Finite Group Databasebeta

← C61×#8995 #29512428

Subgroups — C61×#8995 #29512428

Order 15616.

530 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
1C61×#3035C211yesmaximal, characteristic
2C61×#2906C211yesmaximal, characteristic, complemented
3C61×#1492C211yesmaximal, characteristic, complemented
4C61×#1480C211yesmaximal, characteristic, complemented
5C61×#1476C211yesmaximal, characteristic, complemented
6C61×#1301C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×#135×C61—21no—
9C2×#131×C61—21no—
10C61×#532C2211yescharacteristic
11C4×#41×C61C2211yescharacteristic
12C61×#464—21no—
13C61×#463—21no—
14C61×#462C411yescharacteristic
15C61×#461C411yescharacteristic
16C61×#460C411yescharacteristic
17C61×#459C411yescharacteristic
18C61×#431C2211yescharacteristic
19C61×#424—21no—
20C61×#424—22no—
21C61×#423—21no—
22C61×#423C2211yescharacteristic
23C2×C4⋊C8×C61—21no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#416—21no—
27C2×C4×C8×C61C2211yescharacteristic
28C61×Q8⋊C8—21no—
29C61×D4⋊C8—21no—
30C61×D4⋊C8—21no—
31C61×D4⋊C8—21no—
32C61×D4⋊C8—22no—
33C2×#41×C61—21no—
34C2×#41×C61D411yescharacteristic
35#135×C61—42no—
36#135×C61—42no—
37C2×Q16×C61—21no—
38C2×SD16×C61—21no—
39C2×SD16×C61—21no—
40C2×D8×C61—21no—
41#131×C61—42no—
42#131×C61—42no—
43C2×M16×C61—22no—
44C2×M16×C61—21no—
45C22×C8×C61—22no—
46C22×C8×C61—21no—
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C4⋊Q8×C61C2×C411yescharacteristic
50#127×C61C2×C411yescharacteristic
51#124×C61—21no—
52#121×C61—21no—
53#121×C61—21no—
54C4×Q8×C61C2×C411yescharacteristic
55C4×Q8×C61D411yescharacteristic
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58C4×D4×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61C2×C411yescharacteristic
61C4×D4×C61D411yescharacteristic
62#117×C61—21no—
63#117×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—22no—
67C4⋊C8×C61—22no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61C2×C411yescharacteristic
73C4⋊C8×C61C2×C411yescharacteristic
74C4⋊C8×C61D411yescharacteristic
75C4⋊C8×C61D411yescharacteristic
76C4⋊C8×C61D412yes—
77#103×C61—21no—
78#103×C61—21no—
79#102×C61—21no—
80#102×C61—21no—
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83C4×C8×C61—21no—
84C4×C8×C61—21no—
85#41×C61—21no—
86#41×C61—21no—
87#41×C61—41no—
88#41×C61—41no—
89#41×C61—41no—
90#41×C61—41no—
91#41×C61D812yes—
92#41×C61SD1612yes—
93C2×Q8×C61—21no—
94C2×Q8×C61C22⋊C411yescharacteristic
95C2×D4×C61—21no—
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—21no—
99C2×D4×C61—41no—
100C2×D4×C61C22⋊C411yescharacteristic
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—41no—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C22×C4×C61#4111yescharacteristic
108Q16×C61—42no—
109SD16×C61—42no—
110SD16×C61—42no—
111D8×C61—42no—
112M16×C61—44no—
113M16×C61—41no—
114M16×C61—41no—
115C2×C8×C61—22no—
116C2×C8×C61—21no—
117C2×C8×C61—21no—
118C2×C8×C61—21no—
119C2×C8×C61—22no—
120C2×C8×C61—21no—
121C2×C8×C61—41no—
122C2×C8×C61—44no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61C22⋊C411yescharacteristic
134C4⋊C4×C61C22⋊C411yescharacteristic
135C22⋊C4×C61—21no—
136C22⋊C4×C61—21no—
137C22⋊C4×C61—21no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61—21no—
141C42×C61—21no—
142C42×C61—21no—
143C42×C61C22×C411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C23×C61—21no—
148C23×C61—41no—
149C23×C61#12311yescharacteristic
150Q8×C61—21no—
151Q8×C61—41no—
152Q8×C61—41no—
153Q8×C61#10212yes—
154D4×C61—22no—
155D4×C61—22no—
156D4×C61—21no—
157D4×C61—42no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61—41no—
161D4×C61—41no—
162D4×C61—81no—
163D4×C61—81no—
164D4×C61#10212yes—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—81no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C4×D411yescharacteristic
181C2×C4×C61C4×D411yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×SD1611yescharacteristic
187C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C61#13711yescharacteristic
189C8×C61—42no—
190C8×C61—41no—
191C8×C61—41no—
192C8×C61—41no—
193C8×C61—42no—
194C8×C61—41no—
195C8×C61—81no—
196#8995C6111yesmaximal, characteristic, direct product factor, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—22no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61#38611yescharacteristic
206C22×C61#48011yescharacteristic
207C22×C61#48111yescharacteristic
208C4×C61—22no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61—81no—
215C4×C61C2×#10211yescharacteristic
216C4×C61#41711yescharacteristic
217C4×C61#44311yescharacteristic
218C4×C61#44411yescharacteristic
219C4×C61#44711yescharacteristic
220C4×C61#44811yescharacteristic
221#3035C2×C6111yescharacteristic
222#2906C2×C6111yescharacteristic, complemented
223#1492C2×C6111yescharacteristic, complemented
224#1480C2×C6111yescharacteristic, complemented
225#1476C2×C6111yescharacteristic, complemented
226#1301C2×C6111yescharacteristic, complemented
227#1277C2×C6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—42no—
231C2×C61—161no—
232C2×C61#187411yescharacteristic
233C2×C61#187611yescharacteristic
234C2×C61#188111yescharacteristic
235C2×#135—21no—
236C2×#131—21no—
237#532C22×C6111yescharacteristic
238C4×#41C22×C6111yescharacteristic
239#464—21no—
240#463—21no—
241#462C4×C6111yescharacteristic
242#461C4×C6111yescharacteristic
243#460C4×C6111yescharacteristic
244#459C4×C6111yescharacteristic
245#431C22×C6111yescharacteristic
246#424—21no—
247#424—22no—
248#423—21no—
249#423C22×C6111yescharacteristic
250C2×C4⋊C8—21no—
251C2×C4⋊C8C22×C6111yescharacteristic
252C2×C4⋊C8C22×C6111yescharacteristic
253#416—21no—
254C2×C4×C8C22×C6111yescharacteristic
255Q8⋊C8—21no—
256D4⋊C8—21no—
257D4⋊C8—21no—
258D4⋊C8—21no—
259D4⋊C8—22no—
260C61#899511yescharacteristic, direct product factor, Sylow
261C2×#41—21no—
262C2×#41D4×C6111yescharacteristic
263#135—42no—
264#135—42no—
265C2×Q16—21no—
266C2×SD16—21no—
267C2×SD16—21no—
268C2×D8—21no—
269#131—42no—
270#131—42no—
271C2×M16—22no—
272C2×M16—21no—
273C22×C8—22no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C4⋊Q8C2×C4×C6111yescharacteristic
278#127C2×C4×C6111yescharacteristic
279#124—21no—
280#121—21no—
281#121—21no—
282C4×Q8C2×C4×C6111yescharacteristic
283C4×Q8D4×C6111yescharacteristic
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4C2×C4×C6111yescharacteristic
289C4×D4D4×C6111yescharacteristic
290#117—21no—
291#117D4×C6111yescharacteristic
292C2×C42—21no—
293C2×C42C23×C6111yescharacteristic
294C4⋊C8—22no—
295C4⋊C8—22no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8C2×C4×C6111yescharacteristic
301C4⋊C8C2×C4×C6111yescharacteristic
302C4⋊C8D4×C6111yescharacteristic
303C4⋊C8D4×C6111yescharacteristic
304C4⋊C8D4×C6112yes—
305#103—21no—
306#103—21no—
307#102—21no—
308#102—21no—
309C22⋊C8—21no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313#41—21no—
314#41—21no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41D8×C6112yes—
320#41SD16×C6112yes—
321C2×Q8—21no—
322C2×Q8C22⋊C4×C6111yescharacteristic
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4C22⋊C4×C6111yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4C2×D4×C6111yescharacteristic
334C22×C4#41×C6111yescharacteristic
335C22×C4#41×C6111yescharacteristic
336Q16—42no—
337SD16—42no—
338SD16—42no—
339D8—42no—
340M16—44no—
341M16—41no—
342M16—41no—
343C2×C8—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—44no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊C4×C6111yescharacteristic
362C4⋊C4C22⋊C4×C6111yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42C22×C4×C6111yescharacteristic
372C42C2×D4×C6111yescharacteristic
373C42C2×D4×C6111yescharacteristic
374C42C2×D4×C6111yescharacteristic
375C23—21no—
376C23—41no—
377C23#123×C6111yescharacteristic
378Q8—21no—
379Q8—41no—
380Q8—41no—
381Q8#102×C6112yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—42no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4#102×C6112yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4C2×C22⋊C4×C6111yescharacteristic
408C2×C4C4×D4×C6111yescharacteristic
409C2×C4C4×D4×C6111yescharacteristic
410C2×C4#120×C6111yescharacteristic
411C2×C4#121×C6111yescharacteristic
412C2×C4#121×C6111yescharacteristic
413C2×C4C2×D8×C6111yescharacteristic
414C2×C4C2×SD16×C6111yescharacteristic
415C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
416C2×C4#137×C6111yescharacteristic
417C8—42no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—42no—
422C8—41no—
423C8—81no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C61×#38611yescharacteristic
433C22C61×#48011yescharacteristic
434C22C61×#48111yescharacteristic
435C4—22no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4C2×#102×C6111yescharacteristic
443C4C61×#41711yescharacteristic
444C4C61×#44311yescharacteristic
445C4C61×#44411yescharacteristic
446C4C61×#44711yescharacteristic
447C4C61×#44811yescharacteristic
448C2—21no—
449C2—21no—
450C2—42no—
451C2—161no—
452C2C61×#187411yescharacteristic
453C2C61×#187611yescharacteristic
454C2C61×#188111yescharacteristic
subgroupG/H
centerC2×C4×C61#120
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#386
prime radicalC61×#3035C2
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×#2906C2semidirect
3. C61×#1492C2semidirect
4. C61×#1480C2semidirect
5. C61×#1476C2semidirect
6. C61×#1301C2semidirect
7. C61×#1277C2semidirect
196. #8995C61direct (N × H)
222. #2906C2×C61semidirect
223. #1492C2×C61semidirect
224. #1480C2×C61semidirect
225. #1476C2×C61semidirect
226. #1301C2×C61semidirect
227. #1277C2×C61semidirect
260. C61#8995direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30352
C61×#29062
C61×#14922
C61×#14802
C61×#14762
C61×#13012
C61×#12772
#899561