Finite Group Databasebeta

← C61×#9816 #29513249

Subgroups — C61×#9816 #29513249

Order 15616.

510 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
1C2×C61×#465C211yesmaximal, characteristic
2C61×#1810C211yesmaximal, characteristic, complemented
3C61×#1752C211yesmaximal, characteristic, complemented
4C61×#1508C211yesmaximal, characteristic, complemented
5C61×#1507C211yesmaximal, characteristic
6C61×#1472C211yesmaximal, characteristic, complemented
7C61×#1471C211yesmaximal, characteristic
8C22×SD16×C61C411yescharacteristic, complemented
9C23×C8×C61C2211yescharacteristic
10C2×C22⋊Q8×C61C2211yescharacteristic
11C2×#121×C61C2211yescharacteristic
12C61×#465—21no—
13C61×#465—21no—
14C61×#465—21no—
15C61×#465—21no—
16C2×#108×C61—21no—
17C2×#106×C61C411yescharacteristic, complemented
18C2×#103×C61C411yescharacteristic, complemented
19C2×#102×C61C411yescharacteristic, complemented
20C61×#407C2211yescharacteristic
21C61×#407C2211yescharacteristic
22C2×C22⋊C8×C61C2211yescharacteristic
23C2×#97×C61—21no—
24C4×C22⋊C4×C61C2211yescharacteristic
25C61×#341—21no—
26C61×#336—21no—
27C61×#328—22no—
28C61×#327—22no—
29C61×#324—22no—
30C61×#323—22no—
31C22×Q8×C61C2×C411yescharacteristic
32C22×D4×C61—21no—
33C22×D4×C61C2×C411yescharacteristic
34C23×C4×C61C2311yescharacteristic
35C2×SD16×C61—21no—
36C2×SD16×C61—21no—
37C2×SD16×C61—42no—
38C2×M16×C61—21no—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C22×C8×C61—42no—
42C22×C8×C61C2×C411yescharacteristic
43C22×C8×C61C2×C411yescharacteristic
44C22×C8×C61D411yescharacteristic
45C22×C8×C61D411yescharacteristic
46C22×C8×C61D411yescharacteristic
47C22×C8×C61D411yescharacteristic
48C22⋊Q8×C61—21no—
49C22⋊Q8×C61—21no—
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52#121×C61—21no—
53#121×C61—21no—
54#121×C61—21no—
55#121×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61—21no—
63#108×C61—42no—
64#106×C61—21no—
65#106×C61—21no—
66#103×C61—21no—
67#103×C61—21no—
68#102×C61—21no—
69#102×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61D412yes—
76#97×C61—42no—
77#95×C61D412yes—
78C24×C61—21no—
79C24×C61#4111yescharacteristic
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—41no—
83C2×Q8×C61—41no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—82no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103SD16×C61—42no—
104SD16×C61—42no—
105M16×C61—41no—
106M16×C61—41no—
107M16×C61—41no—
108M16×C61—41no—
109C2×C8×C61—22no—
110C2×C8×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C2×C8×C61C22⋊C411yescharacteristic
121C2×C8×C61C22⋊C411yescharacteristic
122C2×C8×C61C22⋊C411yescharacteristic
123C2×C8×C61C22⋊C411yescharacteristic
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C22⋊C4×C61—42no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C42×C61—41no—
136C42×C61—41no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—42no—
142C23×C61—81no—
143C23×C61—81no—
144C23×C61C4×D411yescharacteristic
145C23×C61#12111yescharacteristic
146C23×C61#12411yescharacteristic
147Q8×C61—41no—
148Q8×C61—41no—
149Q8×C61—81no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—81no—
153D4×C61—82no—
154D4×C61—82no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12711yescharacteristic
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—21no—
180C8×C61—42no—
181C8×C61—81no—
182C8×C61—81no—
183C8×C61#9912yes—
184#9816C6111yesmaximal, characteristic, direct product factor, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—44no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—162no—
197C22×C61#39011yescharacteristic
198C22×C61#44412yes—
199C22×C61#47112yes—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—82no—
204C4×C61—81no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61C2×#9911yescharacteristic
208C4×C61#41011yescharacteristic
209C2×#465C2×C6111yescharacteristic
210#1810C2×C6111yescharacteristic, complemented
211#1752C2×C6111yescharacteristic, complemented
212#1508C2×C6111yescharacteristic, complemented
213#1507C2×C6111yescharacteristic
214#1472C2×C6111yescharacteristic, complemented
215#1471C2×C6111yescharacteristic
216C2×C61—22no—
217C2×C61—22no—
218C2×C61—41no—
219C2×C61—161no—
220C2×C61#196411yescharacteristic
221C2×C61#197511yescharacteristic
222C2×C61#197711yescharacteristic
223C22×SD16C4×C6111yescharacteristic, complemented
224C23×C8C22×C6111yescharacteristic
225C2×C22⋊Q8C22×C6111yescharacteristic
226C2×#121C22×C6111yescharacteristic
227#465—21no—
228#465—21no—
229#465—21no—
230#465—21no—
231C2×#108—21no—
232C2×#106C4×C6111yescharacteristic, complemented
233C2×#103C4×C6111yescharacteristic, complemented
234C2×#102C4×C6111yescharacteristic, complemented
235#407C22×C6111yescharacteristic
236#407C22×C6111yescharacteristic
237C2×C22⋊C8C22×C6111yescharacteristic
238C2×#97—21no—
239C4×C22⋊C4C22×C6111yescharacteristic
240#341—21no—
241#336—21no—
242#328—22no—
243#327—22no—
244#324—22no—
245#323—22no—
246C61#981611yescharacteristic, direct product factor, Sylow
247C22×Q8C2×C4×C6111yescharacteristic
248C22×D4—21no—
249C22×D4C2×C4×C6111yescharacteristic
250C23×C4C23×C6111yescharacteristic
251C2×SD16—21no—
252C2×SD16—21no—
253C2×SD16—42no—
254C2×M16—21no—
255C2×M16—21no—
256C22×C8—21no—
257C22×C8—42no—
258C22×C8C2×C4×C6111yescharacteristic
259C22×C8C2×C4×C6111yescharacteristic
260C22×C8D4×C6111yescharacteristic
261C22×C8D4×C6111yescharacteristic
262C22×C8D4×C6111yescharacteristic
263C22×C8D4×C6111yescharacteristic
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C2×C4×C6111yescharacteristic
274C2×C4⋊C4C2×C4×C6111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C42—21no—
279#108—42no—
280#106—21no—
281#106—21no—
282#103—21no—
283#103—21no—
284#102—21no—
285#102—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8D4×C6112yes—
292#97—42no—
293#95D4×C6112yes—
294C24—21no—
295C24#41×C6111yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—82no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C22×C4×C6111yescharacteristic
314C22×C4C2×D4×C6111yescharacteristic
315C22×C4C2×D4×C6111yescharacteristic
316C22×C4C2×D4×C6111yescharacteristic
317C22×C4C2×D4×C6111yescharacteristic
318C22×C4#41×C6111yescharacteristic
319SD16—42no—
320SD16—42no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8C22⋊C4×C6111yescharacteristic
337C2×C8C22⋊C4×C6111yescharacteristic
338C2×C8C22⋊C4×C6111yescharacteristic
339C2×C8C22⋊C4×C6111yescharacteristic
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C22⋊C4—42no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23C4×D4×C6111yescharacteristic
361C23#121×C6111yescharacteristic
362C23#124×C6111yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—81no—
369D4—82no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C2×C22⋊C4×C6111yescharacteristic
390C2×C4C4×D4×C6111yescharacteristic
391C2×C4#121×C6111yescharacteristic
392C2×C4#127×C6111yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—81no—
398C8—81no—
399C8#99×C6112yes—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22C61×#39011yescharacteristic
413C22C61×#44412yes—
414C22C61×#47112yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—82no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4C2×#99×C6111yescharacteristic
423C4C61×#41011yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2C61×#196411yescharacteristic
429C2C61×#197511yescharacteristic
430C2C61×#197711yescharacteristic
subgroupG/H
center, socleC22×C61#390
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1810C2semidirect
3. C61×#1752C2semidirect
4. C61×#1508C2semidirect
6. C61×#1472C2semidirect
8. C22×SD16×C61C4semidirect
17. C2×#106×C61C4semidirect
18. C2×#103×C61C4semidirect
19. C2×#102×C61C4semidirect
184. #9816C61direct (N × H)
210. #1810C2×C61semidirect
211. #1752C2×C61semidirect
212. #1508C2×C61semidirect
214. #1472C2×C61semidirect
223. C22×SD16C4×C61semidirect
232. C2×#106C4×C61semidirect
233. C2×#103C4×C61semidirect
234. C2×#102C4×C61semidirect
246. C61#9816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4652
C61×#18102
C61×#17522
C61×#15082
C61×#15072
C61×#14722
C61×#14712
#981661