Finite Group Databasebeta

← #29690378

Subgroups — #29690378

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839824C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic
3#21448299C211yesmaximal, characteristic
4#21446542C211yesmaximal, characteristic, complemented
5#21446541C211yesmaximal, characteristic, complemented
6#21446539C211yesmaximal, characteristic, complemented
7#21446538C211yesmaximal, characteristic, complemented
8#21446536C211yesmaximal, characteristic, complemented
9#21446535C211yesmaximal, characteristic, complemented
10#21446534C211yesmaximal, characteristic, complemented
11#21445802C211yesmaximal, characteristic
12#21445800C211yesmaximal, characteristic
13#21445798C211yesmaximal, characteristic
14#21445796C211yesmaximal, characteristic
15C61×#1940C211yesmaximal, characteristic, complemented
16C2×#14519734C2211yescharacteristic
17C2×#14519734C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19#16839824—24no—
20#16839822—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839659C411yescharacteristic
38#16839659C411yescharacteristic
39#16839657C411yescharacteristic
40#16839657C411yescharacteristic
41#16839636C411yescharacteristic
42#16839636C411yescharacteristic
43#16839633C411yescharacteristic
44#16839633C411yescharacteristic
45C4×#11758196C2211yescharacteristic
46C4×#11758196C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519734—41no—
69#14519734—41no—
70#14519734D414yes—
71#14519734Q814yes—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C42×D61—41no—
92C42×D61—41no—
93C4⋊#92418—22no—
94C4⋊#92418—41no—
95C4⋊#92418—41no—
96#14519706—22no—
97#14519706—22no—
98#14519706—41no—
99#14519706—41no—
100#14519706—41no—
101#14519706—41no—
102#14519689—22no—
103#14519689—22no—
104#14519689—22no—
105#14519689—22no—
106#14519687—22no—
107C4×#92418—22no—
108C8×Dic61—22no—
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C4⋊C8×C61—22no—
125C4⋊C8×C61—41no—
126C4⋊C8×C61—41no—
127#97×C61—22no—
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×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×Q812yes—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—41no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61C2×D412yes—
176C42×C61C2×Q812yes—
177#11758198—41no—
178#11758198—41no—
179#11758198C4⋊C414yes—
180#11758198C4⋊C414yes—
181C4⋊Dic61—22no—
182C4⋊Dic61—41no—
183#11758196—22no—
184#11758196—22no—
185#11758196—41no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189#11758196C4⋊C414yes—
190#11758196C4⋊C414yes—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196C4×Dic61—41no—
197C4×Dic61C2×D412yes—
198C4×Dic61C2×Q812yes—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C23×C61C23×C411yescharacteristic
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61C2×C4⋊C412yes—
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×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61C2×C4⋊C412yes—
235C2×C4×C61C2×C4⋊C412yes—
236C2×C4×C61#13112yes—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×Q811yescharacteristic
239C2×C4×C61H(5,𝔽2)11yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×C4×C612−1+411yescharacteristic
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×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61C2×C4⋊C412yes—
261C2×Dic61C2×C4⋊C412yes—
262C2×Dic61C2×C4⋊C412yes—
263C2×Dic61#13112yes—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—44no—
269C4×D61—44no—
270C8×C61—41no—
271C8×C61—41no—
272C8×C61—41no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#21958—611nomaximal, Sylow
279C22×C61C22×C4⋊C411yescharacteristic
280C22×C61#51811yescharacteristic
281C22×C61#51911yescharacteristic
282C22×C61C2×#13111yescharacteristic
283C22×C61C2×#13111yescharacteristic
284C22×C61#56811yescharacteristic
285C22×C61#56811yescharacteristic
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C4×C61—22no—
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61#53711yescharacteristic
300C4×C61#53711yescharacteristic
301C4×C61#54411yescharacteristic
302C4×C61#54411yescharacteristic
303Dic61—22no—
304Dic61—22no—
305Dic61—22no—
306Dic61—22no—
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310C2×#433—611no—
311C2×#433—611no—
312#2296—611no—
313#1940—611no—
314#1940—611no—
315#1940—611no—
316#1940D6111yescharacteristic, complemented
317#1939—611no—
318#1939—611no—
319#1939—611no—
320#1939—611no—
321#1798—611no—
322#1798—611no—
323#1797—611no—
324#1797—611no—
325C2×C61#231611yescharacteristic
326C2×C61#290611yescharacteristic
327C2×C61#290611yescharacteristic
328C2×C61#297711yescharacteristic
329C2×C61#297811yescharacteristic
330C2×C61#298511yescharacteristic
331C2×C61#298511yescharacteristic
332D61—42no—
333C2×#117—611no—
334C2×#117—611no—
335C22×C42—611no—
336#433—1224no—
337#433—1224no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8—611no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8—611no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8C2×D6111yescharacteristic
348C2×C4⋊C8C2×D6111yescharacteristic
349C2×C4⋊C8C2×D6111yescharacteristic
350C2×C22⋊C8—611no—
351C2×C22⋊C8—611no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—611no—
354C2×#97—611no—
355C2×#97C2×D6111yescharacteristic
356C2×C4×C8—611no—
357C2×C4×C8—611no—
358#389—611no—
359#389—611no—
360#389—611no—
361#389—611no—
362#385—611no—
363#385—611no—
364#385—611no—
365#385—611no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4—611no—
368C4×C4⋊C4—611no—
369C4×C4⋊C4C2×D6111yescharacteristic
370#336—611no—
371#336—611no—
372#336—611no—
373#336—611no—
374#336—611no—
375#336—611no—
376#336C2×D6111yescharacteristic
377#336C2×D6111yescharacteristic
378C61#2195811yescharacteristic, complemented, Sylow
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8C22×D6111yescharacteristic
387C22×C8C22×D6111yescharacteristic
388C22×C8C22×D6111yescharacteristic
389C22×C8C22×D6111yescharacteristic
390#117—614no—
391#117—614no—
392#117—2441no—
393#117—2441no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4C4×D6111yescharacteristic
405C2×C4⋊C4C4×D6111yescharacteristic
406C2×C22⋊C4—611no—
407C2×C22⋊C4—611no—
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—2441no—
416C2×C42—2441no—
417C2×C42C22×D6111yescharacteristic
418C2×C42C22×D6111yescharacteristic
419C2×C42C22×D6111yescharacteristic
420C4⋊C8—22no—
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—1222no—
424C4⋊C8—1222no—
425C4⋊C8—1222no—
426C4⋊C8—2441no—
427C4⋊C8—2441no—
428C4⋊C8—2441no—
429C4⋊C8—2441no—
430C4⋊C8—2441no—
431C4⋊C8—2441no—
432C22⋊C8—1222no—
433C22⋊C8—1222no—
434C22⋊C8—1222no—
435C22⋊C8—1222no—
436#97—22no—
437#97—1222no—
438C4×C8—1222no—
439C4×C8—1222no—
440#95—611no—
441#95—611no—
442#95—611no—
443#95—611no—
444#95—611no—
445#95—611no—
446#95C4×D6111yescharacteristic
447#95C4×D6111yescharacteristic
448C24—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—1222no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—2441no—
465C22×C4—2441no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4C2×C4×D6111yescharacteristic
470C22×C4C2×C4×D6111yescharacteristic
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C23×D6111yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—614no—
502C4⋊C4—614no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—2441no—
507C4⋊C4—2441no—
508C4⋊C4—2441no—
509C4⋊C4—2441no—
510C4⋊C4—2441no—
511C22⋊C4—614no—
512C22⋊C4—614no—
513C22⋊C4—2441no—
514C22⋊C4—2441no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—612no—
520C42—612no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—1221no—
525C42—2441no—
526C42—2441no—
527C42D4×D6112yes—
528C42Q8×D6112yes—
529C23—612no—
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23C22×C4×D6111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—2444no—
578C2×C4—2444no—
579C2×C4C4⋊C4×D6112yes—
580C2×C4C4⋊C4×D6112yes—
581C2×C4#1451978512yes—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C2×Q8×D6111yescharacteristic
584C2×C4#1451982211yescharacteristic
585C2×C4#1451982311yescharacteristic
586C2×C4#1451982411yescharacteristic
587C2×C4#1451982511yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—2441no—
593C8—2441no—
594C8—2441no—
595C8—2441no—
596C22—1222no—
597C22—1222no—
598C22—1222no—
599C22—2441no—
600C22—2441no—
601C22—2441no—
602C22—2441no—
603C22C2×C4⋊C4×D6111yescharacteristic
604C22#1684023411yescharacteristic
605C22#1684023811yescharacteristic
606C22#131×D6111yescharacteristic
607C22C2×#1451978511yescharacteristic
608C22#1684052711yescharacteristic
609C22#1684052811yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—1222no—
617C4—1222no—
618C4—1222no—
619C4—1222no—
620C4—2441no—
621C4—2441no—
622C4—2441no—
623C4#1684034111yescharacteristic
624C4#1684034211yescharacteristic
625C4#1684038911yescharacteristic
626C4#1684039211yescharacteristic
627C2—2442no—
628C2#2144843411yescharacteristic
629C2#2145438611yescharacteristic
630C2#2145438811yescharacteristic
631C2#2145487011yescharacteristic
632C2#2145487811yescharacteristic
633C2#2145491211yescharacteristic
634C2#2145491511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1940C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1940D61
hypocenterC61#21958
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
4. #21446542C2semidirect
5. #21446541C2semidirect
6. #21446539C2semidirect
7. #21446538C2semidirect
8. #21446536C2semidirect
9. #21446535C2semidirect
10. #21446534C2semidirect
15. C61×#1940C2semidirect
316. #1940D61semidirect
378. C61#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#168398242
C2×#168398222
#214482992
#214465422
#214465412
#214465392
#214465382
#214465362
#214465352
#214465342
#214458022
#214458002
#214457982
#214457962
C61×#19402
#2195861