Finite Group Databasebeta

← C61×#13308 #29516741

Subgroups — C61×#13308 #29516741

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#510C211yesmaximal, characteristic, complemented
2C2×C61×#473C211yesmaximal, characteristic, complemented
3C61×#3061C211yesmaximal, characteristic
4C2×C61×#359C211yesmaximal, characteristic, complemented
5C2×C61×#358C211yesmaximal, characteristic, complemented
6C2×C61×#350C211yesmaximal, characteristic, complemented
7C61×#1387C211yesmaximal, characteristic, complemented
8C2×#137×C61—21no—
9C2×#135×C61C2211yescharacteristic
10C22×Q16×C61C2211yescharacteristic
11C2×#131×C61C2211yescharacteristic
12C61×#537—21no—
13C61×#510—22no—
14C61×#510—22no—
15C2×Q32×C61—21no—
16C2×SD32×C61—21no—
17C2×M32×C61C2211yescharacteristic
18C22×C16×C61C2211yescharacteristic
19C61×#473—22no—
20C61×#473—22no—
21C61×#468—22no—
22C61×#467—21no—
23C61×#466—21no—
24C2×#108×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C61×#417—21no—
27C2×#101×C61—21no—
28C61×#359—22no—
29C61×#358—22no—
30C61×#350—22no—
31C2×#41×C61—21no—
32C2×#41×C61D411yescharacteristic
33C22×Q8×C61—21no—
34#137×C61—24no—
35#137×C61—42no—
36#135×C61—21no—
37#135×C61—21no—
38#135×C61—21no—
39#135×C61—21no—
40C2×Q16×C61—21no—
41C2×Q16×C61—21no—
42C2×Q16×C61—21no—
43C2×Q16×C61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61—41no—
46C2×Q16×C61D411yescharacteristic
47C2×Q16×C61D412yescomplemented
48C2×SD16×C61—21no—
49C2×SD16×C61—41no—
50C2×D8×C61D411yescharacteristic
51#131×C61—21no—
52#131×C61—21no—
53#131×C61—21no—
54#131×C61—21no—
55C2×M16×C61—21no—
56C2×M16×C61—21no—
57C2×M16×C61D411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61C2311yescharacteristic
60C22⋊Q8×C61—22no—
61C22⋊Q8×C61—41no—
62#121×C61—22no—
63#121×C61—42no—
64#121×C61—41no—
65C2×C4⋊C4×C61—21no—
66Q32×C61—24no—
67SD32×C61—24no—
68M32×C61—21no—
69M32×C61D412yescomplemented
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61—21no—
73C2×C16×C61—21no—
74#108×C61—21no—
75#108×C61D412yescomplemented
76#107×C61—21no—
77#107×C61D412yes—
78#103×C61—22no—
79#102×C61—22no—
80#101×C61—24no—
81#41×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84#41×C61—21no—
85#41×C61—41no—
86#41×C61—41no—
87#41×C61—41no—
88#41×C61—41no—
89C2×Q8×C61—22no—
90C2×Q8×C61—21no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C2×Q8×C61—41no—
94C2×Q8×C61—41no—
95C2×Q8×C61—41no—
96C2×Q8×C61D811yescharacteristic
97C2×D4×C61—21no—
98C2×D4×C61—21no—
99C2×D4×C61—41no—
100C2×D4×C61—42no—
101C2×D4×C61D811yescharacteristic
102C22×C4×C61—21no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61C2×D411yescharacteristic
107Q16×C61—22no—
108Q16×C61—21no—
109Q16×C61—22no—
110Q16×C61—21no—
111Q16×C61—44no—
112Q16×C61—41no—
113Q16×C61—41no—
114SD16×C61—44no—
115SD16×C61—41no—
116SD16×C61—41no—
117D8×C61—21no—
118D8×C61—21no—
119M16×C61—21no—
120M16×C61—22no—
121M16×C61—21no—
122M16×C61—41no—
123M16×C61—41no—
124M16×C61—41no—
125C2×C8×C61—21no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61#4111yescharacteristic
135C4⋊C4×C61—22no—
136C4⋊C4×C61—42no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—42no—
139C22⋊C4×C61—42no—
140C16×C61—22no—
141C16×C61—41no—
142C23×C61—21no—
143C23×C61—41no—
144C23×C61AGL(1,ℤ/8)11yescharacteristic
145Q8×C61—21no—
146Q8×C61—21no—
147Q8×C61—41no—
148Q8×C61—42no—
149Q8×C61—42no—
150Q8×C61—41no—
151Q8×C61—81no—
152Q8×C61—81no—
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—41no—
156D4×C61—41no—
157D4×C61—41no—
158D4×C61—41no—
159D4×C61—81no—
160D4×C61—81no—
161D4×C61—162no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61—161no—
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61#13511yescharacteristic
178C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
179C8×C61—41no—
180C8×C61—42no—
181C8×C61#12011yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61#12111yescharacteristic
184C8×C61#12711yescharacteristic
185#13308C6111yesmaximal, characteristic, direct product factor, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61#44711yescharacteristic
195C22×C61#44911yescharacteristic
196C22×C61#46911yescharacteristic
197C4×C61—41no—
198C4×C61—82no—
199C4×C61—81no—
200C4×C61—82no—
201C4×C61#39211yescharacteristic
202C4×C61#44711yescharacteristic
203C4×C61#44911yescharacteristic
204C4×C61#46611yescharacteristic
205C2×#510C2×C6111yescharacteristic, complemented
206C2×#473C2×C6111yescharacteristic, complemented
207#3061C2×C6111yescharacteristic
208C2×#359C2×C6111yescharacteristic, complemented
209C2×#358C2×C6111yescharacteristic, complemented
210C2×#350C2×C6111yescharacteristic, complemented
211#1387C2×C6111yescharacteristic, complemented
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—81no—
215C2×C61—161no—
216C2×C61#199911yescharacteristic
217C2×C61#219411yescharacteristic
218C2×C61#219511yescharacteristic
219C2×#137—21no—
220C2×#135C22×C6111yescharacteristic
221C22×Q16C22×C6111yescharacteristic
222C2×#131C22×C6111yescharacteristic
223#537—21no—
224#510—22no—
225#510—22no—
226C2×Q32—21no—
227C2×SD32—21no—
228C2×M32C22×C6111yescharacteristic
229C22×C16C22×C6111yescharacteristic
230#473—22no—
231#473—22no—
232#468—22no—
233#467—21no—
234#466—21no—
235C2×#108C22×C6111yescharacteristic
236C2×#107C22×C6111yescharacteristic
237#417—21no—
238C2×#101—21no—
239#359—22no—
240#358—22no—
241#350—22no—
242C61#1330811yescharacteristic, direct product factor, Sylow
243C2×#41—21no—
244C2×#41D4×C6111yescharacteristic
245C22×Q8—21no—
246#137—24no—
247#137—42no—
248#135—21no—
249#135—21no—
250#135—21no—
251#135—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—41no—
258C2×Q16D4×C6111yescharacteristic
259C2×Q16D4×C6112yescomplemented
260C2×SD16—21no—
261C2×SD16—41no—
262C2×D8D4×C6111yescharacteristic
263#131—21no—
264#131—21no—
265#131—21no—
266#131—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16D4×C6111yescharacteristic
270C22×C8—21no—
271C22×C8C23×C6111yescharacteristic
272C22⋊Q8—22no—
273C22⋊Q8—41no—
274#121—22no—
275#121—42no—
276#121—41no—
277C2×C4⋊C4—21no—
278Q32—24no—
279SD32—24no—
280M32—21no—
281M32D4×C6112yescomplemented
282C2×C16—21no—
283C2×C16—21no—
284C2×C16—21no—
285C2×C16—21no—
286#108—21no—
287#108D4×C6112yescomplemented
288#107—21no—
289#107D4×C6112yes—
290#103—22no—
291#102—22no—
292#101—24no—
293#41—21no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—22no—
302C2×Q8—21no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8D8×C6111yescharacteristic
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4D8×C6111yescharacteristic
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C6111yescharacteristic
319Q16—22no—
320Q16—21no—
321Q16—22no—
322Q16—21no—
323Q16—44no—
324Q16—41no—
325Q16—41no—
326SD16—44no—
327SD16—41no—
328SD16—41no—
329D8—21no—
330D8—21no—
331M16—21no—
332M16—22no—
333M16—21no—
334M16—41no—
335M16—41no—
336M16—41no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8C2×D4×C6111yescharacteristic
342C2×C8C2×D4×C6111yescharacteristic
343C2×C8C2×D4×C6111yescharacteristic
344C2×C8C2×D4×C6111yescharacteristic
345C2×C8C2×D4×C6111yescharacteristic
346C2×C8#41×C6111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—42no—
349C4⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C16—22no—
353C16—41no—
354C23—21no—
355C23—41no—
356C23AGL(1,ℤ/8)×C6111yescharacteristic
357Q8—21no—
358Q8—21no—
359Q8—41no—
360Q8—42no—
361Q8—42no—
362Q8—41no—
363Q8—81no—
364Q8—81no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371D4—81no—
372D4—81no—
373D4—162no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—161no—
385C2×C4#120×C6111yescharacteristic
386C2×C4#120×C6111yescharacteristic
387C2×C4#121×C6111yescharacteristic
388C2×C4C2×D8×C6111yescharacteristic
389C2×C4#135×C6111yescharacteristic
390C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
391C8—41no—
392C8—42no—
393C8#120×C6111yescharacteristic
394C8#121×C6111yescharacteristic
395C8#121×C6111yescharacteristic
396C8#127×C6111yescharacteristic
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C61×#44711yescharacteristic
406C22C61×#44911yescharacteristic
407C22C61×#46911yescharacteristic
408C4—41no—
409C4—82no—
410C4—81no—
411C4—82no—
412C4C61×#39211yescharacteristic
413C4C61×#44711yescharacteristic
414C4C61×#44911yescharacteristic
415C4C61×#46611yescharacteristic
416C2—21no—
417C2—21no—
418C2—81no—
419C2—161no—
420C2C61×#199911yescharacteristic
421C2C61×#219411yescharacteristic
422C2C61×#219511yescharacteristic
subgroupG/H
center, socleC22×C61#447
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3061C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#510C2semidirect
2. C2×C61×#473C2semidirect
4. C2×C61×#359C2semidirect
5. C2×C61×#358C2semidirect
6. C2×C61×#350C2semidirect
7. C61×#1387C2semidirect
47. C2×Q16×C61D4semidirect
69. M32×C61D4semidirect
75. #108×C61D4semidirect
185. #13308C61direct (N × H)
205. C2×#510C2×C61semidirect
206. C2×#473C2×C61semidirect
208. C2×#359C2×C61semidirect
209. C2×#358C2×C61semidirect
210. C2×#350C2×C61semidirect
211. #1387C2×C61semidirect
242. C61#13308direct (N × H)
259. C2×Q16D4×C61semidirect
281. M32D4×C61semidirect
287. #108D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5102
C2×C61×#4732
C61×#30612
C2×C61×#3592
C2×C61×#3582
C2×C61×#3502
C61×#13872
#1330861