Finite Group Databasebeta

← #33017185

Subgroups — #33017185

Order 18688.

1278 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×Dic73C211yesmaximal, characteristic
2#22608158C211yesmaximal, characteristic
3#22608157C212yesmaximal
4#22608157C212yesmaximal
5#22608156C212yesmaximal
6#22608156C212yesmaximal
7#22608155C212yesmaximal
8#22608155C212yesmaximal
9C73×#1434C211yesmaximal, characteristic
10C22×C4×Dic73C2211yescharacteristic
11C22×C4×Dic73C2211yescharacteristic
12C22×C4×Dic73C2211yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14C22×C4×Dic73C2211yescharacteristic
15C22×C4×Dic73C2211yescharacteristic
16C2×#14556498C2214yes—
17C2×#14556498C2214yes—
18C2×#14556498C2214yes—
19C2×#14556498C2212yes—
20C2×#14556498C2212yes—
21C2×#14556498C2214yes—
22C2×#14556498C2212yes—
23C42×Dic73C418yescomplemented
24C22×C42×C73C2211yescharacteristic
25C2×#95×C73C2212yes—
26C2×#95×C73C2212yes—
27C2×#95×C73C2212yes—
28C23×Dic73C2314yes—
29C23×Dic73C2311yescharacteristic
30C23×Dic73C2311yescharacteristic
31C23×Dic73C2311yescharacteristic
32C23×Dic73C2311yescharacteristic
33C2×C4×Dic73—24no—
34C2×C4×Dic73—24no—
35C2×C4×Dic73—24no—
36C2×C4×Dic73—24no—
37C2×C4×Dic73—22no—
38C2×C4×Dic73—24no—
39C2×C4×Dic73—22no—
40C2×C4×Dic73C2×C414yes—
41C2×C4×Dic73C2×C414yes—
42C2×C4×Dic73C2×C414yes—
43C2×C4×Dic73C2×C414yes—
44C2×C4×Dic73C2×C414yes—
45C2×C4×Dic73C2×C414yes—
46#14556498—28no—
47#14556498—28no—
48#14556498—28no—
49#14556498—28no—
50#14556498—24no—
51#14556498—24no—
52#14556498—24no—
53C23×C4×C73C2314yes—
54C23×C4×C73C2311yescharacteristic
55C23×C4×C73C2311yescharacteristic
56C23×C4×C73C2311yescharacteristic
57C2×C42×C73—24no—
58C2×C42×C73C2×C414yes—
59#95×C73—24no—
60#95×C73—24no—
61#95×C73—24no—
62C22×Dic73—22no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—22no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73—24no—
73C22×Dic73—24no—
74C22×Dic73—24no—
75C22×Dic73—24no—
76C22×Dic73—24no—
77C22×Dic73—24no—
78C22×Dic73—24no—
79C22×Dic73C22×C412yes—
80C22×Dic73C22×C412yes—
81C22×Dic73C22×C412yes—
82C22×Dic73C22×C412yes—
83C22×Dic73#4114yes—
84C22×Dic73#4114yes—
85C22×Dic73#4114yes—
86C22×Dic73#4114yes—
87C4×Dic73—28no—
88C4×Dic73—28no—
89C4×Dic73—28no—
90C4×Dic73—28no—
91C4×Dic73—28no—
92C4×Dic73—28no—
93C24×C73C2411yescharacteristic
94C22×C4×C73—22no—
95C22×C4×C73—22no—
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73—22no—
99C22×C4×C73—22no—
100C22×C4×C73—24no—
101C22×C4×C73—24no—
102C22×C4×C73—24no—
103C22×C4×C73—24no—
104C22×C4×C73—24no—
105C22×C4×C73—24no—
106C22×C4×C73—24no—
107C22×C4×C73C22×C412yes—
108C22×C4×C73C22×C412yes—
109C22×C4×C73C22×C412yes—
110C22×C4×C73#4112yes—
111C22×C4×C73#4114yes—
112C22×C4×C73#4114yes—
113C22×C4×C73#4112yes—
114C42×C73—28no—
115C23×C73C23×C411yescharacteristic
116C23×C73C2×#4112yes—
117C23×C73C2×#4112yes—
118C23×C73C2×#4112yes—
119C23×C73C2×#4112yes—
120C23×C73C2×#4112yes—
121C23×C73C2×#4111yescharacteristic
122C23×C73C2×#4112yes—
123C23×C73C2×#4111yescharacteristic
124C2×C4×C73—22no—
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73—22no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—24no—
131C2×C4×C73—28no—
132C2×C4×C73—28no—
133C2×C4×C73—24no—
134C2×C4×C73—44no—
135C2×C4×C73—44no—
136C2×C4×C73—44no—
137C2×C4×C73—44no—
138C2×C4×C73—44no—
139C2×C4×C73—44no—
140C2×C4×C73—44no—
141C2×C4×C73#11714yes—
142C2×C4×C73#11714yes—
143C2×C4×C73#11714yes—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—28no—
153C2×Dic73—24no—
154C2×Dic73—24no—
155C2×Dic73—28no—
156C2×Dic73—24no—
157C2×Dic73—24no—
158C2×Dic73—44no—
159C2×Dic73—44no—
160C2×Dic73—44no—
161C2×Dic73—44no—
162C2×Dic73—44no—
163C2×Dic73—44no—
164C2×Dic73—44no—
165C2×Dic73#11714yes—
166C2×Dic73#11714yes—
167C2×Dic73#11714yes—
168C2×Dic73#11714yes—
169C22×C73C2×#11711yescharacteristic
170C22×C73C2×#11711yescharacteristic
171C22×C73C2×#11711yescharacteristic
172C22×C73C2×#11711yescharacteristic
173C22×C73C2×#11711yescharacteristic
174C22×C73C2×#11711yescharacteristic
175C22×C73C2×#11711yescharacteristic
176C22×C73#52914yes—
177C22×C73#52912yes—
178C22×C73#52912yes—
179C22×C73#52912yes—
180C22×C73#52914yes—
181C22×C73#52914yes—
182C22×C73#52912yes—
183C22×C73#52914yes—
184C22×C73#52912yes—
185C22×C73#52912yes—
186C4×C73—24no—
187C4×C73—24no—
188C4×C73—24no—
189C4×C73—84no—
190Dic73—24no—
191Dic73—24no—
192Dic73—24no—
193Dic73—24no—
194Dic73—84no—
195#14690—731nomaximal, Sylow
196C2×C73#228311yescharacteristic
197C2×C73#228311yescharacteristic
198C2×C73#228311yescharacteristic
199C2×C73#228311yescharacteristic
200C2×C73#228311yescharacteristic
201C2×C73#228311yescharacteristic
202C2×C73#228311yescharacteristic
203C2×C73#286514yes—
204C2×C73#286514yes—
205C2×C43—731no—
206#1434—731no—
207#1434—732no—
208#1434—732no—
209#1434—732no—
210#1434—732no—
211#1434—732no—
212#1434—732no—
213#1434D7311yescharacteristic
214C73#1469011yescharacteristic, complemented, Sylow
215C22×C42—731no—
216C22×C42—731no—
217C22×C42—731no—
218C22×C42—731no—
219C22×C42—731no—
220C22×C42—731no—
221C22×C42C2×D7311yescharacteristic
222C2×#95—734no—
223C2×#95—734no—
224C2×#95—734no—
225C2×#95—734no—
226C2×#95—732no—
227C2×#95—732no—
228C2×#95—732no—
229C2×#95C2×D7312yes—
230C2×#95C2×D7312yes—
231C2×#95C2×D7312yes—
232C43—738no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—731no—
236C23×C4—731no—
237C23×C4—734no—
238C23×C4C22×D7314yes—
239C23×C4C22×D7311yescharacteristic
240C23×C4C22×D7311yescharacteristic
241C23×C4C22×D7311yescharacteristic
242C2×C42—24no—
243C2×C42—734no—
244C2×C42—734no—
245C2×C42—734no—
246C2×C42—734no—
247C2×C42—734no—
248C2×C42—734no—
249C2×C42—1464no—
250C2×C42—1464no—
251C2×C42—1464no—
252C2×C42—1464no—
253C2×C42—1462no—
254C2×C42—1464no—
255C2×C42—1462no—
256C2×C42C4×D7314yes—
257#95—24no—
258#95—24no—
259#95—24no—
260#95—1468no—
261#95—1468no—
262#95—1468no—
263#95—1468no—
264#95—1464no—
265#95—1464no—
266#95—1464no—
267C24C23×D7311yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—732no—
284C22×C4—732no—
285C22×C4—734no—
286C22×C4—734no—
287C22×C4—734no—
288C22×C4—734no—
289C22×C4—1464no—
290C22×C4—1464no—
291C22×C4—1464no—
292C22×C4—1464no—
293C22×C4—1464no—
294C22×C4—1464no—
295C22×C4—1464no—
296C22×C4—1462no—
297C22×C4—1462no—
298C22×C4—1462no—
299C22×C4—1462no—
300C22×C4—1461no—
301C22×C4—1461no—
302C22×C4—1462no—
303C22×C4—1462no—
304C22×C4—1461no—
305C22×C4—1461no—
306C22×C4C2×C4×D7312yes—
307C22×C4C2×C4×D7312yes—
308C22×C4C2×C4×D7312yes—
309C22×C4#1192402714yes—
310C22×C4#1192402712yes—
311C22×C4#1192402814yes—
312C22×C4#1192402912yes—
313C42—28no—
314C42—1468no—
315C42—1468no—
316C42—1468no—
317C42—1468no—
318C42—1468no—
319C42—1468no—
320C23C22×C4×D7311yescharacteristic
321C23#41×D7312yes—
322C23#41×D7312yes—
323C23#41×D7312yes—
324C23#41×D7312yes—
325C23C2×#1192402712yes—
326C23C2×#1192402711yescharacteristic
327C23C2×#1192402812yes—
328C23C2×#1192402911yescharacteristic
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—28no—
337C2×C4—28no—
338C2×C4—24no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—2924no—
347C2×C4—2924no—
348C2×C4—2924no—
349C2×C4—2924no—
350C2×C4—2924no—
351C2×C4—2924no—
352C2×C4—2924no—
353C2×C4—734no—
354C2×C4—734no—
355C2×C4—734no—
356C2×C4—734no—
357C2×C4—1468no—
358C2×C4—1464no—
359C2×C4—1464no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4—1462no—
363C2×C4—1462no—
364C2×C4—1462no—
365C2×C4—1462no—
366C2×C4—1462no—
367C2×C4—1462no—
368C2×C4—1468no—
369C2×C4—1464no—
370C2×C4—1464no—
371C2×C4#1455654714yes—
372C2×C4#1455654814yes—
373C2×C4#1455654914yes—
374C22#117×D7311yescharacteristic
375C22#117×D7311yescharacteristic
376C22#117×D7311yescharacteristic
377C22#117×D7311yescharacteristic
378C22C2×#1455654711yescharacteristic
379C22C2×#1455654811yescharacteristic
380C22C2×#1455654911yescharacteristic
381C22#1798911414yes—
382C22#1798911514yes—
383C22#1798911612yes—
384C22#1798911714yes—
385C22#1798911812yes—
386C22#1798911912yes—
387C22#1798912014yes—
388C22#1798912212yes—
389C22#1798912312yes—
390C22#1798912412yes—
391C4—24no—
392C4—24no—
393C4—24no—
394C4—84no—
395C4—5844no—
396C4—1464no—
397C4—1464no—
398C4—1464no—
399C4—1464no—
400C2#2261232211yescharacteristic
401C2#2261232311yescharacteristic
402C2#2261232411yescharacteristic
403C2#2261232511yescharacteristic
404C2#2261232611yescharacteristic
405C2#2261232711yescharacteristic
406C2#2261232811yescharacteristic
407C2#2261831914yes—
408C2#2261832114yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1434C2
socle, prime radical, cosocleC24×C73C24
hypercenter#1434D73
hypocenterC73#14690
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
23. C42×Dic73C4semidirect
214. C73#14690semidirect

Maximal subgroups

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

subgroupindex
C2×C42×Dic732
#226081582
#226081572
#226081562
#226081552
C73×#14342
#1469073