Finite Group Databasebeta

← #29832981

Subgroups — #29832981

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840575C211yesmaximal, characteristic
2#21458921C211yesmaximal, characteristic, complemented
3#21454427C211yesmaximal, characteristic, complemented
4#21447569C211yesmaximal, characteristic, complemented
5#21447567C214yesmaximal, complemented
6#21447566C211yesmaximal, characteristic, complemented
7C2×#16839578C211yesmaximal, characteristic, complemented
8#362×D61C214yesmaximal, complemented
9C2×C61×#362C211yesmaximal, characteristic, complemented
10C2×#14519825—21no—
11#16840575—22no—
12#16840575—22no—
13#16840575C414yes—
14#16840575C414yes—
15C2×#14519809—22no—
16C2×#14519808—21no—
17C2×#14519800C2212yes—
18C2×#14519799C2211yescharacteristic
19C2×Q16×D61C2212yes—
20#16840528—21no—
21C2×#14519783C2211yescharacteristic
22#16840180—22no—
23#16840178—22no—
24C2×#14519717C2211yescharacteristic
25M32×D61C2214yes—
26#16839810—21no—
27#16839809—22no—
28C2×#14519713C2211yescharacteristic
29#108×D61C2214yes—
30#16839579C2212yes—
31#16839578C2214yes—
32#16839577C2212yes—
33#16839576C2212yes—
34#16839574C2212yes—
35C22×Q16×C61C2211yescharacteristic
36C2×M32×C61C2211yescharacteristic
37C2×#108×C61C2211yescharacteristic
38C61×#362C2214yes—
39#14519825—24no—
40#14519825—24no—
41#14519825—42no—
42#14519825—42no—
43C2×#11758226—22no—
44C2×#11758226—41no—
45C2×#11758222—21no—
46C2×#11758222—42no—
47C2×#11758222D411yescharacteristic
48C2×Q8×D61—22no—
49C2×Q8×D61—41no—
50#14519809—28no—
51#14519809—28no—
52#14519808—24no—
53#14519808—24no—
54#14519800—24no—
55#14519800C2×C418yes—
56#14519799—21no—
57#14519799—21no—
58#14519799C2×C412yes—
59#14519799C2×C412yes—
60C2×Dic244C2311yescharacteristic
61C2×#11758202—22no—
62Q16×D61—24no—
63Q16×D61C2×C418yes—
64C2×#11758190—21no—
65C2×#11758201—22no—
66C2×D488C2311yescharacteristic
67#14519785—42no—
68#14519783—42no—
69#14519783C2×C412yes—
70#14519783C2×C412yes—
71#14519783D412yes—
72#14519783D412yes—
73C2×#11758194—21no—
74C2×#11758194D411yescharacteristic
75C2×#11758189D412yes—
76M16×D61—24no—
77C2×C8×D61C2312yes—
78#14519717—21no—
79#14519717C2312yes—
80#14519716—24no—
81C2×#11758185—21no—
82C16×D61—24no—
83#14519713—21no—
84#14519713C2312yes—
85#14519712—24no—
86C22×Q8×C61—21no—
87C2×Q16×C61—21no—
88C2×Q16×C61—21no—
89C2×Q16×C61—21no—
90C2×Q16×C61C2×C412yes—
91C2×Q16×C61C2×C412yes—
92C2×Q16×C61C2312yes—
93C2×M16×C61—21no—
94C22×C8×C61C2311yescharacteristic
95M32×C61—21no—
96M32×C61C2312yes—
97C2×C16×C61—21no—
98#108×C61—21no—
99#108×C61C2312yes—
100C2×Q8×C61—22no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—41no—
104C2×Q8×C61—41no—
105C2×Q8×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61C2×D411yescharacteristic
108C2×C22⋊D61—41no—
109C2×C22⋊D61SD1612yes—
110#11758226—28no—
111#11758226—44no—
112#11758226—44no—
113#11758226—44no—
114Q8×D61—28no—
115Q8×D61—44no—
116Q8×D61—44no—
117Q8×D61—44no—
118#11758222—22no—
119#11758222—22no—
120#11758222—41no—
121#11758222—41no—
122#11758222—48no—
123#11758222—48no—
124#11758222C22⋊C412yes—
125#11758222C22⋊C412yes—
126#11758222D812yes—
127#11758222D812yes—
128C2×D244—21no—
129C2×D244—42no—
130C2×D244SD1611yescharacteristic
131C2×C4×D61—42no—
132C2×C4×D61—41no—
133C2×C4×D61—42no—
134C2×C4×D61C2×D412yes—
135C2×Dic122—21no—
136C2×Dic122—42no—
137C2×Dic122SD1611yescharacteristic
138Q16×C61—22no—
139Q16×C61—22no—
140Q16×C61—22no—
141Q16×C61C22×C414yes—
142M16×C61—22no—
143M16×C61—41no—
144C2×C8×C61—41no—
145C2×C8×C61C22×C411yescharacteristic
146C2×C8×C61C22×C411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2411yescharacteristic
151#11758202—28no—
152#11758201—28no—
153#11758194—22no—
154#11758194—41no—
155#11758194C22⋊C412yes—
156#11758194C22⋊C412yes—
157C2×#92418—41no—
158C2×#92418C2×D412yes—
159Dic244—21no—
160Dic244C22×C412yes—
161D488—21no—
162D488C22×C412yes—
163#11758190—22no—
164#11758190—22no—
165#11758189—44no—
166#11758189C22⋊C414yes—
167#11758189C22⋊C414yes—
168C8×D61—44no—
169C8×D61C22×C414yes—
170C8×D61C2×D414yes—
171C16×C61—22no—
172#11758185—22no—
173C23×C61C2×SD1611yescharacteristic
174C22×D61—41no—
175C22×D61C2×SD1612yes—
176Q8×C61—24no—
177Q8×C61—42no—
178Q8×C61—42no—
179Q8×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61C2×C22⋊C411yescharacteristic
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×SD1611yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C22⋊D61—42no—
190C22⋊D61—42no—
191C22⋊D61#10214yes—
192C22⋊D61#10214yes—
193C2×Dic61—41no—
194C2×Dic61C2×SD1612yes—
195D244—22no—
196D244—48no—
197D244—41no—
198D244#10212yes—
199D244#10212yes—
200C4×D61—48no—
201C4×D61—42no—
202C4×D61—42no—
203C4×D61—48no—
204C4×D61C2×C22⋊C414yes—
205C4×D61C2×D814yes—
206Dic122—22no—
207Dic122—41no—
208Dic122—48no—
209Dic122#10212yes—
210Dic122#10212yes—
211C8×C61—42no—
212C8×C61C2×C22⋊C411yescharacteristic
213C8×C61C2×C22⋊C411yescharacteristic
214C8×C61C23×C411yescharacteristic
215C8×C61C22×D411yescharacteristic
216#92418—42no—
217#92418C2×C22⋊C414yes—
218#33393—611nomaximal, Sylow
219C22×C61—41no—
220C22×C61C2×#10211yescharacteristic
221C22×C61C2×#10211yescharacteristic
222C22×C61C22×SD1611yescharacteristic
223C2×D61—42no—
224C2×D61—42no—
225C2×D61—82no—
226C2×D61C2×#10214yes—
227C4×C61—44no—
228C4×C61C2×#10211yescharacteristic
229C4×C61C2×#10211yescharacteristic
230C4×C61C22×C22⋊C411yescharacteristic
231C4×C61C22×D811yescharacteristic
232Dic61—42no—
233Dic61C2×#10214yes—
234C2×#578—611no—
235#3407—611no—
236#2916—611no—
237#2148—611no—
238#2148—611no—
239#2148—614no—
240C2×#362—614no—
241C2×#362—611no—
242C2×#362D6111yescharacteristic, complemented
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61C22×#10211yescharacteristic
247D61—24no—
248D61—82no—
249C2×2−1+4—1221no—
250#578—614no—
251#578—614no—
252#578—1222no—
253#578—1222no—
254C2×#137—1222no—
255C2×#137—1221no—
256C2×#135—612no—
257C2×#135—611no—
258C22×Q16—612no—
259C22×Q16C2×D6111yescharacteristic
260#568—1221no—
261C2×#131—611no—
262#504—1222no—
263#504—1222no—
264C2×M32—611no—
265C2×M32—614no—
266C2×M32C2×D6111yescharacteristic
267#430—1222no—
268#430—1221no—
269C2×#108—611no—
270C2×#108—614no—
271C2×#108C2×D6111yescharacteristic
272#362—614no—
273#362—612no—
274#362—612no—
275#362C2×D6114yes—
276#361—612no—
277#361—612no—
278C61#3339311yescharacteristic, complemented, Sylow
2792−1+4—1224no—
2802−1+4—1224no—
2812−1+4—2442no—
2822−1+4—2442no—
283C2×#41—611no—
284C2×#41—1222no—
285C2×#41—1221no—
286C2×#41—2442no—
287C2×#41—2441no—
288C22×Q8—21no—
289C22×Q8—1222no—
290C22×Q8—2441no—
291#137—1228no—
292#137—1228no—
293#137—1224no—
294#137—1224no—
295#135—618no—
296#135—612no—
297#135—612no—
298#135—1224no—
299#135—1221no—
300#135—1221no—
301C2×Q16—21no—
302C2×Q16—21no—
303C2×Q16—21no—
304C2×Q16—618no—
305C2×Q16—611no—
306C2×Q16—1224no—
307C2×Q16—1222no—
308C2×Q16C4×D6112yes—
309C2×Q16C4×D6112yes—
310C2×Q16C22×D6112yes—
311C2×SD16—1222no—
312C2×SD16—1221no—
313C2×D8—611no—
314#131—612no—
315#131—612no—
316#131—612no—
317#131—612no—
318#131—2442no—
319#131—2442no—
320C2×M16—21no—
321C2×M16—611no—
322C2×M16—612no—
323C2×M16—1224no—
324C2×M16—1221no—
325C22×C8—612no—
326C22×C8C22×D6111yescharacteristic
327M32—21no—
328M32—612no—
329M32—1224no—
330M32—1221no—
331M32C22×D6112yes—
332C2×C16—21no—
333C2×C16—1224no—
334C2×C16—1221no—
335#108—21no—
336#108—612no—
337#108—1224no—
338#108—1221no—
339#108C22×D6112yes—
340#41—612no—
341#41—612no—
342#41—612no—
343#41—612no—
344#41—1228no—
345#41—1222no—
346#41—1222no—
347#41—2448no—
348#41—2448no—
349#41—2444no—
350#41—2444no—
351#41—2444no—
352#41—2441no—
353#41—2441no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—611no—
361C2×Q8—1228no—
362C2×Q8—1221no—
363C2×Q8—2442no—
364C2×Q8—2444no—
365C2×Q8—2444no—
366C2×Q8—2444no—
367C2×D4—612no—
368C2×D4—611no—
369C2×D4—1221no—
370C2×D4—2442no—
371C2×D4—2441no—
372C22×C4—41no—
373C22×C4—612no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4—2441no—
377C22×C4D4×D6111yescharacteristic
378Q16—22no—
379Q16—22no—
380Q16—22no—
381Q16—612no—
382Q16—1228no—
383Q16—1221no—
384Q16C2×C4×D6114yes—
385SD16—1228no—
386SD16—1222no—
387SD16—1222no—
388D8—612no—
389D8—1221no—
390M16—22no—
391M16—41no—
392M16—612no—
393M16—612no—
394M16—614no—
395M16—614no—
396M16—1222no—
397M16—2444no—
398M16—2441no—
399C2×C8—41no—
400C2×C8—612no—
401C2×C8—614no—
402C2×C8—614no—
403C2×C8—2444no—
404C2×C8—2441no—
405C2×C8C2×C4×D6111yescharacteristic
406C2×C8C2×C4×D6111yescharacteristic
407C2×C8D4×D6111yescharacteristic
408C2×C8D4×D6111yescharacteristic
409C2×C8D4×D6111yescharacteristic
410C2×C8C23×D6111yescharacteristic
411C16—22no—
412C16—1222no—
413C23—612no—
414C23—2441no—
415C23SD16×D6111yescharacteristic
416Q8—24no—
417Q8—42no—
418Q8—42no—
419Q8—42no—
420Q8—612no—
421Q8—612no—
422Q8—1222no—
423Q8—2448no—
424Q8—2441no—
425D4—614no—
426D4—614no—
427D4—612no—
428D4—612no—
429D4—1222no—
430D4—2448no—
431D4—2442no—
432D4—2442no—
433D4—2441no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—612no—
438C2×C4—614no—
439C2×C4—614no—
440C2×C4—2448no—
441C2×C4—2448no—
442C2×C4—2441no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4C22⋊C4×D6111yescharacteristic
446C2×C4C22⋊C4×D6111yescharacteristic
447C2×C4D8×D6111yescharacteristic
448C2×C4D8×D6111yescharacteristic
449C2×C4SD16×D6111yescharacteristic
450C2×C4C2×D4×D6111yescharacteristic
451C8—42no—
452C8—614no—
453C8—2442no—
454C8C22⋊C4×D6111yescharacteristic
455C8C22⋊C4×D6111yescharacteristic
456C8C22×C4×D6111yescharacteristic
457C8C2×D4×D6111yescharacteristic
458C22—41no—
459C22—614no—
460C22—4882no—
461C22—2442no—
462C22—2442no—
463C22#102×D6111yescharacteristic
464C22#102×D6111yescharacteristic
465C22C2×SD16×D6111yescharacteristic
466C4—44no—
467C4—614no—
468C4—2442no—
469C4#102×D6111yescharacteristic
470C4#102×D6111yescharacteristic
471C4C2×C22⋊C4×D6111yescharacteristic
472C4C2×D8×D6111yescharacteristic
473C2—21no—
474C2—21no—
475C2—21no—
476C2—1224no—
477C2—4882no—
478C2C2×#102×D6111yescharacteristic
subgroupG/H
centerC2C2×#102×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC2×C61×#362C2
socleC2×C61C22×#102
prime radicalC2×#16840575C2
cosocleC2×C8×C61C24
hypercenterC2×#362D61
hypocenterC61#33393
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
2. #21458921C2semidirect
3. #21454427C2semidirect
4. #21447569C2semidirect
5. #21447567C2semidirect
6. #21447566C2semidirect
7. C2×#16839578C2semidirect
8. #362×D61C2semidirect
9. C2×C61×#362C2semidirect
242. C2×#362D61semidirect
278. C61#33393semidirect

Maximal subgroups

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

subgroupindex
C2×#168405752
#214589212
#214544272
#214475692
#214475672
#214475662
C2×#168395782
#362×D612
C2×C61×#3622
#3339361