Finite Group Databasebeta

← C73×#11209 #32920613

Subgroups — C73×#11209 #32920613

Order 18688.

842 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#423×C73C211yesmaximal, characteristic
2C73×#2296C211yesmaximal, characteristic
3C2×#339×C73C212yesmaximal
4C2×#339×C73C212yesmaximal
5C4×#95×C73C211yesmaximal, characteristic
6C22×M16×C73C2212yes—
7C2×#117×C73C2211yescharacteristic
8C2×#117×C73C2211yescharacteristic
9C22×C42×C73C2212yes—
10C22×C42×C73C2211yescharacteristic
11#423×C73—24no—
12C2×C4⋊C8×C73—22no—
13#389×C73C412yescomplemented
14#389×C73C412yescomplemented
15#385×C73—22no—
16C4×C4⋊C4×C73—22no—
17C2×#95×C73—22no—
18#339×C73—24no—
19#339×C73—24no—
20C23×C4×C73—22no—
21C23×C4×C73D412yes—
22C23×C4×C73C2311yescharacteristic
23C2×M16×C73—22no—
24C2×M16×C73—22no—
25C2×M16×C73—22no—
26C2×M16×C73—22no—
27C2×M16×C73—22no—
28C2×M16×C73D414yes—
29C22×C8×C73—22no—
30#117×C73—21no—
31#117×C73—21no—
32#117×C73—22no—
33#117×C73—22no—
34#117×C73D412yes—
35#117×C73Q812yes—
36C2×C4⋊C4×C73—22no—
37C2×C4⋊C4×C73—22no—
38C2×C4⋊C4×C73C2×C412yes—
39C2×C4⋊C4×C73C2×C412yes—
40C2×C22⋊C4×C73—21no—
41C2×C22⋊C4×C73—21no—
42C2×C42×C73—22no—
43C2×C42×C73—21no—
44C2×C42×C73—22no—
45C2×C42×C73—22no—
46C2×C42×C73—22no—
47C2×C42×C73—22no—
48C2×C42×C73—22no—
49C2×C42×C73—21no—
50C2×C42×C73—22no—
51C2×C42×C73C2×C411yescharacteristic
52C2×C42×C73C2×C411yescharacteristic
53C2×C42×C73D412yes—
54C2×C42×C73Q814yes—
55C4⋊C8×C73—28no—
56#95×C73—28no—
57#95×C73—22no—
58#95×C73—22no—
59C24×C73C2×D411yescharacteristic
60C22×C4×C73—28no—
61C22×C4×C73—22no—
62C22×C4×C73—24no—
63C22×C4×C73—24no—
64C22×C4×C73—24no—
65C22×C4×C73—22no—
66C22×C4×C73—42no—
67C22×C4×C73—44no—
68C22×C4×C73—42no—
69C22×C4×C73—42no—
70C22×C4×C73C22⋊C412yes—
71C22×C4×C73C22⋊C412yes—
72C22×C4×C73C22×C411yescharacteristic
73C22×C4×C73C2×D411yescharacteristic
74C22×C4×C73C2×D412yes—
75C22×C4×C73C2×D411yescharacteristic
76C22×C4×C73C2×Q811yescharacteristic
77C22×C4×C73C2×Q812yes—
78C22×C4×C73#4111yescharacteristic
79C22×C4×C73#4111yescharacteristic
80C22×C4×C73#4112yes—
81C22×C4×C73#4112yes—
82M16×C73—24no—
83M16×C73—24no—
84M16×C73—42no—
85M16×C73—42no—
86C2×C8×C73—24no—
87C2×C8×C73—42no—
88C2×C8×C73—42no—
89C4⋊C4×C73—22no—
90C4⋊C4×C73—24no—
91C4⋊C4×C73—44no—
92C4⋊C4×C73—44no—
93C4⋊C4×C73C4⋊C414yes—
94C22⋊C4×C73—22no—
95C22⋊C4×C73—22no—
96C22⋊C4×C73—42no—
97C42×C73—22no—
98C42×C73—22no—
99C42×C73—22no—
100C42×C73—22no—
101C42×C73—22no—
102C42×C73—22no—
103C42×C73—24no—
104C42×C73—24no—
105C42×C73—41no—
106C42×C73—42no—
107C42×C73—41no—
108C42×C73—42no—
109C23×C73—22no—
110C23×C73—22no—
111C23×C73C2×C22⋊C411yescharacteristic
112C23×C73#12111yescharacteristic
113C23×C73#12112yes—
114C23×C73C22⋊Q811yescharacteristic
115C23×C73C22⋊Q812yes—
116C2×C4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—28no—
119C2×C4×C73—24no—
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—22no—
123C2×C4×C73—48no—
124C2×C4×C73—48no—
125C2×C4×C73—48no—
126C2×C4×C73—44no—
127C2×C4×C73—44no—
128C2×C4×C73—42no—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73—42no—
133C2×C4×C73#10414yes—
134C2×C4×C73C2×C4⋊C411yescharacteristic
135C2×C4×C73#11711yescharacteristic
136C2×C4×C73C4×D412yes—
137C2×C4×C73C4×Q812yes—
138C2×C4×C73#12011yescharacteristic
139C2×C4×C73#12112yes—
140C2×C4×C73#12111yescharacteristic
141C2×C4×C73C22⋊Q812yes—
142C2×C4×C73C22⋊Q812yes—
143C2×C4×C73C22⋊Q811yescharacteristic
144C2×C4×C73#12312yes—
145C2×C4×C73#12311yescharacteristic
146C2×C4×C73#12411yescharacteristic
147C2×C4×C73#12512yes—
148C2×C4×C73#12512yes—
149C2×C4×C73#12612yes—
150C2×C4×C73C4⋊Q812yes—
151C2×C4×C73C4⋊Q811yescharacteristic
152C8×C73—44no—
153C22×C73—22no—
154C22×C73—22no—
155C22×C73—24no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73#38011yescharacteristic
159C22×C73#38611yescharacteristic
160C22×C73#39111yescharacteristic
161C22×C73#39612yes—
162C22×C73#39812yes—
163C22×C73C2×#10412yes—
164C22×C73#42112yes—
165C4×C73—24no—
166C4×C73—48no—
167C4×C73—44no—
168C4×C73—42no—
169C4×C73—82no—
170C4×C73#38712yes—
171C4×C73#38912yes—
172C4×C73#39411yescharacteristic
173C4×C73#39511yescharacteristic
174C4×C73#39811yescharacteristic
175C4×C73#40011yescharacteristic
176#11209C7311yesmaximal, characteristic, direct product factor, Sylow
177C2×C73—22no—
178C2×C73—22no—
179C2×C73#144111yescharacteristic
180C2×C73#180612yes—
181C2×C73#187112yes—
182C2×C73#199411yescharacteristic
183C2×C73#199511yescharacteristic
184C2×#423C2×C7311yescharacteristic
185#2296C2×C7311yescharacteristic
186C2×#339C2×C7312yes—
187C2×#339C2×C7312yes—
188C4×#95C2×C7311yescharacteristic
189C73#1120911yescharacteristic, direct product factor, Sylow
190C22×M16C22×C7312yes—
191C2×#117C22×C7311yescharacteristic
192C2×#117C22×C7311yescharacteristic
193C22×C42C22×C7312yes—
194C22×C42C22×C7311yescharacteristic
195#423—24no—
196C2×C4⋊C8—22no—
197#389C4×C7312yescomplemented
198#389C4×C7312yescomplemented
199#385—22no—
200C4×C4⋊C4—22no—
201C2×#95—22no—
202#339—24no—
203#339—24no—
204C23×C4—22no—
205C23×C4D4×C7312yes—
206C23×C4C23×C7311yescharacteristic
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16D4×C7314yes—
213C22×C8—22no—
214#117—21no—
215#117—21no—
216#117—22no—
217#117—22no—
218#117D4×C7312yes—
219#117Q8×C7312yes—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4C2×C4×C7312yes—
223C2×C4⋊C4C2×C4×C7312yes—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42—21no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—21no—
234C2×C42—22no—
235C2×C42C2×C4×C7311yescharacteristic
236C2×C42C2×C4×C7311yescharacteristic
237C2×C42D4×C7312yes—
238C2×C42Q8×C7314yes—
239C4⋊C8—28no—
240#95—28no—
241#95—22no—
242#95—22no—
243C24C2×D4×C7311yescharacteristic
244C22×C4—28no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—22no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4C22⋊C4×C7312yes—
255C22×C4C22⋊C4×C7312yes—
256C22×C4C22×C4×C7311yescharacteristic
257C22×C4C2×D4×C7311yescharacteristic
258C22×C4C2×D4×C7312yes—
259C22×C4C2×D4×C7311yescharacteristic
260C22×C4C2×Q8×C7311yescharacteristic
261C22×C4C2×Q8×C7312yes—
262C22×C4#41×C7311yescharacteristic
263C22×C4#41×C7311yescharacteristic
264C22×C4#41×C7312yes—
265C22×C4#41×C7312yes—
266M16—24no—
267M16—24no—
268M16—42no—
269M16—42no—
270C2×C8—24no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—44no—
276C4⋊C4—44no—
277C4⋊C4C4⋊C4×C7314yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—42no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—24no—
288C42—24no—
289C42—41no—
290C42—42no—
291C42—41no—
292C42—42no—
293C23—22no—
294C23—22no—
295C23C2×C22⋊C4×C7311yescharacteristic
296C23#121×C7311yescharacteristic
297C23#121×C7312yes—
298C23C22⋊Q8×C7311yescharacteristic
299C23C22⋊Q8×C7312yes—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—48no—
308C2×C4—44no—
309C2×C4—48no—
310C2×C4—48no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4#104×C7314yes—
318C2×C4C2×C4⋊C4×C7311yescharacteristic
319C2×C4#117×C7311yescharacteristic
320C2×C4C4×D4×C7312yes—
321C2×C4C4×Q8×C7312yes—
322C2×C4#120×C7311yescharacteristic
323C2×C4#121×C7312yes—
324C2×C4#121×C7311yescharacteristic
325C2×C4C22⋊Q8×C7312yes—
326C2×C4C22⋊Q8×C7312yes—
327C2×C4C22⋊Q8×C7311yescharacteristic
328C2×C4#123×C7312yes—
329C2×C4#123×C7311yescharacteristic
330C2×C4#124×C7311yescharacteristic
331C2×C4#125×C7312yes—
332C2×C4#125×C7312yes—
333C2×C4#126×C7312yes—
334C2×C4C4⋊Q8×C7312yes—
335C2×C4C4⋊Q8×C7311yescharacteristic
336C8—44no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—24no—
342C22#380×C7311yescharacteristic
343C22#386×C7311yescharacteristic
344C22#391×C7311yescharacteristic
345C22#396×C7312yes—
346C22#398×C7312yes—
347C22C2×#104×C7312yes—
348C22#421×C7312yes—
349C4—24no—
350C4—48no—
351C4—44no—
352C4—42no—
353C4—82no—
354C4#387×C7312yes—
355C4#389×C7312yes—
356C4#394×C7311yescharacteristic
357C4#395×C7311yescharacteristic
358C4#398×C7311yescharacteristic
359C4#400×C7311yescharacteristic
360C2—22no—
361C2—22no—
362C2C73×#144111yescharacteristic
363C2C73×#180612yes—
364C2C73×#187112yes—
365C2C73×#199411yescharacteristic
366C2C73×#199511yescharacteristic
subgroupG/H
centerC22×C4×C73C2×D4
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C73 ◁ C22×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
13. #389×C73C4semidirect
14. #389×C73C4semidirect
176. #11209C73direct (N × H)
189. C73#11209direct (N × H)
197. #389C4×C73semidirect
198. #389C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#423×C732
C73×#22962
C2×#339×C732
C4×#95×C732
#1120973