Finite Group Databasebeta

← #33248704

Subgroups — #33248704

Order 18688.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C73⋊#564C211yesmaximal, characteristic
2#22613116C212yesmaximal
3#22613115C214yesmaximal
4#22613114C214yesmaximal
5#22613113C214yesmaximal
6#125×Dic73C211yesmaximal, characteristic
7#22612490C214yesmaximal
8#22612488C214yesmaximal
9#22612488C214yesmaximal
10#22612486C212yesmaximal
11C73×#2382C211yesmaximal, characteristic
12C73⋊#564C4116yescomplemented
13C2×#14556583C2212yes—
14C2×#14556582C2214yes—
15C2×#14556581C2214yes—
16C2×#14556581C2214yes—
17#17988486C2212yes—
18#17988485C2214yes—
19#17988484C2214yes—
20#17988484C2214yes—
21#17988483C2212yes—
22#17988483C2212yes—
23#17988482C2214yes—
24#17988482C2214yes—
25#17988474C2214yes—
26#17988474C2214yes—
27#17988473C2214yes—
28#17988472C2214yes—
29#17988472C2214yes—
30#17988471C2214yes—
31#17988471C2214yes—
32#17988470C2214yes—
33#17988470C2214yes—
34#17988469C2214yes—
35#17988469C2214yes—
36#17988468C2214yes—
37#17988468C2214yes—
38#17988453C2211yescharacteristic
39#17988452C2214yes—
40#17988451C2214yes—
41#17988451C2214yes—
42C4⋊C4×Dic73C2212yes—
43C4⋊C4×Dic73C2212yes—
44C4⋊C4×Dic73C2212yes—
45C4⋊C4×Dic73C2214yes—
46C4⋊C4×Dic73C2214yes—
47#17988438C2214yes—
48#17988438C2214yes—
49#17988438C2214yes—
50#17988438C2214yes—
51C42×Dic73C2211yescharacteristic
52C42×Dic73C2214yes—
53C2×#125×C73C2211yescharacteristic
54#389×C73C2214yes—
55#387×C73C2214yes—
56#387×C73C2214yes—
57#382×C73C2212yes—
58#14556583C2×C4116yes—
59#14556582C2×C4132yes—
60#14556581C2×C4132yes—
61#14556581C2×C4132yes—
62C2×C4⋊Dic73C2314yes—
63C2×C4⋊Dic73C2312yes—
64C2×C4⋊Dic73C2312yes—
65C2×C4⋊Dic73C2314yes—
66C2×C4⋊Dic73C2312yes—
67C2×#11924007C2314yes—
68C2×#11924007C2314yes—
69C2×#11924007C2314yes—
70C2×#11924007C2314yes—
71C2×#11924007C2314yes—
72C2×#11924007C2314yes—
73C2×#11924007C2314yes—
74C2×#11924007C2314yes—
75C2×C4×Dic73C2314yes—
76C2×C4×Dic73C2311yescharacteristic
77C2×C4×Dic73C2314yes—
78C2×C4×Dic73C2312yes—
79C2×C4×Dic73C2314yes—
80C2×C4×Dic73C2314yes—
81C2×C4×Dic73C2311yescharacteristic
82C2×C4×Dic73C2312yes—
83C2×C4×Dic73C2314yes—
84C2×C4×Dic73C2314yes—
85#14556498C2314yes—
86#14556498C2314yes—
87#14556498C2314yes—
88#14556498C2314yes—
89#14556498C2314yes—
90#14556498C2314yes—
91#14556498C2314yes—
92#14556498C2314yes—
93#14556498C2314yes—
94#14556498C2314yes—
95#14556498C2314yes—
96#125×C73C2×C418yes—
97C2×C4⋊C4×C73C2312yes—
98C2×C4⋊C4×C73C2312yes—
99C2×C4⋊C4×C73C2314yes—
100C2×C4⋊C4×C73C2312yes—
101C2×C4⋊C4×C73C2314yes—
102C2×C42×C73C2314yes—
103C2×C42×C73C2311yescharacteristic
104#95×C73C2314yes—
105#95×C73C2314yes—
106#95×C73C2314yes—
107#95×C73C2314yes—
108C22×Dic73C2411yescharacteristic
109C22×Dic73C2412yes—
110C22×Dic73C2414yes—
111C22×Dic73C2414yes—
112C22×Dic73C2414yes—
113C22×Dic73C2411yescharacteristic
114C4⋊Dic73—42no—
115C4⋊Dic73—44no—
116C4⋊Dic73C22×C418yes—
117C4⋊Dic73C22×C4116yes—
118C4⋊Dic73C22×C418yes—
119#11924007—44no—
120#11924007—44no—
121#11924007—44no—
122#11924007—44no—
123#11924007C22×C4116yes—
124#11924007C22×C4116yes—
125#11924007C22×C4116yes—
126#11924007C22×C4116yes—
127C4×Dic73—28no—
128C4×Dic73—28no—
129C4×Dic73—22no—
130C4×Dic73—24no—
131C4×Dic73—28no—
132C4×Dic73—44no—
133C4×Dic73—44no—
134C4×Dic73—41no—
135C4×Dic73—42no—
136C4×Dic73C22×C4116yes—
137C22×C4×C73C2414yes—
138C22×C4×C73C2414yes—
139C22×C4×C73C2411yescharacteristic
140C22×C4×C73C2414yes—
141C22×C4×C73C2412yes—
142C4⋊C4×C73—44no—
143C4⋊C4×C73—42no—
144C4⋊C4×C73—42no—
145C4⋊C4×C73C22×C418yes—
146C4⋊C4×C73C22×C4116yes—
147C42×C73—44no—
148C42×C73C22×C414yes—
149C23×C73C2511yescharacteristic
150C2×C4×C73—21no—
151C2×C4×C73—24no—
152C2×C4×C73—22no—
153C2×C4×C73—24no—
154C2×C4×C73—22no—
155C2×C4×C73—21no—
156C2×C4×C73—24no—
157C2×C4×C73—24no—
158C2×C4×C73—24no—
159C2×C4×C73—24no—
160C2×C4×C73—24no—
161C2×C4×C73—24no—
162C2×C4×C73C23×C412yes—
163C2×C4×C73C23×C414yes—
164C2×C4×C73C23×C418yes—
165C2×Dic73—24no—
166C2×Dic73—24no—
167C2×Dic73—24no—
168C2×Dic73—24no—
169C2×Dic73—21no—
170C2×Dic73—22no—
171C2×Dic73—24no—
172C2×Dic73—22no—
173C2×Dic73—22no—
174C2×Dic73—24no—
175C2×Dic73—24no—
176C2×Dic73—22no—
177C2×Dic73C23×C418yes—
178C2×Dic73C23×C418yes—
179C2×Dic732−1+412yes—
180C2×Dic732−1+414yes—
181C22×C73C24×C411yescharacteristic
182C22×C73C2×2−1+411yescharacteristic
183C22×C73C2×2−1+412yes—
184C22×C73#58512yes—
185C22×C73#58511yescharacteristic
186C4×C73—22no—
187C4×C73—28no—
188C4×C73—24no—
189C4×C73—44no—
190C4×C73—44no—
191Dic73—28no—
192Dic73—28no—
193Dic73—41no—
194Dic73—42no—
195Dic73—44no—
196Dic73#56414yescomplemented
197C4×#564—731nomaximal, Sylow
198C2×C73C4×2−1+411yescharacteristic
199C2×C73C4×2−1+412yes—
200C2×C73C2×#56411yescharacteristic
201C2×C73#353111yescharacteristic
202C2×C73#353112yes—
203C2×#564—731no—
204#2382—734no—
205#2382—734no—
206#2382—734no—
207#2382—732no—
208#2382D7311yescharacteristic
209C4×#125—734no—
210C4×#125—734no—
211C4×#125—734no—
212C4×#125—732no—
213C4×#125—731no—
214C73C4×#56411yescharacteristic, complemented, Sylow
215#564—7316no—
216C2×#125—734no—
217C2×#125—734no—
218C2×#125—734no—
219C2×#125—732no—
220C2×#125C2×D7311yescharacteristic
221#389—734no—
222#389—734no—
223#389—732no—
224#389—732no—
225#389—732no—
226#389—734no—
227#389—734no—
228#389—734no—
229#389C2×D7314yes—
230#387—734no—
231#387—734no—
232#387—734no—
233#387—734no—
234#387—734no—
235#387—734no—
236#387—734no—
237#387—734no—
238#387—734no—
239#387—734no—
240#387—734no—
241#387—734no—
242#387—734no—
243#387C2×D7314yes—
244#387C2×D7314yes—
245#382—734no—
246#382—731no—
247#382—734no—
248#382—734no—
249#382C2×D7312yes—
250C4×C4⋊C4—734no—
251C4×C4⋊C4—732no—
252C4×C4⋊C4—734no—
253C4×C4⋊C4—732no—
254C4×C4⋊C4—732no—
255C4×C4⋊C4—734no—
256C4×C4⋊C4—734no—
257C4×C4⋊C4—734no—
258C4×C4⋊C4—734no—
259C43—731no—
260C43—734no—
261#125—7332no—
262#125—7332no—
263#125—7332no—
264#125—7316no—
265#125C4×D7318yes—
266C2×C4⋊C4—734no—
267C2×C4⋊C4—734no—
268C2×C4⋊C4—734no—
269C2×C4⋊C4—734no—
270C2×C4⋊C4—734no—
271C2×C4⋊C4—732no—
272C2×C4⋊C4—734no—
273C2×C4⋊C4—734no—
274C2×C4⋊C4—734no—
275C2×C4⋊C4—734no—
276C2×C4⋊C4—732no—
277C2×C4⋊C4—734no—
278C2×C4⋊C4—732no—
279C2×C4⋊C4C22×D7314yes—
280C2×C4⋊C4C22×D7312yes—
281C2×C4⋊C4C22×D7312yes—
282C2×C4⋊C4C22×D7314yes—
283C2×C4⋊C4C22×D7312yes—
284C2×C42—734no—
285C2×C42—734no—
286C2×C42—732no—
287C2×C42—731no—
288C2×C42—734no—
289C2×C42—734no—
290C2×C42—734no—
291C2×C42—734no—
292C2×C42—732no—
293C2×C42—731no—
294C2×C42C22×D7314yes—
295C2×C42C22×D7311yescharacteristic
296#95—734no—
297#95—734no—
298#95—734no—
299#95—734no—
300#95—734no—
301#95—734no—
302#95—734no—
303#95—734no—
304#95—734no—
305#95—734no—
306#95—734no—
307#95C22×D7314yes—
308#95C22×D7314yes—
309#95C22×D7314yes—
310#95C22×D7314yes—
311C22×C4—731no—
312C22×C4—734no—
313C22×C4—734no—
314C22×C4—731no—
315C22×C4—734no—
316C22×C4—732no—
317C22×C4C23×D7314yes—
318C22×C4C23×D7314yes—
319C22×C4C23×D7314yes—
320C22×C4C23×D7312yes—
321C22×C4C23×D7311yescharacteristic
322C4⋊C4—44no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—2924no—
326C4⋊C4—2924no—
327C4⋊C4—2924no—
328C4⋊C4—2924no—
329C4⋊C4—2924no—
330C4⋊C4—2922no—
331C4⋊C4—7316no—
332C4⋊C4—7316no—
333C4⋊C4—7316no—
334C4⋊C4—7316no—
335C4⋊C4—7316no—
336C4⋊C4—738no—
337C4⋊C4—738no—
338C4⋊C4C2×C4×D7318yes—
339C4⋊C4C2×C4×D73116yes—
340C42—44no—
341C42—2922no—
342C42—2921no—
343C42—2924no—
344C42—2924no—
345C42—7316no—
346C42—1462no—
347C42—1468no—
348C42—1464no—
349C42—1468no—
350C42—1468no—
351C42C2×C4×D7314yes—
352C23C24×D7311yescharacteristic
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—732no—
366C2×C4—734no—
367C2×C4—738no—
368C2×C4—738no—
369C2×C4—1461no—
370C2×C4—1464no—
371C2×C4—1462no—
372C2×C4—1462no—
373C2×C4—1464no—
374C2×C4—1462no—
375C2×C4—1462no—
376C2×C4—1464no—
377C2×C4—1464no—
378C2×C4—1464no—
379C2×C4—1464no—
380C2×C4—1464no—
381C2×C4C22×C4×D7318yes—
382C2×C4C22×C4×D7312yes—
383C2×C4C22×C4×D7314yes—
384C22C23×C4×D7311yescharacteristic
385C222−1+4×D7311yescharacteristic
386C222−1+4×D7312yes—
387C22#1798942212yes—
388C22#1798942411yescharacteristic
389C4—22no—
390C4—28no—
391C4—24no—
392C4—44no—
393C4—44no—
394C4—2921no—
395C4—2924no—
396C4—2922no—
397C4—734no—
398C4—1468no—
399C4—1468no—
400C2#2262314011yescharacteristic
401C2#2262314212yes—
402C2#564×D7311yescharacteristic
403C2#2262407511yescharacteristic
404C2#2262407712yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2382C2
socle, prime radical, cosocleC23×C73C25
hypercenter#2382D73
hypocenterC73C4×#564
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. C73⋊#564C4semidirect
196. Dic73#564semidirect
214. C73C4×#564semidirect

Maximal subgroups

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

subgroupindex
C2×C73⋊#5642
#226131162
#226131152
#226131142
#226131132
#125×Dic732
#226124902
#226124882
#226124862
C73×#23822
C4×#56473