Finite Group Databasebeta

← C61×#18372 #29521805

Subgroups — C61×#18372 #29521805

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3493C211yesmaximal, characteristic
2C61×#3239C212yesmaximal, complemented
3C61×#2628C211yesmaximal, characteristic, complemented
4C61×#1618C214yesmaximal, complemented
5C61×#1617C212yesmaximal, complemented
6C61×#1616C212yesmaximal, complemented
7C61×#1512C212yesmaximal, complemented
8C61×#1464C211yesmaximal, characteristic, complemented
9C61×#556—22no—
10C61×#555—22no—
11C61×#553—22no—
12C61×#552—22no—
13C61×#544C2211yescharacteristic
14C61×#538—21no—
15C61×#538C2212yes—
16C61×#537C2211yescharacteristic
17C2×C4⋊Q8×C61C2211yescharacteristic
18C61×#529—21no—
19C61×#529C2212yes—
20C61×#525—21no—
21C61×#520—21no—
22C2×#117×C61C2211yescharacteristic
23C61×#501—22no—
24C61×#489—22no—
25C61×#484C2214yes—
26C61×#481C2214yes—
27C61×#475—22no—
28C61×#474—22no—
29C61×#432C2212yes—
30C61×#400C2212yes—
31C61×#399C2212yes—
32C61×#395—21no—
33C61×#393—21no—
34C61×#389—21no—
35C61×#382C2211yescharacteristic
36C61×#380—21no—
37C61×#328C2214yes—
38C61×#327C2214yes—
39C61×#324C2212yes—
40C61×#323C2212yes—
41C2×#41×C61—21no—
42C22×Q8×C61—21no—
43C23×C4×C61D411yescharacteristic
44C4⋊Q8×C61—22no—
45C4⋊Q8×C61—22no—
46C4⋊Q8×C61—22no—
47#126×C61—22no—
48#126×C61—22no—
49#126×C61—22no—
50#126×C61—22no—
51#125×C61—21no—
52#125×C61—22no—
53#125×C61D412yes—
54#124×C61—22no—
55#124×C61—21no—
56#124×C61—22no—
57#124×C61D412yes—
58#123×C61—22no—
59#123×C61—22no—
60#123×C61—22no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—22no—
65C22⋊Q8×C61C2312yes—
66#121×C61—22no—
67#121×C61—21no—
68#121×C61—21no—
69#121×C61—22no—
70#121×C61—22no—
71#121×C61—21no—
72#121×C61C2312yes—
73#120×C61—22no—
74C4×Q8×C61—22no—
75C4×Q8×C61—21no—
76C4×Q8×C61D412yes—
77C4×D4×C61—22no—
78C4×D4×C61—21no—
79C4×D4×C61—22no—
80C4×D4×C61—22no—
81C4×D4×C61—22no—
82C4×D4×C61—22no—
83C4×D4×C61D412yes—
84#117×C61—22no—
85#117×C61—22no—
86#117×C61—21no—
87#117×C61—22no—
88#117×C61—22no—
89#117×C61—22no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C4⋊C4×C61C2312yes—
96C2×C4⋊C4×C61C2311yescharacteristic
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61D411yescharacteristic
99C2×C22⋊C4×C61C2311yescharacteristic
100C2×C42×C61D411yescharacteristic
101C2×C42×C61C2311yescharacteristic
102#107×C61—24no—
103#106×C61—24no—
104C4⋊C8×C61—22no—
105#103×C61—24no—
106#102×C61—24no—
107C22⋊C8×C61C2314yes—
108#97×C61—22no—
109#95×C61—22no—
110#95×C61—21no—
111#95×C61—22no—
112#95×C61C2312yes—
113C24×C61C2×D411yescharacteristic
114#41×C61—42no—
115#41×C61—42no—
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—42no—
119C2×Q8×C61—82no—
120C2×Q8×C61C2×D412yes—
121C2×D4×C61—21no—
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61—22no—
125C2×D4×C61—21no—
126C2×D4×C61C2×D412yes—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—41no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C2×C8×C61—24no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—22no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—42no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—82no—
160C4⋊C4×C61C2×D412yes—
161C4⋊C4×C61C2×D412yes—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—82no—
174C42×C61—22no—
175C42×C61—22no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—22no—
179C42×C61C2×D412yes—
180C42×C61C2×D412yes—
181C23×C61—21no—
182C23×C61—22no—
183C23×C61—21no—
184C23×C61—21no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61C22×D411yescharacteristic
188Q8×C61—42no—
189Q8×C61—42no—
190Q8×C61—84no—
191Q8×C61—81no—
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—82no—
197D4×C61—81no—
198D4×C61—82no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—22no—
205C2×C4×C61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—44no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—82no—
222C2×C4×C61—82no—
223C2×C4×C61#12011yescharacteristic
224C2×C4×C61#12011yescharacteristic
225C2×C4×C61#12012yes—
226C2×C4×C61#13712yes—
227C2×C4×C61C22×D412yes—
228C8×C61—44no—
229#18372C6111yesmaximal, characteristic, direct product factor, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—42no—
233C22×C61—41no—
234C22×C61—42no—
235C22×C61—42no—
236C22×C61—41no—
237C22×C61—42no—
238C22×C61—41no—
239C22×C61—81no—
240C22×C61C2×#12011yescharacteristic
241C22×C61C2×#13711yescharacteristic
242C22×C61#57511yescharacteristic
243C4×C61—22no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—22no—
247C4×C61—22no—
248C4×C61—42no—
249C4×C61—41no—
250C4×C61—42no—
251C4×C61—41no—
252C4×C61—42no—
253C4×C61—82no—
254C4×C61—82no—
255#3493C2×C6111yescharacteristic
256#3239C2×C6112yescomplemented
257#2628C2×C6111yescharacteristic, complemented
258#1618C2×C6114yescomplemented
259#1617C2×C6112yescomplemented
260#1616C2×C6112yescomplemented
261#1512C2×C6112yescomplemented
262#1464C2×C6111yescharacteristic, complemented
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—82no—
266C2×C61—81no—
267C2×C61#300711yescharacteristic
268C2×C61#302111yescharacteristic
269C2×C61#302811yescharacteristic
270#556—22no—
271#555—22no—
272#553—22no—
273#552—22no—
274#544C22×C6111yescharacteristic
275#538—21no—
276#538C22×C6112yes—
277#537C22×C6111yescharacteristic
278C2×C4⋊Q8C22×C6111yescharacteristic
279#529—21no—
280#529C22×C6112yes—
281#525—21no—
282#520—21no—
283C2×#117C22×C6111yescharacteristic
284#501—22no—
285#489—22no—
286#484C22×C6114yes—
287#481C22×C6114yes—
288#475—22no—
289#474—22no—
290#432C22×C6112yes—
291#400C22×C6112yes—
292#399C22×C6112yes—
293#395—21no—
294#393—21no—
295#389—21no—
296#382C22×C6111yescharacteristic
297#380—21no—
298#328C22×C6114yes—
299#327C22×C6114yes—
300#324C22×C6112yes—
301#323C22×C6112yes—
302C61#1837211yescharacteristic, direct product factor, Sylow
303C2×#41—21no—
304C22×Q8—21no—
305C23×C4D4×C6111yescharacteristic
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#126—22no—
310#126—22no—
311#126—22no—
312#126—22no—
313#125—21no—
314#125—22no—
315#125D4×C6112yes—
316#124—21no—
317#124—22no—
318#124—22no—
319#124D4×C6112yes—
320#123—22no—
321#123—22no—
322#123—22no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—22no—
327C22⋊Q8C23×C6112yes—
328#121—21no—
329#121—21no—
330#121—22no—
331#121—22no—
332#121—22no—
333#121—21no—
334#121C23×C6112yes—
335#120—22no—
336C4×Q8—22no—
337C4×Q8—21no—
338C4×Q8D4×C6112yes—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—21no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4D4×C6112yes—
346#117—22no—
347#117—22no—
348#117—21no—
349#117—22no—
350#117—22no—
351#117—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C6111yescharacteristic
357C2×C4⋊C4C23×C6112yes—
358C2×C4⋊C4C23×C6111yescharacteristic
359C2×C22⋊C4—22no—
360C2×C22⋊C4D4×C6111yescharacteristic
361C2×C22⋊C4C23×C6111yescharacteristic
362C2×C42D4×C6111yescharacteristic
363C2×C42C23×C6111yescharacteristic
364#107—24no—
365#106—24no—
366C4⋊C8—22no—
367#103—24no—
368#102—24no—
369C22⋊C8C23×C6114yes—
370#97—22no—
371#95—22no—
372#95—21no—
373#95—22no—
374#95C23×C6112yes—
375C24C2×D4×C6111yescharacteristic
376#41—42no—
377#41—42no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8—82no—
382C2×Q8C2×D4×C6112yes—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4C2×D4×C6112yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—41no—
398C22×C4C2×D4×C6111yescharacteristic
399C22×C4C2×D4×C6111yescharacteristic
400C22×C4C2×D4×C6111yescharacteristic
401C22×C4C2×D4×C6111yescharacteristic
402C22×C4C2×D4×C6111yescharacteristic
403C22×C4C24×C6111yescharacteristic
404C2×C8—24no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—42no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—82no—
422C4⋊C4C2×D4×C6112yes—
423C4⋊C4C2×D4×C6112yes—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—82no—
436C42—22no—
437C42—22no—
438C42—21no—
439C42—21no—
440C42—22no—
441C42C2×D4×C6112yes—
442C42C2×D4×C6112yes—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23C22×D4×C6111yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—84no—
453Q8—81no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—81no—
460D4—82no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4#120×C6111yescharacteristic
486C2×C4#120×C6111yescharacteristic
487C2×C4#120×C6112yes—
488C2×C4#137×C6112yes—
489C2×C4C22×D4×C6112yes—
490C8—44no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—81no—
501C22C2×#120×C6111yescharacteristic
502C22C2×#137×C6111yescharacteristic
503C22C61×#57511yescharacteristic
504C4—22no—
505C4—21no—
506C4—21no—
507C4—22no—
508C4—22no—
509C4—42no—
510C4—41no—
511C4—42no—
512C4—41no—
513C4—42no—
514C4—82no—
515C4—82no—
516C2—21no—
517C2—21no—
518C2—81no—
519C2—82no—
520C2C61×#300711yescharacteristic
521C2C61×#302111yescharacteristic
522C2C61×#302811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3493C2
LCSG ▷ C22×C4 ▷ 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×#3239C2semidirect
3. C61×#2628C2semidirect
4. C61×#1618C2semidirect
5. C61×#1617C2semidirect
6. C61×#1616C2semidirect
7. C61×#1512C2semidirect
8. C61×#1464C2semidirect
229. #18372C61direct (N × H)
256. #3239C2×C61semidirect
257. #2628C2×C61semidirect
258. #1618C2×C61semidirect
259. #1617C2×C61semidirect
260. #1616C2×C61semidirect
261. #1512C2×C61semidirect
262. #1464C2×C61semidirect
302. C61#18372direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34932
C61×#32392
C61×#26282
C61×#16182
C61×#16172
C61×#16162
C61×#15122
C61×#14642
#1837261