Finite Group Databasebeta

← #30603303

Subgroups — #30603303

Order 15616.

866 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×#16840772C211yesmaximal, characteristic, complemented
2C2×#16840759C212yesmaximal
3C2×#16840645C212yesmaximal, complemented
4C2×#16840638C211yesmaximal, characteristic, complemented
5#408×D61C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C2×#14519856C2212yes—
8#16840772—24no—
9C2×#14519846—21no—
10C2×#14519845—21no—
11#16840759—24no—
12#16840759—24no—
13C2×#14519842—22no—
14C2×#14519841—22no—
15#16840645—24no—
16#16840638—21no—
17#16840638—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
29C2×#11758213—22no—
30C2×#11758213—22no—
31C2×#11758213—22no—
32C2×#11758213—22no—
33C2×#11758213—22no—
34C2×#11758213D414yes—
35C22×#92420—22no—
36#14519856—22no—
37#14519856—22no—
38#14519856—22no—
39#14519856D414yes—
40C2×C4⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C4×#6923—22no—
43#14519846—24no—
44#14519845—24no—
45#14519842—28no—
46#14519841—28no—
47C2×#11758226D411yescharacteristic
48C2×#11758222—21no—
49C2×#11758222C2×C411yescharacteristic
50C2×#11758224—21no—
51C2×#11758224D411yescharacteristic
52#41×D61—22no—
53#41×D61—22no—
54#41×D61—22no—
55#41×D61—22no—
56C2×Q8×D61Q811yescharacteristic
57C2×D4×D61—21no—
58C2×D4×D61Q811yescharacteristic
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—42no—
87#41×C61—22no—
88#41×C61—22no—
89C2×Q8×C61C4⋊C411yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61C4⋊C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61C22×C411yescharacteristic
94C2×C22⋊D61—21no—
95C2×C22⋊D61—21no—
96C2×C22⋊D61—21no—
97C22×Dic61—21no—
98C22×Dic61#4111yescharacteristic
99#11758226—22no—
100#11758226—22no—
101Q8×D61—22no—
102Q8×D61—22no—
103#11758224—22no—
104#11758224—22no—
105#11758224—42no—
106#11758224—42no—
107D4×D61—22no—
108D4×D61—22no—
109D4×D61—42no—
110D4×D61—42no—
111#11758222—22no—
112#11758222—22no—
113#11758222—41no—
114#11758222—41no—
115#11758222—41no—
116#11758222—41no—
117C2×D244—21no—
118C2×D244C4⋊C411yescharacteristic
119C2×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—21no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61C2×D412yes—
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×D412yes—
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2×Q811yescharacteristic
130C2×C4×D61#4112yes—
131C2×C4×D61#4112yes—
132C2×Dic122—21no—
133C2×Dic122C4⋊C411yescharacteristic
134C22⋊#6923—24no—
135C22⋊#6923—42no—
136C2×#92420—24no—
137C2×#92420—42no—
138C2×#92420—42no—
139C4⋊#6923—24no—
140C4⋊#6923—42no—
141C4×#6923—24no—
142C4×#6923—42no—
143#11758213—24no—
144#11758213—24no—
145#11758213—42no—
146#11758213—42no—
147M16×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—21no—
150C2×C8×C61C22⋊C411yescharacteristic
151C2×C8×C61C22⋊C411yescharacteristic
152#11758194—22no—
153C2×#92418—22no—
154C2×#92418—21no—
155C2×#92418C22⋊C411yescharacteristic
156C2×#92418C22⋊C411yescharacteristic
157#11758189—41no—
158#11758189—41no—
159C8×D61—21no—
160C8×D61—21no—
161C8×D61—22no—
162C8×D61—22no—
163C8×D61—21no—
164C8×D61—21no—
165C8×D61—42no—
166C23×C61—21no—
167C23×C61#11711yescharacteristic
168C22×D61—21no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—42no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61#12111yescharacteristic
175C22×D61#12112yes—
176C22×D61C22⋊Q811yescharacteristic
177C22×D61#12612yes—
178C2×#6923—44no—
179C2×#6923—82no—
180C2×#6923—82no—
181Q8×C61—22no—
182D4×C61—22no—
183D4×C61—42no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61C2×C4⋊C411yescharacteristic
189C2×C4×C61C4×D412yes—
190C2×C4×C61C4×D412yes—
191C22⋊D61—42no—
192C22⋊D61—41no—
193C22⋊D61—41no—
194C22⋊D61—41no—
195C22⋊D61—41no—
196C2×Dic61—21no—
197C2×Dic61—42no—
198C2×Dic61#12111yescharacteristic
199C2×Dic61C22⋊Q811yescharacteristic
200C2×Dic61#12312yes—
201C2×Dic61#12412yes—
202D244—22no—
203D244—41no—
204D244—41no—
205C4×D61—42no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—42no—
209C4×D61#12011yescharacteristic
210C4×D61#12012yes—
211C4×D61#12112yes—
212C4×D61#12112yes—
213C4×D61C22⋊Q812yes—
214C4×D61C22⋊Q812yes—
215C4×D61#12312yes—
216C4×D61#12311yescharacteristic
217C4×D61#12411yescharacteristic
218C4×D61#12711yescharacteristic
219Dic122—22no—
220Dic122—41no—
221Dic122—41no—
222#92420—44no—
223C8×C61—21no—
224C8×C61—21no—
225C8×C61—41no—
226#92418—21no—
227#92418—21no—
228#92418—41no—
229#11104—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61#38011yescharacteristic
236C22×C61#38812yes—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—84no—
247C2×D61#39211yescharacteristic
248C2×D61#39612yes—
249C2×D61#39711yescharacteristic
250#6923—84no—
251C4×C61—41no—
252C4×C61#38512yes—
253C4×C61#38611yescharacteristic
254C4×C61#39011yescharacteristic
255Dic61—41no—
256Dic61#39311yescharacteristic
257Dic61#39412yes—
258Dic61#39911yescharacteristic
259C2×#427—611no—
260C2×#421—612no—
261C2×#408—611no—
262C2×#344—612no—
263C2×#341—611no—
264C2×C61—22no—
265C2×C61—81no—
266C2×C61#143911yescharacteristic
267C2×C61#181411yescharacteristic
268C2×C61#181411yescharacteristic
269D61—21no—
270D61—22no—
271D61—21no—
272D61—81no—
273C22×#41—611no—
274C22×M16—612no—
275C22×M16—611no—
276C23×C8—611no—
277C2×#117—612no—
278#427—1224no—
279C2×#107—1221no—
280C2×#106—1221no—
281#421—1224no—
282#421—1224no—
283C2×#104—1222no—
284C2×#104—1222no—
285#408—611no—
286#408—611no—
287#408—611no—
288#408—1221no—
289#408—1221no—
290#408#692311yescharacteristic, complemented
291C2×C22⋊C8—1221no—
292C2×C22⋊C8—1221no—
293#344—1224no—
294#341—1221no—
295#341—1221no—
296C61#1110411yescharacteristic, complemented, Sylow
297C2×#41—611no—
298C2×#41—611no—
299C2×#41—611no—
300C2×#41—1221no—
301C2×#41—1221no—
302C2×#41—1222no—
303C2×#41—1222no—
304C2×#41—1222no—
305C2×#41—1222no—
306C2×#41C2×#692311yescharacteristic
307C22×Q8—611no—
308C22×D4—611no—
309C22×D4—1221no—
310C23×C4—611no—
311C23×C4—1221no—
312C2×M16—614no—
313C2×M16—611no—
314C2×M16—1221no—
315C2×M16—1222no—
316C2×M16—1222no—
317C2×M16—1222no—
318C2×M16—1222no—
319C2×M16—1222no—
320C2×M16—1222no—
321C2×M16—1222no—
322C2×M16C2×#692311yescharacteristic
323C22×C8—611no—
324C22×C8—611no—
325C22×C8—611no—
326C22×C8—611no—
327C22×C8—611no—
328C22×C8—1222no—
329C22×C8—1222no—
330C22×C8—1221no—
331C22×C8—1222no—
332C22×C8C2×#692311yescharacteristic
333#117—614no—
334#117—1222no—
335#117—1222no—
336#117—1222no—
337C2×C4⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C42—1222no—
340#107—1224no—
341#106—1224no—
342#104—1228no—
343#104—1228no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8—1221no—
352C24—611no—
353C24—1221no—
354#41—22no—
355#41—22no—
356#41—1222no—
357#41—1222no—
358#41—1222no—
359#41—1222no—
360#41—1222no—
361#41—1222no—
362#41—2441no—
363#41—2441no—
364#41—2441no—
365#41—2441no—
366#41—2442no—
367#41—2442no—
368C2×Q8—611no—
369C2×Q8—1221no—
370C2×Q8—1222no—
371C2×Q8—1222no—
372C2×Q8C4⋊#692311yescharacteristic
373C2×D4—21no—
374C2×D4—611no—
375C2×D4—1221no—
376C2×D4—1222no—
377C2×D4—1222no—
378C2×D4—1221no—
379C2×D4—1221no—
380C2×D4—1221no—
381C2×D4—2442no—
382C2×D4—2442no—
383C2×D4C4⋊#692311yescharacteristic
384C22×C4—21no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—612no—
393C22×C4—612no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4C22×#692311yescharacteristic
402M16—22no—
403M16—1224no—
404M16—1224no—
405M16—1222no—
406M16—2441no—
407M16—2441no—
408M16—2442no—
409M16—2442no—
410C2×C8—22no—
411C2×C8—21no—
412C2×C8—611no—
413C2×C8—611no—
414C2×C8—1221no—
415C2×C8—1221no—
416C2×C8—1222no—
417C2×C8—1222no—
418C2×C8—1221no—
419C2×C8—1221no—
420C2×C8—1222no—
421C2×C8—1224no—
422C2×C8—1221no—
423C2×C8—2442no—
424C2×C8—2442no—
425C2×C8—2442no—
426C2×C8C22⋊#692311yescharacteristic
427C2×C8C22⋊#692311yescharacteristic
428C4⋊C4—1224no—
429C4⋊C4—2442no—
430C22⋊C4—1224no—
431C22⋊C4—2442no—
432C42—1224no—
433C42—2442no—
434C23—21no—
435C23—611no—
436C23—611no—
437C23—612no—
438C23—612no—
439C23—1221no—
440C23—2441no—
441C23—2441no—
442C23—2442no—
443C23—2442no—
444C23—2442no—
445C23#1451985611yescharacteristic
446Q8—22no—
447Q8—1222no—
448Q8—2441no—
449Q8—2441no—
450D4—22no—
451D4—42no—
452D4—1222no—
453D4—2441no—
454D4—2441no—
455D4—2441no—
456D4—2441no—
457D4—2441no—
458D4—2441no—
459D4—2442no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—611no—
464C2×C4—611no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—611no—
472C2×C4—612no—
473C2×C4—611no—
474C2×C4—612no—
475C2×C4—611no—
476C2×C4—611no—
477C2×C4—1221no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2444no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4C2×C22⋊#692311yescharacteristic
487C2×C4C2×C4⋊#692311yescharacteristic
488C2×C4D4×#692312yes—
489C2×C4D4×#692312yes—
490C8—21no—
491C8—21no—
492C8—41no—
493C8—1221no—
494C8—1221no—
495C8—2444no—
496C8—2441no—
497C22—21no—
498C22—21no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—611no—
503C22—612no—
504C22—611no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—4884no—
510C22—2442no—
511C22—2442no—
512C22—2441no—
513C22—2441no—
514C22—2441no—
515C22#1684070411yescharacteristic
516C22#1684071212yes—
517C4—41no—
518C4—611no—
519C4—612no—
520C4—611no—
521C4—4884no—
522C4—2441no—
523C4#1684070912yes—
524C4#1684071011yescharacteristic
525C4#1684071411yescharacteristic
526C2—22no—
527C2—81no—
528C2—1221no—
529C2—1222no—
530C2—1221no—
531C2—4881no—
532C2#2146100211yescharacteristic
533C2#2146170511yescharacteristic
534C2#2146170611yescharacteristic
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#11104
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×#16840772C2semidirect
3. C2×#16840645C2semidirect
4. C2×#16840638C2semidirect
21. #16839730C4semidirect
22. #16839729C4semidirect
23. #16839728C4semidirect
28. C61×#408C4semidirect
290. #408#6923semidirect
296. C61#11104semidirect

Maximal subgroups

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

subgroupindex
C2×#168407722
C2×#168407592
C2×#168406452
C2×#168406382
#408×D612
#1110461