Finite Group Databasebeta

← #29585469

Subgroups — #29585469

Order 15616.

1164 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×#16840528C211yesmaximal, characteristic
2C2×#16839744C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5#21445558C211yesmaximal, characteristic, complemented
6#21445557C211yesmaximal, characteristic, complemented
7C2×C61×#344C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840528—22no—
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13C2×#14519785—22no—
14C2×#14519783—22no—
15C22×#11758194C2211yescharacteristic
16C22×#11758194C2211yescharacteristic
17C2×M16×D61C414yescomplemented
18C2×#14519736C2211yescharacteristic
19#16839744—22no—
20#16839744—22no—
21C2×#14519695C412yescomplemented
22C2×#14519693C412yescomplemented
23#16839735—22no—
24#16839735—22no—
25C2×#14519691C414yes—
26#16839534—22no—
27#16839531—22no—
28#16839530—22no—
29C22×M16×C61C2211yescharacteristic
30C22×M16×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#344—22no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222D412yes—
42C2×#11758222D412yes—
43C2×#11758222D412yes—
44C2×#11758222Q812yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61C2×C412yes—
48C22×C4×D61C2×C412yes—
49#14519785—28no—
50#14519785—28no—
51#14519783—28no—
52#14519783—28no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194C2×C412yes—
62C2×#11758194C2×C412yes—
63C2×#11758194D412yes—
64C2×#11758194D412yes—
65C2×#11758189—24no—
66M16×D61—28no—
67M16×D61—28no—
68C22×#92418—21no—
69C22×#92418—21no—
70C2×C8×D61—24no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75C2×C4⋊Dic61—21no—
76C2×C22⋊Dic61C2×C412yes—
77C2×C4×Dic61—21no—
78#14519695—24no—
79#14519693—24no—
80#14519691—28no—
81C23×C4×C61C2311yescharacteristic
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61—21no—
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61C2×C412yes—
91C2×M16×C61C2×C412yes—
92C2×M16×C61D412yes—
93C2×M16×C61D412yes—
94C22×C8×C61—21no—
95C22×C8×C61—21no—
96#117×C61—21no—
97#117×C61—21no—
98#117×C61—21no—
99#117×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C22⋊C4×C61C2×C412yes—
102C2×C42×C61—21no—
103C24×C61C22×C411yescharacteristic
104C23×D61C4212yes—
105C22×C4×C61—22no—
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×Q811yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C2×C22⋊D61—22no—
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61C22⋊C414yes—
125C2×C22⋊D61C4⋊C414yes—
126C22×Dic61—22no—
127C22×Dic61C4212yes—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—22no—
139#11758222—22no—
140#11758222—22no—
141#11758222—22no—
142#11758222—22no—
143#11758222—22no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244C22⋊C412yes—
149C2×D244C4⋊C412yes—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61C22⋊C414yes—
155C2×C4×D61C4⋊C414yes—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22⋊C412yes—
161C2×Dic122C4⋊C412yes—
162M16×C61—22no—
163M16×C61—22no—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61—22no—
167M16×C61—41no—
168M16×C61—41no—
169M16×C61C22⋊C414yes—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—41no—
175C2×C8×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C42×C61—41no—
181C42×C61—41no—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C4⋊Dic61—41no—
185C4⋊Dic61—41no—
186C4×Dic61—41no—
187C4×Dic61—41no—
188#11758194—22no—
189#11758194—22no—
190#11758194—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—41no—
194#11758194—41no—
195#11758194C22⋊C414yes—
196C2×#92418—22no—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—41no—
201C2×#92418—41no—
202#11758189—216no—
203C8×D61—216no—
204C23×C61—81no—
205C23×C61C2×C4211yescharacteristic
206C23×C61C2×C22⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208C23×C61C4×D411yescharacteristic
209C23×C61C4×D411yescharacteristic
210C23×C61C4×D411yescharacteristic
211C23×C61C4×D411yescharacteristic
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—82no—
215C22×D61#9514yes—
216C2×C4×C61—42no—
217C2×C4×C61—82no—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C4⋊C411yescharacteristic
223C2×C4×C61C2×C4⋊C411yescharacteristic
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61#11711yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61#12011yescharacteristic
233C2×C4×C61#12011yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61C22⋊Q811yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61#12311yescharacteristic
243C2×C4×C61#12311yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C22⋊D61—24no—
249C22⋊D61—24no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61—82no—
254C2×Dic61#9514yes—
255D244—22no—
256D244—22no—
257D244—22no—
258D244—22no—
259C4×D61—24no—
260C4×D61—24no—
261C4×D61—24no—
262C4×D61—24no—
263Dic122—22no—
264Dic122—22no—
265Dic122—22no—
266Dic122—22no—
267C8×C61—24no—
268C8×C61—42no—
269#92418—24no—
270#92418—42no—
271#10771—611nomaximal, Sylow
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61C2×#9511yescharacteristic
280C22×C61C4×C22⋊C411yescharacteristic
281C22×C61C4×C22⋊C411yescharacteristic
282C22×C61#38511yescharacteristic
283C22×C61#38511yescharacteristic
284C22×C61#38611yescharacteristic
285C22×C61#38611yescharacteristic
286C2×D61—24no—
287C2×D61—44no—
288C2×D61—82no—
289C2×D61—82no—
290C4×C61—82no—
291C4×C61#37911yescharacteristic
292C4×C61#38011yescharacteristic
293C4×C61#38011yescharacteristic
294C4×C61#38111yescharacteristic
295C4×C61#38511yescharacteristic
296C4×C61#38511yescharacteristic
297C4×C61#38611yescharacteristic
298C4×C61#38611yescharacteristic
299Dic61—24no—
300Dic61—82no—
301C2×#568—611no—
302C2×#413—611no—
303C2×#410—611no—
304C2×#344—611no—
305C2×#344D6111yescharacteristic, complemented
306#1742—611no—
307#1742—611no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61C22⋊#9511yescharacteristic
316D61—44no—
317C22×#41—611no—
318#568—1222no—
319#568—1222no—
320#568—1222no—
321#568—1222no—
322C2×#131—1222no—
323C2×#131—1222no—
324C22×M16—611no—
325C22×M16—611no—
326C22×M16—614no—
327C22×M16C2×D6111yescharacteristic
328C22×M16C2×D6111yescharacteristic
329C2×#117—611no—
330C2×#117C2×D6111yescharacteristic
331#413—1222no—
332#413—1222no—
333C2×#101—612no—
334C2×#100—612no—
335#410—1222no—
336#410—1222no—
337C2×#99—614no—
338#344—22no—
339#344—1222no—
340#343—1222no—
341#343—1222no—
342C61#1077111yescharacteristic, complemented, Sylow
343C2×#41—612no—
344C2×#41—612no—
345C2×#41—612no—
346C2×#41—612no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C22×Q8—611no—
356C22×D4—612no—
357C22×D4—611no—
358C23×C4—612no—
359C23×C4C22×D6111yescharacteristic
360#131—1228no—
361#131—1228no—
362#131—1228no—
363#131—1228no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—612no—
373C2×M16—612no—
374C2×M16—612no—
375C2×M16—612no—
376C2×M16—1224no—
377C2×M16—1228no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1228no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16C4×D6112yes—
388C2×M16C4×D6112yes—
389C2×M16D24412yes—
390C2×M16C22⋊D6112yes—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—1224no—
394C22×C8—1221no—
395C22×C8—1221no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—1221no—
401#117—1221no—
402#117—1221no—
403#117—1221no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—1221no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4C4×D6112yes—
408C2×C42—21no—
409C2×C42—1221no—
410#101—1224no—
411#100—1224no—
412#99—1228no—
413C24—612no—
414C24C2×C4×D6111yescharacteristic
415#41—1222no—
416#41—1222no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—1222no—
430#41—1222no—
431C2×Q8—612no—
432C2×Q8—612no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×D4—614no—
438C2×D4—614no—
439C2×D4—612no—
440C2×D4—612no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—22no—
450C22×C4—612no—
451C22×C4—614no—
452C22×C4—614no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4C2×C4×D6111yescharacteristic
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4C2×D24411yescharacteristic
461C22×C4#1175822211yescharacteristic
462C22×C4#1175822211yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4D4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4D4×D6111yescharacteristic
468C22×C4#1175822411yescharacteristic
469C22×C4Q8×D6111yescharacteristic
470C22×C4#1175822611yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—41no—
478M16—41no—
479M16—614no—
480M16—12216no—
481M16—1222no—
482M16—1222no—
483M16—1222no—
484M16—1222no—
485M16—1222no—
486M16—2441no—
487M16—2441no—
488M16#1175819814yes—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—12216no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—2441no—
501C2×C8—2441no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—2441no—
505C4⋊C4—2441no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C42—41no—
511C42—41no—
512C42—2441no—
513C42—2441no—
514C23—81no—
515C23—614no—
516C23—1222no—
517C23—1222no—
518C23—4882no—
519C23C42×D6111yescharacteristic
520C23C22⋊C4×D6111yescharacteristic
521C23C4⋊C4×D6111yescharacteristic
522C23#1451973711yescharacteristic
523C23C4×C22⋊D6111yescharacteristic
524C23#1451973911yescharacteristic
525C23C4×D24411yescharacteristic
526Q8—1222no—
527Q8—1222no—
528Q8—1222no—
529Q8—1222no—
530D4—1224no—
531D4—1224no—
532D4—1224no—
533D4—1224no—
534D4—1222no—
535D4—1222no—
536D4—1222no—
537D4—1222no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—614no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—1224no—
546C2×C4—1224no—
547C2×C4—4882no—
548C2×C4—2442no—
549C2×C4C22⋊C4×D6111yescharacteristic
550C2×C4C22⋊C4×D6111yescharacteristic
551C2×C4C22⋊C4×D6111yescharacteristic
552C2×C4C2×#1175819811yescharacteristic
553C2×C4C4⋊C4×D6111yescharacteristic
554C2×C4C4⋊C4×D6111yescharacteristic
555C2×C4#1451973411yescharacteristic
556C2×C4#1451973511yescharacteristic
557C2×C4#1451973711yescharacteristic
558C2×C4C4×C22⋊D6111yescharacteristic
559C2×C4#1451973911yescharacteristic
560C2×C4C4×D24411yescharacteristic
561C2×C4#1451974511yescharacteristic
562C2×C4#1451974511yescharacteristic
563C2×C4#1451974711yescharacteristic
564C2×C4#1451974711yescharacteristic
565C2×C4#1451974811yescharacteristic
566C2×C4#1451975011yescharacteristic
567C2×C4#1451975011yescharacteristic
568C2×C4#1451975211yescharacteristic
569C2×C4#1451975311yescharacteristic
570C2×C4#1451975511yescharacteristic
571C2×C4#1451975511yescharacteristic
572C2×C4#1451975711yescharacteristic
573C2×C4#1451975911yescharacteristic
574C2×C4#1451975911yescharacteristic
575C2×C4#1451976211yescharacteristic
576C2×C4#1451976211yescharacteristic
577C8—24no—
578C8—42no—
579C8—1224no—
580C8—2442no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—1224no—
589C22—4882no—
590C22—4882no—
591C22—2444no—
592C22#95×D6111yescharacteristic
593C22#1683960911yescharacteristic
594C22C4×#1175819811yescharacteristic
595C22#1683963311yescharacteristic
596C22#1683963611yescharacteristic
597C22#1683963811yescharacteristic
598C22#1683964011yescharacteristic
599C4—82no—
600C4—1224no—
601C4—4882no—
602C4#1683961711yescharacteristic
603C4#1683961911yescharacteristic
604C4#1683962111yescharacteristic
605C4#1683962411yescharacteristic
606C4#1683963311yescharacteristic
607C4#1683963611yescharacteristic
608C4#1683963811yescharacteristic
609C4#1683964011yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—2444no—
618C2#2144404011yescharacteristic
subgroupG/H
centerC4#16839624
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#344C2
socleC2×C61C22⋊#95
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#344D61
hypocenterC61#10771
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#16839534C2semidirect
5. #21445558C2semidirect
6. #21445557C2semidirect
7. C2×C61×#344C2semidirect
17. C2×M16×D61C4semidirect
21. C2×#14519695C4semidirect
22. C2×#14519693C4semidirect
305. C2×#344D61semidirect
342. C61#10771semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168397442
C2×#168397352
C2×#168395342
#214455582
#214455572
C2×C61×#3442
#1077161