Finite Group Databasebeta

← C73×#33790 #32943194

Subgroups — C73×#33790 #32943194

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3175C211yesmaximal, characteristic, complemented
2C73×#3155C211yesmaximal, characteristic, complemented
3C73×#2250C211yesmaximal, characteristic, complemented
4C73×#2249C211yesmaximal, characteristic, complemented
5C73×#2243C211yesmaximal, characteristic, complemented
6C73×#2240C211yesmaximal, characteristic, complemented
7C73×#2211C211yesmaximal, characteristic, complemented
8C73×#2210C211yesmaximal, characteristic, complemented
9C73×#2207C211yesmaximal, characteristic, complemented
10C73×#2206C211yesmaximal, characteristic, complemented
11C73×#2189C211yesmaximal, characteristic, complemented
12C73×#2187C211yesmaximal, characteristic, complemented
13C73×#2186C211yesmaximal, characteristic, complemented
14C73×#2184C211yesmaximal, characteristic, complemented
15C73×#2164C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C73—21no—
17C2×#135×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19#542×C73—21no—
20#535×C73—21no—
21C2×Q32×C73C2211yescharacteristic, complemented
22C2×SD32×C73C2211yescharacteristic
23C2×SD32×C73C2211yescharacteristic
24C2×SD32×C73C2211yescharacteristic, complemented
25C2×SD32×C73C2211yescharacteristic, complemented
26C2×D16×C73C2211yescharacteristic
27C2×D16×C73C2211yescharacteristic
28C2×D16×C73C2211yescharacteristic, complemented
29#500×C73C2211yescharacteristic, complemented
30#496×C73—21no—
31#496×C73—21no—
32#495×C73C2211yescharacteristic
33#495×C73C2211yescharacteristic
34#495×C73C2211yescharacteristic, complemented
35#493×C73C2211yescharacteristic
36#493×C73C2211yescharacteristic
37#489×C73—21no—
38#468×C73—21no—
39#467×C73C2211yescharacteristic
40#466×C73C2211yescharacteristic
41#440×C73—21no—
42C4×Q16×C73C2211yescharacteristic, complemented
43C4×D8×C73C2211yescharacteristic, complemented
44#405×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic, complemented
46C4⋊C16×C73C2211yescharacteristic, complemented
47#358×C73C2211yescharacteristic, complemented
48#358×C73C2211yescharacteristic, complemented
49#357×C73C2211yescharacteristic
50#357×C73C2211yescharacteristic
51#357×C73C2211yescharacteristic
52#357×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic, complemented
54#357×C73C2211yescharacteristic, complemented
55C22⋊C16×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic, complemented
58C4×C16×C73C2211yescharacteristic, complemented
59C2×#41×C73—21no—
60C22×D4×C73—21no—
61AGL(1,ℤ/8)×C73—44no—
62#135×C73—41no—
63#135×C73—41no—
64C2×Q16×C73C2311yescharacteristic
65C2×Q16×C73C2311yescharacteristic
66C2×SD16×C73—21no—
67C2×SD16×C73—21no—
68C2×SD16×C73—21no—
69C2×SD16×C73—21no—
70C2×D8×C73—21no—
71C2×D8×C73—21no—
72C2×D8×C73—21no—
73C2×D8×C73—41no—
74C2×D8×C73—41no—
75C2×D8×C73C2311yescharacteristic
76C2×D8×C73C2311yescharacteristic
77C2×D8×C73C2311yescharacteristic
78C2×D8×C73C2311yescharacteristic
79C2×M16×C73D411yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C4⋊Q8×C73—21no—
82#127×C73—21no—
83#127×C73—21no—
84#126×C73—41no—
85#124×C73—21no—
86#124×C73—21no—
87#124×C73—21no—
88#124×C73—41no—
89#123×C73—41no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—41no—
92#121×C73—21no—
93#121×C73—41no—
94#121×C73—41no—
95#120×C73—41no—
96#120×C73—41no—
97C4×Q8×C73—21no—
98C4×D4×C73—21no—
99#117×C73D411yescharacteristic
100Q32×C73—41no—
101SD32×C73—41no—
102SD32×C73—41no—
103SD32×C73—41no—
104SD32×C73—41no—
105D16×C73—41no—
106D16×C73—41no—
107D16×C73—41no—
108C2×C16×C73C2311yescharacteristic
109C2×C16×C73C2311yescharacteristic
110C2×C16×C73C2311yescharacteristic
111C2×C16×C73C2311yescharacteristic
112#107×C73—21no—
113#107×C73C2311yescharacteristic
114#107×C73C2311yescharacteristic
115#103×C73—21no—
116#103×C73—21no—
117#102×C73—21no—
118#102×C73—21no—
119#97×C73D411yescharacteristic
120#97×C73D411yescharacteristic
121C4×C8×C73C2311yescharacteristic
122C4×C8×C73C2311yescharacteristic
123C24×C73—41no—
124#41×C73—42no—
125#41×C73—42no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×Q8×C73—41no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×C73—42no—
134C2×D4×C73—42no—
135C2×D4×C73—41no—
136C2×D4×C73—41no—
137C2×D4×C73—41no—
138C2×D4×C73—41no—
139C2×D4×C73—41no—
140C2×D4×C73—41no—
141C2×D4×C73—41no—
142C22×C4×C73—41no—
143C22×C4×C73—41no—
144C22×C4×C73C2×D411yescharacteristic
145Q16×C73—21no—
146Q16×C73—21no—
147Q16×C73—21no—
148Q16×C73—21no—
149SD16×C73—42no—
150SD16×C73—42no—
151SD16×C73—42no—
152SD16×C73—42no—
153D8×C73—21no—
154D8×C73—21no—
155D8×C73—21no—
156D8×C73—21no—
157D8×C73—21no—
158D8×C73—21no—
159D8×C73—21no—
160D8×C73—21no—
161D8×C73—42no—
162D8×C73—42no—
163D8×C73—42no—
164M16×C73—22no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73C2×D411yescharacteristic
168C2×C8×C73C2×D411yescharacteristic
169C2×C8×C73C2×D411yescharacteristic
170C2×C8×C73C2411yescharacteristic
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—41no—
174C4⋊C4×C73—41no—
175C4⋊C4×C73—41no—
176C4⋊C4×C73D811yescharacteristic
177C4⋊C4×C73D811yescharacteristic
178C22⋊C4×C73—41no—
179C22⋊C4×C73—41no—
180C22⋊C4×C73—41no—
181C22⋊C4×C73—41no—
182C22⋊C4×C73—41no—
183C22⋊C4×C73—41no—
184C22⋊C4×C73—41no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73D811yescharacteristic
188C22⋊C4×C73D811yescharacteristic
189C42×C73—41no—
190C42×C73C2×D411yescharacteristic
191C42×C73C2×D411yescharacteristic
192C16×C73—21no—
193C16×C73—21no—
194C16×C73—21no—
195C16×C73—21no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—82no—
201C23×C73—161no—
202C23×C73—161no—
203C23×C73C2×D811yescharacteristic
204Q8×C73—41no—
205Q8×C73—41no—
206Q8×C73—41no—
207Q8×C73—41no—
208Q8×C73—161no—
209D4×C73—41no—
210D4×C73—41no—
211D4×C73—41no—
212D4×C73—41no—
213D4×C73—41no—
214D4×C73—41no—
215D4×C73—41no—
216D4×C73—41no—
217D4×C73—82no—
218D4×C73—82no—
219D4×C73—161no—
220D4×C73—161no—
221D4×C73—161no—
222D4×C73—161no—
223D4×C73—161no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—82no—
231C2×C4×C73—161no—
232C2×C4×C73C2×D811yescharacteristic
233C2×C4×C73C2×D811yescharacteristic
234C2×C4×C73C2×D811yescharacteristic
235C2×C4×C73C2×D811yescharacteristic
236C2×C4×C73C2×D811yescharacteristic
237C2×C4×C73C22×D411yescharacteristic
238C8×C73—21no—
239C8×C73—21no—
240C8×C73AGL(1,ℤ/8)12yes—
241C8×C73H(5,𝔽2)11yescharacteristic
242C8×C73H(5,𝔽2)11yescharacteristic
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—81no—
247C22×C73—81no—
248C22×C73—81no—
249C22×C73—81no—
250C22×C73—81no—
251C22×C73—81no—
252C22×C73—81no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73—81no—
256C22×C73—81no—
257C22×C73—81no—
258C22×C73—164no—
259C22×C73C22×D811yescharacteristic
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—81no—
266C4×C73—81no—
267C4×C73—81no—
268C4×C73—81no—
269C4×C73#53511yescharacteristic
270C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
271#33790C7311yesmaximal, characteristic, direct product factor, Sylow
272C2×C73—41no—
273C2×C73—161no—
274C2×C73—161no—
275C2×C73—161no—
276C2×C73—161no—
277C2×C73#320511yescharacteristic
278C2×C73#341511yescharacteristic
279C2×C73#341611yescharacteristic
280#3175C2×C7311yescharacteristic, complemented
281#3155C2×C7311yescharacteristic, complemented
282#2250C2×C7311yescharacteristic, complemented
283#2249C2×C7311yescharacteristic, complemented
284#2243C2×C7311yescharacteristic, complemented
285#2240C2×C7311yescharacteristic, complemented
286#2211C2×C7311yescharacteristic, complemented
287#2210C2×C7311yescharacteristic, complemented
288#2207C2×C7311yescharacteristic, complemented
289#2206C2×C7311yescharacteristic, complemented
290#2189C2×C7311yescharacteristic, complemented
291#2187C2×C7311yescharacteristic, complemented
292#2186C2×C7311yescharacteristic, complemented
293#2184C2×C7311yescharacteristic, complemented
294#2164C2×C7311yescharacteristic, complemented
295C73#3379011yescharacteristic, direct product factor, Sylow
296C2×AGL(1,ℤ/8)—21no—
297C2×#135C22×C7311yescharacteristic
298C22×D8C22×C7311yescharacteristic
299#542—21no—
300#535—21no—
301C2×Q32C22×C7311yescharacteristic, complemented
302C2×SD32C22×C7311yescharacteristic
303C2×SD32C22×C7311yescharacteristic
304C2×SD32C22×C7311yescharacteristic, complemented
305C2×SD32C22×C7311yescharacteristic, complemented
306C2×D16C22×C7311yescharacteristic
307C2×D16C22×C7311yescharacteristic
308C2×D16C22×C7311yescharacteristic, complemented
309#500C22×C7311yescharacteristic, complemented
310#496—21no—
311#496—21no—
312#495C22×C7311yescharacteristic
313#495C22×C7311yescharacteristic
314#495C22×C7311yescharacteristic, complemented
315#493C22×C7311yescharacteristic
316#493C22×C7311yescharacteristic
317#489—21no—
318#468—21no—
319#467C22×C7311yescharacteristic
320#466C22×C7311yescharacteristic
321#440—21no—
322C4×Q16C22×C7311yescharacteristic, complemented
323C4×D8C22×C7311yescharacteristic, complemented
324#405C22×C7311yescharacteristic
325C4⋊C16C22×C7311yescharacteristic, complemented
326C4⋊C16C22×C7311yescharacteristic, complemented
327#358C22×C7311yescharacteristic, complemented
328#358C22×C7311yescharacteristic, complemented
329#357C22×C7311yescharacteristic
330#357C22×C7311yescharacteristic
331#357C22×C7311yescharacteristic
332#357C22×C7311yescharacteristic
333#357C22×C7311yescharacteristic, complemented
334#357C22×C7311yescharacteristic, complemented
335C22⋊C16C22×C7311yescharacteristic
336C22⋊C16C22×C7311yescharacteristic
337#346C22×C7311yescharacteristic, complemented
338C4×C16C22×C7311yescharacteristic, complemented
339C2×#41—21no—
340C22×D4—21no—
341AGL(1,ℤ/8)—44no—
342#135—41no—
343#135—41no—
344C2×Q16C23×C7311yescharacteristic
345C2×Q16C23×C7311yescharacteristic
346C2×SD16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—21no—
350C2×D8—21no—
351C2×D8—21no—
352C2×D8—21no—
353C2×D8—41no—
354C2×D8—41no—
355C2×D8C23×C7311yescharacteristic
356C2×D8C23×C7311yescharacteristic
357C2×D8C23×C7311yescharacteristic
358C2×D8C23×C7311yescharacteristic
359C2×M16D4×C7311yescharacteristic
360C22×C8C23×C7311yescharacteristic
361C4⋊Q8—21no—
362#127—21no—
363#127—21no—
364#126—41no—
365#124—21no—
366#124—21no—
367#124—21no—
368#124—41no—
369#123—41no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372#121—21no—
373#121—41no—
374#121—41no—
375#120—41no—
376#120—41no—
377C4×Q8—21no—
378C4×D4—21no—
379#117D4×C7311yescharacteristic
380Q32—41no—
381SD32—41no—
382SD32—41no—
383SD32—41no—
384SD32—41no—
385D16—41no—
386D16—41no—
387D16—41no—
388C2×C16C23×C7311yescharacteristic
389C2×C16C23×C7311yescharacteristic
390C2×C16C23×C7311yescharacteristic
391C2×C16C23×C7311yescharacteristic
392#107—21no—
393#107C23×C7311yescharacteristic
394#107C23×C7311yescharacteristic
395#103—21no—
396#103—21no—
397#102—21no—
398#102—21no—
399#97D4×C7311yescharacteristic
400#97D4×C7311yescharacteristic
401C4×C8C23×C7311yescharacteristic
402C4×C8C23×C7311yescharacteristic
403C24—41no—
404#41—42no—
405#41—42no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—41no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4C2×D4×C7311yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—21no—
428Q16—21no—
429SD16—42no—
430SD16—42no—
431SD16—42no—
432SD16—42no—
433D8—21no—
434D8—21no—
435D8—21no—
436D8—21no—
437D8—21no—
438D8—21no—
439D8—21no—
440D8—21no—
441D8—42no—
442D8—42no—
443D8—42no—
444M16—22no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8C2×D4×C7311yescharacteristic
448C2×C8C2×D4×C7311yescharacteristic
449C2×C8C2×D4×C7311yescharacteristic
450C2×C8C24×C7311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4D8×C7311yescharacteristic
457C4⋊C4D8×C7311yescharacteristic
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4D8×C7311yescharacteristic
468C22⋊C4D8×C7311yescharacteristic
469C42—41no—
470C42C2×D4×C7311yescharacteristic
471C42C2×D4×C7311yescharacteristic
472C16—21no—
473C16—21no—
474C16—21no—
475C16—21no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—82no—
481C23—161no—
482C23—161no—
483C23C2×D8×C7311yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—161no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—82no—
498D4—82no—
499D4—161no—
500D4—161no—
501D4—161no—
502D4—161no—
503D4—161no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—82no—
511C2×C4—161no—
512C2×C4C2×D8×C7311yescharacteristic
513C2×C4C2×D8×C7311yescharacteristic
514C2×C4C2×D8×C7311yescharacteristic
515C2×C4C2×D8×C7311yescharacteristic
516C2×C4C2×D8×C7311yescharacteristic
517C2×C4C22×D4×C7311yescharacteristic
518C8—21no—
519C8—21no—
520C8AGL(1,ℤ/8)×C7312yes—
521C8H(5,𝔽2)×C7311yescharacteristic
522C8H(5,𝔽2)×C7311yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—164no—
539C22C22×D8×C7311yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4#535×C7311yescharacteristic
550C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
551C2—41no—
552C2—161no—
553C2—161no—
554C2—161no—
555C2—161no—
556C2C73×#320511yescharacteristic
557C2C73×#341511yescharacteristic
558C2C73×#341611yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3175C2semidirect
2. C73×#3155C2semidirect
3. C73×#2250C2semidirect
4. C73×#2249C2semidirect
5. C73×#2243C2semidirect
6. C73×#2240C2semidirect
7. C73×#2211C2semidirect
8. C73×#2210C2semidirect
9. C73×#2207C2semidirect
10. C73×#2206C2semidirect
11. C73×#2189C2semidirect
12. C73×#2187C2semidirect
13. C73×#2186C2semidirect
14. C73×#2184C2semidirect
15. C73×#2164C2semidirect
21. C2×Q32×C73C22semidirect
24. C2×SD32×C73C22semidirect
25. C2×SD32×C73C22semidirect
28. C2×D16×C73C22semidirect
29. #500×C73C22semidirect
34. #495×C73C22semidirect
42. C4×Q16×C73C22semidirect
43. C4×D8×C73C22semidirect
45. C4⋊C16×C73C22semidirect
46. C4⋊C16×C73C22semidirect
47. #358×C73C22semidirect
48. #358×C73C22semidirect
53. #357×C73C22semidirect
54. #357×C73C22semidirect
57. #346×C73C22semidirect
58. C4×C16×C73C22semidirect
271. #33790C73direct (N × H)
280. #3175C2×C73semidirect
281. #3155C2×C73semidirect
282. #2250C2×C73semidirect
283. #2249C2×C73semidirect
284. #2243C2×C73semidirect
285. #2240C2×C73semidirect
286. #2211C2×C73semidirect
287. #2210C2×C73semidirect
288. #2207C2×C73semidirect
289. #2206C2×C73semidirect
290. #2189C2×C73semidirect
291. #2187C2×C73semidirect
292. #2186C2×C73semidirect
293. #2184C2×C73semidirect
294. #2164C2×C73semidirect
295. C73#33790direct (N × H)
301. C2×Q32C22×C73semidirect
304. C2×SD32C22×C73semidirect
305. C2×SD32C22×C73semidirect
308. C2×D16C22×C73semidirect
309. #500C22×C73semidirect
314. #495C22×C73semidirect
322. C4×Q16C22×C73semidirect
323. C4×D8C22×C73semidirect
325. C4⋊C16C22×C73semidirect
326. C4⋊C16C22×C73semidirect
327. #358C22×C73semidirect
328. #358C22×C73semidirect
333. #357C22×C73semidirect
334. #357C22×C73semidirect
337. #346C22×C73semidirect
338. C4×C16C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#31752
C73×#31552
C73×#22502
C73×#22492
C73×#22432
C73×#22402
C73×#22112
C73×#22102
C73×#22072
C73×#22062
C73×#21892
C73×#21872
C73×#21862
C73×#21842
C73×#21642
#3379073