Finite Group Databasebeta

← #30602545

Subgroups — #30602545

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840759C212yesmaximal
2C2×#16840645C212yesmaximal, complemented
3C2×#16840638C211yesmaximal, characteristic, complemented
4#21461505C211yesmaximal, characteristic, complemented
5C2×#131×D61C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C2×#14519856C2212yes—
8#16840759—24no—
9#16840759C418yescomplemented
10C2×#14519842—22no—
11C2×#14519841—22no—
12#16840645—24no—
13#16840638—21no—
14#16840638—21no—
15#16840636—21no—
16#16840636—21no—
17C2×#41×D61C2211yescharacteristic
18C2×#14519785—21no—
19C2×#14519785C411yescharacteristic, complemented
20C2×#14519784C411yescharacteristic, complemented
21C2×#14519783—21no—
22C2×#14519783C411yescharacteristic, complemented
23#131×D61—24no—
24#131×D61—24no—
25C2×M16×D61—21no—
26C2×M16×D61C2211yescharacteristic
27C22×C8×D61—21no—
28C22×C8×D61C2211yescharacteristic
29C2×#131×C61C411yescharacteristic, complemented
30C2×#11758213—22no—
31C2×#11758213—22no—
32C2×#11758213—22no—
33C2×#11758213—22no—
34C2×#11758213—22no—
35C2×#11758213C2×C414yes—
36C22×#92420—22no—
37#14519856—22no—
38#14519856—22no—
39#14519856—22no—
40#14519856C2×C414yes—
41C2×C4⋊#6923—22no—
42C2×C22⋊#6923—22no—
43C2×C4×#6923—22no—
44#14519842—28no—
45#14519841—28no—
46C2×#11758226D411yescharacteristic
47C2×#11758222—21no—
48C2×#11758222C2×C411yescharacteristic
49C2×#11758224—21no—
50C2×#11758224D411yescharacteristic
51#41×D61—22no—
52#41×D61—22no—
53#41×D61C2×C414yes—
54#41×D61D414yes—
55C2×Q8×D61Q811yescharacteristic
56C2×D4×D61—21no—
57C2×D4×D61Q811yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61C2311yescharacteristic
60#14519785—28no—
61#14519785—22no—
62#14519785—22no—
63#14519784—22no—
64#14519784—22no—
65#14519783—28no—
66#14519783—22no—
67#14519783—22no—
68C2×#11758194—21no—
69C2×#11758194C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73M16×D61—28no—
74M16×D61—22no—
75M16×D61D414yes—
76C22×#92418—21no—
77C22×#92418C2×C411yescharacteristic
78C2×C8×D61—28no—
79C2×C8×D61—21no—
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61D411yescharacteristic
85C2×C8×D61D411yescharacteristic
86C2×C8×D61D411yescharacteristic
87C2×C8×D61D411yescharacteristic
88C2×#41×C61C2×C411yescharacteristic
89#131×C61—22no—
90#131×C61—22no—
91C2×M16×C61—21no—
92C2×M16×C61C2×C411yescharacteristic
93C22×C8×C61—21no—
94C22×C8×C61C2×C411yescharacteristic
95C23×D61—21no—
96C23×D61#4111yescharacteristic
97C22×#6923—42no—
98#41×C61—21no—
99#41×C61—21no—
100#41×C61C4212yes—
101#41×C61C22⋊C412yes—
102C2×Q8×C61C4⋊C411yescharacteristic
103C2×D4×C61—21no—
104C2×D4×C61C4⋊C411yescharacteristic
105C22×C4×C61—21no—
106C22×C4×C61C22×C411yescharacteristic
107C2×C22⋊D61—21no—
108C2×C22⋊D61—21no—
109C2×C22⋊D61—21no—
110C22×Dic61—21no—
111C22×Dic61#4111yescharacteristic
112#11758226—22no—
113#11758226C22⋊C414yes—
114Q8×D61—22no—
115Q8×D61C4⋊C414yes—
116#11758224—24no—
117#11758224—24no—
118#11758224—22no—
119#11758224C22⋊C414yes—
120D4×D61—24no—
121D4×D61—24no—
122D4×D61—22no—
123D4×D61C4⋊C414yes—
124#11758222—21no—
125#11758222—21no—
126#11758222—24no—
127#11758222—24no—
128#11758222C4212yes—
129#11758222C22⋊C412yes—
130C2×D244—21no—
131C2×D244C4⋊C411yescharacteristic
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—24no—
136C2×C4×D61—24no—
137C2×C4×D61C22×C412yes—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D412yes—
140C2×C4×D61C2×D411yescharacteristic
141C2×C4×D61C2×D411yescharacteristic
142C2×C4×D61C2×D412yes—
143C2×C4×D61C2×Q811yescharacteristic
144C2×C4×D61#4112yes—
145C2×Dic122—21no—
146C2×Dic122C4⋊C411yescharacteristic
147C22⋊#6923—24no—
148C22⋊#6923—42no—
149C2×#92420—24no—
150C2×#92420—42no—
151C2×#92420—42no—
152C4⋊#6923—24no—
153C4⋊#6923—42no—
154C4×#6923—24no—
155C4×#6923—42no—
156#11758213—24no—
157#11758213—24no—
158#11758213—42no—
159#11758213—42no—
160M16×C61—24no—
161M16×C61—21no—
162M16×C61C22⋊C412yes—
163C2×C8×C61—24no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C22⋊C411yescharacteristic
168C2×C8×C61C22⋊C411yescharacteristic
169#11758194—24no—
170#11758194—21no—
171#11758194C22⋊C412yes—
172C2×#92418—24no—
173C2×#92418—21no—
174C2×#92418—21no—
175C2×#92418—21no—
176C2×#92418C22⋊C411yescharacteristic
177C2×#92418C22⋊C411yescharacteristic
178#11758189—24no—
179#11758189—24no—
180#11758189—24no—
181C8×D61—24no—
182C8×D61—24no—
183C8×D61—22no—
184C8×D61—24no—
185C8×D61—22no—
186C8×D61—22no—
187C8×D61—22no—
188C23×C61—21no—
189C23×C61#11711yescharacteristic
190C22×D61—21no—
191C22×D61—24no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61C4×D412yes—
197C22×D61#12111yescharacteristic
198C22×D61C22⋊Q811yescharacteristic
199C22×D61#12312yes—
200C2×#6923—44no—
201C2×#6923—82no—
202C2×#6923—82no—
203Q8×C61—21no—
204Q8×C61#9512yes—
205D4×C61—22no—
206D4×C61—22no—
207D4×C61—21no—
208D4×C61#9512yes—
209C2×C4×C61—21no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61C2×C4211yescharacteristic
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C2×C4×C61C2×C4⋊C411yescharacteristic
217C2×C4×C61#11711yescharacteristic
218C22⋊D61—22no—
219C22⋊D61—22no—
220C22⋊D61—24no—
221C22⋊D61—24no—
222C2×Dic61—21no—
223C2×Dic61—24no—
224C2×Dic61C4×D412yes—
225C2×Dic61#12111yescharacteristic
226C2×Dic61C22⋊Q811yescharacteristic
227C2×Dic61#12312yes—
228D244—24no—
229D244—21no—
230D244#9512yes—
231C4×D61—24no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—24no—
235C4×D61C2×C22⋊C412yes—
236C4×D61C2×C4⋊C412yes—
237C4×D61C4×D412yes—
238C4×D61C4×D412yes—
239C4×D61#12012yes—
240C4×D61#12012yes—
241C4×D61#12112yes—
242C4×D61C22⋊Q812yes—
243Dic122—21no—
244Dic122—24no—
245Dic122#9512yes—
246#92420—44no—
247C8×C61—21no—
248C8×C61—22no—
249C8×C61—21no—
250#92418—21no—
251#92418—22no—
252#92418—21no—
253#10773—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—22no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61C4×C22⋊C411yescharacteristic
260C22×C61#38011yescharacteristic
261C22×C61#38111yescharacteristic
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—22no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—48no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61#38512yes—
273C2×D61#38612yes—
274#6923—84no—
275C4×C61—22no—
276C4×C61C2×#9511yescharacteristic
277C4×C61C4×C22⋊C411yescharacteristic
278C4×C61#37911yescharacteristic
279C4×C61#38011yescharacteristic
280Dic61—22no—
281Dic61#38512yes—
282Dic61#38612yes—
283C22×#131—611no—
284C2×#421—612no—
285C2×#344—612no—
286C2×#341—611no—
287#1735—611no—
288C2×C61—21no—
289C2×C61—21no—
290C2×C61—42no—
291C2×C61C22⋊#9511yescharacteristic
292C2×C61#181411yescharacteristic
293C2×C61#181411yescharacteristic
294D61—22no—
295D61—22no—
296D61—42no—
297C22×#41—611no—
298C2×#131—611no—
299C2×#131—611no—
300C2×#131—611no—
301C2×#131—1221no—
302C2×#131—1221no—
303C2×#131—1224no—
304C2×#131—1224no—
305C2×#131#692311yescharacteristic, complemented
306C22×M16—611no—
307C22×M16—612no—
308C22×M16—1221no—
309C23×C8—611no—
310C23×C8—1221no—
311C2×#117—612no—
312#421—618no—
313#421—1224no—
314C2×#104—1222no—
315C2×#104—1222no—
316#344—1224no—
317#341—1221no—
318#341—1221no—
319#340—1221no—
320#340—1221no—
321C61#1077311yescharacteristic, complemented, Sylow
322C2×#41—614no—
323C2×#41—614no—
324C2×#41—611no—
325C2×#41—611no—
326C2×#41—611no—
327C2×#41—1221no—
328C2×#41—1221no—
329C2×#41—1222no—
330C2×#41—1222no—
331C2×#41C2×#692311yescharacteristic
332C22×Q8—611no—
333C22×D4—611no—
334C22×D4—1221no—
335C23×C4—611no—
336C23×C4—1221no—
337#131—22no—
338#131—22no—
339#131—1222no—
340#131—1222no—
341#131—1228no—
342#131—1222no—
343#131—1228no—
344#131—1222no—
345#131—1222no—
346#131—1222no—
347C2×M16—21no—
348C2×M16—611no—
349C2×M16—614no—
350C2×M16—614no—
351C2×M16—1221no—
352C2×M16—1221no—
353C2×M16—1221no—
354C2×M16—1222no—
355C2×M16—1228no—
356C2×M16—1222no—
357C2×M16—1221no—
358C2×M16—1222no—
359C2×M16—1222no—
360C2×M16—1222no—
361C2×M16—1222no—
362C2×M16C2×#692311yescharacteristic
363C22×C8—21no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—1221no—
370C22×C8—1222no—
371C22×C8—1222no—
372C22×C8—1221no—
373C22×C8—1228no—
374C22×C8—1221no—
375C22×C8—1221no—
376C22×C8—1222no—
377C22×C8C2×#692311yescharacteristic
378#117—614no—
379#117—1222no—
380#117—1222no—
381#117—1222no—
382C2×C4⋊C4—1222no—
383C2×C22⋊C4—1222no—
384C2×C42—1222no—
385#104—1228no—
386#104—1228no—
387C24—611no—
388C24—1221no—
389#41—21no—
390#41—21no—
391#41—614no—
392#41—614no—
393#41—612no—
394#41—612no—
395#41—1224no—
396#41—1224no—
397#41—1224no—
398#41—1224no—
399#41—1222no—
400#41—1222no—
401#41—1221no—
402#41—1221no—
403#41C4×#692312yes—
404#41C22⋊#692312yes—
405C2×Q8—614no—
406C2×Q8—611no—
407C2×Q8—1221no—
408C2×Q8—1222no—
409C2×Q8C4⋊#692311yescharacteristic
410C2×D4—21no—
411C2×D4—614no—
412C2×D4—611no—
413C2×D4—1221no—
414C2×D4—1222no—
415C2×D4—1221no—
416C2×D4—1224no—
417C2×D4—1224no—
418C2×D4—1221no—
419C2×D4—1221no—
420C2×D4C4⋊#692311yescharacteristic
421C22×C4—21no—
422C22×C4—611no—
423C22×C4—612no—
424C22×C4—611no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—612no—
431C22×C4—1224no—
432C22×C4—1221no—
433C22×C4—1224no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—2442no—
438C22×C4C22×#692311yescharacteristic
439M16—24no—
440M16—21no—
441M16—612no—
442M16—1224no—
443M16—1224no—
444M16—1224no—
445M16—1224no—
446M16—1221no—
447M16—1224no—
448M16—1224no—
449M16—2442no—
450M16—2442no—
451M16C22⋊#692312yes—
452C2×C8—24no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1222no—
459C2×C8—1222no—
460C2×C8—1222no—
461C2×C8—1222no—
462C2×C8—1224no—
463C2×C8—1224no—
464C2×C8—1224no—
465C2×C8—1224no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1224no—
470C2×C8—2442no—
471C2×C8—2442no—
472C2×C8C22⋊#692311yescharacteristic
473C2×C8C22⋊#692311yescharacteristic
474C4⋊C4—1224no—
475C4⋊C4—2442no—
476C22⋊C4—1224no—
477C22⋊C4—2442no—
478C42—1224no—
479C42—2442no—
480C23—21no—
481C23—611no—
482C23—611no—
483C23—612no—
484C23—612no—
485C23—1224no—
486C23—1221no—
487C23—2441no—
488C23—2441no—
489C23—2442no—
490C23—2442no—
491C23#1451985611yescharacteristic
492Q8—21no—
493Q8—612no—
494Q8—1224no—
495Q8—1221no—
496Q8(C2×#6923)⋊C412yes—
497D4—22no—
498D4—22no—
499D4—21no—
500D4—612no—
501D4—1224no—
502D4—1224no—
503D4—1224no—
504D4—1222no—
505D4—1222no—
506D4—1221no—
507D4(C2×#6923)⋊C412yes—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—1224no—
524C2×C4—1224no—
525C2×C4—1224no—
526C2×C4—1221no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—4882no—
530C2×C4—4882no—
531C2×C4—2444no—
532C2×C4C2×C4×#692311yescharacteristic
533C2×C4C2×C22⋊#692311yescharacteristic
534C2×C4C2×C22⋊#692311yescharacteristic
535C2×C4C2×C22⋊#692311yescharacteristic
536C2×C4C2×C4⋊#692311yescharacteristic
537C2×C4#1451985611yescharacteristic
538C8—21no—
539C8—22no—
540C8—21no—
541C8—1221no—
542C8—1221no—
543C8—1222no—
544C8—2444no—
545C22—21no—
546C22—21no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—612no—
551C22—612no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—1222no—
557C22—2442no—
558C22—2442no—
559C22—2448no—
560C22—2441no—
561C22—2441no—
562C22C4×C22⋊#692311yescharacteristic
563C22#1684070411yescharacteristic
564C22#1684070511yescharacteristic
565C4—22no—
566C4—612no—
567C4—612no—
568C4—1222no—
569C4—4884no—
570C4C2×(C2×#6923)⋊C411yescharacteristic
571C4C4×C22⋊#692311yescharacteristic
572C4#1684070311yescharacteristic
573C4#1684070411yescharacteristic
574C2—21no—
575C2—21no—
576C2—42no—
577C2—1222no—
578C2—1222no—
579C2—2442no—
580C2#2146099311yescharacteristic
581C2#2146170511yescharacteristic
582C2#2146170611yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61#380
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenterC2×#131#6923
hypocenterC61#10773
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. C2×#16840645C2semidirect
3. C2×#16840638C2semidirect
4. #21461505C2semidirect
9. #16840759C4semidirect
19. C2×#14519785C4semidirect
20. C2×#14519784C4semidirect
22. C2×#14519783C4semidirect
29. C2×#131×C61C4semidirect
305. C2×#131#6923semidirect
321. C61#10773semidirect

Maximal subgroups

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

subgroupindex
C2×#168407592
C2×#168406452
C2×#168406382
#214615052
C2×#131×D612
#1077361