Finite Group Databasebeta

← C73×#9520 #32918924

Subgroups — C73×#9520 #32918924

Order 18688.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3003C211yesmaximal, characteristic
2C73×#2976C211yesmaximal, characteristic, complemented
3C73×#1786C211yesmaximal, characteristic, complemented
4C73×#1783C211yesmaximal, characteristic, complemented
5C73×#1513C211yesmaximal, characteristic, complemented
6C73×#1305C211yesmaximal, characteristic, complemented
7C73×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C73C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C73—21no—
10#525×C73C2211yescharacteristic
11#450×C73—21no—
12#450×C73C412yescomplemented
13#447×C73—21no—
14#447×C73C412yescomplemented
15#436×C73—21no—
16#435×C73—21no—
17#435×C73—21no—
18C8×D4×C73—21no—
19#433×C73—21no—
20#418×C73—21no—
21C2×#102×C73—21no—
22C2×#102×C73—21no—
23C2×#100×C73—21no—
24C2×#100×C73—21no—
25#408×C73—21no—
26#407×C73C2211yescharacteristic
27#407×C73C2211yescharacteristic
28#407×C73C2211yescharacteristic
29C2×C22⋊C8×C73C2211yescharacteristic
30#380×C73C2211yescharacteristic
31#328×C73—21no—
32#327×C73—21no—
33C25×C73—21no—
34C2×#41×C73D411yescharacteristic
35C22×D4×C73—21no—
36C22×D4×C73—21no—
37C22×D4×C73—21no—
38C22×D4×C73—21no—
39C22×D4×C73—21no—
40C22×D4×C73—42no—
41C22×D4×C73—42no—
42C22×D4×C73C2×C412yes—
43C23×C4×C73C2311yescharacteristic
44AGL(1,ℤ/8)×C73—42no—
45AGL(1,ℤ/8)×C73—42no—
46C2×SD16×C73—22no—
47C2×D8×C73—22no—
48C2×M16×C73—21no—
49C2×M16×C73—21no—
50C2×M16×C73—21no—
51C2×M16×C73D411yescharacteristic
52C2×M16×C73D411yescharacteristic
53C22×C8×C73—21no—
54C22×C8×C73D411yescharacteristic
55C22×C8×C73D411yescharacteristic
56#123×C73—21no—
57C22⋊Q8×C73C2×C411yescharacteristic
58C22⋊Q8×C73D411yescharacteristic
59#121×C73C2×C411yescharacteristic
60#121×C73D411yescharacteristic
61#120×C73—21no—
62C4×D4×C73—21no—
63C4×D4×C73—21no—
64#117×C73D411yescharacteristic
65C2×C4⋊C4×C73—21no—
66C2×C22⋊C4×C73—21no—
67C4⋊C8×C73—21no—
68C4⋊C8×C73—21no—
69#102×C73—22no—
70#102×C73—22no—
71#102×C73—42no—
72#102×C73—42no—
73#100×C73—42no—
74#100×C73—42no—
75C22⋊C8×C73—21no—
76C22⋊C8×C73—21no—
77C22⋊C8×C73—21no—
78C22⋊C8×C73—21no—
79C22⋊C8×C73—21no—
80C22⋊C8×C73—21no—
81C22⋊C8×C73—21no—
82C22⋊C8×C73—21no—
83C22⋊C8×C73—21no—
84C22⋊C8×C73C2×C412yes—
85#97×C73—21no—
86C4×C8×C73—21no—
87#95×C73—21no—
88C24×C73—22no—
89C24×C73—44no—
90C24×C73—41no—
91C24×C73—41no—
92C24×C73—81no—
93C24×C73—81no—
94C24×C73—82no—
95C24×C73#4111yescharacteristic
96#41×C73—41no—
97#41×C73—41no—
98C2×Q8×C73C22⋊C411yescharacteristic
99C2×D4×C73—22no—
100C2×D4×C73—22no—
101C2×D4×C73—22no—
102C2×D4×C73—22no—
103C2×D4×C73—22no—
104C2×D4×C73—22no—
105C2×D4×C73—21no—
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73—22no—
109C2×D4×C73—22no—
110C2×D4×C73—41no—
111C2×D4×C73—41no—
112C2×D4×C73—41no—
113C2×D4×C73—41no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C2×D4×C73—44no—
117C2×D4×C73—44no—
118C2×D4×C73—44no—
119C2×D4×C73—41no—
120C2×D4×C73—41no—
121C2×D4×C73C22⋊C411yescharacteristic
122C22×C4×C73—21no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73—41no—
126C22×C4×C73C22×C411yescharacteristic
127C22×C4×C73C2×D411yescharacteristic
128C22×C4×C73C2×D411yescharacteristic
129C22×C4×C73C2×D411yescharacteristic
130C22×C4×C73C2×D411yescharacteristic
131C22×C4×C73#4111yescharacteristic
132SD16×C73—44no—
133D8×C73—44no—
134M16×C73—41no—
135M16×C73—41no—
136M16×C73—41no—
137M16×C73—41no—
138M16×C73—41no—
139M16×C73—41no—
140M16×C73—81no—
141C2×C8×C73—22no—
142C2×C8×C73—21no—
143C2×C8×C73—21no—
144C2×C8×C73—21no—
145C2×C8×C73—21no—
146C2×C8×C73—41no—
147C2×C8×C73—41no—
148C2×C8×C73—41no—
149C2×C8×C73—81no—
150C4⋊C4×C73—21no—
151C4⋊C4×C73—21no—
152C4⋊C4×C73—41no—
153C4⋊C4×C73—41no—
154C4⋊C4×C73C22⋊C411yescharacteristic
155C4⋊C4×C73C22⋊C411yescharacteristic
156C22⋊C4×C73—21no—
157C22⋊C4×C73—21no—
158C22⋊C4×C73—21no—
159C22⋊C4×C73—21no—
160C22⋊C4×C73—21no—
161C22⋊C4×C73—81no—
162C42×C73—21no—
163C23×C73—21no—
164C23×C73—21no—
165C23×C73—24no—
166C23×C73—21no—
167C23×C73—41no—
168C23×C73—41no—
169C23×C73—42no—
170C23×C73—42no—
171C23×C73—42no—
172C23×C73—42no—
173C23×C73—42no—
174C23×C73—42no—
175C23×C73—82no—
176C23×C73—82no—
177C23×C73—82no—
178C23×C73—81no—
179C23×C73—81no—
180C23×C73—82no—
181C23×C73—88no—
182C23×C73—88no—
183C23×C73—81no—
184C23×C73—81no—
185C23×C73C4×D411yescharacteristic
186C23×C73#12111yescharacteristic
187C23×C73#12311yescharacteristic
188Q8×C73—41no—
189D4×C73—24no—
190D4×C73—24no—
191D4×C73—41no—
192D4×C73—42no—
193D4×C73—42no—
194D4×C73—42no—
195D4×C73—42no—
196D4×C73—41no—
197D4×C73—41no—
198D4×C73—42no—
199D4×C73—42no—
200D4×C73—81no—
201D4×C73—81no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—81no—
217C2×C4×C73—81no—
218C2×C4×C73—81no—
219C2×C4×C73C2×C22⋊C411yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73#12011yescharacteristic
222C2×C4×C73#12111yescharacteristic
223C8×C73—42no—
224C8×C73—41no—
225C8×C73—41no—
226C8×C73—41no—
227C8×C73—41no—
228C8×C73—81no—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—21no—
232C22×C73—21no—
233C22×C73—21no—
234C22×C73—21no—
235C22×C73—21no—
236C22×C73—21no—
237C22×C73—42no—
238C22×C73—42no—
239C22×C73—41no—
240C22×C73—44no—
241C22×C73—41no—
242C22×C73—41no—
243C22×C73—82no—
244C22×C73—82no—
245C22×C73—82no—
246C22×C73—82no—
247C22×C73—84no—
248C22×C73—84no—
249C22×C73—84no—
250C22×C73—84no—
251C22×C73—82no—
252C22×C73—82no—
253C22×C73#38611yescharacteristic
254C22×C73#47111yescharacteristic
255C22×C73#47211yescharacteristic
256C4×C73—21no—
257C4×C73—21no—
258C4×C73—21no—
259C4×C73—41no—
260C4×C73—41no—
261C4×C73—41no—
262C4×C73—161no—
263C4×C73B(4,𝔽2)11yescharacteristic
264C4×C73B(4,𝔽2)11yescharacteristic
265#9520C7311yesmaximal, characteristic, direct product factor, Sylow
266C2×C73—21no—
267C2×C73—21no—
268C2×C73—41no—
269C2×C73—41no—
270C2×C73—81no—
271C2×C73—84no—
272C2×C73#188911yescharacteristic
273C2×C73#190311yescharacteristic
274C2×C73#190711yescharacteristic
275#3003C2×C7311yescharacteristic
276#2976C2×C7311yescharacteristic, complemented
277#1786C2×C7311yescharacteristic, complemented
278#1783C2×C7311yescharacteristic, complemented
279#1513C2×C7311yescharacteristic, complemented
280#1305C2×C7311yescharacteristic, complemented
281#1293C2×C7311yescharacteristic, complemented
282C73#952011yescharacteristic, direct product factor, Sylow
283C23×D4C22×C7311yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C7311yescharacteristic
286#450—21no—
287#450C4×C7312yescomplemented
288#447—21no—
289#447C4×C7312yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C7311yescharacteristic
302#407C22×C7311yescharacteristic
303#407C22×C7311yescharacteristic
304C2×C22⋊C8C22×C7311yescharacteristic
305#380C22×C7311yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C7311yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C7312yes—
318C23×C4C23×C7311yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C7311yescharacteristic
327C2×M16D4×C7311yescharacteristic
328C22×C8—21no—
329C22×C8D4×C7311yescharacteristic
330C22×C8D4×C7311yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C7311yescharacteristic
333C22⋊Q8D4×C7311yescharacteristic
334#121C2×C4×C7311yescharacteristic
335#121D4×C7311yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C7311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C7312yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C7311yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C7311yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C7311yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C7311yescharacteristic
402C22×C4C2×D4×C7311yescharacteristic
403C22×C4C2×D4×C7311yescharacteristic
404C22×C4C2×D4×C7311yescharacteristic
405C22×C4C2×D4×C7311yescharacteristic
406C22×C4#41×C7311yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C7311yescharacteristic
430C4⋊C4C22⋊C4×C7311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C7311yescharacteristic
461C23#121×C7311yescharacteristic
462C23#123×C7311yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C7311yescharacteristic
495C2×C4C4×D4×C7311yescharacteristic
496C2×C4#120×C7311yescharacteristic
497C2×C4#121×C7311yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C7311yescharacteristic
529C22#471×C7311yescharacteristic
530C22#472×C7311yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C7311yescharacteristic
539C4B(4,𝔽2)×C7311yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C73×#188911yescharacteristic
547C2C73×#190311yescharacteristic
548C2C73×#190711yescharacteristic
subgroupG/H
center, socleC22×C73#386
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC73×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2976C2semidirect
3. C73×#1786C2semidirect
4. C73×#1783C2semidirect
5. C73×#1513C2semidirect
6. C73×#1305C2semidirect
7. C73×#1293C2semidirect
12. #450×C73C4semidirect
14. #447×C73C4semidirect
265. #9520C73direct (N × H)
276. #2976C2×C73semidirect
277. #1786C2×C73semidirect
278. #1783C2×C73semidirect
279. #1513C2×C73semidirect
280. #1305C2×C73semidirect
281. #1293C2×C73semidirect
282. C73#9520direct (N × H)
287. #450C4×C73semidirect
289. #447C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30032
C73×#29762
C73×#17862
C73×#17832
C73×#15132
C73×#13052
C73×#12932
#952073