Finite Group Databasebeta

← #29590219

Subgroups — #29590219

Order 15616.

514 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451562C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443825C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519762—21no—
10C2×#14519752C411yescharacteristic
11C2×C4⋊C4×D61C2211yescharacteristic
12C22⋊C8×D61—21no—
13#16839693C411yescharacteristic
14#16839686—21no—
15#16839684—21no—
16#16839680C411yescharacteristic
17#16839679C2211yescharacteristic
18#16839640—21no—
19#16839621C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—41no—
34M16×D61—24no—
35M16×D61—42no—
36C2×C8×D61—41no—
37C2×C8×D61—41no—
38#14519762—42no—
39#14519762—42no—
40#14519752—41no—
41#14519752—41no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C4⋊C4×D61—41no—
48C4⋊C4×D61—41no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C22⋊#92418—21no—
56#14519689—41no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66C23×D61—21no—
67C23×D61C22⋊C411yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244—81no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—81no—
91C2×C4×D61—81no—
92C2×C4×D61D812yes—
93C2×C4×D61SD1612yes—
94M16×C61—22no—
95M16×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102#11758198—42no—
103#11758198—42no—
104#11758198—41no—
105#11758198—41no—
106#11758198—42no—
107#11758198—81no—
108#11758198—81no—
109C4⋊Dic61—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—42no—
113#11758196—81no—
114#11758194—22no—
115#11758194—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118#11758189—44no—
119C8×D61—44no—
120C8×D61—82no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#9911yescharacteristic
132C22×D61#9911yescharacteristic
133C22×D61#10212yes—
134C22×D61#10412yes—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61#10212yes—
159D244—82no—
160D244—82no—
161D244—82no—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—42no—
167C4×D61—81no—
168C4×D61—81no—
169C4×D61—81no—
170C8×C61—42no—
171C8×C61—81no—
172#92418—42no—
173#92418—81no—
174#11698—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61C2×#9911yescharacteristic
178C22×C61C2×#10211yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61#32712yes—
194C2×D61#32712yes—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—81no—
200C4×C61—81no—
201Dic61—22no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205#2618—611no—
206C2×#343—611no—
207C2×#324—611no—
208#1346—611no—
209#1346D6111yescharacteristic, complemented
210#1345—611no—
211#1345—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61C2×#32711yescharacteristic
215C2×C61#212111yescharacteristic
216C2×C61#213311yescharacteristic
217D61—22no—
218D61—22no—
219D61—161no—
220C22×M16—1221no—
221C2×#123—1221no—
222C2×#121—611no—
223C22×C4⋊C4—611no—
224C2×C22⋊C8—1221no—
225#398—611no—
226#398C2×D6111yescharacteristic
227#396—1221no—
228#396—1221no—
229#394—611no—
230#394—611no—
231#386—1221no—
232#380—611no—
233#343—611no—
234#343—1221no—
235#343C2×D6111yescharacteristic
236#324—611no—
237#324—1221no—
238#324C2×D6111yescharacteristic
239C61#1169811yescharacteristic, complemented, Sylow
240C22×D4—611no—
241C22×D4—1221no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—611no—
245C2×M16—21no—
246C2×M16—1224no—
247C2×M16—1221no—
248C2×M16—2441no—
249C2×M16—2442no—
250C22×C8—2441no—
251C22×C8—2441no—
252#123—2442no—
253#123—2442no—
254#121—2441no—
255#121—2441no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—2441no—
263C2×C4⋊C4—2441no—
264C2×C4⋊C4C4×D6111yescharacteristic
265C2×C4⋊C4C22×D6111yescharacteristic
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C22⋊C8—21no—
273C22⋊C8—1221no—
274C22⋊C8—2441no—
275#95—21no—
276#95—611no—
277#95—1221no—
278#95C4×D6111yescharacteristic
279C24—611no—
280C24—1221no—
281C2×D4—4881no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2442no—
286C2×D4—2442no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1222no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—4881no—
303C22×C4—4881no—
304C22×C4C2×C4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307M16—22no—
308M16—41no—
309M16—1222no—
310M16—2444no—
311M16—2441no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—4882no—
315C2×C8—2444no—
316C2×C8—2441no—
317C2×C8—2441no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—4881no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2442no—
327C22⋊C4—4881no—
328C22⋊C4—4881no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C22⋊C4—2442no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C23—611no—
335C23—611no—
336C23—612no—
337C23—612no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23C22⋊C4×D6111yescharacteristic
348D4—4882no—
349D4—4882no—
350D4—4882no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—612no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4D8×D6111yescharacteristic
382C2×C4SD16×D6111yescharacteristic
383C8—42no—
384C8—81no—
385C8—4881no—
386C8—2442no—
387C22—21no—
388C22—21no—
389C22—612no—
390C22—612no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1221no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—2442no—
403C22—2442no—
404C22#99×D6111yescharacteristic
405C22#102×D6111yescharacteristic
406C22#104×D6111yescharacteristic
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—81no—
413C4—1222no—
414C4—4881no—
415C4—2441no—
416C4—2441no—
417C2—21no—
418C2—21no—
419C2—1222no—
420C2—1222no—
421C2—9761no—
422C2#327×D6111yescharacteristic
423C2#2144746411yescharacteristic
424C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11698
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
2. #343×D61C2semidirect
3. #324×D61C2semidirect
4. #21443825C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1346C2semidirect
209. #1346D61semidirect
239. C61#11698semidirect

Maximal subgroups

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

subgroupindex
#214515622
#343×D612
#324×D612
#214438252
#214438232
#214438212
C61×#13462
#1169861