Finite Group Databasebeta

← D61×#2135 #29832853

Subgroups — D61×#2135 #29832853

Order 15616.

1198 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#536×D61C211yesmaximal, characteristic
2#413×D61C212yesmaximal
3#21447514C211yesmaximal, characteristic, complemented
4#21447513C212yesmaximal, complemented
5#21447512C214yesmaximal, complemented
6#356×D61C214yesmaximal, complemented
7C61×#2135C211yesmaximal, characteristic, complemented
8C2×#41×D61C2211yescharacteristic
9C22×Q8×D61C411yescharacteristic
10C2×M16×D61—22no—
11#16840338C411yescharacteristic
12#16840337C2212yes—
13#16840336C411yescharacteristic
14#16840335—22no—
15#16840334—22no—
16#16840333C2211yescharacteristic
17#16840332C412yes—
18C4⋊Q8×D61C2212yes—
19#124×D61C412yes—
20#123×D61—22no—
21C22⋊Q8×D61—22no—
22#117×D61C411yescharacteristic
23#16839746C2212yes—
24#16839745C2214yes—
25#16839744—22no—
26#16839743—22no—
27#101×D61C2214yes—
28#100×D61—22no—
29#16839561C2214yescomplemented
30#16839560C2218yescomplemented
31C61×#536C2211yescharacteristic
32C61×#413C2212yes—
33C61×#356C2214yescomplemented
34C2×#11758226C2311yescharacteristic
35C2×#11758222C2×C411yescharacteristic
36C2×#11758222D412yes—
37C2×#11758224C2×C411yescharacteristic
38C2×#11758224D412yes—
39#41×D61—42no—
40#41×D61—42no—
41C22×Dic122—21no—
42C22×Dic122C2×C411yescharacteristic
43C2×Q8×D61—21no—
44C2×Q8×D61—21no—
45C2×Q8×D61—42no—
46C2×Q8×D61—42no—
47C2×Q8×D61C2×C412yes—
48C2×Q8×D61C2×C412yes—
49C2×Q8×D61C2311yescharacteristic
50C2×D4×D61C2×C411yescharacteristic
51C2×D4×D61D412yes—
52C22×C4×D61—21no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D412yes—
55C2×#11758194—22no—
56C2×#11758189—42no—
57M16×D61—24no—
58M16×D61—24no—
59M16×D61—42no—
60M16×D61—42no—
61C2×C8×D61—42no—
62#14519777C2×C412yes—
63#14519776—24no—
64#14519775C2×C412yes—
65#14519775C2312yes—
66#14519766C2×C412yes—
67#14519765C2×C412yes—
68#14519764C2×C412yes—
69#14519763—24no—
70#14519762—24no—
71#14519761—22no—
72#14519760—22no—
73#14519759—24no—
74#14519758—22no—
75#14519757—22no—
76#14519756—22no—
77#14519755—24no—
78#14519754—24no—
79#14519753—22no—
80#14519736C2×C411yescharacteristic
81#14519735—21no—
82#14519734C2×C412yes—
83#14519733—21no—
84C4⋊C4×D61—21no—
85C4⋊C4×D61—24no—
86C22⋊C4×D61—21no—
87C22⋊C4×D61—24no—
88C42×D61C2×C412yes—
89#14519696C2314yes—
90#14519695—24no—
91#14519694—22no—
92#14519693—24no—
93C2×#41×C61C2311yescharacteristic
94C22×Q8×C61C2×C411yescharacteristic
95C2×M16×C61—22no—
96C4⋊Q8×C61C2312yes—
97#124×C61C2×C412yes—
98#123×C61—22no—
99C22⋊Q8×C61—22no—
100#117×C61C2×C411yescharacteristic
101#101×C61C2314yes—
102#100×C61—22no—
103C23×D61C22⋊C411yescharacteristic
104C23×D61C22⋊C412yes—
105#41×C61—42no—
106C2×Q8×C61—21no—
107C2×Q8×C61—42no—
108C2×Q8×C61C22×C412yes—
109C2×Q8×C61C2411yescharacteristic
110C2×D4×C61C22×C411yescharacteristic
111C2×D4×C61C2×D412yes—
112C22×C4×C61—21no—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C2×D412yes—
115C2×C22⋊D61C22⋊C412yes—
116C2×C22⋊D61C22⋊C412yes—
117C2×C22⋊D61C22⋊C412yes—
118C22×Dic61—21no—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C412yes—
121#11758226—42no—
122Q8×D61—41no—
123Q8×D61—41no—
124Q8×D61—44no—
125Q8×D61—42no—
126Q8×D61—42no—
127Q8×D61—42no—
128Q8×D61—42no—
129Q8×D61—44no—
130#11758224—42no—
131#11758224—42no—
132#11758224—42no—
133D4×D61—41no—
134D4×D61—41no—
135D4×D61—42no—
136D4×D61—42no—
137#11758222—42no—
138#11758222—42no—
139#11758222—42no—
140C2×D244C22×C411yescharacteristic
141C2×D244C2×D412yes—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C412yes—
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22×C411yescharacteristic
157C2×C4×D61C22×C411yescharacteristic
158C2×C4×D61C2×D412yes—
159C2×C4×D61C2×D412yes—
160C2×Dic122—21no—
161C2×Dic122—22no—
162C2×Dic122—22no—
163C2×Dic122—44no—
164C2×Dic122—42no—
165C2×Dic122C22×C412yes—
166C2×Dic122C22×C411yescharacteristic
167C2×Dic122C2×D412yes—
168M16×C61—24no—
169M16×C61—42no—
170C2×C8×C61—42no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—24no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—24no—
175C42×C61C22×C412yes—
176C22⋊Dic61—21no—
177C22⋊Dic61—24no—
178#11758198—22no—
179#11758198—24no—
180#11758198—24no—
181C4⋊Dic61—21no—
182C4⋊Dic61—24no—
183#11758196—24no—
184#11758196—22no—
185#11758196—24no—
186C4×Dic61—22no—
187C4×Dic61C22×C412yes—
188#11758194—24no—
189#11758194—42no—
190C2×#92418—42no—
191#11758189—44no—
192#11758189—44no—
193C8×D61—44no—
194C8×D61—44no—
195C23×C61C2×C22⋊C412yes—
196C23×C61C2×C22⋊C411yescharacteristic
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—44no—
203C22×D61C2×C22⋊C411yescharacteristic
204C22×D61C2×C22⋊C412yes—
205C22×D61C2×C22⋊C411yescharacteristic
206Q8×C61—41no—
207Q8×C61—42no—
208Q8×C61—42no—
209D4×C61—41no—
210D4×C61—42no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—42no—
217C2×C4×C61C2×C22⋊C411yescharacteristic
218C2×C4×C61C23×C411yescharacteristic
219C2×C4×C61C22×D412yes—
220C22⋊D61—42no—
221C22⋊D61—42no—
222C22⋊D61—42no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—42no—
229C2×Dic61C2×C22⋊C411yescharacteristic
230C2×Dic61C2×C22⋊C412yes—
231C2×Dic61C2×C22⋊C411yescharacteristic
232D244—41no—
233D244—42no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—22no—
244C4×D61—44no—
245C4×D61—44no—
246C4×D61—42no—
247C4×D61—42no—
248C4×D61#9912yes—
249C4×D61#9912yes—
250Dic122—41no—
251Dic122—42no—
252Dic122—44no—
253Dic122—42no—
254Dic122—44no—
255Dic122—42no—
256C8×C61—44no—
257#92418—44no—
258C2×#2135—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—22no—
261C22×C61—41no—
262C22×C61—42no—
263C22×C61C22×C22⋊C411yescharacteristic
264C2×D61—22no—
265C2×D61—21no—
266C2×D61—22no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—44no—
270C2×D61—41no—
271C2×D61—42no—
272C2×D61—82no—
273C2×D61C2×#9911yescharacteristic
274C2×D61C2×#9911yescharacteristic
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—42no—
278C4×C61—42no—
279C4×C61C2×#9912yes—
280Dic61—21no—
281Dic61—22no—
282Dic61—42no—
283Dic61—42no—
284Dic61C2×#9912yes—
285C2×#536—611no—
286C2×#413—612no—
287#2135—612no—
288#2135—614no—
289#2135—611no—
290#2135D6111yescharacteristic, direct product factor
291C2×#356—614no—
292C2×C61—21no—
293C2×C61—41no—
294C2×C61—42no—
295C2×C61C22×#9911yescharacteristic
296D61—21no—
297D61—41no—
298D61—42no—
299D61#213512yesdirect product factor
300C22×#41—611no—
301C23×Q8—611no—
302C22×M16—1222no—
303#536—611no—
304#536—611no—
305#536—612no—
306#536—612no—
307#536—611no—
308#536—1222no—
309#536—1222no—
310#536C2×D6111yescharacteristic
311C2×C4⋊Q8—612no—
312C2×#124—612no—
313C2×#123—1222no—
314C2×C22⋊Q8—1222no—
315C2×#117—611no—
316#413—612no—
317#413—614no—
318#413—1222no—
319#413—1222no—
320#413C2×D6112yes—
321C2×#101—614no—
322C2×#100—1222no—
323#356—614no—
324#356—618no—
325#356C2×D6114yescomplemented
326C61C2×#213511yescharacteristic, complemented, Sylow
327C2×#41—611no—
328C2×#41—611no—
329C2×#41—612no—
330C2×#41—611no—
331C2×#41—612no—
332C2×#41—2442no—
333C2×#41—2442no—
334C2×#41C22×D6111yescharacteristic
335C22×Q8—611no—
336C22×Q8—612no—
337C22×Q8—612no—
338C22×Q8—611no—
339C22×Q8—1221no—
340C22×Q8—1221no—
341C22×Q8—1221no—
342C22×Q8—2442no—
343C22×Q8—2442no—
344C22×Q8C4×D6111yescharacteristic
345C22×D4—611no—
346C22×D4—612no—
347C23×C4—611no—
348C23×C4—612no—
349C23×C4—1221no—
350C2×M16—22no—
351C2×M16—1224no—
352C2×M16—1224no—
353C2×M16—1222no—
354C2×M16—2442no—
355C2×M16—2442no—
356C2×M16—2442no—
357C22×C8—2442no—
358C4⋊Q8—612no—
359C4⋊Q8—612no—
360C4⋊Q8—612no—
361C4⋊Q8—1224no—
362C4⋊Q8C22×D6112yes—
363#124—612no—
364#124—612no—
365#124—612no—
366#124—1224no—
367#124C4×D6112yes—
368#123—22no—
369#123—1224no—
370#123—1222no—
371#123—1224no—
372#123—1222no—
373#123—1222no—
374C22⋊Q8—22no—
375C22⋊Q8—1224no—
376C22⋊Q8—1224no—
377C22⋊Q8—1222no—
378C22⋊Q8—1222no—
379C22⋊Q8—1222no—
380#117—611no—
381#117—612no—
382#117—1221no—
383#117—1221no—
384#117C4×D6111yescharacteristic
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1224no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1224no—
389C2×C42—612no—
390#101—614no—
391#101—1224no—
392#101C22×D6114yes—
393#100—22no—
394#100—1224no—
395#100—1222no—
396C24—612no—
397C24—611no—
398#41—42no—
399#41—2442no—
400#41—2442no—
401#41—2442no—
402#41—2442no—
403#41—2442no—
404#41—2442no—
405#41—2442no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—611no—
409C2×Q8—612no—
410C2×Q8—612no—
411C2×Q8—1222no—
412C2×Q8—1222no—
413C2×Q8—1221no—
414C2×Q8—2442no—
415C2×Q8—2444no—
416C2×Q8—2442no—
417C2×Q8—2442no—
418C2×Q8—2441no—
419C2×Q8—2441no—
420C2×Q8—2444no—
421C2×Q8—2444no—
422C2×Q8—2442no—
423C2×Q8—2442no—
424C2×Q8C2×C4×D6112yes—
425C2×Q8C23×D6111yescharacteristic
426C2×D4—612no—
427C2×D4—612no—
428C2×D4—612no—
429C2×D4—611no—
430C2×D4—612no—
431C2×D4—2442no—
432C2×D4—2442no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4C2×C4×D6111yescharacteristic
436C2×D4D4×D6112yes—
437C22×C4—21no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—612no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—612no—
444C22×C4—612no—
445C22×C4—611no—
446C22×C4—612no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4D4×D6112yes—
461M16—24no—
462M16—42no—
463M16—1224no—
464M16—2444no—
465M16—2444no—
466M16—2442no—
467C2×C8—42no—
468C2×C8—2444no—
469C2×C8—2444no—
470C2×C8—2442no—
471C4⋊C4—24no—
472C4⋊C4—21no—
473C4⋊C4—1222no—
474C4⋊C4—1224no—
475C4⋊C4—1224no—
476C4⋊C4—1224no—
477C4⋊C4—1221no—
478C22⋊C4—21no—
479C22⋊C4—24no—
480C22⋊C4—1222no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C22⋊C4—1221no—
484C22⋊C4—1224no—
485C42—612no—
486C42—1222no—
487C42C2×C4×D6112yes—
488C23—611no—
489C23—612no—
490C23—611no—
491C23—1222no—
492C23—1221no—
493C23—1221no—
494C23—1222no—
495C23—2444no—
496C23—2442no—
497C23C22⋊C4×D6112yes—
498C23C22⋊C4×D6111yescharacteristic
499Q8—41no—
500Q8—42no—
501Q8—42no—
502Q8—2442no—
503Q8—2441no—
504Q8—2442no—
505Q8—2444no—
506Q8—2444no—
507Q8—2442no—
508D4—41no—
509D4—42no—
510D4—2442no—
511D4—2441no—
512D4—2442no—
513D4—2442no—
514D4—2442no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—611no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—612no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2444no—
544C2×C4—2444no—
545C2×C4—2442no—
546C2×C4C22⋊C4×D6111yescharacteristic
547C2×C4C22×C4×D6111yescharacteristic
548C2×C4C2×D4×D6112yes—
549C8—44no—
550C8—2444no—
551C22—21no—
552C22—22no—
553C22—42no—
554C22—41no—
555C22—611no—
556C22—611no—
557C22—1222no—
558C22—1221no—
559C22—1222no—
560C22—4882no—
561C22—2442no—
562C22—2441no—
563C22—2444no—
564C22—2442no—
565C22—2442no—
566C22C2×C22⋊C4×D6111yescharacteristic
567C4—22no—
568C4—21no—
569C4—42no—
570C4—42no—
571C4—612no—
572C4—1222no—
573C4—1221no—
574C4—2442no—
575C4—2442no—
576C4#99×D6112yes—
577C2—21no—
578C2—42no—
579C2—41no—
580C2—612no—
581C2—1221no—
582C2—2442no—
583C2—2441no—
584C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC2C2×#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×Q8C23×D61
FittingC61×#2135C2
socleC2×C61C22×#99
prime radicalC2×#41×D61C22
cosocleC2×Q8×C61C24
hypercenter#2135D61
hypocenterC61C2×#2135
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2135

Complements

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

NH ≅ G/Ntype
3. #21447514C2semidirect
4. #21447513C2semidirect
5. #21447512C2semidirect
6. #356×D61C2semidirect
7. C61×#2135C2semidirect
29. #16839561C22semidirect
30. #16839560C22semidirect
33. C61×#356C22semidirect
290. #2135D61direct (N × H)
299. D61#2135direct (N × H)
325. #356C2×D61semidirect
326. C61C2×#2135semidirect

Maximal subgroups

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

subgroupindex
#536×D612
#413×D612
#214475142
#214475132
#214475122
#356×D612
C61×#21352
C2×#213561