Finite Group Databasebeta

← C61×#10198 #29513631

Subgroups — C61×#10198 #29513631

Order 15616.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3246C211yesmaximal, characteristic
2C61×#3209C211yesmaximal, characteristic, complemented
3C61×#3141C211yesmaximal, characteristic
4C61×#1987C211yesmaximal, characteristic, complemented
5C61×#1986C211yesmaximal, characteristic, complemented
6C61×#1502C211yesmaximal, characteristic
7C61×#1283C211yesmaximal, characteristic, complemented
8C61×#533C2211yescharacteristic
9C61×#532C2211yescharacteristic
10C2×C4⋊Q8×C61C2211yescharacteristic
11C61×#494—21no—
12C61×#489—22no—
13C61×#487—21no—
14C61×#487—21no—
15C61×#486—21no—
16C61×#476—21no—
17C61×#475—21no—
18C61×#465—22no—
19C61×#462—22no—
20C61×#461—21no—
21C61×#460—21no—
22C61×#451—22no—
23C61×#431C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#417—22no—
26C4×M16×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#340—22no—
29C61×#339—22no—
30C61×#327—22no—
31C2×#41×C61—21no—
32C22×Q8×C61—21no—
33C2×Q16×C61—24no—
34C2×SD16×C61—22no—
35C2×M16×C61D412yes—
36C22×C8×C61D412yes—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61D412yes—
41C4⋊Q8×C61D411yescharacteristic
42C4⋊Q8×C61D411yescharacteristic
43C4⋊Q8×C61D411yescharacteristic
44#127×C61D411yescharacteristic
45#125×C61—21no—
46#124×C61—21no—
47C22⋊Q8×C61—21no—
48C22⋊Q8×C61—21no—
49#121×C61—21no—
50#121×C61—21no—
51C4×Q8×C61—21no—
52C4×Q8×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55#117×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61#106×C61—22no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65#103×C61—24no—
66#103×C61—24no—
67#103×C61—22no—
68#102×C61—24no—
69#102×C61—22no—
70C22⋊C8×C61D412yes—
71#97×C61—21no—
72C4×C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61—21no—
75#41×C61—42no—
76#41×C61—42no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—22no—
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—82no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93Q16×C61—84no—
94SD16×C61—82no—
95M16×C61—22no—
96M16×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—42no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C42×C61—42no—
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124C23×C61—41no—
125C23×C61#12711yescharacteristic
126Q8×C61—42no—
127Q8×C61—44no—
128Q8×C61—42no—
129Q8×C61—41no—
130Q8×C61—41no—
131Q8×C61—82no—
132D4×C61—42no—
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—81no—
136D4×C61—81no—
137D4×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—81no—
147C2×C4×C61—82no—
148C2×C4×C61—81no—
149C2×C4×C61—82no—
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#13512yes—
157C2×C4×C61#13712yes—
158C8×C61—42no—
159C8×C61—42no—
160C8×C61—42no—
161#10198C6111yesmaximal, characteristic, direct product factor, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61#39211yescharacteristic
168C22×C61#49511yescharacteristic
169C22×C61#49711yescharacteristic
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—82no—
174C4×C61—81no—
175C4×C61—82no—
176C4×C61—81no—
177C4×C61—81no—
178C4×C61#45212yes—
179C4×C61#45511yescharacteristic
180C4×C61#45611yescharacteristic
181C4×C61#46412yes—
182#3246C2×C6111yescharacteristic
183#3209C2×C6111yescharacteristic, complemented
184#3141C2×C6111yescharacteristic
185#1987C2×C6111yescharacteristic, complemented
186#1986C2×C6111yescharacteristic, complemented
187#1502C2×C6111yescharacteristic
188#1283C2×C6111yescharacteristic, complemented
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—161no—
192C2×C61#200711yescharacteristic
193C2×C61#200811yescharacteristic
194C2×C61#201511yescharacteristic
195#533C22×C6111yescharacteristic
196#532C22×C6111yescharacteristic
197C2×C4⋊Q8C22×C6111yescharacteristic
198#494—21no—
199#489—22no—
200#487—21no—
201#487—21no—
202#486—21no—
203#476—21no—
204#475—21no—
205#465—22no—
206#462—22no—
207#461—21no—
208#460—21no—
209#451—22no—
210#431C22×C6111yescharacteristic
211C2×C4⋊C8C22×C6111yescharacteristic
212#417—22no—
213C4×M16C22×C6111yescharacteristic
214C4×C4⋊C4C22×C6111yescharacteristic
215#340—22no—
216#339—22no—
217#327—22no—
218C61#1019811yescharacteristic, direct product factor, Sylow
219C2×#41—21no—
220C22×Q8—21no—
221C2×Q16—24no—
222C2×SD16—22no—
223C2×M16D4×C6112yes—
224C22×C8D4×C6112yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C6112yes—
229C4⋊Q8D4×C6111yescharacteristic
230C4⋊Q8D4×C6111yescharacteristic
231C4⋊Q8D4×C6111yescharacteristic
232#127D4×C6111yescharacteristic
233#125—21no—
234#124—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237#121—21no—
238#121—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C6111yescharacteristic
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253#103—24no—
254#103—24no—
255#103—22no—
256#102—24no—
257#102—22no—
258C22⋊C8D4×C6112yes—
259#97—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—21no—
263#41—42no—
264#41—42no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C6111yescharacteristic
279C22×C4C2×D4×C6111yescharacteristic
280C22×C4C2×D4×C6111yescharacteristic
281Q16—84no—
282SD16—82no—
283M16—22no—
284M16—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—42no—
308C42C2×D4×C6111yescharacteristic
309C42C2×D4×C6111yescharacteristic
310C42C2×D4×C6111yescharacteristic
311C42#41×C6111yescharacteristic
312C23—41no—
313C23#127×C6111yescharacteristic
314Q8—42no—
315Q8—44no—
316Q8—42no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320D4—42no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4#120×C6111yescharacteristic
339C2×C4#120×C6111yescharacteristic
340C2×C4#120×C6111yescharacteristic
341C2×C4#121×C6111yescharacteristic
342C2×C4#121×C6111yescharacteristic
343C2×C4#121×C6111yescharacteristic
344C2×C4#135×C6112yes—
345C2×C4#137×C6112yes—
346C8—42no—
347C8—42no—
348C8—42no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C61×#39211yescharacteristic
355C22C61×#49511yescharacteristic
356C22C61×#49711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4C61×#45212yes—
366C4C61×#45511yescharacteristic
367C4C61×#45611yescharacteristic
368C4C61×#46412yes—
369C2—21no—
370C2—21no—
371C2—161no—
372C2C61×#200711yescharacteristic
373C2C61×#200811yescharacteristic
374C2C61×#201511yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C2×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×#3209C2semidirect
4. C61×#1987C2semidirect
5. C61×#1986C2semidirect
7. C61×#1283C2semidirect
161. #10198C61direct (N × H)
183. #3209C2×C61semidirect
185. #1987C2×C61semidirect
186. #1986C2×C61semidirect
188. #1283C2×C61semidirect
218. C61#10198direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32462
C61×#32092
C61×#31412
C61×#19872
C61×#19862
C61×#15022
C61×#12832
#1019861