Finite Group Databasebeta

← #30603297

Subgroups — #30603297

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840772C211yesmaximal, characteristic, complemented
2C2×#16840741C212yesmaximal
3#21461505C211yesmaximal, characteristic, complemented
4C2×#16840630C212yesmaximal, complemented
5C2×#16839727C211yesmaximal, characteristic
6C2×#14519856C2212yes—
7C2×#14519856C2212yes—
8#16840772—24no—
9C2×#14519846—21no—
10C2×#14519845—21no—
11#16840741—24no—
12#16840741—24no—
13C2×#14519836—22no—
14C2×#14519835—22no—
15#16840636—21no—
16#16840636—21no—
17#16840630—24no—
18C22×#11758222C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16839727—21no—
22#16839727—21no—
23#16839727—21no—
24#16839727—21no—
25C2×C22⋊#92418C411yescharacteristic, complemented
26C2×#14519689C411yescharacteristic, complemented
27C2×#14519689C411yescharacteristic, complemented
28C2×C22⋊C8×C61C411yescharacteristic, complemented
29#14519856—22no—
30#14519856—22no—
31#14519856—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35#14519856D414yes—
36#14519856D414yes—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C22⋊#6923—22no—
40C2×C22⋊#6923—22no—
41C2×C4×#6923—22no—
42C2×C4×#6923—22no—
43#14519846—24no—
44#14519845—24no—
45#14519836—28no—
46#14519835—28no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C22×Dic122Q811yescharacteristic
56C22×D244D411yescharacteristic
57C22×C22⋊D61D411yescharacteristic
58C22×C22⋊D61Q811yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—21no—
62C2×#11758189—21no—
63C2×#11758189—22no—
64C2×#11758189—22no—
65C22×#92418C2×C411yescharacteristic
66C22×#92418C2×C411yescharacteristic
67C2×C8×D61—22no—
68C2×C8×D61—22no—
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—
79C23×C4×C61C2×C411yescharacteristic
80C22×C8×C61C2×C411yescharacteristic
81C22×C8×C61C2×C411yescharacteristic
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C24×C61C4⋊C411yescharacteristic
85C23×D61C4⋊C411yescharacteristic
86C23×D61C2×D411yescharacteristic
87C22×#6923—42no—
88C22×#6923—42no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61C4⋊C411yescharacteristic
94C22×C4×C61C22×C411yescharacteristic
95C2×C22⋊D61—22no—
96C2×C22⋊D61—21no—
97C2×C22⋊D61—21no—
98C2×C22⋊D61—22no—
99C2×C22⋊D61—22no—
100C2×C22⋊D61—21no—
101C2×C22⋊D61—21no—
102C2×C22⋊D61—22no—
103C22×Dic61C4⋊C411yescharacteristic
104C22×Dic61C2×Q811yescharacteristic
105#11758222—41no—
106#11758222—42no—
107#11758222—42no—
108#11758222—42no—
109#11758222—41no—
110#11758222—42no—
111#11758222—42no—
112#11758222—41no—
113#11758222—42no—
114#11758222—41no—
115C2×D244—22no—
116C2×D244—21no—
117C2×D244—21no—
118C2×D244—22no—
119C2×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61C2×D412yes—
124C2×C4×D61C2×D411yescharacteristic
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×D412yes—
127C2×C4×D61#4111yescharacteristic
128C2×C4×D61#4112yes—
129C2×C4×D61#4112yes—
130C2×C4×D61#4111yescharacteristic
131C2×Dic122—22no—
132C2×Dic122—21no—
133C2×Dic122—21no—
134C2×Dic122—22no—
135C22⋊#6923—24no—
136C22⋊#6923—24no—
137C22⋊#6923—42no—
138C22⋊#6923—42no—
139C4⋊#6923—24no—
140C4⋊#6923—24no—
141C4⋊#6923—42no—
142C4⋊#6923—42no—
143C4×#6923—24no—
144C4×#6923—24no—
145C4×#6923—42no—
146C4×#6923—42no—
147C2×C8×C61—22no—
148C2×C8×C61—21no—
149C2×C8×C61—22no—
150C2×C8×C61C22⋊C411yescharacteristic
151C2×C8×C61C22⋊C411yescharacteristic
152C2×#92418—22no—
153C2×#92418—21no—
154C2×#92418—22no—
155C2×#92418C22⋊C411yescharacteristic
156C2×#92418C22⋊C411yescharacteristic
157#11758189—42no—
158#11758189—41no—
159#11758189—41no—
160C8×D61—21no—
161C8×D61—21no—
162C8×D61—22no—
163C8×D61—22no—
164C8×D61—21no—
165C8×D61—21no—
166C23×C61—21no—
167C23×C61—22no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61C2×C4⋊C411yescharacteristic
171C22×D61—21no—
172C22×D61—22no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61#12012yes—
178C22×D61#12111yescharacteristic
179C22×D61#12111yescharacteristic
180C22×D61#12312yes—
181C2×#6923—44no—
182C2×#6923—44no—
183C2×#6923—82no—
184C2×#6923—82no—
185C2×#6923—82no—
186C2×#6923—82no—
187C2×C4×C61—21no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—41no—
192C2×C4×C61C2×C22⋊C411yescharacteristic
193C2×C4×C61#11711yescharacteristic
194C2×C4×C61C4×D412yes—
195C2×C4×C61C4×D412yes—
196C22⋊D61—41no—
197C22⋊D61—42no—
198C22⋊D61—41no—
199C22⋊D61—41no—
200C22⋊D61—42no—
201C22⋊D61—41no—
202C2×Dic61—21no—
203C2×Dic61—22no—
204C2×Dic61C22⋊Q812yes—
205C2×Dic61C22⋊Q811yescharacteristic
206C2×Dic61C22⋊Q811yescharacteristic
207C2×Dic61C22⋊Q812yes—
208D244—41no—
209D244—42no—
210D244—41no—
211C4×D61—41no—
212C4×D61—42no—
213C4×D61—41no—
214C4×D61#12011yescharacteristic
215C4×D61#12112yes—
216C4×D61#12112yes—
217C4×D61#12112yes—
218C4×D61#12311yescharacteristic
219C4×D61#12312yes—
220C4×D61#12412yes—
221C4×D61#12411yescharacteristic
222C4×D61#12612yes—
223C4×D61#12711yescharacteristic
224Dic122—41no—
225Dic122—42no—
226Dic122—41no—
227C8×C61—21no—
228C8×C61—21no—
229C8×C61—41no—
230#92418—21no—
231#92418—21no—
232#92418—41no—
233#11098—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—82no—
240C22×C61#38011yescharacteristic
241C22×C61#38512yes—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—82no—
252C2×D61#39211yescharacteristic
253C2×D61#39412yes—
254C2×D61#39711yescharacteristic
255#6923—84no—
256#6923—84no—
257C4×C61—41no—
258C4×C61#38611yescharacteristic
259C4×C61#38812yes—
260C4×C61#39011yescharacteristic
261Dic61—41no—
262Dic61#39311yescharacteristic
263Dic61#39612yes—
264Dic61#39911yescharacteristic
265C2×#427—611no—
266C2×#410—612no—
267C2×#408—611no—
268#1735—611no—
269C2×H(3,ℤ/4)—612no—
270C2×C61—22no—
271C2×C61—81no—
272C2×C61#143911yescharacteristic
273C2×C61#181211yescharacteristic
274C2×C61#181211yescharacteristic
275D61—21no—
276D61—22no—
277D61—21no—
278D61—81no—
279C22×#41—611no—
280C22×M16—611no—
281C23×C8—611no—
282C2×#117—612no—
283C2×#117—612no—
284#427—1224no—
285C2×#107—1221no—
286C2×#106—1221no—
287#410—1224no—
288#410—1224no—
289C2×#99—1222no—
290C2×#99—1222no—
291#408—1221no—
292#408—1221no—
293#408—1221no—
294#408—1221no—
295C2×C22⋊C8—611no—
296C2×C22⋊C8—611no—
297C2×C22⋊C8—611no—
298C2×C22⋊C8#692311yescharacteristic, complemented
299#340—1221no—
300#340—1221no—
301H(3,ℤ/4)—1224no—
302C61#1109811yescharacteristic, complemented, Sylow
303C2×#41—1221no—
304C2×#41—1221no—
305C2×#41—1222no—
306C2×#41—1222no—
307C2×#41—1221no—
308C2×#41—1221no—
309C2×#41—1222no—
310C2×#41—1222no—
311C22×Q8—611no—
312C22×D4—611no—
313C22×D4—611no—
314C22×D4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4C2×#692311yescharacteristic
318C2×M16—1222no—
319C2×M16—1221no—
320C2×M16—1221no—
321C2×M16—1222no—
322C22×C8—611no—
323C22×C8—611no—
324C22×C8—611no—
325C22×C8—611no—
326C22×C8—611no—
327C22×C8—611no—
328C22×C8—1222no—
329C22×C8—1222no—
330C22×C8C2×#692311yescharacteristic
331C22×C8C2×#692311yescharacteristic
332#117—614no—
333#117—614no—
334#117—1222no—
335#117—1222no—
336#117—1222no—
337#117—1222no—
338#117—1222no—
339#117—1222no—
340C2×C4⋊C4—1222no—
341C2×C4⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1222no—
344C2×C42—1222no—
345C2×C42—1222no—
346#107—1224no—
347#106—1224no—
348#99—1228no—
349#99—1228no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—1221no—
353C22⋊C8—1221no—
354C22⋊C8—1221no—
355C22⋊C8—1221no—
356C22⋊C8—1221no—
357C22⋊C8—1221no—
358C24—611no—
359C24—611no—
360C24C4⋊#692311yescharacteristic
361#41—2441no—
362#41—2442no—
363#41—2441no—
364#41—2442no—
365#41—2442no—
366#41—2442no—
367#41—2442no—
368#41—2442no—
369#41—2441no—
370#41—2441no—
371C2×Q8—1221no—
372C2×Q8—1221no—
373C2×Q8—1222no—
374C2×Q8—1222no—
375C2×D4—1222no—
376C2×D4—1221no—
377C2×D4—1221no—
378C2×D4—1222no—
379C2×D4—1221no—
380C2×D4—1221no—
381C2×D4—1222no—
382C2×D4—1222no—
383C2×D4—1222no—
384C2×D4—1221no—
385C2×D4—1221no—
386C2×D4—1222no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—612no—
397C22×C4—612no—
398C22×C4—612no—
399C22×C4—612no—
400C22×C4—611no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1222no—
404C22×C4—1222no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4C4⋊#692311yescharacteristic
408C22×C4C22×#692311yescharacteristic
409M16—2442no—
410M16—2441no—
411M16—2441no—
412C2×C8—22no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8—611no—
416C2×C8—611no—
417C2×C8—1221no—
418C2×C8—1221no—
419C2×C8—1222no—
420C2×C8—1222no—
421C2×C8—1221no—
422C2×C8—1221no—
423C2×C8—1222no—
424C2×C8—1221no—
425C2×C8—1222no—
426C2×C8C22⋊#692311yescharacteristic
427C2×C8C22⋊#692311yescharacteristic
428C4⋊C4—1224no—
429C4⋊C4—1224no—
430C4⋊C4—2442no—
431C4⋊C4—2442no—
432C22⋊C4—1224no—
433C22⋊C4—1224no—
434C22⋊C4—2442no—
435C22⋊C4—2442no—
436C42—1224no—
437C42—1224no—
438C42—2442no—
439C42—2442no—
440C23—21no—
441C23—22no—
442C23—41no—
443C23—41no—
444C23—611no—
445C23—611no—
446C23—612no—
447C23—612no—
448C23—1222no—
449C23—1221no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23C2×C4⋊#692311yescharacteristic
455Q8—2441no—
456Q8—2442no—
457Q8—2441no—
458D4—2441no—
459D4—2442no—
460D4—2441no—
461D4—2441no—
462D4—2442no—
463D4—2441no—
464D4—2441no—
465D4—2442no—
466D4—2441no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—611no—
477C2×C4—612no—
478C2×C4—611no—
479C2×C4—612no—
480C2×C4—612no—
481C2×C4—612no—
482C2×C4—612no—
483C2×C4—612no—
484C2×C4—611no—
485C2×C4—611no—
486C2×C4—1221no—
487C2×C4—1222no—
488C2×C4—4882no—
489C2×C4—4882no—
490C2×C4—4882no—
491C2×C4—4882no—
492C2×C4—2444no—
493C2×C4—2444no—
494C2×C4—2441no—
495C2×C4—2442no—
496C2×C4—2441no—
497C2×C4C2×C22⋊#692311yescharacteristic
498C2×C4#1451985611yescharacteristic
499C2×C4D4×#692312yes—
500C2×C4D4×#692312yes—
501C8—21no—
502C8—21no—
503C8—41no—
504C8—1221no—
505C8—1221no—
506C8—2441no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—82no—
513C22—611no—
514C22—612no—
515C22—611no—
516C22—1221no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—4882no—
521C22—2442no—
522C22—2442no—
523C22—2441no—
524C22—2441no—
525C22—2441no—
526C22#1684070411yescharacteristic
527C22#1684070912yes—
528C4—41no—
529C4—611no—
530C4—612no—
531C4—611no—
532C4—4884no—
533C4—4884no—
534C4—2441no—
535C4#1684071011yescharacteristic
536C4#1684071212yes—
537C4#1684071411yescharacteristic
538C2—22no—
539C2—81no—
540C2—1221no—
541C2—1222no—
542C2—1221no—
543C2—4881no—
544C2#2146100211yescharacteristic
545C2#2146170111yescharacteristic
546C2#2146170211yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC22×#11758222C22
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16840772C2semidirect
3. #21461505C2semidirect
4. C2×#16840630C2semidirect
25. C2×C22⋊#92418C4semidirect
26. C2×#14519689C4semidirect
27. C2×#14519689C4semidirect
28. C2×C22⋊C8×C61C4semidirect
298. C2×C22⋊C8#6923semidirect
302. C61#11098semidirect

Maximal subgroups

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

subgroupindex
C2×#168407722
C2×#168407412
#214615052
C2×#168406302
C2×#168397272
#1109861