Finite Group Databasebeta

← #29690522

Subgroups — #29690522

Order 15616.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839822C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic
3#21448314C211yesmaximal, characteristic
4#21446541C211yesmaximal, characteristic, complemented
5#21446541C211yesmaximal, characteristic, complemented
6#21446536C211yesmaximal, characteristic, complemented
7#21446536C211yesmaximal, characteristic, complemented
8#21446003C211yesmaximal, characteristic
9#21446003C211yesmaximal, characteristic
10#21445998C211yesmaximal, characteristic
11#21445998C211yesmaximal, characteristic
12#21445973C211yesmaximal, characteristic, complemented
13#21445970C211yesmaximal, characteristic, complemented
14#21445935C211yesmaximal, characteristic, complemented
15C61×#1832C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19#16839822—24no—
20#16839787—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839651C411yescharacteristic
38#16839651C411yescharacteristic
39#16839651C411yescharacteristic
40#16839651C411yescharacteristic
41#16839644C411yescharacteristic
42#16839644C411yescharacteristic
43#16839644C411yescharacteristic
44#16839644C411yescharacteristic
45C4×#11758196C2211yescharacteristic
46C4×#11758196C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×#11758198C2211yescharacteristic
49C42×Dic61C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#376C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758189—22no—
63C2×#11758189—41no—
64C2×#11758189—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C2×C8×D61—22no—
70C2×C8×D61—41no—
71C2×C8×D61—41no—
72#14519734D414yes—
73#14519734Q814yes—
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C4⋊#92418—22no—
94C4⋊#92418—22no—
95C4⋊#92418—41no—
96C4⋊#92418—41no—
97C4⋊#92418—41no—
98C4⋊#92418—41no—
99#14519706—22no—
100#14519706—22no—
101#14519706—41no—
102#14519706—41no—
103#14519706—41no—
104#14519706—41no—
105#14519689—22no—
106#14519689—22no—
107#14519687—22no—
108C8×Dic61—22no—
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C4⋊C8×C61—22no—
125C4⋊C8×C61—22no—
126#95×C61C2×C411yescharacteristic
127#95×C61C2×C411yescharacteristic
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130C23×D61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×Q812yes—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C42×C61—21no—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61C2×D412yes—
168C42×C61C2×Q812yes—
169#11758198—22no—
170#11758198—22no—
171#11758198—41no—
172#11758198—41no—
173#11758198C4⋊C414yes—
174#11758198C4⋊C414yes—
175#11758196—22no—
176#11758196—22no—
177#11758196—41no—
178#11758196—41no—
179#11758196C4⋊C414yes—
180#11758196C4⋊C414yes—
181C4×Dic61—21no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—41no—
188C4×Dic61—41no—
189C4×Dic61C2×D412yes—
190C4×Dic61C2×Q812yes—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203#11758189—44no—
204C8×D61—44no—
205C23×C61C23×C411yescharacteristic
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61C2×C4⋊C412yes—
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—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61C2×C4⋊C412yes—
230C2×C4×C61C2×C4⋊C412yes—
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×Q811yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C61H(5,𝔽2)11yescharacteristic
235C2×C4×C612−1+411yescharacteristic
236C2×C4×C612−1+411yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61C2×C4⋊C412yes—
254C2×Dic61C2×C4⋊C412yes—
255C2×Dic61C2×C4⋊C412yes—
256C2×Dic61#13112yes—
257C2×Dic61#13112yes—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C8×C61—41no—
263C8×C61—41no—
264C8×C61—41no—
265C8×C61—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#92418—41no—
270#21980—611nomaximal, Sylow
271C22×C61C22×C4⋊C411yescharacteristic
272C22×C61#52011yescharacteristic
273C22×C61#52011yescharacteristic
274C22×C61C2×#13111yescharacteristic
275C22×C61C2×#13111yescharacteristic
276C22×C61#56811yescharacteristic
277C22×C61#56811yescharacteristic
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C4×C61—22no—
286C4×C61—22no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61#53511yescharacteristic
292C4×C61#53611yescharacteristic
293C4×C61#54411yescharacteristic
294C4×C61#54411yescharacteristic
295Dic61—22no—
296Dic61—22no—
297Dic61—22no—
298Dic61—22no—
299Dic61—22no—
300Dic61—41no—
301Dic61—41no—
302C2×#433—611no—
303C2×#424—611no—
304#2298—611no—
305#1940—611no—
306#1940—611no—
307#1939—611no—
308#1939—611no—
309#1851—611no—
310#1851—611no—
311#1850—611no—
312#1850—611no—
313#1843—611no—
314#1842—611no—
315#1832D6111yescharacteristic, complemented
316#1831—611no—
317C2×C61#231711yescharacteristic
318C2×C61#290611yescharacteristic
319C2×C61#290611yescharacteristic
320C2×C61#299211yescharacteristic
321C2×C61#299311yescharacteristic
322C2×C61#299411yescharacteristic
323C2×C61#299511yescharacteristic
324D61—42no—
325C22×M16—611no—
326C23×C8—611no—
327C2×#117—611no—
328#433—1224no—
329#424—1224no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—611no—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8C2×D6111yescharacteristic
343C2×C4⋊C8C2×D6111yescharacteristic
344C2×C22⋊C8—611no—
345C2×C22⋊C8—611no—
346C2×#97—611no—
347C2×C4×C8—611no—
348#388—611no—
349#388—611no—
350#388—611no—
351#388—611no—
352#387—611no—
353#387—611no—
354#387—611no—
355#387—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—611no—
358C4×C22⋊C4—611no—
359C4×C22⋊C4—611no—
360#376C2×D6111yescharacteristic
361C43—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336C2×D6111yescharacteristic
367#336C2×D6111yescharacteristic
368#336C2×D6111yescharacteristic
369#336C2×D6111yescharacteristic
370C61#2198011yescharacteristic, complemented, Sylow
371C23×C4—611no—
372C2×M16—1222no—
373C2×M16—2441no—
374C2×M16—2441no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—1222no—
380C22×C8—2441no—
381C22×C8—2441no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384C22×C8C22×D6111yescharacteristic
385C22×C8C22×D6111yescharacteristic
386#117—614no—
387#117—614no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C22⋊C4—611no—
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C22⋊C4—611no—
398C2×C22⋊C4—611no—
399C2×C22⋊C4—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42C22×D6111yescharacteristic
408C2×C42C22×D6111yescharacteristic
409C2×C42C22×D6111yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—22no—
412C4⋊C8—1222no—
413C4⋊C8—1222no—
414C4⋊C8—1222no—
415C4⋊C8—1222no—
416C4⋊C8—2441no—
417C4⋊C8—2441no—
418C4⋊C8—2441no—
419C4⋊C8—2441no—
420C4⋊C8—2441no—
421C4⋊C8—2441no—
422C4⋊C8—2441no—
423C4⋊C8—2441no—
424C22⋊C8—1222no—
425C22⋊C8—1222no—
426#97—1222no—
427C4×C8—1222no—
428#95—611no—
429#95—611no—
430#95—611no—
431#95—611no—
432#95—611no—
433#95—611no—
434#95—611no—
435#95—611no—
436#95C4×D6111yescharacteristic
437#95C4×D6111yescharacteristic
438#95C4×D6111yescharacteristic
439#95C4×D6111yescharacteristic
440C24—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4C2×C4×D6111yescharacteristic
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C2×C4×D6111yescharacteristic
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4C23×D6111yescharacteristic
461M16—2444no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—2444no—
487C4⋊C4—614no—
488C4⋊C4—614no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C22⋊C4—614no—
494C22⋊C4—614no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—612no—
504C42—612no—
505C42—1222no—
506C42—1222no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—2441no—
512C42—2441no—
513C42D4×D6112yes—
514C42Q8×D6112yes—
515C23—612no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—1221no—
521C23—1221no—
522C23C22×C4×D6111yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—612no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4C4⋊C4×D6112yes—
565C2×C4C4⋊C4×D6112yes—
566C2×C4C2×D4×D6111yescharacteristic
567C2×C4C2×Q8×D6111yescharacteristic
568C2×C4#1451982311yescharacteristic
569C2×C4#1451982311yescharacteristic
570C2×C4#1451982411yescharacteristic
571C2×C4#1451982411yescharacteristic
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—2441no—
577C8—2441no—
578C8—2441no—
579C8—2441no—
580C22—1222no—
581C22—1222no—
582C22—1222no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22C2×C4⋊C4×D6111yescharacteristic
588C22#1684024211yescharacteristic
589C22#1684024211yescharacteristic
590C22#131×D6111yescharacteristic
591C22#131×D6111yescharacteristic
592C22#1684052711yescharacteristic
593C22#1684052711yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—1222no—
601C4—1222no—
602C4—1222no—
603C4—1222no—
604C4—1222no—
605C4—2441no—
606C4—2441no—
607C4#1684033011yescharacteristic
608C4#1684033211yescharacteristic
609C4#1684039211yescharacteristic
610C4#1684039211yescharacteristic
611C2—2442no—
612C2#2144844411yescharacteristic
613C2#2145438611yescharacteristic
614C2#2145438611yescharacteristic
615C2#2145495311yescharacteristic
616C2#2145496211yescharacteristic
617C2#2145497311yescharacteristic
618C2#2145498411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1832C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1832D61
hypocenterC61#21980
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1832

Complements

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

NH ≅ G/Ntype
4. #21446541C2semidirect
5. #21446541C2semidirect
6. #21446536C2semidirect
7. #21446536C2semidirect
12. #21445973C2semidirect
13. #21445970C2semidirect
14. #21445935C2semidirect
15. C61×#1832C2semidirect
315. #1832D61semidirect
370. C61#21980semidirect

Maximal subgroups

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

subgroupindex
C2×#168398222
C2×#168397872
#214483142
#214465412
#214465362
#214460032
#214459982
#214459732
#214459702
#214459352
C61×#18322
#2198061