Finite Group Databasebeta

← C73×#33835 #32943239

Subgroups — C73×#33835 #32943239

Order 18688.

670 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C73C211yesmaximal, characteristic, complemented
2C2×#508×C73C211yesmaximal, characteristic, complemented
3C73×#3285C211yesmaximal, characteristic, complemented
4C73×#3283C211yesmaximal, characteristic, complemented
5C73×#2251C211yesmaximal, characteristic, complemented
6C73×#2220C211yesmaximal, characteristic, complemented
7C73×#2216C211yesmaximal, characteristic, complemented
8C73×#2210C211yesmaximal, characteristic, complemented
9C73×#2209C211yesmaximal, characteristic, complemented
10C73×#2189C211yesmaximal, characteristic, complemented
11C73×#2189C211yesmaximal, characteristic, complemented
12C73×#2188C211yesmaximal, characteristic, complemented
13C73×#2186C211yesmaximal, characteristic, complemented
14C73×#2175C211yesmaximal, characteristic, complemented
15C73×#2168C211yesmaximal, characteristic, complemented
16C2×#135×C73C2211yescharacteristic
17C2×#135×C73C2211yescharacteristic
18C2×#135×C73C2211yescharacteristic
19C22×Q16×C73C2211yescharacteristic
20#548×C73—21no—
21#547×C73—21no—
22#510×C73—24no—
23#508×C73—24no—
24C2×Q32×C73C2211yescharacteristic
25C2×Q32×C73C2211yescharacteristic
26C2×Q32×C73C2211yescharacteristic
27C2×Q32×C73C2211yescharacteristic
28C2×SD32×C73C2211yescharacteristic
29C2×SD32×C73C2211yescharacteristic
30C2×SD32×C73C2211yescharacteristic
31C2×SD32×C73C2211yescharacteristic
32C2×D16×C73C2211yescharacteristic
33C2×M32×C73C2211yescharacteristic
34C22×C16×C73C2211yescharacteristic
35#495×C73C2211yescharacteristic
36#494×C73C2211yescharacteristic
37#467×C73C2211yescharacteristic
38#467×C73C2211yescharacteristic
39#467×C73C2211yescharacteristic
40#466×C73C2211yescharacteristic
41#464×C73—21no—
42#461×C73—21no—
43#452×C73—21no—
44#452×C73—21no—
45#452×C73—21no—
46#448×C73—21no—
47C4×Q16×C73C2211yescharacteristic
48C4×D8×C73C2211yescharacteristic
49C8×D4×C73C2211yescharacteristic
50#366×C73C2211yescharacteristic
51C4⋊C16×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#358×C73C2211yescharacteristic
54#358×C73C2211yescharacteristic
55#358×C73C2211yescharacteristic
56#357×C73C2211yescharacteristic
57#357×C73C2211yescharacteristic
58C22⋊C16×C73C2211yescharacteristic
59C22⋊C16×C73C2211yescharacteristic
60#346×C73C2211yescharacteristic
61C2×#41×C73—21no—
62C2×#41×C73—21no—
63C2×#41×C73—21no—
64C22×Q8×C73—21no—
65#135×C73—22no—
66#135×C73—22no—
67#135×C73—22no—
68#135×C73—41no—
69#135×C73—41no—
70#135×C73—41no—
71C2×Q16×C73—22no—
72C2×Q16×C73—21no—
73C2×Q16×C73—21no—
74C2×Q16×C73—41no—
75C2×Q16×C73C2311yescharacteristic
76C2×Q16×C73C2311yescharacteristic
77C2×Q16×C73C2311yescharacteristic
78C2×Q16×C73C2311yescharacteristic
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×SD16×C73—21no—
82C2×SD16×C73—21no—
83C2×D8×C73C2311yescharacteristic
84C2×D8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C4⋊Q8×C73—21no—
88#124×C73—21no—
89#124×C73—41no—
90#123×C73—41no—
91#123×C73—41no—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73—21no—
94C22⋊Q8×C73—21no—
95C22⋊Q8×C73—41no—
96#121×C73—21no—
97#121×C73—41no—
98#121×C73—41no—
99C4×Q8×C73—21no—
100C4×D4×C73—21no—
101C4×D4×C73—41no—
102C4×D4×C73D411yescharacteristic
103C2×C4⋊C4×C73—41no—
104Q32×C73—22no—
105Q32×C73—22no—
106Q32×C73—22no—
107Q32×C73—41no—
108SD32×C73—22no—
109SD32×C73—22no—
110SD32×C73—41no—
111SD32×C73D414yescomplemented
112D16×C73—22no—
113M32×C73—22no—
114C2×C16×C73—22no—
115C2×C16×C73C2311yescharacteristic
116C2×C16×C73C2311yescharacteristic
117C2×C16×C73C2311yescharacteristic
118C2×C16×C73C2311yescharacteristic
119#107×C73C2311yescharacteristic
120#107×C73C2311yescharacteristic
121C4⋊C8×C73D411yescharacteristic
122#103×C73—21no—
123#103×C73—21no—
124#103×C73—21no—
125#103×C73—21no—
126#102×C73—21no—
127#102×C73—21no—
128C22⋊C8×C73D411yescharacteristic
129C22⋊C8×C73D411yescharacteristic
130C4×C8×C73C2311yescharacteristic
131#41×C73—42no—
132#41×C73—42no—
133#41×C73—42no—
134#41×C73—81no—
135#41×C73—81no—
136#41×C73—81no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—42no—
142C2×Q8×C73—41no—
143C2×Q8×C73—81no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—41no—
147C2×D4×C73—41no—
148C2×D4×C73—41no—
149C2×D4×C73—41no—
150C2×D4×C73D811yescharacteristic
151C22×C4×C73—41no—
152C22×C4×C73—41no—
153C22×C4×C73—41no—
154C22×C4×C73—41no—
155C22×C4×C73—41no—
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158Q16×C73—21no—
159Q16×C73—21no—
160Q16×C73—21no—
161Q16×C73—21no—
162Q16×C73—21no—
163Q16×C73—21no—
164Q16×C73—21no—
165Q16×C73—42no—
166Q16×C73—81no—
167Q16×C73C2×D412yes—
168SD16×C73—42no—
169SD16×C73—42no—
170SD16×C73—42no—
171SD16×C73—81no—
172D8×C73—21no—
173D8×C73—21no—
174D8×C73—21no—
175D8×C73C2×D412yes—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73C2×D411yescharacteristic
181C2×C8×C73C2×D411yescharacteristic
182C2×C8×C73C2×D411yescharacteristic
183C2×C8×C73C2411yescharacteristic
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—41no—
187C4⋊C4×C73—41no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73—41no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73D811yescharacteristic
193C22⋊C4×C73—41no—
194C22⋊C4×C73—41no—
195C22⋊C4×C73—41no—
196C22⋊C4×C73—41no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C22⋊C4×C73D811yescharacteristic
201C22⋊C4×C73D811yescharacteristic
202C42×C73—41no—
203C42×C73C2×D411yescharacteristic
204C16×C73—21no—
205C16×C73—21no—
206C16×C73—21no—
207C16×C73C2×D412yes—
208C23×C73—41no—
209C23×C73—41no—
210C23×C73C2×D811yescharacteristic
211C23×C73C2×D811yescharacteristic
212Q8×C73—22no—
213Q8×C73—41no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—41no—
217Q8×C73—41no—
218Q8×C73—41no—
219Q8×C73—41no—
220Q8×C73—82no—
221D4×C73—22no—
222D4×C73—41no—
223D4×C73—41no—
224D4×C73—41no—
225D4×C73—41no—
226D4×C73—82no—
227D4×C73—82no—
228D4×C73—82no—
229D4×C73—82no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—82no—
241C2×C4×C73—82no—
242C2×C4×C73—82no—
243C2×C4×C73—82no—
244C2×C4×C73—82no—
245C2×C4×C73C2×D811yescharacteristic
246C2×C4×C73C2×D811yescharacteristic
247C2×C4×C73C2×D811yescharacteristic
248C2×C4×C73C2×D811yescharacteristic
249C2×C4×C73C22×D411yescharacteristic
250C8×C73—21no—
251C8×C73—21no—
252C8×C73—21no—
253C8×C73C22×D411yescharacteristic
254C8×C73H(5,𝔽2)11yescharacteristic
255C22×C73—21no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—42no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73—81no—
265C22×C73—81no—
266C22×C73—81no—
267C22×C73C22×D811yescharacteristic
268C4×C73—21no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—42no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73D4211yescharacteristic
279C4×C73#57611yescharacteristic
280#33835C7311yesmaximal, characteristic, direct product factor, Sylow
281C2×C73—41no—
282C2×C73—41no—
283C2×C73—82no—
284C2×C73—161no—
285C2×C73D4×D811yescharacteristic
286C2×C73#341411yescharacteristic
287C2×C73#341711yescharacteristic
288C2×#510C2×C7311yescharacteristic, complemented
289C2×#508C2×C7311yescharacteristic, complemented
290#3285C2×C7311yescharacteristic, complemented
291#3283C2×C7311yescharacteristic, complemented
292#2251C2×C7311yescharacteristic, complemented
293#2220C2×C7311yescharacteristic, complemented
294#2216C2×C7311yescharacteristic, complemented
295#2210C2×C7311yescharacteristic, complemented
296#2209C2×C7311yescharacteristic, complemented
297#2189C2×C7311yescharacteristic, complemented
298#2189C2×C7311yescharacteristic, complemented
299#2188C2×C7311yescharacteristic, complemented
300#2186C2×C7311yescharacteristic, complemented
301#2175C2×C7311yescharacteristic, complemented
302#2168C2×C7311yescharacteristic, complemented
303C73#3383511yescharacteristic, direct product factor, Sylow
304C2×#135C22×C7311yescharacteristic
305C2×#135C22×C7311yescharacteristic
306C2×#135C22×C7311yescharacteristic
307C22×Q16C22×C7311yescharacteristic
308#548—21no—
309#547—21no—
310#510—24no—
311#508—24no—
312C2×Q32C22×C7311yescharacteristic
313C2×Q32C22×C7311yescharacteristic
314C2×Q32C22×C7311yescharacteristic
315C2×Q32C22×C7311yescharacteristic
316C2×SD32C22×C7311yescharacteristic
317C2×SD32C22×C7311yescharacteristic
318C2×SD32C22×C7311yescharacteristic
319C2×SD32C22×C7311yescharacteristic
320C2×D16C22×C7311yescharacteristic
321C2×M32C22×C7311yescharacteristic
322C22×C16C22×C7311yescharacteristic
323#495C22×C7311yescharacteristic
324#494C22×C7311yescharacteristic
325#467C22×C7311yescharacteristic
326#467C22×C7311yescharacteristic
327#467C22×C7311yescharacteristic
328#466C22×C7311yescharacteristic
329#464—21no—
330#461—21no—
331#452—21no—
332#452—21no—
333#452—21no—
334#448—21no—
335C4×Q16C22×C7311yescharacteristic
336C4×D8C22×C7311yescharacteristic
337C8×D4C22×C7311yescharacteristic
338#366C22×C7311yescharacteristic
339C4⋊C16C22×C7311yescharacteristic
340#358C22×C7311yescharacteristic
341#358C22×C7311yescharacteristic
342#358C22×C7311yescharacteristic
343#358C22×C7311yescharacteristic
344#357C22×C7311yescharacteristic
345#357C22×C7311yescharacteristic
346C22⋊C16C22×C7311yescharacteristic
347C22⋊C16C22×C7311yescharacteristic
348#346C22×C7311yescharacteristic
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C22×Q8—21no—
353#135—22no—
354#135—22no—
355#135—22no—
356#135—41no—
357#135—41no—
358#135—41no—
359C2×Q16—22no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—41no—
363C2×Q16C23×C7311yescharacteristic
364C2×Q16C23×C7311yescharacteristic
365C2×Q16C23×C7311yescharacteristic
366C2×Q16C23×C7311yescharacteristic
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8C23×C7311yescharacteristic
372C2×D8C23×C7311yescharacteristic
373C22×C8C23×C7311yescharacteristic
374C22×C8C23×C7311yescharacteristic
375C4⋊Q8—21no—
376#124—21no—
377#124—41no—
378#123—41no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384#121—21no—
385#121—41no—
386#121—41no—
387C4×Q8—21no—
388C4×D4—21no—
389C4×D4—41no—
390C4×D4D4×C7311yescharacteristic
391C2×C4⋊C4—41no—
392Q32—22no—
393Q32—22no—
394Q32—22no—
395Q32—41no—
396SD32—22no—
397SD32—22no—
398SD32—41no—
399SD32D4×C7314yescomplemented
400D16—22no—
401M32—22no—
402C2×C16—22no—
403C2×C16C23×C7311yescharacteristic
404C2×C16C23×C7311yescharacteristic
405C2×C16C23×C7311yescharacteristic
406C2×C16C23×C7311yescharacteristic
407#107C23×C7311yescharacteristic
408#107C23×C7311yescharacteristic
409C4⋊C8D4×C7311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416C22⋊C8D4×C7311yescharacteristic
417C22⋊C8D4×C7311yescharacteristic
418C4×C8C23×C7311yescharacteristic
419#41—42no—
420#41—42no—
421#41—42no—
422#41—81no—
423#41—81no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—42no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4D8×C7311yescharacteristic
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4C2×D4×C7311yescharacteristic
445C22×C4C2×D4×C7311yescharacteristic
446Q16—21no—
447Q16—21no—
448Q16—21no—
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—21no—
453Q16—42no—
454Q16—81no—
455Q16C2×D4×C7312yes—
456SD16—42no—
457SD16—42no—
458SD16—42no—
459SD16—81no—
460D8—21no—
461D8—21no—
462D8—21no—
463D8C2×D4×C7312yes—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8C2×D4×C7311yescharacteristic
469C2×C8C2×D4×C7311yescharacteristic
470C2×C8C2×D4×C7311yescharacteristic
471C2×C8C24×C7311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4D8×C7311yescharacteristic
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4D8×C7311yescharacteristic
489C22⋊C4D8×C7311yescharacteristic
490C42—41no—
491C42C2×D4×C7311yescharacteristic
492C16—21no—
493C16—21no—
494C16—21no—
495C16C2×D4×C7312yes—
496C23—41no—
497C23—41no—
498C23C2×D8×C7311yescharacteristic
499C23C2×D8×C7311yescharacteristic
500Q8—22no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—82no—
509D4—22no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—82no—
515D4—82no—
516D4—82no—
517D4—82no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4C2×D8×C7311yescharacteristic
534C2×C4C2×D8×C7311yescharacteristic
535C2×C4C2×D8×C7311yescharacteristic
536C2×C4C2×D8×C7311yescharacteristic
537C2×C4C22×D4×C7311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8C22×D4×C7311yescharacteristic
542C8H(5,𝔽2)×C7311yescharacteristic
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—42no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C22×D8×C7311yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—42no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4D42×C7311yescharacteristic
567C4#576×C7311yescharacteristic
568C2—41no—
569C2—41no—
570C2—82no—
571C2—161no—
572C2D4×D8×C7311yescharacteristic
573C2C73×#341411yescharacteristic
574C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×D4×C73 ◁ C8×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#510×C73C2semidirect
2. C2×#508×C73C2semidirect
3. C73×#3285C2semidirect
4. C73×#3283C2semidirect
5. C73×#2251C2semidirect
6. C73×#2220C2semidirect
7. C73×#2216C2semidirect
8. C73×#2210C2semidirect
9. C73×#2209C2semidirect
10. C73×#2189C2semidirect
11. C73×#2189C2semidirect
12. C73×#2188C2semidirect
13. C73×#2186C2semidirect
14. C73×#2175C2semidirect
15. C73×#2168C2semidirect
111. SD32×C73D4semidirect
280. #33835C73direct (N × H)
288. C2×#510C2×C73semidirect
289. C2×#508C2×C73semidirect
290. #3285C2×C73semidirect
291. #3283C2×C73semidirect
292. #2251C2×C73semidirect
293. #2220C2×C73semidirect
294. #2216C2×C73semidirect
295. #2210C2×C73semidirect
296. #2209C2×C73semidirect
297. #2189C2×C73semidirect
298. #2189C2×C73semidirect
299. #2188C2×C73semidirect
300. #2186C2×C73semidirect
301. #2175C2×C73semidirect
302. #2168C2×C73semidirect
303. C73#33835direct (N × H)
399. SD32D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C732
C2×#508×C732
C73×#32852
C73×#32832
C73×#22512
C73×#22202
C73×#22162
C73×#22102
C73×#22092
C73×#21892
C73×#21882
C73×#21862
C73×#21752
C73×#21682
#3383573