Finite Group Databasebeta

← C4×C73⋊#564 #33248705

Subgroups — C4×C73⋊#564 #33248705

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#22613117C211yesmaximal, characteristic
3#22613116C212yesmaximal
4#22613115C214yesmaximal
5#22613114C214yesmaximal
6#22613113C214yesmaximal
7C4×#14556583C212yesmaximal
8C4×#14556582C214yesmaximal
9C4×#14556581C214yesmaximal
10C4×#14556581C214yesmaximal
11C4×#125×C73C211yesmaximal, characteristic
12C73⋊#564C4116yesdirect product factor
13C2×#14556583C2212yes—
14C2×#14556582C2214yes—
15C2×#14556581C2214yes—
16C2×#14556581C2214yes—
17#17988486C2214yes—
18#17988485C2212yes—
19#17988485C2212yes—
20#17988484C2214yes—
21#17988484C2214yes—
22#17988483C2214yes—
23#17988482C2214yes—
24#17988482C2214yes—
25#17988474C2214yes—
26#17988474C2214yes—
27#17988473C2214yes—
28#17988473C2214yes—
29#17988472C2214yes—
30#17988472C2214yes—
31#17988471C2214yes—
32#17988471C2214yes—
33#17988470C2214yes—
34#17988470C2214yes—
35#17988469C2214yes—
36#17988469C2214yes—
37#17988468C2214yes—
38#17988468C2214yes—
39#17988453C2212yes—
40#17988452C2214yes—
41#17988451C2214yes—
42#17988451C2214yes—
43C4×#11924007C2214yes—
44C4×#11924007C2214yes—
45C4×#11924007C2214yes—
46C4×#11924007C2214yes—
47C4×C4⋊Dic73C2212yes—
48C4×C4⋊Dic73C2214yes—
49C4×C4⋊Dic73C2212yes—
50C42×Dic73C2214yes—
51C2×#125×C73C2211yescharacteristic
52#389×C73C2212yes—
53#387×C73C2214yes—
54#382×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2212yes—
56C4×C4⋊C4×C73C2214yes—
57C43×C73C2211yescharacteristic
58#14556583C2×C4116yes—
59#14556582C2×C4132yes—
60#14556581C2×C4132yes—
61#14556581C2×C4132yes—
62C2×C4⋊Dic73C2314yes—
63C2×C4⋊Dic73C2312yes—
64C2×C4⋊Dic73C2312yes—
65C2×C4⋊Dic73C2312yes—
66C2×C4⋊Dic73C2314yes—
67C2×C4⋊Dic73C2312yes—
68C2×#11924007C2314yes—
69C2×#11924007C2314yes—
70C2×#11924007C2314yes—
71C2×#11924007C2314yes—
72C2×#11924007C2314yes—
73C2×#11924007C2314yes—
74C2×#11924007C2314yes—
75C2×#11924007C2314yes—
76C2×C4×Dic73C2314yes—
77C2×C4×Dic73C2314yes—
78C2×C4×Dic73C2314yes—
79C2×C4×Dic73C2314yes—
80C2×C4×Dic73C2314yes—
81C2×C4×Dic73C2314yes—
82#14556498C2314yes—
83#14556498C2314yes—
84#14556498C2314yes—
85#14556498C2314yes—
86#14556498C2314yes—
87#14556498C2314yes—
88#14556498C2314yes—
89#14556498C2314yes—
90#14556498C2314yes—
91#14556498C2314yes—
92#14556498C2314yes—
93#14556498C2314yes—
94#125×C73C2×C418yes—
95C2×C4⋊C4×C73C2312yes—
96C2×C4⋊C4×C73C2314yes—
97C2×C4⋊C4×C73C2314yes—
98C2×C4⋊C4×C73C2312yes—
99C2×C42×C73C2314yes—
100C2×C42×C73C2312yes—
101C2×C42×C73C2311yescharacteristic
102C2×C42×C73C2312yes—
103C2×C42×C73C2311yescharacteristic
104C2×C42×C73C2311yescharacteristic
105#95×C73C2314yes—
106#95×C73C2314yes—
107#95×C73C2314yes—
108C22×Dic73C2414yes—
109C22×Dic73C2414yes—
110C22×Dic73C2414yes—
111C22×Dic73C2414yes—
112C4⋊Dic73—42no—
113C4⋊Dic73—44no—
114C4⋊Dic73—42no—
115C4⋊Dic73C22×C418yes—
116C4⋊Dic73C22×C4116yes—
117C4⋊Dic73C22×C418yes—
118#11924007—44no—
119#11924007—44no—
120#11924007—44no—
121#11924007—44no—
122#11924007C22×C4116yes—
123#11924007C22×C4116yes—
124#11924007C22×C4116yes—
125#11924007C22×C4116yes—
126C4×Dic73—28no—
127C4×Dic73—28no—
128C4×Dic73—44no—
129C4×Dic73—44no—
130C4×Dic73—44no—
131C4×Dic73C22×C4116yes—
132C22×C4×C73C2411yescharacteristic
133C22×C4×C73C2414yes—
134C22×C4×C73C2412yes—
135C22×C4×C73C2412yes—
136C22×C4×C73C2414yes—
137C22×C4×C73C2411yescharacteristic
138C22×C4×C73C2411yescharacteristic
139C4⋊C4×C73—42no—
140C4⋊C4×C73—44no—
141C4⋊C4×C73C22×C418yes—
142C4⋊C4×C73C22×C4116yes—
143C42×C73—28no—
144C42×C73—24no—
145C42×C73—22no—
146C42×C73—41no—
147C42×C73—42no—
148C42×C73C22×C414yes—
149C23×C73C2511yescharacteristic
150C2×C4×C73—22no—
151C2×C4×C73—24no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—22no—
155C2×C4×C73—24no—
156C2×C4×C73—24no—
157C2×C4×C73—22no—
158C2×C4×C73—21no—
159C2×C4×C73—22no—
160C2×C4×C73—22no—
161C2×C4×C73—22no—
162C2×C4×C73—24no—
163C2×C4×C73—24no—
164C2×C4×C73C23×C412yes—
165C2×C4×C73C23×C414yes—
166C2×C4×C73C23×C418yes—
167C2×C4×C732−1+414yes—
168C2×C4×C732−1+412yes—
169C2×Dic73—24no—
170C2×Dic73—24no—
171C2×Dic73—24no—
172C2×Dic73—24no—
173C2×Dic73—24no—
174C2×Dic73—24no—
175C2×Dic73—24no—
176C2×Dic73—24no—
177C2×Dic73—24no—
178C2×Dic73—24no—
179C2×Dic73C23×C418yes—
180C2×Dic73C23×C418yes—
181C22×C73C24×C411yescharacteristic
182C22×C73C2×2−1+412yes—
183C22×C73C2×2−1+411yescharacteristic
184C22×C73#58511yescharacteristic
185C22×C73#58512yes—
186C4×C73—24no—
187C4×C73—28no—
188C4×C73—22no—
189C4×C73—42no—
190C4×C73—44no—
191C4×C73—41no—
192C4×C73#56414yescomplemented
193Dic73—28no—
194Dic73—28no—
195Dic73—44no—
196Dic73—44no—
197C4×#564—731nomaximal, Sylow
198C2×C73C4×2−1+412yes—
199C2×C73C4×2−1+411yescharacteristic
200C2×C73C2×#56411yescharacteristic
201C2×C73#353112yes—
202C2×C73#353111yescharacteristic
203C2×#564—731no—
204#2382—734no—
205#2382—734no—
206#2382—734no—
207#2382—732no—
208#2382—731no—
209C4×#125—734no—
210C4×#125—734no—
211C4×#125—734no—
212C4×#125—732no—
213C4×#125D7311yescharacteristic
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—734no—
224#389—734no—
225#389—732no—
226#389—732no—
227#389—734no—
228#389—734no—
229#389C2×D7312yes—
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#387—734no—
244#387C2×D7314yes—
245#382—734no—
246#382—732no—
247#382—734no—
248#382—734no—
249#382C2×D7311yescharacteristic
250C4×C4⋊C4—734no—
251C4×C4⋊C4—732no—
252C4×C4⋊C4—732no—
253C4×C4⋊C4—734no—
254C4×C4⋊C4—734no—
255C4×C4⋊C4—734no—
256C4×C4⋊C4—734no—
257C4×C4⋊C4C2×D7314yes—
258C4×C4⋊C4C2×D7312yes—
259C43—734no—
260C43C2×D7311yescharacteristic
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—732no—
273C2×C4⋊C4—734no—
274C2×C4⋊C4—734no—
275C2×C4⋊C4—734no—
276C2×C4⋊C4—734no—
277C2×C4⋊C4—734no—
278C2×C4⋊C4—732no—
279C2×C4⋊C4—732no—
280C2×C4⋊C4C22×D7314yes—
281C2×C4⋊C4C22×D7312yes—
282C2×C4⋊C4C22×D7312yes—
283C2×C4⋊C4C22×D7314yes—
284C2×C42—734no—
285C2×C42—734no—
286C2×C42—734no—
287C2×C42—734no—
288C2×C42—734no—
289C2×C42—734no—
290C2×C42C22×D7314yes—
291C2×C42C22×D7312yes—
292C2×C42C22×D7311yescharacteristic
293C2×C42C22×D7311yescharacteristic
294C2×C42C22×D7312yes—
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#95—734no—
308#95C22×D7314yes—
309#95C22×D7314yes—
310#95C22×D7314yes—
311C22×C4—734no—
312C22×C4—734no—
313C22×C4—734no—
314C22×C4—734no—
315C22×C4C23×D7312yes—
316C22×C4C23×D7314yes—
317C22×C4C23×D7311yescharacteristic
318C22×C4C23×D7311yescharacteristic
319C22×C4C23×D7314yes—
320C22×C4C23×D7312yes—
321C22×C4C23×D7311yescharacteristic
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—2924no—
325C4⋊C4—2924no—
326C4⋊C4—2924no—
327C4⋊C4—2924no—
328C4⋊C4—2922no—
329C4⋊C4—2922no—
330C4⋊C4—2924no—
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—28no—
341C42—24no—
342C42—22no—
343C42—41no—
344C42—42no—
345C42—2924no—
346C42—2924no—
347C42—2924no—
348C42—7316no—
349C42—1468no—
350C42—1468no—
351C42C2×C4×D7314yes—
352C23C24×D7311yescharacteristic
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—738no—
368C2×C4—738no—
369C2×C4—1464no—
370C2×C4—1464no—
371C2×C4—1464no—
372C2×C4—1464no—
373C2×C4—1464no—
374C2×C4—1464no—
375C2×C4—1464no—
376C2×C4—1464no—
377C2×C4—1464no—
378C2×C4—1464no—
379C2×C4C22×C4×D7318yes—
380C2×C4C22×C4×D7314yes—
381C2×C4C22×C4×D7312yes—
382C2×C4#1455663814yes—
383C2×C4#1455663912yes—
384C22C23×C4×D7311yescharacteristic
385C22C2×#1455663812yes—
386C22C2×#1455663911yescharacteristic
387C22#1798942311yescharacteristic
388C22#1798942312yes—
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—2924no—
396C4—2924no—
397C4—1468no—
398C4—1468no—
399C4C73⋊#56414yesdirect product factor
400C2C4×#1455663812yes—
401C2C4×#1455663911yescharacteristic
402C2C2×C73⋊#56411yescharacteristic
403C2#2262407612yes—
404C2#2262407811yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×#125×C73C2
socle, prime radical, cosocleC23×C73C25
hypercenterC4×#125D73
hypocenterC73C4×#564
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
12. C73⋊#564C4direct (N × H)
192. C4×C73#564semidirect
214. C73C4×#564semidirect
399. C4C73⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C73⋊#5642
#226131172
#226131162
#226131152
#226131142
#226131132
C4×#145565832
C4×#145565822
C4×#145565812
C4×#125×C732
C4×#56473