Finite Group Databasebeta

← #29574029

Subgroups — #29574029

Order 15616.

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

normal subgroups only

This group has 458 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#21454858C211yesmaximal, characteristic
2#21446114C211yesmaximal, characteristic
3#21446026C211yesmaximal, characteristic, complemented
4#21446023C211yesmaximal, characteristic, complemented
5#21444135C211yesmaximal, characteristic
6#21443707C211yesmaximal, characteristic, complemented
7C61×#1298C211yesmaximal, characteristic, complemented
8C22×#11758194C2211yescharacteristic
9C2×C4×C22⋊D61C2211yescharacteristic
10#16839838—21no—
11#16839838—21no—
12#16839837—21no—
13#16839837—21no—
14#16839812—21no—
15C2×#14519713—21no—
16C2×#14519712—21no—
17#16839726C2211yescharacteristic
18#16839724—21no—
19C2×C22⋊#92418C2211yescharacteristic
20C2×#14519689—21no—
21#16839527—21no—
22#16839526—21no—
23#16839516—21no—
24#16839487C412yes—
25#16839485C412yes—
26C61×#407C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C22×C22⋊D61Q811yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—42no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C2×#11758189—21no—
37C2×#11758189—21no—
38C22×#92418—21no—
39C22×#92418—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C2×#11758196C2×C411yescharacteristic
45C2×C22⋊Dic61Q811yescharacteristic
46C2×#11758198C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519713—42no—
49#14519712—42no—
50#14519706—21no—
51#14519706—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418C2×C412yes—
56#14519689—21no—
57#14519689—21no—
58#14519689—42no—
59C8×Dic61—21no—
60C8×Dic61—21no—
61C23×C4×C61C2311yescharacteristic
62C2×M16×C61D411yescharacteristic
63C2×M16×C61D411yescharacteristic
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61C2×C412yes—
72C24×C61C2×Q811yescharacteristic
73C23×D61C4⋊C411yescharacteristic
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×C22⋊D61—21no—
83C2×C22⋊D61—21no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—41no—
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C4⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C22⋊Dic61—21no—
104C22⋊Dic61—21no—
105#11758198—21no—
106#11758198—21no—
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111#11758194—22no—
112#11758194—22no—
113#11758194—41no—
114#11758194—41no—
115#11758194—41no—
116#11758194—41no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125#11758189—81no—
126#11758189—81no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61C2×C4⋊C411yescharacteristic
132C23×C61C22⋊Q811yescharacteristic
133C23×C61C22⋊Q811yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—41no—
138C22×D61—41no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C22⋊D61—42no—
153C22⋊D61—42no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61#10812yescomplemented
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—81no—
164C8×C61—42no—
165C8×C61—41no—
166C8×C61—41no—
167C8×C61—81no—
168#92418—42no—
169#92418—41no—
170#92418—42no—
171#92418—41no—
172#8860—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61#38511yescharacteristic
184C22×C61C2×#10811yescharacteristic
185C22×C61#43011yescharacteristic
186C2×D61—42no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61B(4,𝔽2)11yescharacteristic
195C4×C61#45811yescharacteristic
196Dic61—22no—
197Dic61—41no—
198Dic61—41no—
199#2975—611no—
200#1870—611no—
201#1855—611no—
202#1855—611no—
203#1459—611no—
204#1298—611no—
205#1298D6111yescharacteristic, complemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—41no—
209C2×C61—41no—
210C2×C61#185511yescharacteristic
211C2×C61#185811yescharacteristic
212C2×C61#186711yescharacteristic
213D61—81no—
214C22×M16—611no—
215C2×C4×D4—611no—
216#436—1221no—
217#436—1221no—
218#436—1221no—
219#436—1221no—
220#431—1221no—
221C2×#108—1221no—
222C2×#108—1221no—
223#407—611no—
224#407—1221no—
225#407C2×D6111yescharacteristic
226C2×C22⋊C8—611no—
227C2×C22⋊C8—1221no—
228C2×C22⋊C8C2×D6111yescharacteristic
229C2×C22⋊C8C2×D6111yescharacteristic
230#341—1221no—
231#341—1221no—
232#336—1221no—
233#324—612no—
234#323—612no—
235C61#886011yescharacteristic, complemented, Sylow
236C22×D4—611no—
237C23×C4—611no—
238C23×C4C22×D6111yescharacteristic
239C2×M16—611no—
240C2×M16—611no—
241C2×M16—1221no—
242C2×M16—1221no—
243C2×M16—1221no—
244C2×M16—1221no—
245C2×M16—2442no—
246C2×M16D24411yescharacteristic
247C2×M16D24411yescharacteristic
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—1221no—
251C22×C8—1221no—
252C4×D4—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C42—611no—
260#108—2442no—
261#108—2442no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—612no—
270C22⋊C8—1221no—
271C22⋊C8—1221no—
272C22⋊C8—1221no—
273C22⋊C8—1221no—
274C22⋊C8—1221no—
275C22⋊C8—2442no—
276C22⋊C8C4×D6112yes—
277C4×C8—1221no—
278C4×C8—1221no—
279C24—611no—
280C24Q8×D6111yescharacteristic
281C2×D4—1222no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—2441no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4C2×C4×D6111yescharacteristic
295C22×C4C2×D24411yescharacteristic
296C22×C4#1175822211yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4#1175822411yescharacteristic
300M16—41no—
301M16—41no—
302M16—1222no—
303M16—1222no—
304M16—4881no—
305M16—4881no—
306M16—2441no—
307M16—2441no—
308M16—2441no—
309M16—2441no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—1222no—
319C2×C8—1222no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C42—1221no—
333C42—1221no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—2441no—
342C23—2441no—
343C23C4⋊C4×D6111yescharacteristic
344C23#1451975511yescharacteristic
345C23#1451975711yescharacteristic
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—612no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—4881no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4#1451973711yescharacteristic
368C2×C4C4×D24411yescharacteristic
369C2×C4#1451974711yescharacteristic
370C2×C4#1451975911yescharacteristic
371C8—42no—
372C8—41no—
373C8—41no—
374C8—81no—
375C8—2442no—
376C8—2442no—
377C8—2441no—
378C8—2441no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—4881no—
390C22—2442no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22#1683963611yescharacteristic
395C22#108×D6111yescharacteristic
396C22#1683980911yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—1222no—
401C4—2441no—
402C4—2441no—
403C4#1683995011yescharacteristic
404C4#1683995311yescharacteristic
405C2—21no—
406C2—21no—
407C2—41no—
408C2—41no—
409C2—4881no—
410C2#2144602511yescharacteristic
411C2#2144604011yescharacteristic
412C2#2144610111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1298C2
socleC22×C61#385
prime radicalC22×C22⋊D61Q8
cosocleC23×C4×C61C23
hypercenter#1298D61
hypocenterC61#8860
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1298

Complements

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

NH ≅ G/Ntype
3. #21446026C2semidirect
4. #21446023C2semidirect
6. #21443707C2semidirect
7. C61×#1298C2semidirect
160. C2×Dic61#108semidirect
205. #1298D61semidirect
235. C61#8860semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214461142
#214460262
#214460232
#214441352
#214437072
C61×#12982
#886061