Finite Group Databasebeta

← #29582323

Subgroups — #29582323

Order 15616.

676 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839963C211yesmaximal, characteristic
2C2×#16839962C211yesmaximal, characteristic
3#21451189C211yesmaximal, characteristic, complemented
4#21446625C211yesmaximal, characteristic
5C2×#16839494C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C22×#11758201—21no—
10C2×#14519774C2211yescharacteristic
11C2×C4×Dic122C2211yescharacteristic
12#16839963—22no—
13#16839963—22no—
14#16839962—22no—
15#16839962—22no—
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519699—21no—
18C2×#14519699—22no—
19C2×#14519697—21no—
20#16839695—22no—
21#16839669—21no—
22#16839668—21no—
23#16839660—21no—
24#16839658—21no—
25#16839632C2211yescharacteristic
26#16839494—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×Dic122D411yescharacteristic
32C22×D244—21no—
33C22×D244—21no—
34C22×D244—21no—
35C2×#11758190—24no—
36C2×#11758190—42no—
37C2×#11758190—42no—
38C2×#11758201—24no—
39C2×#11758201—42no—
40C2×#11758201—42no—
41C22×#92418—21no—
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774D412yes—
46C4×Dic122—21no—
47C4×Dic122—21no—
48C4×Dic122—21no—
49C4×Dic122—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61D411yescharacteristic
53C2×C4⋊Dic61D412yes—
54C2×#11758196—21no—
55C2×#11758196—22no—
56C2×C4×Dic61—21no—
57C4⋊#92418—21no—
58C4⋊#92418D412yes—
59#14519699—24no—
60#14519699—44no—
61#14519697—24no—
62#14519684—22no—
63#14519684—22no—
64#14519684—22no—
65C22×Q8×C61D411yescharacteristic
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61D412yes—
78C4×C8×C61—21no—
79C4×C8×C61—21no—
80C23×D61—41no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61SD1612yescomplemented
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C2×D244—22no—
96C2×D244—22no—
97C2×D244—22no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122—21no—
114C2×Dic122—21no—
115C2×Dic122—21no—
116C2×Dic122SD1612yescomplemented
117C2×C8×C61—22no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—41no—
127C42×C61—41no—
128C42×C61—41no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133#11758201—48no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—41no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139C4⋊Dic61—41no—
140C4⋊Dic61—42no—
141#11758196—41no—
142#11758196—41no—
143#11758196—82no—
144C4×Dic61—41no—
145C4×Dic61—41no—
146C2×#92418—22no—
147C2×#92418—41no—
148C2×#92418—41no—
149#11758190—48no—
150C23×C61#12011yescharacteristic
151C22×D61—42no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61—81no—
155C22×D61—81no—
156C22×D61—81no—
157C22×D61—81no—
158Q8×C61—22no—
159Q8×C61—22no—
160Q8×C61—41no—
161Q8×C61—41no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—22no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12711yescharacteristic
176C2×C4×C61C2×SD1611yescharacteristic
177C2×C4×C61C2×SD1611yescharacteristic
178C2×C4×C61#13511yescharacteristic
179C2×C4×C61#13511yescharacteristic
180C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C61#13711yescharacteristic
183C2×C4×C61#13711yescharacteristic
184C2×Dic61—22no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—41no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193D244—44no—
194D244—42no—
195D244—42no—
196D244—42no—
197D244—42no—
198D244—82no—
199D244—81no—
200D244—81no—
201D244—81no—
202D244—81no—
203Dic122—22no—
204Dic122—22no—
205Dic122—41no—
206Dic122—41no—
207C8×C61—42no—
208C8×C61—42no—
209#92418—42no—
210#10230—611nomaximal, Sylow
211C22×C61#39211yescharacteristic
212C22×C61#44811yescharacteristic
213C22×C61#44811yescharacteristic
214C22×C61#44911yescharacteristic
215C22×C61#44911yescharacteristic
216C22×C61#45311yescharacteristic
217C22×C61#45411yescharacteristic
218C2×D61—82no—
219C2×D61—82no—
220C2×D61—82no—
221C2×D61—161no—
222C2×D61—161no—
223C2×D61—161no—
224C2×D61—161no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—42no—
228C4×C61—81no—
229C4×C61#45011yescharacteristic
230C4×C61#45011yescharacteristic
231C4×C61#45211yescharacteristic
232C4×C61#45211yescharacteristic
233C4×C61#46511yescharacteristic
234C4×C61#46511yescharacteristic
235C4×C61#46811yescharacteristic
236C4×C61#46811yescharacteristic
237Dic61—42no—
238Dic61—82no—
239Dic61—81no—
240C2×#460—611no—
241C2×#460—611no—
242#2582—611no—
243#1957—611no—
244C2×Q8⋊C8—611no—
245C2×Q8⋊C8D6111yescharacteristic, complemented
246#1296—611no—
247C2×C61#162011yescharacteristic
248C2×C61#162311yescharacteristic
249C2×C61#162611yescharacteristic
250C2×C61#162611yescharacteristic
251C2×C61#200011yescharacteristic
252C2×C61#200011yescharacteristic
253C2×C61#200611yescharacteristic
254D61—162no—
255C22×SD16—1221no—
256C22×SD16—1221no—
257C2×#127—611no—
258C2×C4×Q8—611no—
259C2×C4×Q8C2×D6111yescharacteristic
260#460—1222no—
261#460—1222no—
262#460—1222no—
263#460—1222no—
264C2×C4⋊C8—611no—
265C2×C4⋊C8C2×D6111yescharacteristic
266C2×#102—1221no—
267C2×#102—1221no—
268C2×#102—1222no—
269C2×C4×C8C2×D6111yescharacteristic
270#398—1222no—
271#391—1221no—
272#391—1221no—
273#389—1221no—
274#389—1221no—
275#384—611no—
276Q8⋊C8—22no—
277Q8⋊C8—1222no—
278C61#1023011yescharacteristic, complemented, Sylow
279C22×Q8—611no—
280C22×Q8D24411yescharacteristic
281C22×D4—1221no—
282C22×D4—1221no—
283C22×D4—1221no—
284C2×SD16—1224no—
285C2×SD16—1224no—
286C2×SD16—2442no—
287C2×SD16—2442no—
288C2×SD16—2442no—
289C2×SD16—2442no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—1221no—
293#127—612no—
294#127—1221no—
295#127—1221no—
296#127—1221no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C4×Q8—1221no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—612no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4D24411yescharacteristic
313C2×C42—21no—
314C2×C42—1221no—
315C2×C42C22×D6111yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—612no—
318C4⋊C8—1221no—
319C4⋊C8C22⋊D6112yes—
320#102—1224no—
321#102—1224no—
322#102—2444no—
323C4×C8—21no—
324C4×C8—21no—
325#95—1222no—
326#95—1222no—
327#95—1222no—
328C24—2441no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—612no—
335C2×Q8—1221no—
336C2×Q8—1221no—
337C2×Q8—1221no—
338C2×Q8—1221no—
339C2×Q8—1221no—
340C2×Q8#1175819012yescomplemented
341C2×D4—1222no—
342C2×D4—1222no—
343C2×D4—1222no—
344C2×D4—2442no—
345C2×D4—2442no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—1221no—
360C22×C4—1222no—
361C22×C4—1221no—
362C22×C4C2×D24411yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365SD16—2448no—
366SD16—2448no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—1222no—
374C2×C8—2441no—
375C2×C8—2441no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—4882no—
383C4⋊C4—2442no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C42—41no—
391C42—41no—
392C42—2441no—
393C42—2441no—
394C42#1175822211yescharacteristic
395C42D4×D6111yescharacteristic
396C42D4×D6111yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C23—4881no—
399C23—4881no—
400C23—4881no—
401C23—4881no—
402C23—4881no—
403C23—4881no—
404C23—2442no—
405C23#1451974711yescharacteristic
406Q8—22no—
407Q8—22no—
408Q8—41no—
409Q8—41no—
410Q8—1222no—
411Q8—1222no—
412Q8—2441no—
413Q8—2441no—
414D4—4882no—
415D4—4881no—
416D4—4881no—
417D4—4881no—
418D4—4881no—
419D4—2444no—
420D4—2442no—
421D4—2442no—
422D4—2442no—
423D4—2442no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—1222no—
433C2×C4—2441no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4#1451974511yescharacteristic
442C2×C4#1451974711yescharacteristic
443C2×C4#1451975011yescharacteristic
444C2×C4#1451975011yescharacteristic
445C2×C4#1451975111yescharacteristic
446C2×C4#1451977311yescharacteristic
447C2×C4SD16×D6111yescharacteristic
448C2×C4C2×#1175819011yescharacteristic
449C2×C4#1451979911yescharacteristic
450C2×C4#1451980011yescharacteristic
451C2×C4#1451980411yescharacteristic
452C2×C4#1451980511yescharacteristic
453C2×C4#1451980911yescharacteristic
454C2×C4#1451981011yescharacteristic
455C8—42no—
456C8—42no—
457C8—2442no—
458C22—9761no—
459C22—9761no—
460C22—9761no—
461C22—9761no—
462C22—4882no—
463C22—4882no—
464C22—4882no—
465C22#1683967111yescharacteristic
466C22#1683990211yescharacteristic
467C22#1683990311yescharacteristic
468C22#1683990911yescharacteristic
469C22#1683991011yescharacteristic
470C22#1683993111yescharacteristic
471C22#1683993611yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—81no—
476C4—4882no—
477C4—4881no—
478C4—2442no—
479C4#1683991111yescharacteristic
480C4#1683991511yescharacteristic
481C4#1683992311yescharacteristic
482C4#1683992611yescharacteristic
483C4#1683999111yescharacteristic
484C4#1683999411yescharacteristic
485C4#1684000811yescharacteristic
486C4#1684001111yescharacteristic
487C2—9762no—
488C2#2144488011yescharacteristic
489C2#2144489911yescharacteristic
490C2#2144491711yescharacteristic
491C2#2144491811yescharacteristic
492C2#2144682111yescharacteristic
493C2#2144682411yescharacteristic
494C2#2144686211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenterC2×Q8⋊C8D61
hypocenterC61#10230
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #21451189C2semidirect
5. C2×#16839494C2semidirect
6. #21443703C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
86. C2×Q8×C61SD16semidirect
116. C2×Dic122SD16semidirect
245. C2×Q8⋊C8D61semidirect
278. C61#10230semidirect
340. C2×Q8#11758190semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
C2×#168399622
#214511892
#214466252
C2×#168394942
#214437032
C2×C61×Q8⋊C82
#1023061