185#9053C6111yesmaximal, characteristic, direct product factor, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—42no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61#38611yescharacteristic
195C22×C61#45911yescharacteristic
196C22×C61#46311yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—42no—
201C4×C61—82no—
202C4×C61—81no—
203C4×C61C4×D811yescharacteristic
204C4×C61#44211yescharacteristic
205C4×C61#44311yescharacteristic
206C4×C61#44411yescharacteristic
207C4×C61#44711yescharacteristic
208C4×C61#44911yescharacteristic
209#3169C2×C6111yescharacteristic
210#2935C2×C6111yescharacteristic, complemented
211#1980C2×C6111yescharacteristic, complemented
212#1502C2×C6111yescharacteristic, complemented
213#1480C2×C6111yescharacteristic, complemented
214#1279C2×C6111yescharacteristic, complemented
215#1278C2×C6111yescharacteristic, complemented
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—82no—
219C2×C61—161no—
220C2×C61#187611yescharacteristic
221C2×C61#187911yescharacteristic
222C2×C61#188411yescharacteristic
223C2×#131—21no—
224#532C22×C6111yescharacteristic
225#532C22×C6111yescharacteristic
226#500C4×C6111yescharacteristic, complemented
227#493C4×C6111yescharacteristic, complemented
228#486C4×C6111yescharacteristic, complemented
229#486C4×C6111yescharacteristic, complemented
230#466—22no—
231C4×D8—22no—
232#436—21no—
233#435—22no—
234C8×D4—21no—
235#431C22×C6111yescharacteristic
236C2×C4⋊C8C22×C6111yescharacteristic
237C2×#104—21no—
238C2×#104—21no—
239#408—21no—
240C4×M16C22×C6111yescharacteristic
241C2×C4×C8C22×C6111yescharacteristic
242C4×C4⋊C4C22×C6111yescharacteristic
243#327—22no—
244D4⋊C8—21no—
245D4⋊C8—21no—
246C61#905311yescharacteristic, direct product factor, Sylow
247C2×#41—21no—
248C2×#41—21no—
249C2×D8—22no—
250#131—42no—
251#131—42no—
252C2×M16—22no—
253C2×M16D4×C6111yescharacteristic
254C2×M16D4×C6111yescharacteristic
255C22×C8—22no—
256C22×C8—21no—
257C22×C8—21no—
258C4⋊Q8C2×C4×C6111yescharacteristic
259C4⋊Q8C2×C4×C6111yescharacteristic
260#127C2×C4×C6111yescharacteristic
261#127C2×C4×C6111yescharacteristic
262#124—21no—
263#124—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121D4×C6112yes—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4D4×C6112yes—
272C2×C4⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C6111yescharacteristic
275#107—22no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8D4×C6111yescharacteristic
279C4⋊C8D4×C6111yescharacteristic
280#104—42no—
281#104—42no—
282#102—22no—
283#102—22no—
284C22⋊C8—22no—
285C22⋊C8—22no—
286C22⋊C8—21no—
287#97—21no—
288C4×C8—21no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8C2×C4×C6111yescharacteristic
292C4×C8C2×C4×C6111yescharacteristic
293#95—21no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊C4×C6112yes—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C2×D4×C6111yescharacteristic
316C22×C4C2×D4×C6111yescharacteristic
317C22×C4#41×C6111yescharacteristic
318D8—44no—
319M16—21no—
320M16—21no—
321M16—21no—
322M16—44no—
323M16D8×C6112yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—42no—
331C2×C8—44no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4C22⋊C4×C6112yes—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—41no—
346C42—41no—
347C42C22×C4×C6111yescharacteristic
348C42C2×D4×C6111yescharacteristic
349C42C2×D4×C6111yescharacteristic
350C42#41×C6111yescharacteristic
351C23—22no—
352C23—41no—
353C23#121×C6111yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—41no—
357Q8—41no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—42no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—81no—
371D4—81no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4C2×C22⋊C4×C6111yescharacteristic
385C2×C4C4×D4×C6111yescharacteristic
386C2×C4C4×D4×C6111yescharacteristic
387C2×C4#120×C6111yescharacteristic
388C2×C4#121×C6111yescharacteristic
389C2×C4#123×C6111yescharacteristic
390C2×C4C2×D8×C6111yescharacteristic
391C2×C4#135×C6111yescharacteristic
392C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
393C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
394C8—22no—
395C8—22no—
396C8—41no—
397C8—41no—
398C8—41no—
399C8—41no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C61×#38611yescharacteristic
410C22C61×#45911yescharacteristic
411C22C61×#46311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—82no—
417C4—81no—
418C4C4×D8×C6111yescharacteristic
419C4C61×#44211yescharacteristic
420C4C61×#44311yescharacteristic
421C4C61×#44411yescharacteristic
422C4C61×#44711yescharacteristic
423C4C61×#44911yescharacteristic
424C2—21no—
425C2—21no—
426C2—82no—
427C2—161no—
428C2C61×#187611yescharacteristic
429C2C61×#187911yescharacteristic
430C2C61×#188411yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#386
prime radicalC61×#3169C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2935C2semidirect
3. C61×#1980C2semidirect
4. C61×#1502C2semidirect
5. C61×#1480C2semidirect
6. C61×#1279C2semidirect
7. C61×#1278C2semidirect
11. C61×#500C4semidirect
12. C61×#493C4semidirect
13. C61×#486C4semidirect
14. C61×#486C4semidirect
107. M16×C61D8semidirect
185. #9053C61direct (N × H)
210. #2935C2×C61semidirect
211. #1980C2×C61semidirect
212. #1502C2×C61semidirect
213. #1480C2×C61semidirect
214. #1279C2×C61semidirect
215. #1278C2×C61semidirect
226. #500C4×C61semidirect
227. #493C4×C61semidirect
228. #486C4×C61semidirect
229. #486C4×C61semidirect
246. C61#9053direct (N × H)
323. M16D8×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31692
C61×#29352
C61×#19802
C61×#15022
C61×#14802
C61×#12792
C61×#12782
#905361