Finite Group Databasebeta

← #30603230

Subgroups — #30603230

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2C22×#14519838C212yesmaximal
3C2×#16840642C212yesmaximal
4#21461482C211yesmaximal, characteristic
5C2×#16839666C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840765—24no—
9C2×#14519844—21no—
10C2×C4⋊#92420—21no—
11C2×#14519838—24no—
12C2×#14519838—24no—
13C2×#14519838—24no—
14#16840642—24no—
15#16840628—21no—
16#16840628—21no—
17C23×Dic122C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839666—21no—
21#16839666—21no—
22#16839666—21no—
23#16839666—21no—
24C2×#14519684C411yescharacteristic
25C2×#14519684C411yescharacteristic
26C2×#14519684C411yescharacteristic
27C2×#95×C61C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217—22no—
34C2×#11758217—22no—
35C2×#11758217—22no—
36C2×#11758217—22no—
37C2×#11758217—22no—
38C2×#11758217D414yes—
39C2×#11758217D414yes—
40C22×#92420—22no—
41C22×#92420—22no—
42#14519844—24no—
43C4⋊#92420—24no—
44#14519838—216no—
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—21no—
48C22×Dic122—21no—
49C22×Dic122—21no—
50C22×Dic122—21no—
51C22×Dic122—22no—
52C22×Dic122—22no—
53C22×Dic122D412yes—
54C22×Dic122Q812yes—
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2311yescharacteristic
59C2×#11758196—22no—
60C2×#11758196—21no—
61C2×#11758196—21no—
62C2×#11758196—22no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—22no—
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C2×C4×Dic61D411yescharacteristic
68C2×C4×Dic61D411yescharacteristic
69#14519684—21no—
70#14519684—21no—
71#14519684—21no—
72#14519684—21no—
73#14519684—21no—
74#14519684—21no—
75C23×C4×C61C2×C411yescharacteristic
76C23×C4×C61C2×C411yescharacteristic
77C23×C4×C61C2×C411yescharacteristic
78#95×C61—21no—
79#95×C61—21no—
80C24×C61C22×C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C4⋊C412yes—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—21no—
102C22×Dic61—22no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C412yes—
109C22×Dic61C2×D412yes—
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D412yes—
112C22×Dic61C2×D411yescharacteristic
113C22×Dic61C2×D411yescharacteristic
114C22×Dic61C2×Q811yescharacteristic
115C22×Dic61#4111yescharacteristic
116C22×Dic61#4112yes—
117C22×Dic61#4111yescharacteristic
118C22×Dic61#4112yes—
119C2×Dic122—24no—
120C2×Dic122—22no—
121C2×Dic122—22no—
122C2×Dic122—24no—
123C2×Dic122—22no—
124C2×Dic122—22no—
125C2×Dic122—24no—
126C2×Dic122—24no—
127C2×Dic122—41no—
128C2×Dic122—42no—
129C2×Dic122—42no—
130C2×Dic122—42no—
131C2×Dic122—42no—
132C2×Dic122—41no—
133C2×Dic122—42no—
134C2×Dic122—41no—
135C2×Dic122—42no—
136C2×Dic122—41no—
137#11758217—24no—
138#11758217—24no—
139#11758217—24no—
140#11758217—24no—
141#11758217—42no—
142#11758217—42no—
143#11758217—42no—
144#11758217—42no—
145C2×#92420—24no—
146C2×#92420—24no—
147C2×#92420—42no—
148C2×#92420—42no—
149C2×#92420—42no—
150C2×#92420—42no—
151#11758196—42no—
152#11758196—41no—
153#11758196—41no—
154C4×Dic61—21no—
155C4×Dic61—21no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61C2×C22⋊C411yescharacteristic
165C23×C61C2×C4⋊C411yescharacteristic
166C23×C61#11711yescharacteristic
167C23×C61C4×D412yes—
168C23×C61C4×D412yes—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—44no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—82no—
184C2×C4×C61#10112yescomplemented
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—22no—
188C2×Dic61—24no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—44no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—82no—
200C2×Dic61#10112yescomplemented
201C2×Dic61#12011yescharacteristic
202C2×Dic61#12012yes—
203C2×Dic61#12112yes—
204C2×Dic61#12111yescharacteristic
205C2×Dic61#12111yescharacteristic
206C2×Dic61#12112yes—
207C2×Dic61#12112yes—
208C2×Dic61C22⋊Q812yes—
209C2×Dic61C22⋊Q811yescharacteristic
210C2×Dic61C22⋊Q811yescharacteristic
211C2×Dic61C22⋊Q812yes—
212C2×Dic61#12312yes—
213C2×Dic61#12312yes—
214C2×Dic61#12311yescharacteristic
215C2×Dic61#12412yes—
216C2×Dic61#12411yescharacteristic
217C2×Dic61#12612yes—
218C2×Dic61#12711yescharacteristic
219Dic122—42no—
220Dic122—42no—
221Dic122—44no—
222Dic122—44no—
223Dic122—42no—
224Dic122—42no—
225#92420—44no—
226#92420—44no—
227#11045—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—22no—
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—22no—
236C22×C61#38011yescharacteristic
237C22×C61#38512yes—
238C22×C61#38611yescharacteristic
239C22×C61#38812yes—
240C22×C61#39011yescharacteristic
241C22×C61C2×#10111yescharacteristic
242C22×C61C2×#10111yescharacteristic
243C22×C61#41311yescharacteristic
244C22×C61#41311yescharacteristic
245C4×C61—22no—
246C4×C61—41no—
247C4×C61—42no—
248C4×C61—81no—
249Dic61—22no—
250Dic61—41no—
251Dic61—42no—
252Dic61—81no—
253Dic61#39211yescharacteristic
254Dic61#39311yescharacteristic
255Dic61#39412yes—
256Dic61#39612yes—
257Dic61#39711yescharacteristic
258Dic61#39911yescharacteristic
259C2×#423—611no—
260C22×#101—612no—
261C2×#391—611no—
262C2×#343—612no—
263#1728—611no—
264C2×C61—22no—
265C2×C61—22no—
266C2×C61#143911yescharacteristic
267C2×C61#180111yescharacteristic
268C2×C61#180111yescharacteristic
269C2×C61#190111yescharacteristic
270C2×C61#190111yescharacteristic
271C2×C61#196611yescharacteristic
272C2×C61#196711yescharacteristic
273C23×Q8—611no—
274C22×M16—612no—
275C22×M16—612no—
276C22×C4⋊C4—611no—
277C22×C42—611no—
278#423—1224no—
279C2×C4⋊C8—1221no—
280C2×C4⋊C8—1221no—
281C2×#101—1224no—
282C2×#101—1224no—
283C2×#101—1224no—
284#391—1221no—
285#391—1221no—
286#391—1221no—
287#391—1221no—
288C2×#95—611no—
289C2×#95—611no—
290C2×#95—611no—
291C2×#95#692311yescharacteristic
292#343—1224no—
293#336—1221no—
294#336—1221no—
295C61#1104511yescharacteristic, complemented, Sylow
296C22×Q8—612no—
297C22×Q8—612no—
298C22×Q8—1221no—
299C22×Q8—1221no—
300C22×Q8—1222no—
301C22×Q8—1222no—
302C22×Q8—1221no—
303C22×Q8—1221no—
304C22×Q8—1222no—
305C22×Q8—1222no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4C2×#692311yescharacteristic
311C23×C4C2×#692311yescharacteristic
312C23×C4C2×#692311yescharacteristic
313C2×M16—614no—
314C2×M16—614no—
315C2×M16—1222no—
316C2×M16—1222no—
317C2×M16—1222no—
318C2×M16—1222no—
319C2×M16—1222no—
320C2×M16—1222no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16—1222no—
324C2×M16—1222no—
325C22×C8—1222no—
326C22×C8—1222no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4—1222no—
331C2×C42—611no—
332C2×C42—611no—
333C2×C42—611no—
334C2×C42—611no—
335C2×C42—1222no—
336C2×C42—1222no—
337C4⋊C8—1224no—
338C4⋊C8—1224no—
339#101—12216no—
340#95—21no—
341#95—21no—
342#95—1221no—
343#95—1221no—
344#95—1221no—
345#95—1221no—
346#95—1221no—
347#95—1221no—
348C24C22×#692311yescharacteristic
349C2×Q8—1224no—
350C2×Q8—1222no—
351C2×Q8—1222no—
352C2×Q8—1222no—
353C2×Q8—1222no—
354C2×Q8—1224no—
355C2×Q8—1224no—
356C2×Q8—1224no—
357C2×Q8—2441no—
358C2×Q8—2442no—
359C2×Q8—2441no—
360C2×Q8—2442no—
361C2×Q8—2442no—
362C2×Q8—2442no—
363C2×Q8—2442no—
364C2×Q8—2442no—
365C2×Q8—2441no—
366C2×Q8—2441no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—612no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—612no—
391C22×C4—1222no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—1222no—
397C22×C4—1222no—
398C22×C4—1221no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4C4⋊#692312yes—
403C22×C4C22⋊#692311yescharacteristic
404C22×C4C22⋊#692311yescharacteristic
405M16—1224no—
406M16—1224no—
407M16—1224no—
408M16—1224no—
409M16—2442no—
410M16—2442no—
411M16—2442no—
412M16—2442no—
413C2×C8—1224no—
414C2×C8—1224no—
415C2×C8—2442no—
416C2×C8—2442no—
417C2×C8—2442no—
418C2×C8—2442no—
419C4⋊C4—2442no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C42—1221no—
423C42—1221no—
424C42—1222no—
425C42—1221no—
426C42—1222no—
427C42—1221no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23C2×C22⋊#692311yescharacteristic
433C23C2×C4⋊#692311yescharacteristic
434C23#1451985611yescharacteristic
435C23D4×#692312yes—
436C23D4×#692312yes—
437Q8—2442no—
438Q8—2442no—
439Q8—2444no—
440Q8—2444no—
441Q8—2442no—
442Q8—2442no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—44no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—82no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—611no—
461C2×C4—611no—
462C2×C4—612no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—611no—
467C2×C4—612no—
468C2×C4—611no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—612no—
472C2×C4—612no—
473C2×C4—612no—
474C2×C4—611no—
475C2×C4—611no—
476C2×C4—612no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1222no—
480C2×C4—1224no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—4882no—
485C2×C4—2444no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2442no—
491C2×C4—2441no—
492C2×C4#1451983812yescomplemented
493C8—2444no—
494C8—2444no—
495C22—22no—
496C22—22no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22#1684070411yescharacteristic
504C22#1684070912yes—
505C22#1684071011yescharacteristic
506C22#1684071212yes—
507C22#1684071411yescharacteristic
508C22C2×#1451983811yescharacteristic
509C22D61⋊#10111yescharacteristic
510C22#1684074811yescharacteristic
511C22#1684074911yescharacteristic
512C4—22no—
513C4—42no—
514C4—41no—
515C4—81no—
516C4—611no—
517C4—611no—
518C4—612no—
519C4—612no—
520C4—611no—
521C4—611no—
522C4—1222no—
523C4—4881no—
524C4—2442no—
525C4—2441no—
526C2—22no—
527C2—22no—
528C2#2146100211yescharacteristic
529C2#2146168511yescharacteristic
530C2#2146168611yescharacteristic
531C2#2146184611yescharacteristic
532C2#2146184711yescharacteristic
533C2#2146196211yescharacteristic
534C2#2146196311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#11045
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
184. C2×C4×C61#101semidirect
200. C2×Dic61#101semidirect
295. C61#11045semidirect
492. C2×C4#14519838semidirect

Maximal subgroups

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

subgroupindex
C2×#168407652
C22×#145198382
C2×#168406422
#214614822
C2×#168396662
#1104561