Finite Group Databasebeta

← #29578115

Subgroups — #29578115

Order 15616.

412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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#21455992C211yesmaximal, characteristic
2#21454799C211yesmaximal, characteristic
3#21444451C211yesmaximal, characteristic
4#21444265C211yesmaximal, characteristic, complemented
5#21444162C211yesmaximal, characteristic, complemented
6#21443692C211yesmaximal, characteristic, complemented
7C61×#1308C211yesmaximal, characteristic, complemented
8#16840296C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840098C411yescharacteristic
11#16840081C411yescharacteristic
12#16840070—21no—
13#16839985—21no—
14#16839920C411yescharacteristic
15#16839903C411yescharacteristic
16#16839891—21no—
17#16839870—21no—
18#16839864—21no—
19#16839837—21no—
20#16839836—21no—
21#16839832—21no—
22#16839824—21no—
23#16839819C2211yescharacteristic
24#16839719—21no—
25C4×#11758194C2211yescharacteristic
26#16839503—21no—
27#16839501—21no—
28#16839492—21no—
29#16839492—21no—
30#16839487—21no—
31#16839487—21no—
32C61×#432C2211yescharacteristic
33C61×#432C2211yescharacteristic
34C61×#432C2211yescharacteristic
35C22×Dic122C2×C411yescharacteristic
36C2×Dic244—21no—
37C2×#11758190—21no—
38C2×#11758194—21no—
39C2×#11758189—21no—
40C2×C8×D61—21no—
41#14519771—21no—
42#14519769D411yescharacteristic
43#14519765D411yescharacteristic
44#14519760—21no—
45#14519756C2×C411yescharacteristic
46#14519751C2×C411yescharacteristic
47C4×Dic122—21no—
48C4×Dic122—21no—
49C4×Dic122—21no—
50C4×Dic122—21no—
51C4×Dic122D411yescharacteristic
52C4×D244D411yescharacteristic
53C4×C22⋊D61—21no—
54#14519734—21no—
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×#11758196—21no—
57C2×C4×Dic61—21no—
58#14519711—21no—
59#14519709—21no—
60C4⋊#92418—21no—
61#14519706—21no—
62#14519706—21no—
63#14519702—21no—
64#14519702—21no—
65#14519702—21no—
66#14519699—21no—
67C22⋊#92418—21no—
68#14519689—21no—
69#14519689—21no—
70#14519688—21no—
71#14519688—21no—
72#14519687—21no—
73C4×#92418D411yescharacteristic
74C4×#92418D411yescharacteristic
75C8×Dic61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61C2×C411yescharacteristic
82C22⋊C8×C61C2×C411yescharacteristic
83C22⋊C8×C61D411yescharacteristic
84C22⋊C8×C61D411yescharacteristic
85#97×C61—21no—
86#97×C61—21no—
87#97×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C2×D244C22⋊C411yescharacteristic
95C2×C4×D61—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—42no—
99C2×Dic122C22⋊C411yescharacteristic
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—41no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C22⋊Dic61—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61C22⋊C411yescharacteristic
117C4⋊Dic61C22⋊C411yescharacteristic
118#11758196—21no—
119#11758196—21no—
120#11758196—21no—
121#11758196—21no—
122#11758196—41no—
123#11758196—41no—
124C4×Dic61—21no—
125C4×Dic61—41no—
126C4×Dic61—41no—
127#11758194—42no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—41no—
131Dic244—42no—
132#11758190—42no—
133#11758189—42no—
134C8×D61—42no—
135C23×C61C4×D411yescharacteristic
136C22×D61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C22⋊D61—81no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—81no—
155D244—41no—
156C4×D61—41no—
157C4×D61—41no—
158Dic122—22no—
159Dic122—22no—
160Dic122—41no—
161Dic122—41no—
162Dic122—41no—
163C8×C61—41no—
164C8×C61—41no—
165C8×C61—41no—
166C8×C61—41no—
167C8×C61—81no—
168#92418—22no—
169#92418—41no—
170#92418—81no—
171#9531—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61#38611yescharacteristic
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185Dic61—42no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—81no—
190#3117—611no—
191#2967—611no—
192#1535—611no—
193#1491—611no—
194#1467—611no—
195#1308D6111yescharacteristic, complemented
196#1291—611no—
197C2×C61—41no—
198C2×C61#189111yescharacteristic
199C2×C61#190211yescharacteristic
200C2×C61#190611yescharacteristic
201D61—81no—
202#529—611no—
203C2×C4×Q8—611no—
204#484—611no—
205#481—611no—
206#479—1221no—
207#464—1221no—
208#451—611no—
209#448—611no—
210#446—1221no—
211#441—1221no—
212#440—1221no—
213#436—1221no—
214#435—1221no—
215#435—1221no—
216#433—1221no—
217#432—611no—
218#432C2×D6111yescharacteristic
219#432C2×D6111yescharacteristic
220#432C2×D6111yescharacteristic
221#405—1221no—
222C4×M16—611no—
223#330—1221no—
224#329—1221no—
225Q8⋊C8—1221no—
226Q8⋊C8—1221no—
227#324—1221no—
228#324—1221no—
229C61#953111yescharacteristic, complemented, Sylow
230C22×Q8—611no—
231C2×Q16—1221no—
232C2×SD16—1221no—
233C2×M16—1221no—
234C2×M16—1221no—
235C22×C8—1221no—
236#126—1221no—
237#125—611no—
238#124—611no—
239#123—1221no—
240C22⋊Q8—611no—
241#121—611no—
242C4×Q8—611no—
243C4×Q8—1221no—
244C4×Q8—1221no—
245C4×Q8—1221no—
246C4×Q8—1221no—
247C4×D4—611no—
248C4×D4—1221no—
249#117—1221no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C42—1221no—
253C2×C42C22×D6111yescharacteristic
254#107—1221no—
255#106—1221no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262#103—1221no—
263#103—1221no—
264#103—1221no—
265#102—1221no—
266C22⋊C8—21no—
267C22⋊C8—1221no—
268C22⋊C8—1221no—
269C22⋊C8—1221no—
270C22⋊C8C4×D6111yescharacteristic
271C22⋊C8C4×D6111yescharacteristic
272C22⋊C8D24411yescharacteristic
273C22⋊C8D24411yescharacteristic
274#97—21no—
275#97—21no—
276#97—21no—
277#97—1221no—
278#97—1221no—
279#97—1221no—
280C4×C8—611no—
281C4×C8—611no—
282C4×C8—1221no—
283C2×Q8—611no—
284C2×Q8—1221no—
285C2×Q8—1221no—
286C2×Q8—2442no—
287C2×D4—611no—
288C2×D4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4C2×D24411yescharacteristic
294C22×C4#1175822211yescharacteristic
295Q16—2442no—
296SD16—2442no—
297M16—2442no—
298M16—2442no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—2442no—
307C2×C8—2441no—
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C42—1221no—
324C42—2441no—
325C42—2441no—
326C42D4×D6111yescharacteristic
327C42D4×D6111yescharacteristic
328C42D4×D6111yescharacteristic
329C42#1175822611yescharacteristic
330C23—1221no—
331C23C4×D24411yescharacteristic
332Q8—1222no—
333Q8—1222no—
334Q8—2441no—
335Q8—2441no—
336Q8—2441no—
337D4—4881no—
338D4—2441no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—1222no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—4881no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4C22⋊C4×D6111yescharacteristic
353C2×C4#1451973911yescharacteristic
354C2×C4#1451974711yescharacteristic
355C2×C4#1451975011yescharacteristic
356C2×C4#1451975211yescharacteristic
357C2×C4#1451976211yescharacteristic
358C8—41no—
359C8—41no—
360C8—41no—
361C8—41no—
362C8—81no—
363C8—1222no—
364C8—4881no—
365C8—2441no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22#1683964011yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—4881no—
380C4—2442no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C2—41no—
385C2—4881no—
386C2#2144623611yescharacteristic
387C2#2144629111yescharacteristic
388C2#2144632111yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1308C2
socleC22×C61#386
prime radical#14519751C2×C4
cosocleC2×C42×C61C23
hypercenter#1308D61
hypocenterC61#9531
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
4. #21444265C2semidirect
5. #21444162C2semidirect
6. #21443692C2semidirect
7. C61×#1308C2semidirect
195. #1308D61semidirect
229. C61#9531semidirect

Maximal subgroups

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

subgroupindex
#214559922
#214547992
#214444512
#214442652
#214441622
#214436922
C61×#13082
#953161