Finite Group Databasebeta

← C61×#11203 #29514636

Subgroups — C61×#11203 #29514636

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#385C211yesmaximal, characteristic
2C2×C61×#380C211yesmaximal, characteristic
3C2×C61×#342C212yesmaximal
4C2×C61×#342C212yesmaximal
5C61×C22⋊#95C211yesmaximal, characteristic
6C24×C4×C61C2211yescharacteristic
7C22×C4⋊C4×C61—21no—
8C22×C4⋊C4×C61C412yescomplemented
9C22×C22⋊C4×C61C2211yescharacteristic
10C22×C22⋊C4×C61C2212yes—
11C22×C22⋊C4×C61C2212yes—
12C22×C22⋊C4×C61C2211yescharacteristic
13C61×#385—21no—
14C61×#385—22no—
15C61×#385—21no—
16C61×#380—24no—
17C2×#95×C61—21no—
18C2×#95×C61—22no—
19C2×#95×C61C412yescomplemented
20C61×#342—24no—
21C61×#342—24no—
22C25×C61C2311yescharacteristic
23C23×C4×C61—22no—
24C23×C4×C61—22no—
25C23×C4×C61—22no—
26C23×C4×C61—22no—
27C23×C4×C61—44no—
28C23×C4×C61C2×C412yes—
29C23×C4×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61C2×C412yes—
32C23×C4×C61D411yescharacteristic
33C23×C4×C61D412yes—
34C23×C4×C61D411yescharacteristic
35C2×C4⋊C4×C61—24no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—44no—
39C2×C4⋊C4×C61—44no—
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—21no—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—22no—
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61—22no—
47C2×C22⋊C4×C61—22no—
48C2×C22⋊C4×C61—22no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—22no—
53C2×C22⋊C4×C61—22no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—22no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61D414yes—
59C2×C22⋊C4×C61D412yes—
60C2×C22⋊C4×C61Q814yes—
61C2×C22⋊C4×C61Q812yes—
62#95×C61—24no—
63#95×C61—22no—
64#95×C61—22no—
65#95×C61—44no—
66C24×C61—42no—
67C24×C61—42no—
68C24×C61C22×C411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C24×C61C2×D411yescharacteristic
71C24×C61C2×D411yescharacteristic
72C24×C61C2×D412yes—
73C24×C61C2×Q811yescharacteristic
74C24×C61C2×Q812yes—
75C24×C61#4111yescharacteristic
76C24×C61#4111yescharacteristic
77C24×C61#4112yes—
78C24×C61#4112yes—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—24no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—24no—
85C22×C4×C61—21no—
86C22×C4×C61—24no—
87C22×C4×C61—21no—
88C22×C4×C61—24no—
89C22×C4×C61—24no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—24no—
93C22×C4×C61—24no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61—48no—
100C22×C4×C61—48no—
101C22×C4×C61—42no—
102C22×C4×C61—42no—
103C22×C4×C61—44no—
104C22×C4×C61—44no—
105C22×C4×C61—44no—
106C22×C4×C61—44no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61C22⋊C412yes—
114C22×C4×C61C22⋊C412yes—
115C22×C4×C61C4⋊C414yescomplemented
116C4⋊C4×C61—48no—
117C4⋊C4×C61—44no—
118C4⋊C4×C61—44no—
119C22⋊C4×C61—22no—
120C22⋊C4×C61—22no—
121C22⋊C4×C61—22no—
122C22⋊C4×C61—22no—
123C22⋊C4×C61—24no—
124C22⋊C4×C61—24no—
125C22⋊C4×C61—24no—
126C22⋊C4×C61—24no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—42no—
129C22⋊C4×C61—42no—
130C22⋊C4×C61—42no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—42no—
133C22⋊C4×C61—42no—
134C23×C61—22no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—42no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—42no—
145C23×C61—44no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—44no—
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61C2×C4⋊C411yescharacteristic
152C23×C61#11711yescharacteristic
153C23×C61C4×D412yes—
154C23×C61C4×Q812yes—
155C23×C61#12011yescharacteristic
156C23×C61#12111yescharacteristic
157C23×C61#12111yescharacteristic
158C23×C61#12112yes—
159C23×C61#12112yes—
160C23×C61C22⋊Q811yescharacteristic
161C23×C61C22⋊Q811yescharacteristic
162C23×C61C22⋊Q812yes—
163C23×C61C22⋊Q812yes—
164C23×C61C22⋊Q812yes—
165C23×C61#12311yescharacteristic
166C23×C61#12312yes—
167C23×C61#12411yescharacteristic
168C23×C61#12512yes—
169C23×C61#12512yes—
170C23×C61#12612yes—
171C23×C61C4⋊Q811yescharacteristic
172C23×C61C4⋊Q812yes—
173C2×C4×C61—24no—
174C2×C4×C61—24no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—24no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—48no—
182C2×C4×C61—48no—
183C2×C4×C61—44no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—44no—
189C2×C4×C61—44no—
190C2×C4×C61—44no—
191C2×C4×C61—48no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—44no—
195C2×C4×C61—44no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61—84no—
199C2×C4×C61—84no—
200C2×C4×C61—82no—
201C2×C4×C61—82no—
202C2×C4×C61—84no—
203C2×C4×C61—82no—
204C2×C4×C61—82no—
205C2×C4×C61#9914yes—
206#11203C6111yesmaximal, characteristic, direct product factor, Sylow
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—21no—
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—21no—
221C22×C61—24no—
222C22×C61—22no—
223C22×C61—24no—
224C22×C61—22no—
225C22×C61—42no—
226C22×C61—42no—
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—42no—
230C22×C61—42no—
231C22×C61—42no—
232C22×C61—42no—
233C22×C61#38011yescharacteristic
234C22×C61#38611yescharacteristic
235C22×C61#38712yes—
236C22×C61#38912yes—
237C22×C61#39111yescharacteristic
238C22×C61#39411yescharacteristic
239C22×C61#39511yescharacteristic
240C22×C61#39612yes—
241C22×C61#39811yescharacteristic
242C22×C61#39812yes—
243C22×C61#40011yescharacteristic
244C22×C61C2×#9912yes—
245C22×C61#41012yes—
246C4×C61—24no—
247C4×C61—44no—
248C4×C61—42no—
249C4×C61—84no—
250C4×C61—84no—
251C4×C61—81no—
252C4×C61—81no—
253C2×#385C2×C6111yescharacteristic
254C2×#380C2×C6111yescharacteristic
255C2×#342C2×C6112yes—
256C2×#342C2×C6112yes—
257C22⋊#95C2×C6111yescharacteristic
258C2×C61—21no—
259C2×C61—22no—
260C2×C61—22no—
261C2×C61—22no—
262C2×C61—21no—
263C2×C61—21no—
264C2×C61—22no—
265C2×C61—21no—
266C2×C61#144111yescharacteristic
267C2×C61#179912yes—
268C2×C61#189811yescharacteristic
269C2×C61#189911yescharacteristic
270C2×C61#199612yes—
271C24×C4C22×C6111yescharacteristic
272C22×C4⋊C4—21no—
273C22×C4⋊C4C4×C6112yescomplemented
274C22×C22⋊C4C22×C6111yescharacteristic
275C22×C22⋊C4C22×C6112yes—
276C22×C22⋊C4C22×C6112yes—
277C22×C22⋊C4C22×C6111yescharacteristic
278#385—21no—
279#385—22no—
280#385—21no—
281#380—24no—
282C2×#95—21no—
283C2×#95—22no—
284C2×#95C4×C6112yescomplemented
285#342—24no—
286#342—24no—
287C61#1120311yescharacteristic, direct product factor, Sylow
288C25C23×C6111yescharacteristic
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—44no—
294C23×C4C2×C4×C6112yes—
295C23×C4C2×C4×C6111yescharacteristic
296C23×C4C2×C4×C6111yescharacteristic
297C23×C4C2×C4×C6112yes—
298C23×C4D4×C6111yescharacteristic
299C23×C4D4×C6112yes—
300C23×C4D4×C6111yescharacteristic
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4D4×C6114yes—
325C2×C22⋊C4D4×C6112yes—
326C2×C22⋊C4Q8×C6114yes—
327C2×C22⋊C4Q8×C6112yes—
328#95—24no—
329#95—22no—
330#95—22no—
331#95—44no—
332C24—42no—
333C24—42no—
334C24C22×C4×C6111yescharacteristic
335C24C2×D4×C6111yescharacteristic
336C24C2×D4×C6111yescharacteristic
337C24C2×D4×C6111yescharacteristic
338C24C2×D4×C6112yes—
339C24C2×Q8×C6111yescharacteristic
340C24C2×Q8×C6112yes—
341C24#41×C6111yescharacteristic
342C24#41×C6111yescharacteristic
343C24#41×C6112yes—
344C24#41×C6112yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—21no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—48no—
366C22×C4—48no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4C22⋊C4×C6112yes—
380C22×C4C22⋊C4×C6112yes—
381C22×C4C4⋊C4×C6114yescomplemented
382C4⋊C4—48no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—41no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—41no—
398C22⋊C4—42no—
399C22⋊C4—42no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—44no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—44no—
416C23C2×C22⋊C4×C6111yescharacteristic
417C23C2×C4⋊C4×C6111yescharacteristic
418C23#117×C6111yescharacteristic
419C23C4×D4×C6112yes—
420C23C4×Q8×C6112yes—
421C23#120×C6111yescharacteristic
422C23#121×C6111yescharacteristic
423C23#121×C6111yescharacteristic
424C23#121×C6112yes—
425C23#121×C6112yes—
426C23C22⋊Q8×C6111yescharacteristic
427C23C22⋊Q8×C6111yescharacteristic
428C23C22⋊Q8×C6112yes—
429C23C22⋊Q8×C6112yes—
430C23C22⋊Q8×C6112yes—
431C23#123×C6111yescharacteristic
432C23#123×C6112yes—
433C23#124×C6111yescharacteristic
434C23#125×C6112yes—
435C23#125×C6112yes—
436C23#126×C6112yes—
437C23C4⋊Q8×C6111yescharacteristic
438C23C4⋊Q8×C6112yes—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—48no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—48no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—84no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4#99×C6114yes—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—22no—
482C22—21no—
483C22—22no—
484C22—22no—
485C22—21no—
486C22—24no—
487C22—22no—
488C22—24no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22C61×#38011yescharacteristic
499C22C61×#38611yescharacteristic
500C22C61×#38712yes—
501C22C61×#38912yes—
502C22C61×#39111yescharacteristic
503C22C61×#39411yescharacteristic
504C22C61×#39511yescharacteristic
505C22C61×#39612yes—
506C22C61×#39811yescharacteristic
507C22C61×#39812yes—
508C22C61×#40011yescharacteristic
509C22C2×#99×C6112yes—
510C22C61×#41012yes—
511C4—24no—
512C4—44no—
513C4—42no—
514C4—84no—
515C4—84no—
516C4—81no—
517C4—81no—
518C2—21no—
519C2—22no—
520C2—22no—
521C2—22no—
522C2—21no—
523C2—21no—
524C2—22no—
525C2—21no—
526C2C61×#144111yescharacteristic
527C2C61×#179912yes—
528C2C61×#189811yescharacteristic
529C2C61×#189911yescharacteristic
530C2C61×#199612yes—
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC24C22×C4×C61
Frattini, cosocleC25C23×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C4⋊C4×C61C4semidirect
19. C2×#95×C61C4semidirect
115. C22×C4×C61C4⋊C4semidirect
206. #11203C61direct (N × H)
273. C22×C4⋊C4C4×C61semidirect
284. C2×#95C4×C61semidirect
287. C61#11203direct (N × H)
381. C22×C4C4⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3852
C2×C61×#3802
C2×C61×#3422
C61×C22⋊#952
#1120361