Finite Group Databasebeta

← C73×#9681 #32919085

Subgroups — C73×#9681 #32919085

Order 18688.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2850C211yesmaximal, characteristic
2C4×C22⋊C8×C73C211yesmaximal, characteristic, complemented
3C2×#328×C73C212yesmaximal, complemented
4C2×#327×C73C212yesmaximal
5C73×#1434C211yesmaximal, characteristic, complemented
6C2×#124×C73C411yescharacteristic, complemented
7C2×C22⋊Q8×C73C2211yescharacteristic
8C2×#121×C73C2211yescharacteristic
9C22×C42×C73C2211yescharacteristic
10C2×C22⋊C8×C73C2212yes—
11C2×C4×C8×C73—21no—
12#391×C73C411yescharacteristic, complemented
13#390×C73C411yescharacteristic, complemented
14#388×C73—21no—
15#388×C73—21no—
16#386×C73—21no—
17#386×C73—21no—
18#382×C73C411yescharacteristic, complemented
19C2×#95×C73—21no—
20C2×#95×C73—21no—
21C2×#95×C73C2212yes—
22#336×C73—21no—
23#328×C73—24no—
24#327×C73—24no—
25C22×Q8×C73C2×C411yescharacteristic
26C22×D4×C73—21no—
27C22×D4×C73C2×C411yescharacteristic
28C23×C4×C73—22no—
29C23×C4×C73D411yescharacteristic
30C23×C4×C73D411yescharacteristic
31C23×C4×C73C2311yescharacteristic
32C22×C8×C73—22no—
33#124×C73—42no—
34C22⋊Q8×C73—22no—
35C22⋊Q8×C73—22no—
36#121×C73—22no—
37#121×C73—22no—
38C2×C4⋊C4×C73—21no—
39C2×C4⋊C4×C73C2×C411yescharacteristic
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C22⋊C4×C73—21no—
42C2×C22⋊C4×C73—21no—
43C2×C22⋊C4×C73—21no—
44C2×C22⋊C4×C73—21no—
45C2×C22⋊C4×C73—21no—
46C2×C22⋊C4×C73—21no—
47C2×C42×C73—42no—
48C2×C42×C73C2×C411yescharacteristic
49C2×C42×C73C2×C411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73D411yescharacteristic
52C22⋊C8×C73—22no—
53C22⋊C8×C73D414yes—
54C4×C8×C73—42no—
55#95×C73—24no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—22no—
61#95×C73—22no—
62#95×C73—42no—
63C24×C73—21no—
64C24×C73C2×D411yescharacteristic
65C2×Q8×C73—22no—
66C2×Q8×C73—41no—
67C2×Q8×C73—41no—
68C2×D4×C73—22no—
69C2×D4×C73—41no—
70C2×D4×C73—41no—
71C2×D4×C73—41no—
72C2×D4×C73—41no—
73C2×D4×C73—42no—
74C2×D4×C73—42no—
75C22×C4×C73—22no—
76C22×C4×C73—22no—
77C22×C4×C73—22no—
78C22×C4×C73—22no—
79C22×C4×C73—24no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73—41no—
87C22×C4×C73—42no—
88C22×C4×C73—42no—
89C22×C4×C73—42no—
90C22×C4×C73—42no—
91C22×C4×C73—42no—
92C22×C4×C73—42no—
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22×C411yescharacteristic
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D412yes—
100C22×C4×C73#4112yes—
101C2×C8×C73—24no—
102C2×C8×C73—42no—
103C2×C8×C73—42no—
104C4⋊C4×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—42no—
107C22⋊C4×C73—42no—
108C22⋊C4×C73—42no—
109C22⋊C4×C73—41no—
110C22⋊C4×C73—41no—
111C22⋊C4×C73—42no—
112C22⋊C4×C73—42no—
113C22⋊C4×C73—42no—
114C42×C73—22no—
115C42×C73—22no—
116C42×C73—41no—
117C42×C73—41no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—41no—
123C23×C73—41no—
124C23×C73—41no—
125C23×C73—41no—
126C23×C73—41no—
127C23×C73—41no—
128C23×C73—41no—
129C23×C73C2×C22⋊C411yescharacteristic
130C23×C73#12411yescharacteristic
131C23×C73#12711yescharacteristic
132C23×C73#13512yes—
133C23×C73#13512yes—
134Q8×C73—82no—
135D4×C73—82no—
136D4×C73—82no—
137D4×C73—82no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—42no—
153C2×C4×C73—42no—
154C2×C4×C73—44no—
155C2×C4×C73—44no—
156C2×C4×C73—44no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73—41no—
160C2×C4×C73—41no—
161C2×C4×C73—41no—
162C2×C4×C73—41no—
163C2×C4×C73—41no—
164C2×C4×C73—41no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—41no—
168C2×C4×C73—82no—
169C2×C4×C73—82no—
170C2×C4×C73—82no—
171C2×C4×C73—82no—
172C2×C4×C73#9912yes—
173C2×C4×C73#10412yes—
174C2×C4×C73C4×D412yes—
175C2×C4×C73#12112yes—
176C8×C73—44no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—81no—
186C22×C73—81no—
187C22×C73—81no—
188C22×C73—81no—
189C22×C73—81no—
190C22×C73—81no—
191C22×C73—81no—
192C22×C73#39011yescharacteristic
193C22×C73C2×#9911yescharacteristic
194C22×C73#41011yescharacteristic
195C22×C73#41611yescharacteristic
196C22×C73#41611yescharacteristic
197C22×C73C2×#10411yescharacteristic
198C22×C73#42111yescharacteristic
199C22×C73#48812yes—
200C22×C73#49512yes—
201C4×C73—22no—
202C4×C73—22no—
203C4×C73—22no—
204C4×C73—22no—
205C4×C73—41no—
206C4×C73—41no—
207C4×C73—84no—
208C4×C73—81no—
209C4×C73—81no—
210C4×C73—81no—
211#9681C7311yesmaximal, characteristic, direct product factor, Sylow
212C2×C73—22no—
213C2×C73—22no—
214C2×C73—161no—
215C2×C73#150011yescharacteristic
216C2×C73#150111yescharacteristic
217C2×C73#151611yescharacteristic
218C2×C73#152111yescharacteristic
219C2×C73#195811yescharacteristic
220C2×C73#196411yescharacteristic
221C2×C73#198011yescharacteristic
222#2850C2×C7311yescharacteristic
223C4×C22⋊C8C2×C7311yescharacteristic, complemented
224C2×#328C2×C7312yescomplemented
225C2×#327C2×C7312yes—
226#1434C2×C7311yescharacteristic, complemented
227C73#968111yescharacteristic, direct product factor, Sylow
228C2×#124C4×C7311yescharacteristic, complemented
229C2×C22⋊Q8C22×C7311yescharacteristic
230C2×#121C22×C7311yescharacteristic
231C22×C42C22×C7311yescharacteristic
232C2×C22⋊C8C22×C7312yes—
233C2×C4×C8—21no—
234#391C4×C7311yescharacteristic, complemented
235#390C4×C7311yescharacteristic, complemented
236#388—21no—
237#388—21no—
238#386—21no—
239#386—21no—
240#382C4×C7311yescharacteristic, complemented
241C2×#95—21no—
242C2×#95—21no—
243C2×#95C22×C7312yes—
244#336—21no—
245#328—24no—
246#327—24no—
247C22×Q8C2×C4×C7311yescharacteristic
248C22×D4—21no—
249C22×D4C2×C4×C7311yescharacteristic
250C23×C4—22no—
251C23×C4D4×C7311yescharacteristic
252C23×C4D4×C7311yescharacteristic
253C23×C4C23×C7311yescharacteristic
254C22×C8—22no—
255#124—42no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258#121—22no—
259#121—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C2×C4×C7311yescharacteristic
262C2×C4⋊C4C2×C4×C7311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C42—42no—
270C2×C42C2×C4×C7311yescharacteristic
271C2×C42C2×C4×C7311yescharacteristic
272C2×C42D4×C7311yescharacteristic
273C2×C42D4×C7311yescharacteristic
274C22⋊C8—22no—
275C22⋊C8D4×C7314yes—
276C4×C8—42no—
277#95—24no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—22no—
283#95—22no—
284#95—42no—
285C24—21no—
286C24C2×D4×C7311yescharacteristic
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4C22⋊C4×C7311yescharacteristic
316C22×C4C22⋊C4×C7311yescharacteristic
317C22×C4C22⋊C4×C7311yescharacteristic
318C22×C4C22⋊C4×C7311yescharacteristic
319C22×C4C22×C4×C7311yescharacteristic
320C22×C4C2×D4×C7311yescharacteristic
321C22×C4C2×D4×C7312yes—
322C22×C4#41×C7312yes—
323C2×C8—24no—
324C2×C8—42no—
325C2×C8—42no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C42—22no—
337C42—22no—
338C42—41no—
339C42—41no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23C2×C22⋊C4×C7311yescharacteristic
352C23#124×C7311yescharacteristic
353C23#127×C7311yescharacteristic
354C23#135×C7312yes—
355C23#135×C7312yes—
356Q8—82no—
357D4—82no—
358D4—82no—
359D4—82no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4#99×C7312yes—
395C2×C4#104×C7312yes—
396C2×C4C4×D4×C7312yes—
397C2×C4#121×C7312yes—
398C8—44no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22#390×C7311yescharacteristic
415C22C2×#99×C7311yescharacteristic
416C22#410×C7311yescharacteristic
417C22#416×C7311yescharacteristic
418C22#416×C7311yescharacteristic
419C22C2×#104×C7311yescharacteristic
420C22#421×C7311yescharacteristic
421C22#488×C7312yes—
422C22#495×C7312yes—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—84no—
430C4—81no—
431C4—81no—
432C4—81no—
433C2—22no—
434C2—22no—
435C2—161no—
436C2C73×#150011yescharacteristic
437C2C73×#150111yescharacteristic
438C2C73×#151611yescharacteristic
439C2C73×#152111yescharacteristic
440C2C73×#195811yescharacteristic
441C2C73×#196411yescharacteristic
442C2C73×#198011yescharacteristic
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. C4×C22⋊C8×C73C2semidirect
3. C2×#328×C73C2semidirect
5. C73×#1434C2semidirect
6. C2×#124×C73C4semidirect
12. #391×C73C4semidirect
13. #390×C73C4semidirect
18. #382×C73C4semidirect
211. #9681C73direct (N × H)
223. C4×C22⋊C8C2×C73semidirect
224. C2×#328C2×C73semidirect
226. #1434C2×C73semidirect
227. C73#9681direct (N × H)
228. C2×#124C4×C73semidirect
234. #391C4×C73semidirect
235. #390C4×C73semidirect
240. #382C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28502
C4×C22⋊C8×C732
C2×#328×C732
C2×#327×C732
C73×#14342
#968173