Finite Group Databasebeta

← C73×#9057 #32918461

Subgroups — C73×#9057 #32918461

Order 18688.

690 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C73C211yesmaximal, characteristic
2C73×#2366C211yesmaximal, characteristic
3C73×#1988C211yesmaximal, characteristic, complemented
4C73×#1981C211yesmaximal, characteristic, complemented
5C2×#331×C73C211yesmaximal, characteristic
6C73×#1279C211yesmaximal, characteristic, complemented
7C73×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C73C2211yescharacteristic
9C2×#127×C73C2211yescharacteristic
10C2×C4×D4×C73—21no—
11C2×C4×D4×C73—21no—
12#486×C73—22no—
13#486×C73C414yescomplemented
14C2×C4⋊C8×C73C2211yescharacteristic
15C2×C4⋊C8×C73C2211yescharacteristic
16C2×#103×C73—21no—
17C2×#103×C73—21no—
18C2×#102×C73—22no—
19C2×C4×C8×C73C2211yescharacteristic
20#390×C73—21no—
21#390×C73—21no—
22#386×C73—22no—
23C4×C4⋊C4×C73C2211yescharacteristic
24C4×C4⋊C4×C73C2211yescharacteristic
25#340×C73—21no—
26#340×C73—21no—
27#331×C73—22no—
28C22×Q8×C73—21no—
29C22×D4×C73—21no—
30C22×D4×C73—21no—
31C22×D4×C73D412yes—
32C23×C4×C73—22no—
33C22×C8×C73—21no—
34C22×C8×C73—21no—
35C22×C8×C73—21no—
36C4⋊Q8×C73—21no—
37C4⋊Q8×C73—21no—
38C4⋊Q8×C73—21no—
39C4⋊Q8×C73C2×C412yescomplemented
40#127×C73—21no—
41#127×C73—21no—
42#127×C73C2×C412yes—
43#127×C73D412yes—
44C4×D4×C73—42no—
45C4×D4×C73—42no—
46C4×D4×C73—42no—
47C4×D4×C73—42no—
48C2×C4⋊C4×C73—21no—
49C2×C4⋊C4×C73—21no—
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C22⋊C4×C73—22no—
55C2×C22⋊C4×C73—22no—
56C2×C22⋊C4×C73—22no—
57C2×C42×C73—21no—
58C2×C42×C73—21no—
59C2×C42×C73C2311yescharacteristic
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73—21no—
64#103×C73—42no—
65#103×C73—42no—
66#102×C73—28no—
67C4×C8×C73—21no—
68C4×C8×C73C2×C412yescomplemented
69#95×C73—21no—
70#95×C73—21no—
71C24×C73—22no—
72C2×Q8×C73—22no—
73C2×Q8×C73—41no—
74C2×Q8×C73—41no—
75C2×Q8×C73—41no—
76C2×Q8×C73—41no—
77C2×Q8×C73—41no—
78C2×D4×C73—22no—
79C2×D4×C73—22no—
80C2×D4×C73—22no—
81C2×D4×C73—22no—
82C2×D4×C73—22no—
83C2×D4×C73—42no—
84C2×D4×C73—42no—
85C2×D4×C73—41no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
88C2×D4×C73—41no—
89C2×D4×C73—41no—
90C2×D4×C73—41no—
91C2×D4×C73—41no—
92C2×D4×C73—41no—
93C2×D4×C73C22⋊C414yes—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—44no—
99C22×C4×C73—44no—
100C22×C4×C73—41no—
101C22×C4×C73—82no—
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C2×C8×C73—22no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73—41no—
113C2×C8×C73—41no—
114C4⋊C4×C73—21no—
115C4⋊C4×C73—21no—
116C4⋊C4×C73—22no—
117C4⋊C4×C73—22no—
118C4⋊C4×C73—21no—
119C4⋊C4×C73—21no—
120C4⋊C4×C73—21no—
121C4⋊C4×C73—21no—
122C4⋊C4×C73—41no—
123C4⋊C4×C73—41no—
124C4⋊C4×C73D812yes—
125C4⋊C4×C73SD1612yes—
126C22⋊C4×C73—44no—
127C22⋊C4×C73—44no—
128C22⋊C4×C73—82no—
129C42×C73—41no—
130C42×C73—41no—
131C42×C73—41no—
132C42×C73—41no—
133C42×C73C22×C411yescharacteristic
134C42×C73C2×D411yescharacteristic
135C42×C73#4111yescharacteristic
136C42×C73#4111yescharacteristic
137C23×C73—24no—
138C23×C73—42no—
139C23×C73—42no—
140C23×C73—42no—
141C23×C73—42no—
142C23×C73—42no—
143C23×C73—42no—
144C23×C73#12011yescharacteristic
145Q8×C73—42no—
146Q8×C73—42no—
147Q8×C73—81no—
148Q8×C73—81no—
149D4×C73—44no—
150D4×C73—42no—
151D4×C73—42no—
152D4×C73—42no—
153D4×C73—42no—
154D4×C73—42no—
155D4×C73—42no—
156D4×C73—42no—
157D4×C73—42no—
158D4×C73—82no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—22no—
162C2×C4×C73—22no—
163C2×C4×C73—41no—
164C2×C4×C73—41no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—42no—
168C2×C4×C73—41no—
169C2×C4×C73—41no—
170C2×C4×C73—41no—
171C2×C4×C73—41no—
172C2×C4×C73—41no—
173C2×C4×C73—41no—
174C2×C4×C73—88no—
175C2×C4×C73—81no—
176C2×C4×C73—81no—
177C2×C4×C73C2×C22⋊C411yescharacteristic
178C2×C4×C73C4×D411yescharacteristic
179C2×C4×C73C4×D411yescharacteristic
180C2×C4×C73#12111yescharacteristic
181C2×C4×C73#12111yescharacteristic
182C2×C4×C73#12311yescharacteristic
183C2×C4×C73C2×D811yescharacteristic
184C2×C4×C73C2×SD1611yescharacteristic
185C2×C4×C73#13511yescharacteristic
186C2×C4×C73#13511yescharacteristic
187C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C73#13711yescharacteristic
191C8×C73—42no—
192C8×C73—81no—
193C8×C73—81no—
194C22×C73—44no—
195C22×C73—44no—
196C22×C73—44no—
197C22×C73—82no—
198C22×C73—82no—
199C22×C73—82no—
200C22×C73—82no—
201C22×C73#38611yescharacteristic
202C22×C73#44711yescharacteristic
203C22×C73#44911yescharacteristic
204C22×C73#45011yescharacteristic
205C22×C73#45211yescharacteristic
206C22×C73#45511yescharacteristic
207C22×C73#45511yescharacteristic
208C4×C73—21no—
209C4×C73—21no—
210C4×C73—42no—
211C4×C73—42no—
212C4×C73—82no—
213C4×C73—81no—
214C4×C73—81no—
215C4×C73C4×D811yescharacteristic
216C4×C73C4×SD1611yescharacteristic
217C4×C73#44011yescharacteristic
218C4×C73#44211yescharacteristic
219C4×C73#45911yescharacteristic
220C4×C73#46111yescharacteristic
221C4×C73#46311yescharacteristic
222C4×C73#46311yescharacteristic
223#9057C7311yesmaximal, characteristic, direct product factor, Sylow
224C2×C73—84no—
225C2×C73#163911yescharacteristic
226C2×C73#164011yescharacteristic
227C2×C73#164111yescharacteristic
228C2×C73#164211yescharacteristic
229C2×C73#187711yescharacteristic
230C2×C73#187911yescharacteristic
231C2×C73#188511yescharacteristic
232C2×#486C2×C7311yescharacteristic
233#2366C2×C7311yescharacteristic
234#1988C2×C7311yescharacteristic, complemented
235#1981C2×C7311yescharacteristic, complemented
236C2×#331C2×C7311yescharacteristic
237#1279C2×C7311yescharacteristic, complemented
238#1279C2×C7311yescharacteristic, complemented
239C73#905711yescharacteristic, direct product factor, Sylow
240C2×C4⋊Q8C22×C7311yescharacteristic
241C2×#127C22×C7311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244#486—22no—
245#486C4×C7314yescomplemented
246C2×C4⋊C8C22×C7311yescharacteristic
247C2×C4⋊C8C22×C7311yescharacteristic
248C2×#103—21no—
249C2×#103—21no—
250C2×#102—22no—
251C2×C4×C8C22×C7311yescharacteristic
252#390—21no—
253#390—21no—
254#386—22no—
255C4×C4⋊C4C22×C7311yescharacteristic
256C4×C4⋊C4C22×C7311yescharacteristic
257#340—21no—
258#340—21no—
259#331—22no—
260C22×Q8—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4D4×C7312yes—
264C23×C4—22no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8C2×C4×C7312yescomplemented
272#127—21no—
273#127—21no—
274#127C2×C4×C7312yes—
275#127D4×C7312yes—
276C4×D4—42no—
277C4×D4—42no—
278C4×D4—42no—
279C4×D4—42no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C7311yescharacteristic
283C2×C4⋊C4D4×C7311yescharacteristic
284C2×C4⋊C4D4×C7311yescharacteristic
285C2×C4⋊C4D4×C7311yescharacteristic
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42C23×C7311yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296#103—42no—
297#103—42no—
298#102—28no—
299C4×C8—21no—
300C4×C8C2×C4×C7312yescomplemented
301#95—21no—
302#95—21no—
303C24—22no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C22⋊C4×C7314yes—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—44no—
331C22×C4—44no—
332C22×C4—41no—
333C22×C4—82no—
334C22×C4C2×D4×C7311yescharacteristic
335C22×C4C2×D4×C7311yescharacteristic
336C22×C4C2×D4×C7311yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4D8×C7312yes—
357C4⋊C4SD16×C7312yes—
358C22⋊C4—44no—
359C22⋊C4—44no—
360C22⋊C4—82no—
361C42—41no—
362C42—41no—
363C42—41no—
364C42—41no—
365C42C22×C4×C7311yescharacteristic
366C42C2×D4×C7311yescharacteristic
367C42#41×C7311yescharacteristic
368C42#41×C7311yescharacteristic
369C23—24no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23#120×C7311yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—44no—
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—82no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—88no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4C2×C22⋊C4×C7311yescharacteristic
410C2×C4C4×D4×C7311yescharacteristic
411C2×C4C4×D4×C7311yescharacteristic
412C2×C4#121×C7311yescharacteristic
413C2×C4#121×C7311yescharacteristic
414C2×C4#123×C7311yescharacteristic
415C2×C4C2×D8×C7311yescharacteristic
416C2×C4C2×SD16×C7311yescharacteristic
417C2×C4#135×C7311yescharacteristic
418C2×C4#135×C7311yescharacteristic
419C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
420C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
421C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
422C2×C4#137×C7311yescharacteristic
423C8—42no—
424C8—81no—
425C8—81no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22#386×C7311yescharacteristic
434C22#447×C7311yescharacteristic
435C22#449×C7311yescharacteristic
436C22#450×C7311yescharacteristic
437C22#452×C7311yescharacteristic
438C22#455×C7311yescharacteristic
439C22#455×C7311yescharacteristic
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—82no—
445C4—81no—
446C4—81no—
447C4C4×D8×C7311yescharacteristic
448C4C4×SD16×C7311yescharacteristic
449C4#440×C7311yescharacteristic
450C4#442×C7311yescharacteristic
451C4#459×C7311yescharacteristic
452C4#461×C7311yescharacteristic
453C4#463×C7311yescharacteristic
454C4#463×C7311yescharacteristic
455C2—84no—
456C2C73×#163911yescharacteristic
457C2C73×#164011yescharacteristic
458C2C73×#164111yescharacteristic
459C2C73×#164211yescharacteristic
460C2C73×#187711yescharacteristic
461C2C73×#187911yescharacteristic
462C2C73×#188511yescharacteristic
subgroupG/H
center, socleC23×C73#120
commutatorC42C22×C4×C73
Frattini, cosocleC2×C42C23×C73
prime radicalC2×#127×C73C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#1988C2semidirect
4. C73×#1981C2semidirect
6. C73×#1279C2semidirect
7. C73×#1279C2semidirect
13. #486×C73C4semidirect
39. C4⋊Q8×C73C2×C4semidirect
68. C4×C8×C73C2×C4semidirect
223. #9057C73direct (N × H)
234. #1988C2×C73semidirect
235. #1981C2×C73semidirect
237. #1279C2×C73semidirect
238. #1279C2×C73semidirect
239. C73#9057direct (N × H)
245. #486C4×C73semidirect
271. C4⋊Q8C2×C4×C73semidirect
300. C4×C8C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C732
C73×#23662
C73×#19882
C73×#19812
C2×#331×C732
C73×#12792
#905773