Finite Group Databasebeta

← #29687968

Subgroups — #29687968

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839886C211yesmaximal, characteristic, complemented
2C2×#16839837C211yesmaximal, characteristic
3#21449106C211yesmaximal, characteristic
4#21446757C211yesmaximal, characteristic, complemented
5#21446615C211yesmaximal, characteristic
6#21446428C211yesmaximal, characteristic, complemented
7#21446425C211yesmaximal, characteristic, complemented
8#21446424C211yesmaximal, characteristic, complemented
9#21445937C211yesmaximal, characteristic, complemented
10#21445605C211yesmaximal, characteristic, complemented
11#21445603C211yesmaximal, characteristic, complemented
12#21445601C211yesmaximal, characteristic, complemented
13#21445599C211yesmaximal, characteristic, complemented
14#21445505C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20#16839886—24no—
21#16839837—24no—
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839704C411yescharacteristic
37#16839703C411yescharacteristic
38#16839691C411yescharacteristic
39#16839690C411yescharacteristic
40#16839678C411yescharacteristic
41#16839677C411yescharacteristic
42#16839675C411yescharacteristic
43#16839674C411yescharacteristic
44C4×#11758198C2211yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47#16839608C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C4×Dic122—22no—
75C4×Dic122—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519706—22no—
94#14519706—22no—
95#14519706—22no—
96C22⋊#92418—22no—
97#14519689—22no—
98#14519689—22no—
99#14519689—22no—
100#14519688—22no—
101#14519687—22no—
102#14519687—22no—
103C4×#92418—22no—
104C8×Dic61—22no—
105C8×Dic61—22no—
106C8×Dic61D414yes—
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126C4⋊C8×C61—22no—
127C22⋊C8×C61—22no—
128C22⋊C8×C61—22no—
129C4×C8×C61—22no—
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—41no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×Dic122—22no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61C2×D412yes—
176C2×C8×C61#4112yes—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—41no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—41no—
186#11758198—22no—
187#11758198—22no—
188#11758198—22no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61C2×D412yes—
200C4×Dic61#4112yes—
201#11758194—44no—
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×#92418C2×D412yes—
211C2×#92418#4112yes—
212C2×#92418#4112yes—
213C2×#92418#4112yes—
214#11758189—44no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61C23×C411yescharacteristic
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61#13112yes—
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C22⋊D61—44no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61C4×D412yes—
275C2×Dic61C4×D412yes—
276C2×Dic61#13112yes—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281Dic122—28no—
282C8×C61—22no—
283C8×C61—22no—
284C8×C61—41no—
285C8×C61—41no—
286#92418—22no—
287#92418—41no—
288#92418—41no—
289#92418#12414yes—
290#21639—611nomaximal, Sylow
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61C2×C4×D411yescharacteristic
299C22×C61C4×#4111yescharacteristic
300C22×C61C4×#4111yescharacteristic
301C22×C61C2×#13111yescharacteristic
302C22×C61C2×#13111yescharacteristic
303C22×C61#56811yescharacteristic
304C22×C61#56811yescharacteristic
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C4×C61—22no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61C2×#12411yescharacteristic
318C4×C61#52911yescharacteristic
319C4×C61#52911yescharacteristic
320C4×C61#53211yescharacteristic
321Dic61—22no—
322Dic61—22no—
323Dic61—22no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61—41no—
328C2×C8×Q8—611no—
329C2×#436—611no—
330#2398—611no—
331#1985—611no—
332#1955—611no—
333#1923—611no—
334#1923—611no—
335#1923—611no—
336#1923D6111yescharacteristic, complemented
337#1832—611no—
338#1753—611no—
339#1753—611no—
340#1753—611no—
341#1753—611no—
342#1726—611no—
343C2×C61—81no—
344C2×C61C4×#12411yescharacteristic
345C2×C61#292911yescharacteristic
346C2×C61#293011yescharacteristic
347C2×C61#296911yescharacteristic
348C2×C61#296911yescharacteristic
349C2×C61#296911yescharacteristic
350C2×C61#296911yescharacteristic
351D61—81no—
352C22×M16—611no—
353C22×M16—611no—
354C2×C4×Q8—611no—
355C2×C4×D4—611no—
356C8×Q8—1224no—
357#436—1224no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8—611no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8C2×D6111yescharacteristic
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×C22⋊C8C2×D6111yescharacteristic
367C2×C22⋊C8C2×D6111yescharacteristic
368C2×#97—611no—
369C2×#97—611no—
370C2×#97—611no—
371C2×C4×C8—611no—
372C2×C4×C8—611no—
373C2×C4×C8—611no—
374C2×C4×C8—611no—
375C2×C4×C8C2×D6111yescharacteristic
376#400—611no—
377#400—611no—
378#397—611no—
379#397—611no—
380#394—611no—
381#394—611no—
382#393—611no—
383#393—611no—
384C4×C22⋊C4—611no—
385C4×C22⋊C4—611no—
386C4×C22⋊C4—611no—
387C4×C22⋊C4C2×D6111yescharacteristic
388#376—611no—
389#336—611no—
390#336—611no—
391#336—611no—
392#336—611no—
393#336—611no—
394#336—611no—
395#336C2×D6111yescharacteristic
396#336C2×D6111yescharacteristic
397C61#2163911yescharacteristic, complemented, Sylow
398C22×Q8—611no—
399C22×D4—611no—
400C23×C4—611no—
401C23×C4C22×D6111yescharacteristic
402C2×M16—1222no—
403C2×M16—1222no—
404C2×M16—1222no—
405C2×M16—1222no—
406C2×M16—1222no—
407C2×M16—1222no—
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8C22×D6111yescharacteristic
413C22×C8C22×D6111yescharacteristic
414C22×C8C22×D6111yescharacteristic
415C22×C8C22×D6111yescharacteristic
416C4×Q8—1222no—
417C4×Q8—1222no—
418C4×D4—1222no—
419C4×D4—1222no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4C4×D6111yescharacteristic
433C2×C22⋊C4C4×D6111yescharacteristic
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42C22×D6111yescharacteristic
438C2×C42C22×D6111yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—1222no—
441C4⋊C8—1222no—
442C4⋊C8—1222no—
443C22⋊C8—22no—
444C22⋊C8—22no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447C22⋊C8—1222no—
448C22⋊C8—1222no—
449#97—1222no—
450#97—1222no—
451#97—1222no—
452C4×C8—22no—
453C4×C8—614no—
454C4×C8—1222no—
455C4×C8—1222no—
456C4×C8—1222no—
457#95—611no—
458#95—611no—
459#95—611no—
460#95—611no—
461#95—611no—
462#95—611no—
463#95—611no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95C4×D6111yescharacteristic
468#95C4×D6111yescharacteristic
469C24—611no—
470C24C2×C4×D6111yescharacteristic
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×Q8—1222no—
474C2×D4—1222no—
475C2×D4—2441no—
476C2×D4—2441no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4C2×C4×D6111yescharacteristic
498C22×C4C2×C4×D6111yescharacteristic
499C22×C4C2×C4×D6111yescharacteristic
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502M16—2444no—
503M16—2444no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—612no—
515C2×C8—612no—
516C2×C8—612no—
517C2×C8—612no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8D4×D6112yes—
527C2×C8#1175822412yes—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—2441no—
540C22⋊C4—2441no—
541C22⋊C4—2441no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—612no—
547C42—612no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23C22×C4×D6111yescharacteristic
567Q8—1228no—
568D4—2444no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4#1451978312yes—
613C2×C4C2×D4×D6111yescharacteristic
614C2×C4#41×D6111yescharacteristic
615C2×C4#41×D6111yescharacteristic
616C2×C4#41×D6111yescharacteristic
617C2×C4#41×D6111yescharacteristic
618C2×C4C2×#1175822411yescharacteristic
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—614no—
624C8—1222no—
625C8—2441no—
626C8—2441no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—2441no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22C4×D4×D6111yescharacteristic
642C22C4×#1175822411yescharacteristic
643C22#1684023011yescharacteristic
644C22#131×D6111yescharacteristic
645C22C2×#1451978311yescharacteristic
646C22#1684052711yescharacteristic
647C22#1684052811yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—1222no—
654C4—1222no—
655C4—1222no—
656C4—2441no—
657C4—2441no—
658C4—2441no—
659C4—2441no—
660C4#124×D6111yescharacteristic
661C4#1684028911yescharacteristic
662C4#1684029511yescharacteristic
663C4#1684030711yescharacteristic
664C2—81no—
665C2—4881no—
666C2#2144836011yescharacteristic
667C2#2145450811yescharacteristic
668C2#2145451911yescharacteristic
669C2#2145481611yescharacteristic
670C2#2145481711yescharacteristic
671C2#2145482011yescharacteristic
672C2#2145482111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1923C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1923D61
hypocenterC61#21639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16839886C2semidirect
4. #21446757C2semidirect
6. #21446428C2semidirect
7. #21446425C2semidirect
8. #21446424C2semidirect
9. #21445937C2semidirect
10. #21445605C2semidirect
11. #21445603C2semidirect
12. #21445601C2semidirect
13. #21445599C2semidirect
14. #21445505C2semidirect
15. C61×#1923C2semidirect
336. #1923D61semidirect
397. C61#21639semidirect

Maximal subgroups

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

subgroupindex
C2×#168398862
C2×#168398372
#214491062
#214467572
#214466152
#214464282
#214464252
#214464242
#214459372
#214456052
#214456032
#214456012
#214455992
#214455052
C61×#19232
#2163961