Finite Group Databasebeta

← #29731925

Subgroups — #29731925

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840063C211yesmaximal, characteristic
2#21451207C211yesmaximal, characteristic, complemented
3#21451177C211yesmaximal, characteristic
4#21447317C211yesmaximal, characteristic, complemented
5#21447307C211yesmaximal, characteristic, complemented
6#21447206C211yesmaximal, characteristic
7#21447192C211yesmaximal, characteristic
8#21446784C211yesmaximal, characteristic, complemented
9#21446589C211yesmaximal, characteristic, complemented
10#21446562C211yesmaximal, characteristic, complemented
11#21446557C211yesmaximal, characteristic, complemented
12#21446516C211yesmaximal, characteristic
13#21446516C211yesmaximal, characteristic
14C4×#14519699C211yesmaximal, characteristic
15C2×C61×#446C211yesmaximal, characteristic, complemented
16C2×#14519769C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840063—24no—
19C2×#14519711C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27#16839697—21no—
28#16839693—21no—
29#16839681—21no—
30#16839673—21no—
31#16839664C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839657—21no—
40#16839657—21no—
41#16839633—21no—
42#16839633—21no—
43#16839628C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#446—24no—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63#14519769—22no—
64#14519769—22no—
65C4×D244—22no—
66C4×D244—22no—
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88#14519711—22no—
89#14519711—22no—
90#14519709—22no—
91#14519709—22no—
92#14519699—22no—
93#14519699—22no—
94#14519699—22no—
95#14519699Q814yescomplemented
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C22×Q8×C61D411yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C4×Q8×C61—22no—
111C4×Q8×C61—22no—
112C2×C4⋊C4×C61D411yescharacteristic
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C4⋊C8×C61—22no—
119C4⋊C8×C61—22no—
120C4⋊C8×C61D414yes—
121#97×C61—22no—
122#97×C61—22no—
123C4×C8×C61—22no—
124C23×D61—21no—
125C2×Q8×C61—22no—
126C2×Q8×C61—41no—
127C2×Q8×C61—41no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244C2×Q812yes—
148C2×C4×D61—42no—
149C2×C4×D61—81no—
150C2×C4×D61—81no—
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×C61C2×D412yes—
161C2×C8×C61C2×D412yes—
162C2×C8×C61C2×Q812yes—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61C2×D412yes—
171C42×C61#4112yes—
172#11758198—42no—
173#11758198—42no—
174#11758198—42no—
175#11758198—81no—
176#11758198—81no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C2×Q812yes—
190C4⋊Dic61#4112yes—
191#11758196—42no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195#11758196—81no—
196#11758196—81no—
197#11758196—81no—
198#11758196—81no—
199C4×Dic61—81no—
200C23×C61C22×D411yescharacteristic
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208Q8×C61—44no—
209C2×C4×C61—21no—
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—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61#12112yes—
226C2×C4×C61#12112yes—
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×Q811yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C612−1+411yescharacteristic
232C2×C4×C612−1+411yescharacteristic
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
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—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254D244—22no—
255D244—22no—
256D244—41no—
257D244—41no—
258C4×D61—84no—
259C8×C61—22no—
260C8×C61—22no—
261C8×C61—22no—
262C8×C61—41no—
263#25475—611nomaximal, Sylow
264C22×C61C2×#12111yescharacteristic
265C22×C61#54811yescharacteristic
266C22×C61D4×Q811yescharacteristic
267C22×C61#57511yescharacteristic
268C22×C61#57511yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—81no—
277C2×D61—81no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61#53311yescharacteristic
285C4×C61#54111yescharacteristic
286C4×C61#54711yescharacteristic
287C4×C61D4×Q811yescharacteristic
288Dic61—42no—
289Dic61—42no—
290Dic61—81no—
291Dic61—81no—
292Dic61—81no—
293Dic61—81no—
294Dic61—81no—
295C2×#478—611no—
296C2×#446D6111yescharacteristic, complemented
297#2584—611no—
298#2580—611no—
299#2088—611no—
300#2086—611no—
301#2067—611no—
302#2065—611no—
303#1991—611no—
304#1949—611no—
305#1944—611no—
306#1943—611no—
307#1936—611no—
308#1936—611no—
309C4×#102—611no—
310C2×C61#242911yescharacteristic
311C2×C61#305411yescharacteristic
312C2×C61#306211yescharacteristic
313C2×C61#337011yescharacteristic
314C2×C61#337111yescharacteristic
315C2×C61#338811yescharacteristic
316C2×C61#338911yescharacteristic
317D61—82no—
318C2×#125—611no—
319C2×C4×Q8C2×D6111yescharacteristic
320C2×C4×D4—611no—
321#478—1224no—
322#446—24no—
323C2×#107—611no—
324C2×#107—611no—
325C2×#106—611no—
326C2×#106—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328C2×C4⋊C8C2×D6111yescharacteristic
329C2×C4⋊C8C2×D6111yescharacteristic
330C2×#102—611no—
331C2×#102—611no—
332C2×#102—611no—
333C2×#102—611no—
334C2×#97C2×D6111yescharacteristic
335C2×#97C2×D6111yescharacteristic
336C2×C4×C8C2×D6111yescharacteristic
337#399—1221no—
338#398—1221no—
339#395—1221no—
340#393—1221no—
341#390—611no—
342#390—611no—
343#389—611no—
344#389—611no—
345#389—611no—
346#389—611no—
347#389—611no—
348#389—611no—
349#389—1221no—
350#389—1221no—
351#385—1221no—
352#385—1221no—
353#382—611no—
354C4×C4⋊C4—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363C61#2547511yescharacteristic, complemented, Sylow
364C22×Q8D24411yescharacteristic
365C22×D4—611no—
366C23×C4—1221no—
367C22×C8C22×D6111yescharacteristic
368C22×C8C22×D6111yescharacteristic
369C22×C8C22×D6111yescharacteristic
370C22×C8C22×D6111yescharacteristic
371#125—1222no—
372#125—1222no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—1222no—
376C4×D4—1222no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4D24411yescharacteristic
393C2×C4⋊C4D24411yescharacteristic
394C2×C4⋊C4D24411yescharacteristic
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C42—1221no—
401C2×C42C22×D6111yescharacteristic
402C2×C42C22×D6111yescharacteristic
403C2×C42C22×D6111yescharacteristic
404#107—1222no—
405#107—1222no—
406#106—1222no—
407#106—1222no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410C4⋊C8C22⋊D6114yes—
411#102—614no—
412#102—1222no—
413#102—1222no—
414#102—1222no—
415#97—22no—
416#97—22no—
417C4×C8—22no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427C24—1221no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×D4—612no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—4881no—
445C22×C4—4881no—
446C22×C4—2442no—
447C22×C4C2×D24411yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4C2×D24411yescharacteristic
450C22×C4C2×D24411yescharacteristic
451C22×C4C2×D24411yescharacteristic
452C22×C4C2×D24411yescharacteristic
453C22×C4C23×D6111yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8Q8×D6112yes—
464C2×C8C2×C22⋊D6112yes—
465C2×C8C2×C22⋊D6112yes—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—612no—
470C4⋊C4—612no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—4881no—
484C4⋊C4—4881no—
485C4⋊C4—4881no—
486C4⋊C4—4881no—
487C4⋊C4—2442no—
488C4⋊C4—2442no—
489C4⋊C4—2442no—
490C4⋊C4—2442no—
491C22⋊C4—4881no—
492C22⋊C4—4881no—
493C22⋊C4—2442no—
494C22⋊C4—2442no—
495C22⋊C4—2442no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—4881no—
501C42#1175822212yes—
502C42C2×C22⋊D6112yes—
503C23—1222no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23—2441no—
510C23C22×D24411yescharacteristic
511Q8—44no—
512D4—1222no—
513D4—1222no—
514D4—2441no—
515D4—2441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
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—1222no—
533C2×C4—1222no—
534C2×C4—4884no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4#1451975112yes—
555C2×C4#1451975112yes—
556C2×C4C22×C22⋊D6111yescharacteristic
557C2×C4C2×Q8×D6111yescharacteristic
558C2×C4#41×D6111yescharacteristic
559C2×C4C2×#1175822211yescharacteristic
560C2×C4#1451982411yescharacteristic
561C2×C4#1451982511yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—4881no—
567C22—4881no—
568C22—4881no—
569C22—4881no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C2×#1451975111yescharacteristic
574C22#1684042411yescharacteristic
575C22Q8×D24411yescharacteristic
576C22#1684056211yescharacteristic
577C22#1684056211yescharacteristic
578C22#1684056711yescharacteristic
579C22#1684057411yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—4881no—
587C4—4881no—
588C4—4881no—
589C4—4881no—
590C4—4881no—
591C4—2442no—
592C4—2442no—
593C4#1684031611yescharacteristic
594C4#1684037011yescharacteristic
595C4#1684041111yescharacteristic
596C4Q8×C22⋊D6111yescharacteristic
597C2—4882no—
598C2#2144941211yescharacteristic
599C2#2145542811yescharacteristic
600C2#2145549911yescharacteristic
601C2#2145857411yescharacteristic
602C2#2145858911yescharacteristic
603C2#2145876611yescharacteristic
604C2#2145877911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#446C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#446D61
hypocenterC61#25475
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21451207C2semidirect
4. #21447317C2semidirect
5. #21447307C2semidirect
8. #21446784C2semidirect
9. #21446589C2semidirect
10. #21446562C2semidirect
11. #21446557C2semidirect
15. C2×C61×#446C2semidirect
95. #14519699Q8semidirect
296. C2×#446D61semidirect
363. C61#25475semidirect

Maximal subgroups

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

subgroupindex
C2×#168400632
#214512072
#214511772
#214473172
#214473072
#214472062
#214471922
#214467842
#214465892
#214465622
#214465572
#214465162
C4×#145196992
C2×C61×#4462
#2547561