Finite Group Databasebeta

← #29587207

Subgroups — #29587207

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839789C211yesmaximal, characteristic, complemented
2C2×#16839735C211yesmaximal, characteristic
3#21454263C211yesmaximal, characteristic
4C2×#16839730C211yesmaximal, characteristic
5C2×#16839534C211yesmaximal, characteristic, complemented
6#21445517C211yesmaximal, characteristic, complemented
7C2×C61×#344C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839789—22no—
13#16839789—22no—
14C2×C4⋊#92418—22no—
15#16839735—22no—
16#16839735—22no—
17C2×#14519691C414yes—
18#16839730—22no—
19#16839730—22no—
20#16839730—22no—
21#16839728—22no—
22#16839725—22no—
23C2×#14519689—22no—
24#16839534—22no—
25#16839516—22no—
26C22×M16×C61C2211yescharacteristic
27C22×M16×C61C2211yescharacteristic
28C2×#117×C61C2211yescharacteristic
29C61×#344—22no—
30C2×#11758222—21no—
31C2×#11758222—21no—
32C2×#11758222—21no—
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×#11758222—21no—
42C22×Dic122Q811yescharacteristic
43C22×D244Q811yescharacteristic
44C22×C22⋊D61C2×C412yes—
45C22×C4×D61D412yes—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418D412yes—
59C22×#92418D412yes—
60#14519736—21no—
61#14519736—21no—
62#14519736—21no—
63#14519736—21no—
64C2×C4⋊Dic61—21no—
65C2×C22⋊Dic61C2×C412yes—
66C2×C4×Dic61—21no—
67C4⋊#92418—28no—
68#14519691—28no—
69#14519689—28no—
70#14519689—28no—
71C23×C4×C61C2311yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61D412yes—
84C22×C8×C61—21no—
85C22×C8×C61D412yes—
86#117×C61—21no—
87#117×C61—21no—
88#117×C61D412yes—
89#117×C61D412yes—
90C2×C4⋊C4×C61—21no—
91C2×C22⋊C4×C61C2×C412yes—
92C2×C42×C61—21no—
93C24×C61C22×C411yescharacteristic
94C23×D61C4⋊C412yes—
95C22×C4×C61—22no—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×Q811yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C2×C22⋊D61—22no—
111C2×C22⋊D61—22no—
112C2×C22⋊D61—22no—
113C2×C22⋊D61—22no—
114C2×C22⋊D61—22no—
115C2×C22⋊D61—22no—
116C22×Dic61—22no—
117C22×Dic61C4⋊C412yes—
118#11758222—41no—
119#11758222—41no—
120#11758222—41no—
121#11758222—41no—
122#11758222—41no—
123#11758222—41no—
124#11758222—41no—
125#11758222—41no—
126#11758222—41no—
127#11758222—41no—
128#11758222—41no—
129#11758222—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152M16×C61—22no—
153M16×C61—22no—
154M16×C61—41no—
155M16×C61—41no—
156M16×C61—41no—
157M16×C61—41no—
158M16×C61—41no—
159M16×C61—41no—
160C2×C8×C61—22no—
161C2×C8×C61—22no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—41no—
165C2×C8×C61—41no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61C22⋊C414yes—
170C42×C61—22no—
171C42×C61—22no—
172C22⋊Dic61—22no—
173C22⋊Dic61—22no—
174C4⋊Dic61—41no—
175C4⋊Dic61—41no—
176C4×Dic61—41no—
177C4×Dic61—41no—
178#11758194—41no—
179#11758194—41no—
180#11758194—41no—
181#11758194—41no—
182C2×#92418—22no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—41no—
189C2×#92418—41no—
190C2×#92418—41no—
191C2×#92418—41no—
192C23×C61—42no—
193C23×C61C2×C22⋊C411yescharacteristic
194C23×C61C2×C4⋊C411yescharacteristic
195C23×C61#11711yescharacteristic
196C23×C61C4×D411yescharacteristic
197C23×C61C4×D411yescharacteristic
198C23×C61C4×D411yescharacteristic
199C23×C61C4×D411yescharacteristic
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—44no—
204C2×C4×C61—24no—
205C2×C4×C61—44no—
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12111yescharacteristic
210C2×C4×C61#12111yescharacteristic
211C2×C4×C61#12111yescharacteristic
212C2×C4×C61#12111yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61#12111yescharacteristic
217C2×C4×C61C22⋊Q811yescharacteristic
218C2×C4×C61C22⋊Q811yescharacteristic
219C2×C4×C61C22⋊Q811yescharacteristic
220C2×C4×C61C22⋊Q811yescharacteristic
221C2×C4×C61C22⋊Q811yescharacteristic
222C2×C4×C61C22⋊Q811yescharacteristic
223C2×C4×C61#12311yescharacteristic
224C2×C4×C61#12311yescharacteristic
225C2×C4×C61#12311yescharacteristic
226C2×C4×C61#12311yescharacteristic
227C2×C4×C61#12311yescharacteristic
228C2×C4×C61#12411yescharacteristic
229C2×C4×C61#12411yescharacteristic
230C2×C4×C61#12411yescharacteristic
231C2×C4×C61#12611yescharacteristic
232C2×C4×C61#12611yescharacteristic
233C2×C4×C61#12711yescharacteristic
234C22⋊D61—42no—
235C22⋊D61—42no—
236C22⋊D61—42no—
237C22⋊D61—42no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—44no—
242C2×Dic61—42no—
243D244—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247C4×D61—42no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—42no—
251Dic122—41no—
252Dic122—41no—
253Dic122—41no—
254Dic122—41no—
255C8×C61—42no—
256C8×C61—42no—
257#92418—42no—
258#92418—42no—
259#11088—611nomaximal, Sylow
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61#38011yescharacteristic
268C22×C61#38511yescharacteristic
269C22×C61#38511yescharacteristic
270C22×C61#38611yescharacteristic
271C22×C61#38811yescharacteristic
272C22×C61#38811yescharacteristic
273C22×C61#39011yescharacteristic
274C2×D61—44no—
275C2×D61—44no—
276C2×D61—42no—
277C2×D61—82no—
278C4×C61—44no—
279C4×C61#39211yescharacteristic
280C4×C61#39311yescharacteristic
281C4×C61#39411yescharacteristic
282C4×C61#39411yescharacteristic
283C4×C61#39611yescharacteristic
284C4×C61#39611yescharacteristic
285C4×C61#39711yescharacteristic
286C4×C61#39911yescharacteristic
287Dic61—42no—
288Dic61—82no—
289C2×#424—611no—
290C2×#410—611no—
291#2879—611no—
292C2×#408—611no—
293C2×#344—611no—
294C2×#344D6111yescharacteristic, complemented
295#1729—611no—
296C2×C61—21no—
297C2×C61—21no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—21no—
301C2×C61—21no—
302C2×C61#143911yescharacteristic
303C2×C61#186812yes—
304D61—82no—
305C22×#41—611no—
306C22×M16—611no—
307C22×M16C2×D6111yescharacteristic
308C22×M16C2×D6111yescharacteristic
309C23×C8—611no—
310C2×#117—611no—
311C2×#117C2×D6111yescharacteristic
312#424—1222no—
313#424—1222no—
314C2×C4⋊C8—1222no—
315#410—1222no—
316#410—1222no—
317C2×#99—614no—
318#408—1222no—
319#408—1222no—
320#408—1222no—
321#408—1222no—
322#407—1222no—
323C2×C22⋊C8—1222no—
324#344—22no—
325#344—1222no—
326#336—1222no—
327C61#1108811yescharacteristic, complemented, Sylow
328C2×#41—1221no—
329C2×#41—1221no—
330C2×#41—1221no—
331C2×#41—1221no—
332C2×#41—1221no—
333C2×#41—1221no—
334C2×#41—1221no—
335C2×#41—1221no—
336C2×#41—1221no—
337C2×#41—1221no—
338C2×#41—1221no—
339C2×#41—1221no—
340C22×Q8—611no—
341C22×D4—612no—
342C22×D4—611no—
343C23×C4—612no—
344C23×C4C22×D6111yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16D24412yes—
363C22×C8—21no—
364C22×C8—612no—
365C22×C8—612no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C22×C8—1221no—
372C22×C8D24412yes—
373#117—21no—
374#117—21no—
375#117—1221no—
376#117—1221no—
377#117—1221no—
378#117—1221no—
379#117D24412yes—
380#117C22⋊D6112yes—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—1221no—
383C2×C22⋊C4—612no—
384C2×C22⋊C4C4×D6112yes—
385C2×C42—21no—
386C2×C42—1221no—
387C4⋊C8—1228no—
388#99—1228no—
389C22⋊C8—1228no—
390C22⋊C8—1228no—
391C24—612no—
392C24C2×C4×D6111yescharacteristic
393#41—2441no—
394#41—2441no—
395#41—2441no—
396#41—2441no—
397#41—2441no—
398#41—2441no—
399#41—2441no—
400#41—2441no—
401#41—2441no—
402#41—2441no—
403#41—2441no—
404#41—2441no—
405#41—2441no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409C2×Q8—1221no—
410C2×Q8—1221no—
411C2×Q8—1221no—
412C2×Q8—1221no—
413C2×Q8—1221no—
414C2×Q8—1221no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1221no—
422C2×D4—1221no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C22×C4—22no—
428C22×C4—612no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4C2×D24411yescharacteristic
437C22×C4C2×D24411yescharacteristic
438C22×C4C2×D24411yescharacteristic
439C22×C4#1175822211yescharacteristic
440C22×C4#1175822211yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443C22×C4D4×D6111yescharacteristic
444C22×C4#1175822411yescharacteristic
445C22×C4#1175822411yescharacteristic
446C22×C4#1175822411yescharacteristic
447C22×C4Q8×D6111yescharacteristic
448C22×C4#1175822611yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450M16—22no—
451M16—22no—
452M16—41no—
453M16—41no—
454M16—41no—
455M16—41no—
456M16—41no—
457M16—41no—
458M16—2441no—
459M16—2441no—
460M16—2441no—
461M16—2441no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—1222no—
469C2×C8—1222no—
470C2×C8—1222no—
471C2×C8—1222no—
472C2×C8—1222no—
473C2×C8—1222no—
474C2×C8—2441no—
475C2×C8—2441no—
476C2×C8—2441no—
477C2×C8—2441no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C22⋊C4—22no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C22⋊C4#1175819814yes—
486C42—22no—
487C42—22no—
488C42—2441no—
489C42—2441no—
490C23—42no—
491C23—1222no—
492C23—1222no—
493C23—1222no—
494C23—2444no—
495C23C2×#1175819811yescharacteristic
496C23C4⋊C4×D6111yescharacteristic
497C23#1451973511yescharacteristic
498C23#1451973711yescharacteristic
499C23#1451973711yescharacteristic
500C23C4×D24411yescharacteristic
501C23C4×D24411yescharacteristic
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—2442no—
507D4—2442no—
508D4—2442no—
509D4—2442no—
510D4—2441no—
511D4—2441no—
512D4—2441no—
513D4—2441no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1222no—
519C2×C4—2444no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2442no—
523C2×C4—2442no—
524C2×C4—2442no—
525C2×C4#1451974711yescharacteristic
526C2×C4#1451974711yescharacteristic
527C2×C4#1451974711yescharacteristic
528C2×C4#1451974811yescharacteristic
529C2×C4#1451974911yescharacteristic
530C2×C4#1451974911yescharacteristic
531C2×C4#1451975111yescharacteristic
532C2×C4#1451975111yescharacteristic
533C2×C4#1451975211yescharacteristic
534C2×C4#1451975211yescharacteristic
535C2×C4#1451975211yescharacteristic
536C2×C4#1451975311yescharacteristic
537C2×C4#1451975511yescharacteristic
538C2×C4#1451975511yescharacteristic
539C2×C4#1451975711yescharacteristic
540C2×C4#1451975711yescharacteristic
541C2×C4#1451975711yescharacteristic
542C2×C4#1451975911yescharacteristic
543C2×C4#1451975911yescharacteristic
544C2×C4#1451976111yescharacteristic
545C2×C4#1451976111yescharacteristic
546C2×C4#1451976111yescharacteristic
547C2×C4#1451976311yescharacteristic
548C2×C4#1451976311yescharacteristic
549C2×C4#1451976511yescharacteristic
550C2×C4#1451977211yescharacteristic
551C2×C4#1451977211yescharacteristic
552C2×C4#1451977411yescharacteristic
553C8—42no—
554C8—42no—
555C8—2442no—
556C8—2442no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—4882no—
565C22—2444no—
566C22—2444no—
567C22—2442no—
568C22#1683961911yescharacteristic
569C22#1683963611yescharacteristic
570C22#1683963611yescharacteristic
571C22#1683963911yescharacteristic
572C22#1683965411yescharacteristic
573C22#1683965411yescharacteristic
574C22#1683966411yescharacteristic
575C4—44no—
576C4—4882no—
577C4—2442no—
578C4#1683967211yescharacteristic
579C4#1683967511yescharacteristic
580C4#1683967811yescharacteristic
581C4#1683967811yescharacteristic
582C4#1683968411yescharacteristic
583C4#1683968411yescharacteristic
584C4#1683968911yescharacteristic
585C4#1683969911yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—4882no—
593C2#2144406511yescharacteristic
594C2#2144610612yes—
subgroupG/H
centerC2×C4#14519747
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#344C2
socleC22×C61#385
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#344D61
hypocenterC61#11088
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16839789C2semidirect
5. C2×#16839534C2semidirect
6. #21445517C2semidirect
7. C2×C61×#344C2semidirect
294. C2×#344D61semidirect
327. C61#11088semidirect

Maximal subgroups

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

subgroupindex
C2×#168397892
C2×#168397352
#214542632
C2×#168397302
C2×#168395342
#214455172
C2×C61×#3442
#1108861