Finite Group Databasebeta

← #29697765

Subgroups — #29697765

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839805C211yesmaximal, characteristic
2#21448686C211yesmaximal, characteristic
3#21446554C211yesmaximal, characteristic, complemented
4#21446549C211yesmaximal, characteristic, complemented
5#21446408C211yesmaximal, characteristic, complemented
6#21446404C211yesmaximal, characteristic, complemented
7#21446397C211yesmaximal, characteristic, complemented
8#21446387C211yesmaximal, characteristic, complemented
9#21445914C211yesmaximal, characteristic
10#21445907C211yesmaximal, characteristic
11#21445850C211yesmaximal, characteristic
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519708C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic
15C61×#2347C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×#14519733—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19#16839805C418yescomplemented
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519688C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839660C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839647—21no—
32#16839647—21no—
33#16839623—21no—
34#16839622C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36C4×C4⋊Dic61C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C61×#389C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#388—21no—
54C61×#383—21no—
55C61×#380C2211yescharacteristic
56C4×C4⋊C4×C61—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C23×Dic61—21no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194C2×C414yes—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519733—44no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61C2×C414yes—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81#14519710—22no—
82#14519710C2×C414yes—
83#14519710C2×C414yes—
84#14519708—22no—
85#14519708C2×C414yes—
86#14519708C2×C414yes—
87C22⋊#92418—22no—
88#14519688—22no—
89C4×#92418—22no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95C23×C4×C61C2311yescharacteristic
96#117×C61—22no—
97#117×C61C2×C414yes—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61D411yescharacteristic
107C2×C22⋊C4×C61D411yescharacteristic
108C2×C42×C61—21no—
109C2×C42×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61#4112yes—
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—24no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—42no—
143C22×Dic61—42no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—42no—
151C4⋊C4×C61—42no—
152C4⋊C4×C61C22×C412yes—
153C4⋊C4×C61C22×C412yes—
154C22⋊C4×C61—24no—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61—81no—
158C42×C61—24no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—81no—
164C42×C61—81no—
165C22⋊Dic61—42no—
166C4⋊Dic61—24no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61C22×C412yes—
174C4⋊Dic61C22×C412yes—
175#11758196—42no—
176#11758196—42no—
177C4×Dic61—42no—
178C4×Dic61—42no—
179#11758194—28no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418C22×C412yes—
189C2×#92418C22×C412yes—
190C2×#92418#4112yes—
191C2×#92418#4112yes—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61C4×D412yes—
199C23×C61C22×D411yescharacteristic
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C4×D412yes—
230C2×C4×C61AGL(1,ℤ/8)12yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C612−1+411yescharacteristic
236C2×C4×C612−1+411yescharacteristic
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—48no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250#92418—22no—
251#92418—41no—
252#92418—41no—
253#92418#11714yescomplemented
254#22622—611nomaximal, Sylow
255C22×C61—22no—
256C22×C61—22no—
257C22×C61—22no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61C2×C4×D411yescharacteristic
263C22×C61#54711yescharacteristic
264C22×C61#54711yescharacteristic
265C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C61#57511yescharacteristic
267C22×C61#57711yescharacteristic
268C22×C61#57811yescharacteristic
269C4×C61—22no—
270C4×C61—22no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—42no—
275C4×C61—42no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61C2×#11711yescharacteristic
279C4×C61#51911yescharacteristic
280C4×C61#55211yescharacteristic
281C4×C61#55211yescharacteristic
282Dic61—42no—
283Dic61—42no—
284Dic61—81no—
285Dic61—81no—
286C2×#428—611no—
287#2347D6111yescharacteristic
288#2344—611no—
289#1943—611no—
290#1942—611no—
291#1921—611no—
292#1920—611no—
293#1919—611no—
294#1918—611no—
295#1825—611no—
296#1824—611no—
297#1809—611no—
298#1776—611no—
299C4×#106—611no—
300#1753—611no—
301C2×C61—42no—
302C2×C61#234411yescharacteristic
303C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
304C2×C61#294711yescharacteristic
305C2×C61#334511yescharacteristic
306C2×C61#334911yescharacteristic
307C2×C61#335111yescharacteristic
308C2×C61#335311yescharacteristic
309C22×M16—611no—
310C2×#117—1221no—
311C2×#117C2×D6111yescharacteristic
312C22×C4⋊C4—611no—
313#428—618no—
314C2×#107—611no—
315C2×#107—611no—
316C2×#107—611no—
317C2×#106—611no—
318C2×#106—611no—
319C2×#106—611no—
320C2×C22⋊C8—611no—
321C2×#97—611no—
322C2×C4×C8—611no—
323#389—611no—
324#389—611no—
325#389C2×D6111yescharacteristic
326#389C2×D6111yescharacteristic
327#388—21no—
328#388—21no—
329#387—1221no—
330#387—1221no—
331#383—21no—
332#381—1221no—
333#380—611no—
334#380C2×D6111yescharacteristic
335C4×C4⋊C4—21no—
336C4×C4⋊C4—611no—
337C4×C4⋊C4—611no—
338C4×C4⋊C4C2×D6111yescharacteristic
339C4×C4⋊C4C2×D6111yescharacteristic
340C4×C22⋊C4C2×D6111yescharacteristic
341#340—611no—
342#340—611no—
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#336—611no—
352#336—611no—
353C61#2262211yescharacteristic, complemented, Sylow
354C23×C4—1221no—
355C23×C4C22×D6111yescharacteristic
356C2×M16—614no—
357C2×M16—1222no—
358C2×M16—1222no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—611no—
363#117—22no—
364#117—2444no—
365#117C4×D6114yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—614no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4C22⋊D6111yescharacteristic
385C2×C22⋊C4C22⋊D6111yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—1221no—
390C2×C42—1221no—
391C2×C42C22×D6111yescharacteristic
392C2×C42C22×D6111yescharacteristic
393#107—614no—
394#107—614no—
395#107—1222no—
396#106—614no—
397#106—614no—
398#106—1222no—
399C22⋊C8—1222no—
400#97—1222no—
401C4×C8—1222no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95C22⋊D6111yescharacteristic
413#95C22⋊D6111yescharacteristic
414C24C2×C22⋊D6111yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1224no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4C2×C4×D6112yes—
431C22×C4#1175822212yes—
432C22×C4C2×C22⋊D6111yescharacteristic
433C22×C4C2×C22⋊D6111yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435C22×C4C2×C22⋊D6111yescharacteristic
436C22×C4C2×C22⋊D6111yescharacteristic
437C22×C4C23×D6111yescharacteristic
438M16—1228no—
439C2×C8—612no—
440C2×C8—612no—
441C2×C8—612no—
442C2×C8—612no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—612no—
460C4⋊C4—612no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1224no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—2442no—
469C4⋊C4—2442no—
470C4⋊C4C2×C4×D6112yes—
471C4⋊C4C2×C4×D6112yes—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—81no—
476C22⋊C4—2442no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—24no—
482C42—81no—
483C42—81no—
484C42—2442no—
485C42—2442no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C4×C22⋊D6112yes—
493C23C22×C22⋊D6111yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2448no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C4×C22⋊D6112yes—
537C2×C4#1451980212yes—
538C2×C4C22×C4×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C2×C4#41×D6111yescharacteristic
541C2×C4C2×#1175822211yescharacteristic
542C2×C4#1451982411yescharacteristic
543C2×C4#1451982411yescharacteristic
544C8—614no—
545C8—1222no—
546C8—2441no—
547C8—2441no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C4×C22⋊D6111yescharacteristic
556C22#1684041111yescharacteristic
557C22#1684041111yescharacteristic
558C22C2×#1451980211yescharacteristic
559C22#1684056011yescharacteristic
560C22#1684057311yescharacteristic
561C22#1684057711yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—4881no—
572C4—4881no—
573C4—2442no—
574C4—2442no—
575C4#117×D6111yescharacteristic
576C4#1684023911yescharacteristic
577C4#1684044511yescharacteristic
578C4#1684044511yescharacteristic
579C2—42no—
580C2#2144868911yescharacteristic
581C2C4×#1451980211yescharacteristic
582C2#2145465811yescharacteristic
583C2#2145828311yescharacteristic
584C2#2145834311yescharacteristic
585C2#2145837311yescharacteristic
586C2#2145839711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2347C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#2347D61
hypocenterC61#22622
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #21446554C2semidirect
4. #21446549C2semidirect
5. #21446408C2semidirect
6. #21446404C2semidirect
7. #21446397C2semidirect
8. #21446387C2semidirect
12. #21445717C2semidirect
13. C4×#14519708C2semidirect
19. #16839805C4semidirect
253. #92418#117semidirect
353. C61#22622semidirect

Maximal subgroups

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

subgroupindex
C2×#168398052
#214486862
#214465542
#214465492
#214464082
#214464042
#214463972
#214463872
#214459142
#214459072
#214458502
#214457172
C4×#145197082
#214456032
C61×#23472
#2262261