Finite Group Databasebeta

← #34031057

Subgroups — #34031057

Order 18688.

1800 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626477C213yesmaximal
2#22626466C216yesmaximal
3#22626465C216yesmaximal
4#22626431C216yesmaximal
5#22626425C216yesmaximal
6#125×#64408C213yesmaximal
7#564×D73C211yesmaximal, characteristic
8#17989538C2213yes—
9#17989538C2213yes—
10#17989538C2216yes—
11#17989538C2216yes—
12#17989538C2216yes—
13#17989538C2216yes—
14#17989536C2216yes—
15#17989536C2216yes—
16#17989536C2216yes—
17#17989536C2216yes—
18#17989536C2216yes—
19#17989536C2216yes—
20#17989536C2216yes—
21#17989536C2216yes—
22#17989536C2216yes—
23#17989536C2216yes—
24#17989533C2212yes—
25#17989532C2212yes—
26#17989531C2213yes—
27C4⋊C4×#64408C2216yes—
28C4⋊C4×#64408C2213yes—
29C4⋊C4×#64408C2216yes—
30C4⋊C4×#64408C2213yes—
31C4⋊C4×#64408C2216yes—
32C4⋊C4×#64408C2216yes—
33C4×C4⋊#64408C2216yes—
34#17989523C2216yes—
35C42×#64408C2211yescharacteristic
36C73⋊#564C413yescomplemented
37C73⋊#564C416yescomplemented
38C73⋊#564C416yescomplemented
39#125×D73C2213yes—
40#125×D73C2216yes—
41#125×D73C2216yes—
42#564×C73C411yescharacteristic, complemented
43C2×C4⋊#64408C2316yes—
44C2×C4⋊#64408C2316yes—
45C2×C4⋊#64408C2313yes—
46C2×C4⋊#64408C2313yes—
47C2×C4⋊#64408C2316yes—
48C2×C4⋊#64408C2316yes—
49C2×C4×#64408C2313yes—
50C2×C4×#64408C2316yes—
51C2×C4×#64408C2313yes—
52C2×C4×#64408C2316yes—
53C2×C4×#64408C2316yes—
54C2×C4×#64408C2316yes—
55(C2×#64408)⋊C4C2316yes—
56(C2×#64408)⋊C4C2316yes—
57(C2×#64408)⋊C4C2316yes—
58(C2×#64408)⋊C4C2316yes—
59(C2×#64408)⋊C4C2316yes—
60(C2×#64408)⋊C4C2316yes—
61(C2×#64408)⋊C4C2316yes—
62(C2×#64408)⋊C4C2316yes—
63(C2×#64408)⋊C4C2316yes—
64(C2×#64408)⋊C4C2316yes—
65#14556583C2×C413yes—
66#14556583C2×C416yes—
67#14556583C2×C416yes—
68#14556582C2×C413yes—
69#14556582C2×C413yes—
70#14556582C2×C416yes—
71#14556582C2×C416yes—
72#14556582C2×C416yes—
73#14556582C2×C416yes—
74#14556581C2×C416yes—
75#14556581C2×C416yes—
76#14556581C2×C416yes—
77#14556581C2×C416yes—
78#14556581C2×C416yes—
79#14556581C2×C416yes—
80#14556581C2×C416yes—
81#14556581C2×C416yes—
82#14556581C2×C416yes—
83#14556581C2×C416yes—
84C4⋊C4×D73C2316yes—
85C4⋊C4×D73C2313yes—
86C4⋊C4×D73C2316yes—
87C4⋊C4×D73C2313yes—
88C4⋊C4×D73C2316yes—
89C4⋊C4×D73C2316yes—
90C42×D73C2311yescharacteristic
91C42×D73C2312yes—
92C42×D73C2312yes—
93#125×C73C2×C413yes—
94#125×C73C2×C416yes—
95#125×C73C2×C416yes—
96C22×#64408C2416yes—
97C22×#64408C2416yes—
98C22×#64408C2411yescharacteristic
99C22×#64408C2413yes—
100C4⋊#64408—212no—
101C4⋊#64408—46no—
102C4⋊#64408—43no—
103C4⋊#64408—46no—
104C4⋊#64408—46no—
105C4⋊#64408—43no—
106C4×#64408—26no—
107C4×#64408—212no—
108C4×#64408—46no—
109C4×#64408—46no—
110C4×#64408—43no—
111C4×#64408—46no—
112C2×C4×D73C2413yes—
113C2×C4×D73C2416yes—
114C2×C4×D73C2416yes—
115C4⋊Dic73C22×C416yes—
116C4⋊Dic73C22×C413yes—
117C4⋊Dic73C22×C416yes—
118C4⋊Dic73C22×C413yes—
119C4⋊Dic73C22×C416yes—
120C4⋊Dic73C22×C416yes—
121#11924007C22×C416yes—
122#11924007C22×C416yes—
123#11924007C22×C416yes—
124#11924007C22×C416yes—
125#11924007C22×C416yes—
126#11924007C22×C416yes—
127#11924007C22×C416yes—
128#11924007C22×C416yes—
129#11924007C22×C416yes—
130#11924007C22×C416yes—
131C4×Dic73C22×C413yes—
132C4×Dic73C22×C416yes—
133C4×Dic73C22×C416yes—
134C4⋊C4×C73C22×C413yes—
135C4⋊C4×C73C22×C416yes—
136C4⋊C4×C73C22×C416yes—
137C4⋊C4×C73C22×C413yes—
138C4⋊C4×C73C22×C416yes—
139C4⋊C4×C73C22×C416yes—
140C42×C73C22×C411yescharacteristic
141C42×C73C22×C412yes—
142C42×C73C22×C412yes—
143C22×D73C2511yescharacteristic
144C2×#64408—23no—
145C2×#64408—23no—
146C2×#64408—26no—
147C2×#64408—26no—
148C2×#64408—26no—
149C2×#64408—26no—
150C2×#64408—26no—
151C2×#64408—23no—
152C2×#64408—26no—
153C2×#644082−1+416yes—
154C2×C4×C73C23×C413yes—
155C2×C4×C73C23×C416yes—
156C2×C4×C73C23×C416yes—
157C2×Dic73C23×C413yes—
158C2×Dic73C23×C416yes—
159C2×Dic73C23×C416yes—
160C4×D73—23no—
161C4×D73—26no—
162C4×D73—26no—
163C4×D73—26no—
164C4×D73—23no—
165C4×D73—26no—
166C22×C73C24×C411yescharacteristic
167C2×D73C2×2−1+413yes—
168C2×D73#58513yes—
169#64408—26no—
170#64408—46no—
171#64408—46no—
172#64408—41no—
173C4×C73—23no—
174C4×C73—26no—
175C4×C73—26no—
176Dic73—23no—
177Dic73—26no—
178Dic73—26no—
179#34530—731nomaximal, Sylow
180C2×C73C4×2−1+413yes—
181D73#356313yes—
182D73#356711yescharacteristic
183C2×#564—731no—
184#2382—733no—
185#2371—736no—
186#2370—736no—
187#2336—736no—
188#2330—736no—
189C4×#125—733no—
190C73#3453011yescharacteristic, complemented, Sylow
191#564—736no—
192#564—736no—
193#564—733no—
194#564#6440811yescharacteristic, complemented
195C2×#125—733no—
196C2×#125—736no—
197C2×#125—736no—
198#389—733no—
199#389—733no—
200#389—736no—
201#389—736no—
202#389—736no—
203#389—736no—
204#387—736no—
205#387—736no—
206#387—736no—
207#387—736no—
208#387—736no—
209#387—736no—
210#387—736no—
211#387—736no—
212#387—736no—
213#387—736no—
214#384—732no—
215#383—732no—
216#382—733no—
217C4×C4⋊C4—736no—
218C4×C4⋊C4—733no—
219C4×C4⋊C4—736no—
220C4×C4⋊C4—733no—
221C4×C4⋊C4—736no—
222C4×C4⋊C4—736no—
223C4×C4⋊C4—736no—
224#376—736no—
225C43—731no—
226#125—736no—
227#125—736no—
228#125—736no—
229#125—736no—
230#125—736no—
231#125—736no—
232#125—736no—
233#125—736no—
234#125—736no—
235#125—736no—
236#125—733no—
237#125—733no—
238#125—736no—
239#125—736no—
240#125—736no—
241#125—736no—
242#125—733no—
243#125—736no—
244#125—736no—
245#125C2×#6440813yes—
246#125C2×#6440816yes—
247#125C2×#6440816yes—
248C2×C4⋊C4—733no—
249C2×C4⋊C4—733no—
250C2×C4⋊C4—736no—
251C2×C4⋊C4—736no—
252C2×C4⋊C4—736no—
253C2×C4⋊C4—733no—
254C2×C4⋊C4—736no—
255C2×C4⋊C4—736no—
256C2×C4⋊C4—733no—
257C2×C4⋊C4—736no—
258C2×C4⋊C4—736no—
259C2×C4⋊C4—736no—
260C2×C42—733no—
261C2×C42—736no—
262C2×C42—736no—
263C2×C42—736no—
264C2×C42—731no—
265C2×C42—732no—
266C2×C42—732no—
267C2×C42—733no—
268C2×C42—736no—
269#95—736no—
270#95—736no—
271#95—736no—
272#95—736no—
273#95—736no—
274#95—736no—
275#95—736no—
276#95—736no—
277#95—736no—
278#95—736no—
279C22×C4—733no—
280C22×C4—736no—
281C22×C4—736no—
282C22×C4—733no—
283C22×C4—736no—
284C22×C4—736no—
285C22×C4—731no—
286C4⋊C4—2926no—
287C4⋊C4—2923no—
288C4⋊C4—2926no—
289C4⋊C4—2926no—
290C4⋊C4—2923no—
291C4⋊C4—736no—
292C4⋊C4—736no—
293C4⋊C4—736no—
294C4⋊C4—736no—
295C4⋊C4—736no—
296C4⋊C4—736no—
297C4⋊C4—736no—
298C4⋊C4—736no—
299C4⋊C4—736no—
300C4⋊C4—736no—
301C4⋊C4—733no—
302C4⋊C4—736no—
303C4⋊C4—736no—
304C4⋊C4—733no—
305C4⋊C4—736no—
306C4⋊C4—736no—
307C4⋊C4—14612no—
308C4⋊C4C22×#6440813yes—
309C4⋊C4C22×#6440816yes—
310C4⋊C4C22×#6440816yes—
311C4⋊C4C22×#6440813yes—
312C4⋊C4C22×#6440816yes—
313C4⋊C4C22×#6440816yes—
314C42—2926no—
315C42—2926no—
316C42—2926no—
317C42—2923no—
318C42—733no—
319C42—736no—
320C42—736no—
321C42—14612no—
322C42—1466no—
323C42C22×#6440811yescharacteristic
324C42C22×#6440812yes—
325C42C22×#6440812yes—
326C23—731no—
327C2×C4—736no—
328C2×C4—736no—
329C2×C4—733no—
330C2×C4—736no—
331C2×C4—1466no—
332C2×C4—1466no—
333C2×C4—1463no—
334C2×C4—1466no—
335C2×C4—1463no—
336C2×C4—1466no—
337C2×C4—1466no—
338C2×C4—1466no—
339C2×C4—1466no—
340C2×C4—1463no—
341C2×C4—1466no—
342C2×C4—1466no—
343C2×C4—1466no—
344C2×C4—1463no—
345C2×C4—1463no—
346C2×C4C23×#6440816yes—
347C2×C4C23×#6440813yes—
348C2×C4C23×#6440816yes—
349C22—733no—
350C22—733no—
351C22C24×#6440811yescharacteristic
352C4—26no—
353C4—26no—
354C4—23no—
355C4—2926no—
356C4—2921no—
357C4—2926no—
358C4—1466no—
359C4—1466no—
360C4—1463no—
361C4—1466no—
362C2—731no—
363C2—733no—
364C22−1+4×#6440813yes—
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#564×C73C4
prime radical, cosocleC22×D73C25
hypercenter#564#64408
hypocenterC73#34530
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
36. C73⋊#564C4semidirect
37. C73⋊#564C4semidirect
38. C73⋊#564C4semidirect
42. #564×C73C4semidirect
190. C73#34530semidirect
194. #564#64408semidirect

Maximal subgroups

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

subgroupindex
#226264772
#226264662
#226264652
#226264312
#226264252
#125×#644082
#564×D732
#3453073