Finite Group Databasebeta

← #29685001

Subgroups — #29685001

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840290C211yesmaximal, characteristic
2C2×#16839813C211yesmaximal, characteristic, complemented
3C2×#16839714C211yesmaximal, characteristic, complemented
4#21446753C212yesmaximal, complemented
5#21446611C212yesmaximal, complemented
6#21446115C212yesmaximal, complemented
7#21446113C212yesmaximal, complemented
8#21445588C211yesmaximal, characteristic, complemented
9#21445586C211yesmaximal, characteristic, complemented
10#21445585C211yesmaximal, characteristic, complemented
11C61×#1750C211yesmaximal, characteristic, complemented
12C22×#11758189C2212yes—
13#16840290—24no—
14#16840290—24no—
15C2×#14519772C411yescharacteristic
16C2×#14519770C411yescharacteristic
17C2×#14519767C411yescharacteristic
18C2×#14519763C411yescharacteristic
19C2×#14519762C411yescharacteristic
20C2×#14519759C411yescharacteristic
21C2×#14519755C411yescharacteristic
22C2×#14519750C411yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×#14519734C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29#16839813—24no—
30C2×#14519706C2212yes—
31C2×C22⋊#92418C2212yes—
32C2×#14519689C2212yes—
33C2×#14519689C2212yes—
34C2×#14519689C2212yes—
35#16839714—24no—
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38C2×C8×Dic61C2212yes—
39#16839517C2212yes—
40#16839516C2212yes—
41#16839516C2212yes—
42C2×#117×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2212yes—
44C2×#97×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C61×#336C2212yes—
47C22×Dic122C2×C411yescharacteristic
48C22×D244C2×C411yescharacteristic
49C22×C22⋊D61C2×C411yescharacteristic
50C22×C22⋊D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C22×C4×D61C2311yescharacteristic
55C2×#11758189—24no—
56C2×#11758189—24no—
57C2×#11758189—24no—
58C22×#92418C2312yes—
59C22×#92418C2312yes—
60#14519772—24no—
61#14519770—24no—
62#14519767—24no—
63#14519763—24no—
64#14519762—24no—
65#14519759—24no—
66#14519755—24no—
67#14519750—24no—
68C4×Dic122—22no—
69C4×Dic122—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76#14519734—22no—
77#14519734—22no—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61D414yes—
99C42×D61D414yes—
100#14519706—24no—
101C22⋊#92418—24no—
102#14519689—24no—
103#14519689—24no—
104#14519689—24no—
105#14519688—22no—
106C4×#92418—22no—
107C8×Dic61—24no—
108C23×C4×C61C2311yescharacteristic
109C22×C8×C61C2312yes—
110C22×C8×C61C2312yes—
111#117×C61—22no—
112#117×C61—22no—
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C22⋊C4×C61C2×C411yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C22⋊C8×C61—24no—
120#97×C61—22no—
121C4×C8×C61—22no—
122C24×C61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
124C23×D61C22×C411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C2×C22⋊D61—22no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61—24no—
138C2×C22⋊D61—42no—
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C2×D244—22no—
146C2×D244—42no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—24no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—42no—
155C2×C4×D61C22⋊C414yes—
156C2×C4×D61C22⋊C414yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×Dic122—22no—
160C2×Dic122—24no—
161C2×C8×C61—22no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61#4114yes—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61C2×D412yes—
174C42×C61C2×D412yes—
175C22⋊Dic61—22no—
176C22⋊Dic61—22no—
177#11758198—22no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61C22⋊C414yes—
194C4×Dic61C22⋊C414yes—
195C4×Dic61C2×D412yes—
196C4×Dic61C2×D412yes—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418#4114yes—
203#11758189—216no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—22no—
208C23×C61—22no—
209C23×C61C23×C411yescharacteristic
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61C2×C22⋊C412yes—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61C2×C22⋊C412yes—
232C2×C4×C61C2×C22⋊C412yes—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4112yes—
236C2×C4×C61C2×#4112yes—
237C22⋊D61—44no—
238C22⋊D61—44no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61C2×C22⋊C412yes—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61#13114yes—
253D244—44no—
254C4×D61—24no—
255C4×D61—24no—
256C4×D61—28no—
257C4×D61—44no—
258C4×D61—42no—
259C4×D61—42no—
260Dic122—44no—
261C8×C61—24no—
262C8×C61—42no—
263#92418—24no—
264#92418—42no—
265#21378—611nomaximal, Sylow
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—41no—
271C22×C61C22×C22⋊C411yescharacteristic
272C22×C61C4×#4111yescharacteristic
273C22×C61C4×#4111yescharacteristic
274C22×C61C2×#13112yes—
275C22×C61#56812yes—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—41no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61#52512yes—
292C4×C61#53212yes—
293Dic61—22no—
294Dic61—22no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298Dic61#40814yes—
299C2×#529—611no—
300C2×#431—611no—
301C2×C4×M16—611no—
302#1984—612no—
303#1954—612no—
304#1870—612no—
305#1870—612no—
306#1750—611no—
307#1750—611no—
308#1750—611no—
309#1750D6111yescharacteristic, complemented
310C2×C61—81no—
311C2×C61#229711yescharacteristic
312C2×C61C2×#40811yescharacteristic
313C2×C61#287911yescharacteristic
314C2×C61#296912yes—
315C2×C61#296912yes—
316D61—42no—
317D61—81no—
318C22×M16—612no—
319#529—1224no—
320#529—1224no—
321C2×#126—611no—
322C2×#126—611no—
323C2×#125—611no—
324C2×#124—611no—
325C2×#123—611no—
326C2×#123—611no—
327C2×C22⋊Q8—611no—
328C2×#121—611no—
329C2×C4×Q8—611no—
330C2×C4×D4—611no—
331C2×C4×D4—611no—
332C2×C4×D4—611no—
333C2×#117—611no—
334C2×#117C2×D6111yescharacteristic
335C22×C42—611no—
336#431—1224no—
337C2×C4⋊C8—612no—
338C2×C22⋊C8—612no—
339C2×C22⋊C8—612no—
340C2×C22⋊C8—612no—
341C2×C22⋊C8—612no—
342C2×C22⋊C8C2×D6112yes—
343C4×M16—1224no—
344C2×#97—611no—
345C2×#97C2×D6111yescharacteristic
346C2×C4×C8—612no—
347C2×C4×C8—611no—
348C2×C4×C8C2×D6111yescharacteristic
349#336—612no—
350#336—612no—
351#336—612no—
352#336C2×D6112yes—
353C61#2137811yescharacteristic, complemented, Sylow
354C22×Q8—611no—
355C22×D4—611no—
356C22×D4—611no—
357C22×D4—611no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4C22×D6111yescharacteristic
363C2×M16—1224no—
364C2×M16—1224no—
365C2×M16—1224no—
366C22×C8—612no—
367C22×C8—612no—
368C22×C8C22×D6112yes—
369C22×C8C22×D6112yes—
370#126—1224no—
371#126—1224no—
372#125—1224no—
373#124—1224no—
374#123—1224no—
375#123—1224no—
376C22⋊Q8—1224no—
377#121—1224no—
378C4×Q8—1222no—
379C4×Q8—1222no—
380C4×D4—1222no—
381C4×D4—1222no—
382C4×D4—1222no—
383C4×D4—1222no—
384C4×D4—1222no—
385C4×D4—1222no—
386#117—22no—
387#117—22no—
388#117—1222no—
389#117—1222no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4C4×D6111yescharacteristic
399C2×C4⋊C4C4×D6111yescharacteristic
400C2×C22⋊C4—611no—
401C2×C22⋊C4—611no—
402C2×C22⋊C4—611no—
403C2×C22⋊C4—611no—
404C2×C22⋊C4—611no—
405C2×C22⋊C4—611no—
406C2×C22⋊C4—611no—
407C2×C22⋊C4—611no—
408C2×C22⋊C4C4×D6111yescharacteristic
409C2×C22⋊C4C4×D6111yescharacteristic
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—614no—
414C2×C42—614no—
415C2×C42—611no—
416C2×C42C22×D6111yescharacteristic
417C2×C42C22×D6111yescharacteristic
418C4⋊C8—1224no—
419C22⋊C8—24no—
420C22⋊C8—1224no—
421C22⋊C8—1224no—
422C22⋊C8—1224no—
423C22⋊C8—1224no—
424#97—22no—
425#97—1222no—
426C4×C8—22no—
427C4×C8—1224no—
428C4×C8—1222no—
429C24—611no—
430C24—611no—
431C24C2×C4×D6111yescharacteristic
432C2×Q8—1222no—
433C2×Q8—1224no—
434C2×D4—1222no—
435C2×D4—1222no—
436C2×D4—1224no—
437C2×D4—1222no—
438C2×D4—2442no—
439C2×D4—2442no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—614no—
450C22×C4—614no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—1224no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—2442no—
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C23×D6111yescharacteristic
468M16—12216no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—614no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C2×C8—1222no—
479C2×C8—1222no—
480C2×C8#1175822214yes—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C42—21no—
502C42—21no—
503C42—612no—
504C42—612no—
505C42—614no—
506C42—614no—
507C42—1221no—
508C42—1221no—
509C42D4×D6112yes—
510C42D4×D6112yes—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—22no—
516C23—612no—
517C23—1221no—
518C23—1221no—
519C23—1222no—
520C23—1222no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23—1222no—
525C23—1222no—
526C23C22×C4×D6111yescharacteristic
527Q8—2444no—
528D4—2444no—
529D4—2444no—
530D4—2444no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—612no—
543C2×C4—614no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—1228no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1222no—
550C2×C4—1224no—
551C2×C4—1224no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—2444no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4C22⋊C4×D6112yes—
563C2×C4C22⋊C4×D6112yes—
564C2×C4C2×D4×D6111yescharacteristic
565C2×C4C2×D4×D6111yescharacteristic
566C2×C4#41×D6112yes—
567C2×C4C2×#1175822212yes—
568C8—24no—
569C8—42no—
570C8—1224no—
571C8—2442no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—1222no—
578C22—1222no—
579C22—1222no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2442no—
584C22—2442no—
585C22—2442no—
586C22—2442no—
587C22C2×C22⋊C4×D6111yescharacteristic
588C22#1684023011yescharacteristic
589C22C4×#1175822211yescharacteristic
590C22#131×D6112yes—
591C22#1684052712yes—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—614no—
598C4—1222no—
599C4—1222no—
600C4—2441no—
601C4—2441no—
602C4—2441no—
603C4#1684027112yes—
604C4#1684030912yes—
605C2—81no—
606C2—4881no—
607C2—2442no—
608C2#2144830511yescharacteristic
609C2#408×D6111yescharacteristic
610C2#2145426111yescharacteristic
611C2#2145481912yes—
612C2#2145482112yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1750C2
prime radicalC2×#14519750C4
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#21378
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#16839813C2semidirect
3. C2×#16839714C2semidirect
4. #21446753C2semidirect
5. #21446611C2semidirect
6. #21446115C2semidirect
7. #21446113C2semidirect
8. #21445588C2semidirect
9. #21445586C2semidirect
10. #21445585C2semidirect
11. C61×#1750C2semidirect
309. #1750D61semidirect
353. C61#21378semidirect

Maximal subgroups

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

subgroupindex
C2×#168402902
C2×#168398132
C2×#168397142
#214467532
#214466112
#214461152
#214461132
#214455882
#214455862
#214455852
C61×#17502
#2137861