Finite Group Databasebeta

← C73×#9148 #32918552

Subgroups — C73×#9148 #32918552

Order 18688.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2854C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
3C73×#1817C211yesmaximal, characteristic, complemented
4C2×#327×C73C212yesmaximal
5C73×#1294C212yesmaximal, complemented
6C2×#123×C73—21no—
7C2×#121×C73C2211yescharacteristic
8C22×C4⋊C4×C73—21no—
9C22×C42×C73—21no—
10C22×C42×C73C2211yescharacteristic
11C2×C22⋊C8×C73C2212yes—
12#390×C73C412yescomplemented
13#389×C73C412yescomplemented
14#388×C73—22no—
15#386×C73—21no—
16#380×C73C2211yescharacteristic
17C4×C4⋊C4×C73—24no—
18C2×#95×C73C2212yes—
19#336×C73—22no—
20#327×C73—24no—
21C22×D4×C73—21no—
22C22×D4×C73C2×C411yescharacteristic
23C23×C4×C73—22no—
24C23×C4×C73D411yescharacteristic
25C23×C4×C73D411yescharacteristic
26C23×C4×C73C2311yescharacteristic
27C22×C8×C73—22no—
28#123×C73—42no—
29#123×C73—42no—
30#121×C73—22no—
31#121×C73—22no—
32C2×C4⋊C4×C73—24no—
33C2×C4⋊C4×C73—28no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73C2×C411yescharacteristic
36C2×C4⋊C4×C73C2×C412yes—
37C2×C22⋊C4×C73—21no—
38C2×C22⋊C4×C73—22no—
39C2×C22⋊C4×C73—22no—
40C2×C22⋊C4×C73—21no—
41C2×C42×C73—22no—
42C2×C42×C73—22no—
43C2×C42×C73—24no—
44C2×C42×C73—42no—
45C2×C42×C73—42no—
46C2×C42×C73C2×C412yes—
47C2×C42×C73D412yes—
48C22⋊C8×C73—22no—
49C22⋊C8×C73—22no—
50#95×C73—22no—
51#95×C73—22no—
52#95×C73—21no—
53#95×C73D414yes—
54C24×C73—21no—
55C24×C73C2×D411yescharacteristic
56C2×D4×C73—22no—
57C2×D4×C73—42no—
58C2×D4×C73—41no—
59C2×D4×C73—41no—
60C2×D4×C73—41no—
61C2×D4×C73—41no—
62C2×D4×C73—41no—
63C2×D4×C73—41no—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—24no—
71C22×C4×C73—28no—
72C22×C4×C73—24no—
73C22×C4×C73—22no—
74C22×C4×C73—21no—
75C22×C4×C73—42no—
76C22×C4×C73—44no—
77C22×C4×C73—42no—
78C22×C4×C73—42no—
79C22×C4×C73C22⋊C412yes—
80C22×C4×C73C22⋊C412yes—
81C22×C4×C73D812yes—
82C22×C4×C73SD1612yes—
83C22×C4×C73C22×C411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D412yes—
86C22×C4×C73#4112yes—
87C2×C8×C73—44no—
88C2×C8×C73—42no—
89C4⋊C4×C73—216no—
90C4⋊C4×C73—22no—
91C4⋊C4×C73—42no—
92C4⋊C4×C73—44no—
93C22⋊C4×C73—41no—
94C22⋊C4×C73—41no—
95C22⋊C4×C73—44no—
96C22⋊C4×C73—44no—
97C22⋊C4×C73—42no—
98C42×C73—24no—
99C42×C73—24no—
100C42×C73—48no—
101C23×C73—22no—
102C23×C73—22no—
103C23×C73—41no—
104C23×C73—42no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—42no—
108C23×C73C2×C22⋊C411yescharacteristic
109C23×C73#12011yescharacteristic
110C23×C73#12311yescharacteristic
111C23×C73C2×D811yescharacteristic
112C23×C73C2×SD1611yescharacteristic
113C23×C73AGL(1,ℤ/8)11yescharacteristic
114C23×C73#13711yescharacteristic
115D4×C73—82no—
116D4×C73—81no—
117D4×C73—81no—
118D4×C73—81no—
119D4×C73—81no—
120C2×C4×C73—24no—
121C2×C4×C73—24no—
122C2×C4×C73—22no—
123C2×C4×C73—22no—
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—22no—
131C2×C4×C73—22no—
132C2×C4×C73—28no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73—44no—
136C2×C4×C73—48no—
137C2×C4×C73—48no—
138C2×C4×C73—44no—
139C2×C4×C73—41no—
140C2×C4×C73—42no—
141C2×C4×C73—42no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—42no—
145C2×C4×C73#10214yes—
146C2×C4×C73#10414yes—
147C2×C4×C73C4×D412yes—
148C2×C4×C73#12112yes—
149C8×C73—82no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—22no—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—81no—
159C22×C73—81no—
160C22×C73—81no—
161C22×C73—82no—
162C22×C73—82no—
163C22×C73#38611yescharacteristic
164C22×C73#41012yes—
165C22×C73C2×#10211yescharacteristic
166C22×C73#41711yescharacteristic
167C22×C73C2×#10412yes—
168C22×C73#44711yescharacteristic
169C22×C73#44811yescharacteristic
170C22×C73#48011yescharacteristic
171C22×C73#48111yescharacteristic
172C4×C73—24no—
173C4×C73—24no—
174C4×C73—22no—
175C4×C73—22no—
176C4×C73—48no—
177C4×C73—81no—
178C4×C73—82no—
179#9148C7311yesmaximal, characteristic, direct product factor, Sylow
180C2×C73—21no—
181C2×C73—21no—
182C2×C73—21no—
183C2×C73—21no—
184C2×C73—161no—
185C2×C73#150212yes—
186C2×C73#150912yes—
187C2×C73#187411yescharacteristic
188C2×C73#189611yescharacteristic
189C2×C73#189911yescharacteristic
190#2854C2×C7311yescharacteristic
191C2×C4×C4⋊C4C2×C7311yescharacteristic, complemented
192#1817C2×C7311yescharacteristic, complemented
193C2×#327C2×C7312yes—
194#1294C2×C7312yescomplemented
195C73#914811yescharacteristic, direct product factor, Sylow
196C2×#123—21no—
197C2×#121C22×C7311yescharacteristic
198C22×C4⋊C4—21no—
199C22×C42—21no—
200C22×C42C22×C7311yescharacteristic
201C2×C22⋊C8C22×C7312yes—
202#390C4×C7312yescomplemented
203#389C4×C7312yescomplemented
204#388—22no—
205#386—21no—
206#380C22×C7311yescharacteristic
207C4×C4⋊C4—24no—
208C2×#95C22×C7312yes—
209#336—22no—
210#327—24no—
211C22×D4—21no—
212C22×D4C2×C4×C7311yescharacteristic
213C23×C4—22no—
214C23×C4D4×C7311yescharacteristic
215C23×C4D4×C7311yescharacteristic
216C23×C4C23×C7311yescharacteristic
217C22×C8—22no—
218#123—42no—
219#123—42no—
220#121—22no—
221#121—22no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C2×C4×C7311yescharacteristic
226C2×C4⋊C4C2×C4×C7312yes—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—24no—
234C2×C42—42no—
235C2×C42—42no—
236C2×C42C2×C4×C7312yes—
237C2×C42D4×C7312yes—
238C22⋊C8—22no—
239C22⋊C8—22no—
240#95—22no—
241#95—22no—
242#95—21no—
243#95D4×C7314yes—
244C24—21no—
245C24C2×D4×C7311yescharacteristic
246C2×D4—22no—
247C2×D4—42no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—44no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4C22⋊C4×C7312yes—
270C22×C4C22⋊C4×C7312yes—
271C22×C4D8×C7312yes—
272C22×C4SD16×C7312yes—
273C22×C4C22×C4×C7311yescharacteristic
274C22×C4C2×D4×C7311yescharacteristic
275C22×C4C2×D4×C7312yes—
276C22×C4#41×C7312yes—
277C2×C8—44no—
278C2×C8—42no—
279C4⋊C4—216no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—44no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—42no—
288C42—24no—
289C42—24no—
290C42—48no—
291C23—22no—
292C23—22no—
293C23—41no—
294C23—42no—
295C23—41no—
296C23—41no—
297C23—42no—
298C23C2×C22⋊C4×C7311yescharacteristic
299C23#120×C7311yescharacteristic
300C23#123×C7311yescharacteristic
301C23C2×D8×C7311yescharacteristic
302C23C2×SD16×C7311yescharacteristic
303C23AGL(1,ℤ/8)×C7311yescharacteristic
304C23#137×C7311yescharacteristic
305D4—82no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—28no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—48no—
326C2×C4—48no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4#102×C7314yes—
336C2×C4#104×C7314yes—
337C2×C4C4×D4×C7312yes—
338C2×C4#121×C7312yes—
339C8—82no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—82no—
349C22—82no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22#386×C7311yescharacteristic
354C22#410×C7312yes—
355C22C2×#102×C7311yescharacteristic
356C22#417×C7311yescharacteristic
357C22C2×#104×C7312yes—
358C22#447×C7311yescharacteristic
359C22#448×C7311yescharacteristic
360C22#480×C7311yescharacteristic
361C22#481×C7311yescharacteristic
362C4—24no—
363C4—24no—
364C4—22no—
365C4—22no—
366C4—48no—
367C4—82no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2C73×#150212yes—
375C2C73×#150912yes—
376C2C73×#187411yescharacteristic
377C2C73×#189611yescharacteristic
378C2C73×#189911yescharacteristic
subgroupG/H
center, socleC23×C73C2×C22⋊C4
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊C4×C73C2semidirect
3. C73×#1817C2semidirect
5. C73×#1294C2semidirect
12. #390×C73C4semidirect
13. #389×C73C4semidirect
179. #9148C73direct (N × H)
191. C2×C4×C4⋊C4C2×C73semidirect
192. #1817C2×C73semidirect
194. #1294C2×C73semidirect
195. C73#9148direct (N × H)
202. #390C4×C73semidirect
203. #389C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28542
C2×C4×C4⋊C4×C732
C73×#18172
C2×#327×C732
C73×#12942
#914873