Finite Group Databasebeta

← #29598364

Subgroups — #29598364

Order 15616.

448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455458C211yesmaximal, characteristic
2#21447513C211yesmaximal, characteristic, complemented
3#21447510C211yesmaximal, characteristic
4#21447474C211yesmaximal, characteristic, complemented
5#21447470C211yesmaximal, characteristic
6#21445619C211yesmaximal, characteristic, complemented
7C61×#1813C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic, complemented
9#16840333C2211yescharacteristic
10#16840326C2211yescharacteristic
11#16840008—21no—
12#16840008—21no—
13#16839991—21no—
14#16839991—21no—
15#16839800C411yescharacteristic, complemented
16#16839772C411yescharacteristic, complemented
17#16839768C411yescharacteristic, complemented
18#16839746C2211yescharacteristic
19#16839736C2211yescharacteristic
20#16839717—21no—
21#16839560—22no—
22#16839558—22no—
23#16839553—22no—
24#16839550—22no—
25#16839533—21no—
26C2×#131×C61C2211yescharacteristic
27C2×#108×C61—21no—
28C61×#413C2211yescharacteristic
29C61×#413C2211yescharacteristic
30C61×#338—21no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C2×#11758190—21no—
34C2×#11758190—21no—
35C2×#11758190—41no—
36C2×#11758190—41no—
37C2×#11758194—21no—
38#14519775—21no—
39#14519773—21no—
40#14519766—21no—
41#14519764—21no—
42#14519758—21no—
43#14519758—21no—
44#14519756—21no—
45#14519756—21no—
46#14519751—21no—
47#14519751—21no—
48#14519745—21no—
49#14519745—21no—
50#14519736—21no—
51#14519736C2×C411yescharacteristic
52#14519736C2×C411yescharacteristic
53#14519711—21no—
54#14519709—21no—
55#14519702—21no—
56#14519702—21no—
57#14519699—21no—
58#14519699—21no—
59#14519696D412yes—
60#14519694—21no—
61#14519692—21no—
62#14519692D412yes—
63#14519687—41no—
64C8×Dic61—41no—
65C2×#41×C61C2311yescharacteristic
66#131×C61—41no—
67#131×C61—41no—
68C2×M16×C61—21no—
69C2×M16×C61—21no—
70C2×M16×C61C2×C411yescharacteristic
71C2×M16×C61D411yescharacteristic
72C2×M16×C61D411yescharacteristic
73C22×C8×C61C2×C411yescharacteristic
74C22×C8×C61D411yescharacteristic
75C22×C8×C61D411yescharacteristic
76#108×C61—41no—
77#108×C61—41no—
78#101×C61—21no—
79#101×C61—21no—
80#100×C61—21no—
81#100×C61—21no—
82C23×D61—21no—
83#41×C61—41no—
84#41×C61—41no—
85C2×Q8×C61C2×D411yescharacteristic
86C2×D4×C61C2×D411yescharacteristic
87C2×D4×C61#4111yescharacteristic
88C2×D4×C61#4111yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C22×Dic61—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—41no—
98C2×D244—41no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103M16×C61—41no—
104M16×C61—41no—
105M16×C61—41no—
106M16×C61—41no—
107M16×C61—41no—
108M16×C61—41no—
109M16×C61—41no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—21no—
115C2×C8×C61—21no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61C22⋊C411yescharacteristic
119C2×C8×C61C22⋊C411yescharacteristic
120C2×C8×C61C22⋊C411yescharacteristic
121C2×C8×C61C22⋊C411yescharacteristic
122C22⋊Dic61—21no—
123C22⋊Dic61—21no—
124C22⋊Dic61—22no—
125C22⋊Dic61—41no—
126C22⋊Dic61—41no—
127#11758198—41no—
128#11758198—41no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—41no—
132#11758196—41no—
133#11758196—41no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—41no—
137#11758194—22no—
138#11758194—41no—
139C2×#92418—41no—
140#11758190—42no—
141#11758190—41no—
142#11758190—41no—
143C23×C61C4×D411yescharacteristic
144C23×C61#12111yescharacteristic
145C23×C61#12411yescharacteristic
146C22×D61—41no—
147C22×D61—81no—
148C22×D61—161no—
149Q8×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61C2×C22⋊C411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12711yescharacteristic
163C22⋊D61—161no—
164C22⋊D61—161no—
165C2×Dic61—42no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—81no—
170D244—41no—
171D244—41no—
172D244—81no—
173Dic122—41no—
174Dic122—41no—
175Dic122—81no—
176C8×C61—21no—
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—81no—
180C8×C61—81no—
181C8×C61#9911yescharacteristic
182C8×C61#9911yescharacteristic
183#92418—42no—
184#13232—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61#39011yescharacteristic
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—162no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61C2×#9911yescharacteristic
200C4×C61#41011yescharacteristic
201Dic61—81no—
202Dic61—81no—
203Dic61—82no—
204Dic61—81no—
205#3057—611no—
206#2135—611no—
207#2134—611no—
208#2123—611no—
209#2122—611no—
210#1813D6111yescharacteristic, complemented
211#1757—611no—
212C2×C61—21no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61#196411yescharacteristic
217D61—161no—
218C22×SD16—611no—
219C2×#131C2×D6111yescharacteristic
220#536—611no—
221#535—611no—
222#468—1221no—
223#468—1221no—
224#465—1221no—
225#465—1221no—
226C2×#108—21no—
227#427—611no—
228#419—611no—
229#418—611no—
230#413—611no—
231#413C2×D6111yescharacteristic
232#413C2×D6111yescharacteristic
233#410—611no—
234#405—1221no—
235#356—1222no—
236#355—1222no—
237#352—1222no—
238AΣL(1,𝔽16)—1222no—
239#344—1221no—
240#338—21no—
241C61#1323211yescharacteristic, complemented, Sylow
242C2×#41C22×D6111yescharacteristic
243C22×Q8—611no—
244C22×D4—611no—
245C2×SD16—1221no—
246C2×SD16—1221no—
247C2×SD16—2441no—
248C2×SD16—2441no—
249#131—41no—
250#131—41no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—1221no—
254C2×M16C4×D6111yescharacteristic
255C2×M16D24411yescharacteristic
256C2×M16C22⋊D6111yescharacteristic
257C22×C8C4×D6111yescharacteristic
258C22×C8D24411yescharacteristic
259C22×C8C22⋊D6111yescharacteristic
260C4⋊Q8—1221no—
261#127—1221no—
262#124—1221no—
263#124—1221no—
264#123—1221no—
265#123—1221no—
266C22⋊Q8—1221no—
267C22⋊Q8—1221no—
268#121—1221no—
269#121—1221no—
270#120—1221no—
271#120—1221no—
272#117—611no—
273#117—611no—
274#117—1221no—
275#108—41no—
276#108—41no—
277#107—1221no—
278#106—1221no—
279#103—1221no—
280#103—1221no—
281#102—1221no—
282#102—1221no—
283#101—21no—
284#101—21no—
285#101—612no—
286#100—21no—
287#100—21no—
288#100—1221no—
289#99—612no—
290#99—1221no—
291#97—2441no—
292C4×C8—2441no—
293C24—1221no—
294#41—41no—
295#41—41no—
296C2×Q8—1221no—
297C2×Q8—1221no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×Q8D4×D6111yescharacteristic
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4D4×D6111yescharacteristic
308C2×D4#1175822611yescharacteristic
309C2×D4#1175822611yescharacteristic
310C22×C4—1221no—
311C22×C4C2×C4×D6111yescharacteristic
312C22×C4C2×D24411yescharacteristic
313C22×C4C2×C22⋊D6111yescharacteristic
314SD16—2442no—
315SD16—2441no—
316SD16—2441no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—1222no—
325M16—2441no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—2441no—
335C2×C8#1175819811yescharacteristic
336C2×C8#1175819811yescharacteristic
337C2×C8#1175819811yescharacteristic
338C2×C8#1175819811yescharacteristic
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1222no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C42—1221no—
352C42—1221no—
353C42—2441no—
354C23—9761no—
355C23—4881no—
356C23—2441no—
357C23#1451973911yescharacteristic
358C23#1451975211yescharacteristic
359C23#1451976611yescharacteristic
360Q8—41no—
361Q8—4881no—
362Q8—2441no—
363Q8—2441no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—9761no—
368D4—9761no—
369D4—4881no—
370D4—2441no—
371D4—2441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—4881no—
379C2×C4—2442no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4C2×#1175819811yescharacteristic
384C2×C4#1451973911yescharacteristic
385C2×C4#1451975211yescharacteristic
386C2×C4#1451977311yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—81no—
391C8—81no—
392C8—2442no—
393C8#1451969111yescharacteristic
394C8#1451969111yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—9762no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22#1683966311yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—4881no—
410C4—4881no—
411C4—4882no—
412C4—4881no—
413C4C2×#1451969111yescharacteristic
414C4#1683973511yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—9761no—
420C2#2144665411yescharacteristic
subgroupG/H
centerC2#21446654
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#1813C2
socleC2×C61#1964
prime radical#16840326C22
cosocleC2×#41×C61C23
hypercenter#1813D61
hypocenterC61#13232
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1813

Complements

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

NH ≅ G/Ntype
2. #21447513C2semidirect
4. #21447474C2semidirect
6. #21445619C2semidirect
7. C61×#1813C2semidirect
8. C22×#11758190C4semidirect
15. #16839800C4semidirect
16. #16839772C4semidirect
17. #16839768C4semidirect
210. #1813D61semidirect
241. C61#13232semidirect

Maximal subgroups

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

subgroupindex
#214554582
#214475132
#214475102
#214474742
#214474702
#214456192
C61×#18132
#1323261