Finite Group Databasebeta

← C73×#10263 #32919667

Subgroups — C73×#10263 #32919667

Order 18688.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C73C211yesmaximal, characteristic
2C2×#462×C73C211yesmaximal, characteristic, complemented
3C2×#460×C73C211yesmaximal, characteristic
4C73×#1984C211yesmaximal, characteristic, complemented
5C2×#332×C73C211yesmaximal, characteristic, complemented
6C2×#331×C73C211yesmaximal, characteristic
7C73×#1277C211yesmaximal, characteristic, complemented
8C22×Q16×C73—21no—
9C22×SD16×C73—21no—
10C2×C4⋊Q8×C73C2211yescharacteristic
11C2×#127×C73C2211yescharacteristic
12C2×C4×Q8×C73C2211yescharacteristic
13#486×C73—22no—
14#486×C73—22no—
15#462×C73—22no—
16#462×C73—22no—
17#460×C73—22no—
18#460×C73—22no—
19C2×C4⋊C8×C73C2211yescharacteristic
20C2×C4⋊C8×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×#103×C73—21no—
23C2×#102×C73—22no—
24C2×#102×C73—21no—
25C2×C4×C8×C73C2211yescharacteristic
26#336×C73—22no—
27#332×C73—22no—
28#331×C73—22no—
29C22×Q8×C73—21no—
30C22×Q8×C73D411yescharacteristic
31C22×D4×C73—21no—
32C22×D4×C73—21no—
33C22×D4×C73—21no—
34C2×Q16×C73—24no—
35C2×Q16×C73—42no—
36C2×Q16×C73—42no—
37C2×SD16×C73—24no—
38C2×SD16×C73—42no—
39C2×SD16×C73—42no—
40C22×C8×C73—21no—
41C22×C8×C73—21no—
42C22×C8×C73—21no—
43C22×C8×C73D412yes—
44C4⋊Q8×C73—21no—
45C4⋊Q8×C73—21no—
46C4⋊Q8×C73—21no—
47C4⋊Q8×C73D412yes—
48#127×C73—21no—
49#127×C73—21no—
50#127×C73—21no—
51#127×C73D412yes—
52C4×Q8×C73—21no—
53C4×Q8×C73—21no—
54C4×Q8×C73—21no—
55C4×Q8×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C4⋊C4×C73D411yescharacteristic
60C2×C42×C73—21no—
61C2×C42×C73C2311yescharacteristic
62C4⋊C8×C73—21no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65C4⋊C8×C73—21no—
66C4⋊C8×C73D412yes—
67C4⋊C8×C73D412yes—
68#103×C73—24no—
69#102×C73—24no—
70#102×C73—28no—
71C4×C8×C73—21no—
72C4×C8×C73—21no—
73C24×C73—41no—
74C2×Q8×C73—21no—
75C2×Q8×C73—21no—
76C2×Q8×C73—21no—
77C2×Q8×C73—22no—
78C2×Q8×C73—21no—
79C2×Q8×C73—21no—
80C2×Q8×C73—41no—
81C2×Q8×C73—41no—
82C2×Q8×C73—41no—
83C2×Q8×C73—41no—
84C2×Q8×C73—41no—
85C2×Q8×C73D812yes—
86C2×D4×C73—22no—
87C2×D4×C73—22no—
88C2×D4×C73—22no—
89C2×D4×C73—41no—
90C2×D4×C73—41no—
91C2×D4×C73—41no—
92C2×D4×C73—41no—
93C2×D4×C73—41no—
94C2×D4×C73—42no—
95C2×D4×C73—41no—
96C2×D4×C73—41no—
97C2×D4×C73—42no—
98C2×D4×C73—82no—
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101C22×C4×C73—41no—
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73#4111yescharacteristic
105Q16×C73—48no—
106SD16×C73—48no—
107C2×C8×C73—22no—
108C2×C8×C73—22no—
109C2×C8×C73—22no—
110C2×C8×C73—22no—
111C2×C8×C73—22no—
112C2×C8×C73—41no—
113C2×C8×C73—41no—
114C2×C8×C73—41no—
115C2×C8×C73—41no—
116C2×C8×C73—41no—
117C2×C8×C73—42no—
118C4⋊C4×C73—22no—
119C4⋊C4×C73—21no—
120C4⋊C4×C73—21no—
121C4⋊C4×C73—22no—
122C4⋊C4×C73—41no—
123C4⋊C4×C73—41no—
124C4⋊C4×C73—41no—
125C4⋊C4×C73—41no—
126C42×C73—41no—
127C42×C73—41no—
128C42×C73C2×D411yescharacteristic
129C42×C73C2×D411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C42×C73C2×D411yescharacteristic
132C23×C73—42no—
133C23×C73—82no—
134C23×C73—81no—
135C23×C73—81no—
136C23×C73—82no—
137C23×C73#12111yescharacteristic
138Q8×C73—22no—
139Q8×C73—22no—
140Q8×C73—41no—
141Q8×C73—41no—
142Q8×C73—42no—
143Q8×C73—42no—
144Q8×C73—81no—
145Q8×C73—81no—
146D4×C73—42no—
147D4×C73—42no—
148D4×C73—44no—
149D4×C73—82no—
150D4×C73—82no—
151D4×C73—81no—
152D4×C73—81no—
153D4×C73—81no—
154D4×C73—81no—
155C2×C4×C73—22no—
156C2×C4×C73—22no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—42no—
161C2×C4×C73—42no—
162C2×C4×C73—81no—
163C2×C4×C73—81no—
164C2×C4×C73#12011yescharacteristic
165C2×C4×C73#12011yescharacteristic
166C2×C4×C73#12011yescharacteristic
167C2×C4×C73#12111yescharacteristic
168C2×C4×C73#12111yescharacteristic
169C2×C4×C73#12711yescharacteristic
170C2×C4×C73C2×D811yescharacteristic
171C2×C4×C73#13511yescharacteristic
172C2×C4×C73#13512yes—
173C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C73#13712yes—
176C8×C73—42no—
177C8×C73—42no—
178C8×C73—42no—
179C8×C73—81no—
180C22×C73—82no—
181C22×C73—82no—
182C22×C73—82no—
183C22×C73—162no—
184C22×C73—162no—
185C22×C73#39211yescharacteristic
186C22×C73#46412yes—
187C22×C73#46611yescharacteristic
188C22×C73#46911yescharacteristic
189C22×C73#47112yes—
190C4×C73—21no—
191C4×C73—21no—
192C4×C73—42no—
193C4×C73—82no—
194C4×C73—81no—
195C4×C73#44711yescharacteristic
196C4×C73#44711yescharacteristic
197C4×C73#44911yescharacteristic
198C4×C73#44911yescharacteristic
199C4×C73#45212yes—
200C4×C73#49511yescharacteristic
201C4×C73#49711yescharacteristic
202#10263C7311yesmaximal, characteristic, direct product factor, Sylow
203C2×C73—162no—
204C2×C73#168212yes—
205C2×C73#170212yes—
206C2×C73#199911yescharacteristic
207C2×C73#201511yescharacteristic
208C2×C73#201911yescharacteristic
209C2×#486C2×C7311yescharacteristic
210C2×#462C2×C7311yescharacteristic, complemented
211C2×#460C2×C7311yescharacteristic
212#1984C2×C7311yescharacteristic, complemented
213C2×#332C2×C7311yescharacteristic, complemented
214C2×#331C2×C7311yescharacteristic
215#1277C2×C7311yescharacteristic, complemented
216C73#1026311yescharacteristic, direct product factor, Sylow
217C22×Q16—21no—
218C22×SD16—21no—
219C2×C4⋊Q8C22×C7311yescharacteristic
220C2×#127C22×C7311yescharacteristic
221C2×C4×Q8C22×C7311yescharacteristic
222#486—22no—
223#486—22no—
224#462—22no—
225#462—22no—
226#460—22no—
227#460—22no—
228C2×C4⋊C8C22×C7311yescharacteristic
229C2×C4⋊C8C22×C7311yescharacteristic
230C2×C4⋊C8C22×C7311yescharacteristic
231C2×#103—21no—
232C2×#102—22no—
233C2×#102—21no—
234C2×C4×C8C22×C7311yescharacteristic
235#336—22no—
236#332—22no—
237#331—22no—
238C22×Q8—21no—
239C22×Q8D4×C7311yescharacteristic
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C2×Q16—24no—
244C2×Q16—42no—
245C2×Q16—42no—
246C2×SD16—24no—
247C2×SD16—42no—
248C2×SD16—42no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8D4×C7312yes—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8D4×C7312yes—
257#127—21no—
258#127—21no—
259#127—21no—
260#127D4×C7312yes—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4D4×C7311yescharacteristic
269C2×C42—21no—
270C2×C42C23×C7311yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C7312yes—
276C4⋊C8D4×C7312yes—
277#103—24no—
278#102—24no—
279#102—28no—
280C4×C8—21no—
281C4×C8—21no—
282C24—41no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8D8×C7312yes—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—82no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4C2×D4×C7311yescharacteristic
312C22×C4C2×D4×C7311yescharacteristic
313C22×C4#41×C7311yescharacteristic
314Q16—48no—
315SD16—48no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—42no—
327C4⋊C4—22no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C42—41no—
336C42—41no—
337C42C2×D4×C7311yescharacteristic
338C42C2×D4×C7311yescharacteristic
339C42C2×D4×C7311yescharacteristic
340C42C2×D4×C7311yescharacteristic
341C23—42no—
342C23—82no—
343C23—81no—
344C23—81no—
345C23—82no—
346C23#121×C7311yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—42no—
353Q8—81no—
354Q8—81no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—82no—
359D4—82no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#120×C7311yescharacteristic
374C2×C4#120×C7311yescharacteristic
375C2×C4#120×C7311yescharacteristic
376C2×C4#121×C7311yescharacteristic
377C2×C4#121×C7311yescharacteristic
378C2×C4#127×C7311yescharacteristic
379C2×C4C2×D8×C7311yescharacteristic
380C2×C4#135×C7311yescharacteristic
381C2×C4#135×C7312yes—
382C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
383C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
384C2×C4#137×C7312yes—
385C8—42no—
386C8—42no—
387C8—42no—
388C8—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—162no—
393C22—162no—
394C22#392×C7311yescharacteristic
395C22#464×C7312yes—
396C22#466×C7311yescharacteristic
397C22#469×C7311yescharacteristic
398C22#471×C7312yes—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—82no—
403C4—81no—
404C4#447×C7311yescharacteristic
405C4#447×C7311yescharacteristic
406C4#449×C7311yescharacteristic
407C4#449×C7311yescharacteristic
408C4#452×C7312yes—
409C4#495×C7311yescharacteristic
410C4#497×C7311yescharacteristic
411C2—162no—
412C2C73×#168212yes—
413C2C73×#170212yes—
414C2C73×#199911yescharacteristic
415C2C73×#201511yescharacteristic
416C2C73×#201911yescharacteristic
subgroupG/H
center, socleC23×C73#121
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC2×#127×C73C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#462×C73C2semidirect
4. C73×#1984C2semidirect
5. C2×#332×C73C2semidirect
7. C73×#1277C2semidirect
202. #10263C73direct (N × H)
210. C2×#462C2×C73semidirect
212. #1984C2×C73semidirect
213. C2×#332C2×C73semidirect
215. #1277C2×C73semidirect
216. C73#10263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#486×C732
C2×#462×C732
C2×#460×C732
C73×#19842
C2×#332×C732
C2×#331×C732
C73×#12772
#1026373