Finite Group Databasebeta

← #30603304

Subgroups — #30603304

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#108C211yesmaximal, characteristic, complemented
2C2×#16840753C212yesmaximal
3C2×#16840641C212yesmaximal, complemented
4C2×#16840636C211yesmaximal, characteristic, complemented
5#408×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C22×C4⋊#6923C2212yes—
8C2×#14519848—21no—
9D61⋊#108—24no—
10C2×#14519847—21no—
11#16840753—24no—
12#16840753—24no—
13C2×#14519840—22no—
14C2×#14519839—22no—
15#16840641—24no—
16#16840636—21no—
17#16840636—21no—
18C2×#41×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16839730C411yescharacteristic, complemented
22#16839729C411yescharacteristic, complemented
23#16839728C411yescharacteristic, complemented
24#16839727—21no—
25#16839727—21no—
26C22⋊C8×D61—21no—
27C22⋊C8×D61—21no—
28C61×#408C411yescharacteristic, complemented
29C23×#6923—22no—
30C2×#11758213—22no—
31D61⋊M16—22no—
32D61⋊M16—22no—
33D61⋊M16—22no—
34D61⋊M16D414yes—
35C2×#11758217—22no—
36C2×D61⋊C8—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923—22no—
40C2×C4⋊#6923—22no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923D414yes—
43#14519848—24no—
44#14519847—24no—
45#14519840—28no—
46#14519839—28no—
47C2×#11758226Q811yescharacteristic
48C2×#11758222—21no—
49C2×#11758222C2×C411yescharacteristic
50C2×#11758224—21no—
51C2×#11758224Q811yescharacteristic
52#41×D61—22no—
53#41×D61—22no—
54#41×D61—22no—
55#41×D61—22no—
56C2×Q8×D61D411yescharacteristic
57C2×D4×D61—21no—
58C2×D4×D61D411yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61C2311yescharacteristic
61C2×#11758194C2×C411yescharacteristic
62C2×#11758189—21no—
63M16×D61—22no—
64M16×D61—22no—
65C22×#92418C2×C411yescharacteristic
66C2×C8×D61—22no—
67C2×C8×D61—22no—
68C2×C8×D61—21no—
69C2×C8×D61D411yescharacteristic
70C2×C8×D61D411yescharacteristic
71C2×C8×D61D411yescharacteristic
72C2×C8×D61D411yescharacteristic
73C22⋊#92418—21no—
74C22⋊#92418—21no—
75#14519689—21no—
76#14519689—21no—
77#14519689—21no—
78#14519689—21no—
79C2×#41×C61C2×C411yescharacteristic
80C2×M16×C61C2×C411yescharacteristic
81C22×C8×C61C2×C411yescharacteristic
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C23×D61—21no—
85C23×D61#4111yescharacteristic
86C22×#6923—24no—
87C22×#6923—42no—
88C22×#6923—42no—
89C22×#6923—82no—
90C22×#6923—82no—
91#41×C61—22no—
92#41×C61—22no—
93C2×Q8×C61C4⋊C411yescharacteristic
94C2×D4×C61—21no—
95C2×D4×C61C4⋊C411yescharacteristic
96C22×C4×C61—21no—
97C22×C4×C61C22×C411yescharacteristic
98C2×C22⋊D61—21no—
99C2×C22⋊D61—21no—
100C2×C22⋊D61—21no—
101C22×Dic61—21no—
102C22×Dic61#4111yescharacteristic
103#11758226—22no—
104#11758226—22no—
105Q8×D61—22no—
106Q8×D61—22no—
107#11758224—22no—
108#11758224—22no—
109#11758224—42no—
110#11758224—42no—
111D4×D61—22no—
112D4×D61—22no—
113D4×D61—42no—
114D4×D61—42no—
115#11758222—22no—
116#11758222—22no—
117#11758222—41no—
118#11758222—41no—
119#11758222—41no—
120#11758222—41no—
121C2×D244—21no—
122C2×D244C4⋊C411yescharacteristic
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61C2×D412yes—
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61C2×D412yes—
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×Q811yescharacteristic
134C2×C4×D61#4112yes—
135C2×C4×D61#4112yes—
136C2×Dic122—21no—
137C2×Dic122C4⋊C411yescharacteristic
138#11758217—24no—
139#11758217—42no—
140C2×#92420—42no—
141C4⋊#6923—24no—
142C4⋊#6923—24no—
143C4⋊#6923—42no—
144C4⋊#6923—42no—
145#11758213—24no—
146#11758213—42no—
147D61⋊C8—24no—
148D61⋊C8—42no—
149M16×C61—22no—
150C2×C8×C61—22no—
151C2×C8×C61—21no—
152C2×C8×C61C22⋊C411yescharacteristic
153C2×C8×C61C22⋊C411yescharacteristic
154#11758194—22no—
155C2×#92418—22no—
156C2×#92418—21no—
157C2×#92418C22⋊C411yescharacteristic
158C2×#92418C22⋊C411yescharacteristic
159#11758189—41no—
160#11758189—41no—
161C8×D61—21no—
162C8×D61—21no—
163C8×D61—22no—
164C8×D61—22no—
165C8×D61—21no—
166C8×D61—21no—
167C8×D61—42no—
168C23×C61—21no—
169C23×C61#11711yescharacteristic
170C22×D61—22no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—42no—
175C22×D61—42no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61#12111yescharacteristic
179C22×D61C22⋊Q811yescharacteristic
180C22×D61#12312yes—
181C22×D61#12412yes—
182C2×#6923—44no—
183C2×#6923—84no—
184C2×#6923—82no—
185C2×#6923—82no—
186C2×#6923—84no—
187Q8×C61—22no—
188D4×C61—22no—
189D4×C61—42no—
190C2×C4×C61—21no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61C2×C22⋊C411yescharacteristic
194C2×C4×C61C2×C4⋊C411yescharacteristic
195C2×C4×C61C4×D412yes—
196C2×C4×C61C4×D412yes—
197C22⋊D61—42no—
198C22⋊D61—41no—
199C22⋊D61—41no—
200C22⋊D61—41no—
201C22⋊D61—41no—
202C2×Dic61—21no—
203C2×Dic61—42no—
204C2×Dic61#12112yes—
205C2×Dic61#12111yescharacteristic
206C2×Dic61C22⋊Q811yescharacteristic
207C2×Dic61#12612yes—
208D244—22no—
209D244—41no—
210D244—41no—
211C4×D61—42no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—42no—
215C4×D61#12012yes—
216C4×D61#12011yescharacteristic
217C4×D61#12112yes—
218C4×D61#12112yes—
219C4×D61C22⋊Q812yes—
220C4×D61C22⋊Q812yes—
221C4×D61#12312yes—
222C4×D61#12311yescharacteristic
223C4×D61#12411yescharacteristic
224C4×D61#12711yescharacteristic
225Dic122—22no—
226Dic122—41no—
227Dic122—41no—
228#92420—44no—
229C8×C61—21no—
230C8×C61—21no—
231C8×C61—41no—
232#92418—21no—
233#92418—21no—
234#92418—41no—
235#11105—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61#38011yescharacteristic
242C22×C61#38812yes—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—82no—
253C2×D61—82no—
254C2×D61#39311yescharacteristic
255C2×D61#39412yes—
256C2×D61#39911yescharacteristic
257C2×D61#47112yes—
258C2×D61#47211yescharacteristic
259C2×D61#47311yescharacteristic
260#6923—84no—
261C4×C61—41no—
262C4×C61#38512yes—
263C4×C61#38611yescharacteristic
264C4×C61#39011yescharacteristic
265Dic61—41no—
266Dic61#39211yescharacteristic
267Dic61#39612yes—
268Dic61#39711yescharacteristic
269C22×#108—611no—
270C2×#417—612no—
271C2×#408—611no—
272C2×#343—612no—
273C2×#340—611no—
274C2×C61—22no—
275C2×C61—81no—
276C2×C61#143911yescharacteristic
277C2×C61#181511yescharacteristic
278C2×C61#181611yescharacteristic
279D61—21no—
280D61—21no—
281D61—81no—
282D61#205112yes—
283D61#205212yes—
284C22×#41—611no—
285C22×M16—612no—
286C22×M16—611no—
287C23×C8—611no—
288C22×C4⋊C4—612no—
289C2×#108—1221no—
290C2×#108—1221no—
291C2×#108—1224no—
292#417—1224no—
293#417—1224no—
294C2×#103—1222no—
295C2×#102—1222no—
296#408—611no—
297#408—611no—
298#408—611no—
299#408—1221no—
300#408—1221no—
301#408#692311yescharacteristic, complemented
302C2×C22⋊C8—1221no—
303C2×C22⋊C8—1221no—
304#343—1224no—
305#340—1221no—
306#340—1221no—
307C61#1110511yescharacteristic, complemented, Sylow
308C2×#41—611no—
309C2×#41—611no—
310C2×#41—611no—
311C2×#41—1221no—
312C2×#41—1221no—
313C2×#41—1222no—
314C2×#41—1222no—
315C2×#41—1222no—
316C2×#41—1222no—
317C2×#41C2×#692311yescharacteristic
318C22×Q8—611no—
319C22×D4—611no—
320C22×D4—1221no—
321C23×C4—611no—
322C23×C4—1221no—
323C23×C4—1222no—
324C2×M16—614no—
325C2×M16—611no—
326C2×M16—1221no—
327C2×M16—1222no—
328C2×M16—1222no—
329C2×M16—1222no—
330C2×M16—1222no—
331C2×M16—1222no—
332C2×M16—1222no—
333C2×M16—1222no—
334C2×M16C2×#692311yescharacteristic
335C22×C8—611no—
336C22×C8—611no—
337C22×C8—611no—
338C22×C8—611no—
339C22×C8—611no—
340C22×C8—1222no—
341C22×C8—1222no—
342C22×C8—1221no—
343C22×C8—1222no—
344C22×C8C2×#692311yescharacteristic
345C2×C4⋊C4—614no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1222no—
348C2×C4⋊C4—1222no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4—1222no—
351#108—1224no—
352#108—1224no—
353#103—1228no—
354#102—1228no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—1221no—
358C22⋊C8—1221no—
359C22⋊C8—1221no—
360C22⋊C8—1221no—
361C22⋊C8—1221no—
362C22⋊C8—1221no—
363C24—611no—
364C24—1221no—
365#41—22no—
366#41—22no—
367#41—1222no—
368#41—1222no—
369#41—1222no—
370#41—1222no—
371#41—1222no—
372#41—1222no—
373#41—2441no—
374#41—2441no—
375#41—2441no—
376#41—2441no—
377#41—2442no—
378#41—2442no—
379C2×Q8—611no—
380C2×Q8—1221no—
381C2×Q8—1222no—
382C2×Q8—1222no—
383C2×Q8C4⋊#692311yescharacteristic
384C2×D4—21no—
385C2×D4—611no—
386C2×D4—1221no—
387C2×D4—1222no—
388C2×D4—1222no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—1221no—
392C2×D4—2442no—
393C2×D4—2442no—
394C2×D4C4⋊#692311yescharacteristic
395C22×C4—21no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—612no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1224no—
410C22×C4—4882no—
411C22×C4—4882no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4—2442no—
416C22×C4C22×#692311yescharacteristic
417M16—22no—
418M16—1224no—
419M16—1224no—
420M16—1222no—
421M16—2441no—
422M16—2441no—
423M16—2442no—
424M16—2442no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8—611no—
428C2×C8—611no—
429C2×C8—1221no—
430C2×C8—1221no—
431C2×C8—1222no—
432C2×C8—1222no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1222no—
436C2×C8—1224no—
437C2×C8—1221no—
438C2×C8—2442no—
439C2×C8—2442no—
440C2×C8—2442no—
441C2×C8C22⋊#692311yescharacteristic
442C2×C8C22⋊#692311yescharacteristic
443C4⋊C4—1224no—
444C4⋊C4—1224no—
445C4⋊C4—2442no—
446C4⋊C4—2442no—
447C23—21no—
448C23—611no—
449C23—611no—
450C23—612no—
451C23—612no—
452C23—1221no—
453C23—1222no—
454C23—1221no—
455C23—1221no—
456C23—2442no—
457C23—2442no—
458C23—2441no—
459C23—2441no—
460C23#1451985611yescharacteristic
461Q8—22no—
462Q8—1222no—
463Q8—2441no—
464Q8—2441no—
465D4—22no—
466D4—42no—
467D4—1222no—
468D4—2441no—
469D4—2441no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473D4—2441no—
474D4—2442no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—612no—
481C2×C4—612no—
482C2×C4—612no—
483C2×C4—612no—
484C2×C4—612no—
485C2×C4—612no—
486C2×C4—611no—
487C2×C4—612no—
488C2×C4—611no—
489C2×C4—612no—
490C2×C4—611no—
491C2×C4—611no—
492C2×C4—1221no—
493C2×C4—4882no—
494C2×C4—4882no—
495C2×C4—4884no—
496C2×C4—4884no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2444no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4C2×C22⋊#692311yescharacteristic
504C2×C4C2×C4⋊#692311yescharacteristic
505C2×C4D4×#692312yes—
506C2×C4D4×#692312yes—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—1221no—
511C8—1221no—
512C8—2444no—
513C8—2441no—
514C22—21no—
515C22—21no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—612no—
520C22—612no—
521C22—611no—
522C22—611no—
523C22—611no—
524C22—611no—
525C22—1222no—
526C22—1222no—
527C22—1222no—
528C22—1222no—
529C22—1221no—
530C22—1221no—
531C22—4882no—
532C22—4882no—
533C22—2441no—
534C22—2441no—
535C22—2441no—
536C22#1684070411yescharacteristic
537C22#1684071212yes—
538C4—41no—
539C4—611no—
540C4—612no—
541C4—611no—
542C4—4884no—
543C4—2441no—
544C4#1684070912yes—
545C4#1684071011yescharacteristic
546C4#1684071411yescharacteristic
547C2—22no—
548C2—81no—
549C2—612no—
550C2—612no—
551C2—1221no—
552C2—1221no—
553C2—4881no—
554C2#2146100211yescharacteristic
555C2#2146170711yescharacteristic
556C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61#380
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#408#6923
hypocenterC61#11105
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊#108C2semidirect
3. C2×#16840641C2semidirect
4. C2×#16840636C2semidirect
21. #16839730C4semidirect
22. #16839729C4semidirect
23. #16839728C4semidirect
28. C61×#408C4semidirect
301. #408#6923semidirect
307. C61#11105semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1082
C2×#168407532
C2×#168406412
C2×#168406362
#408×D612
#1110561